the tev gamma-ray binary psr b1259-63€¦ · doctor rerum naturalium (dr. rer. nat.) im fach...

The TeV γ-Ray Binary PSR B1259-63

Observations with the High Energy Stereoscopic System in the years2005-2007

D I S S E R T A T I O N

zur Erlangung des akademischen Grades

doctor rerum naturalium (Dr. rer. nat.)im Fach Physik

eingereicht an derMathematisch-Naturwissenschaftlichen Fakultät I

der Humboldt-Universität zu Berlin

vonHerrn Dipl.-Ing. Matthias Kerschhaggl

geboren am 20.11.1977 in Graz

Präsident der der Humboldt-Universität zu Berlin:Prof. Dr. Dr. h.c. Christoph Markschies

Dekan der Mathematisch-Naturwissenschaftlichen Fakultät I:Prof. Dr. rer. nat., habil. Lutz-Helmut Schön

Gutachter:1. Prof. Dr. rer. nat. habil. Thomas Lohse2. Prof. Dr. rer. nat. habil. Hermann Kolanoski3. Prof. Dr. rer. nat. Marek Kowalski

eingereicht am: 25. November 2009Tag der mündlichen Prüfung: 6. April 2010

Widmung

Berlin am 25.11.2009

An dieser Stelle möchte ich meinem Doktorvater und Chef Herrn Prof. Dr. ThomasLohse, der diese Arbeit durch ein hohes Maß an Unterstützung und Betreuung trotzteils widriger finanzieller Umstände erst ermöglicht hat, recht herzlich danken: Ich habein den letzten 4 Jahren sehr viel über Physik und Statistik aber auch in zahlreichenmittäglichen Kaffeeplauschen das ein oder andere Interessante über Mathematik gel-ernt. Die Arbeit der vergangnen Jahre in seiner Gruppe und unter seiner Anleitung hatsehr viel Spass gemacht, nicht zuletzt deshalb weil hier ein wirklich gutes Betriebsklimaherrscht. Solche nicht unwesentlichen Rahmenbedingungen sind keineswegs selbstver-ständlich!Herrn Dr. Ulli Schwanke möchte ich für die erstklassige Betreuung und die vielen fach-lichen Diskussionen zu meiner Arbeit sowie für das Korrekturlesen danken. Ich hätte denEinstieg in das für mich damals neue Fachgebiet wohl kaum ohne seine Hilfe geschafft.Den Herren Prof. Dr. Felix Aharonian und Dr. Dimitry Khangulyan möchte ich für diefruchtbare Zusammenarbeit und Unterstützung auf dem Gebiet der theoretischen Mod-ellierung von Binärsystemen danken. Herrn Dr. M. de Naurois danke ich für die guteZusammenarbeit und Crosscheck Analyse.Mein Dank gilt auch all meinen Kollegen, allen voran Matt Dalton, Arne Schönwald,Manuel Paz Arribas, Iurii Sush und Matthias Füßling für gute Zusammenarbeit, zahlre-iche humorvolle Spaziergänge und Aktivitäten in Zeiten fachlicher Innovationssätti-gung und gelebte Integration gegenüber Wissenschatlern mit Migrationshintergrund.Matthias Füßling möchte ich überdies für seine Hilfe in Computerangelenheiten meinenDank aussprechen.Unserer Sekretärin und gutem Geist der Arbeitsgruppe Veronika Fetting möchte ich fürdie vielfache Unterstützung bei administrativen Fragestellungen herzlich danken. HerrnOlf Epler gilt mein Dank für seine Arbeit als Systemadministrator und Unterstützungbei der Betreuung diverser Praktikumsversuche.Wie wohl in den meisten Danksagungen dürfen an dieser Stelle natürlich nicht meine El-tern für ihre uneingeschränkte Unterstützung so wie meine liebe Oma fehlen, die mich injungen Jahren unermüdlich mit leckeren Lungauer Knödeln gemästet hat, wohl wissend,daß diese sich intelligenzförderlich auf das zerebrale Wachstum auswirken und somit dieeigentliche Grundlage für diese Arbeit gelegt wurde.

iii

Abstract

PSRB1259−63/SS2883 is a binary system where a 48 ms pulsar orbits a massiveBe star with a period of 3.4 years. The system exhibits variable, non-thermal radi-ation around periastron on the highly eccentric orbit (e = 0.87) visible from radioto very high energies (VHE; E > 100GeV). When being detected in TeV γ-rayswith the High Energy Stereoscopic System (H.E.S.S.) in 2004 it became known asthe first variable galactic VHE source.This thesis presents VHE data from PSR B1259−63 as taken during the years 2005,2006 and before as well as shortly after the 2007 periastron passage. These dataextend the knowledge of the lightcurve of this object to all phases of the binaryorbit. The lightcurve constrains physical mechanisms present in this TeV source.Observations of VHE γ-rays with the H.E.S.S. telescope array using the Imaging At-mospheric Cherenkov Technique were performed. The H.E.S.S. instrument featuresan angular resolution of < 0.1 and an energy resolution of < 20 %. Gamma-rayevents in an energy range of 0.5 − 70TeV were recorded. From these data, energyspectra and lightcurve with a monthly time sampling were extracted.VHE γ-ray emission from PSRB1259−63 was detected with an overall significanceof 9.5 standard deviations using 55 h of exposure, obtained from April to August2007. The monthly flux of γ-rays during the observation period was measured,yielding VHE lightcurve data for the early pre-periastron phase of the system forthe first time. No spectral variability was found on timescales of months. The spec-trum is described by a power law with a photon index of Γ = 2.8± 0.2stat± 0.2sysand flux normalisation Φ0 = (1.1± 0.1stat ± 0.2sys)× 10−12TeV−1cm−2s−1.PSRB1259−63 was also monitored in 2005 and 2006, far from periastron passage,comprising 8.9 h and 7.5h of exposure, respectively. No significant excess of γ-raysis seen in those observations.PSRB1259−63 has been re-confirmed as a variable TeV γ-ray emitter. The firmdetection of VHE photons emitted at a true anomaly θ ≈ −0.35 of the pulsar orbit,i.e. already ∼ 50 days prior to the periastron passage, disfavors the stellar disc tar-get scenario as a primary emission mechanism, based on current knowledge aboutthe companion star’s disc inclination, extension, and density profile.In a phenomenological study indirect evidence that PSRB1259−63 could in fact bea periodical VHE emitter is presented using the TeV data discussed in this work.While the TeV energy flux level seems to be only dependent on the binary sepa-ration this behavior is not seen in X-rays. Moreover, model calculations based oninverse compton (IC) scattering of shock accelerated pulsar wind electrons and UVphotons were performed. The model presented accounts for non-radiative lossespossibly at work in the region where the pulsar wind is shocked by stellar outflowsand particles are accelerated to very high energies. The presented results show apeculiar non-radiative cooling profile around periastron dominating the VHE emis-sion in PSRB1259−63. The discrepancy between the γ-ray and X-ray lightcurvescould be a sign for synchrotron radiation as origin of the X-ray emission.

Keywords:VHE gamma-rays, gamma-ray astronomy - H.E.S.S., TeV binaries, pulsars -PSRB1259−63

iv

Zusammenfassung

PSRB1259−63/SS2883 ist ein Binärsystem in welchem ein Pulsar mit 48 ms Pe-riodendauer um einen massereichen Be-Stern mit einer Umlaufdauer von 3.4 Jahrenkreist. Dieses System weist variable, nicht thermische Strahlung um den Periastrondes hoch exzentrischen Orbits (e = 0.87) auf, welche vom Radiobereich bis zu sehrhohen Energien (engl. very-high-energy VHE; E > 100GeV) sichtbar ist. Seit dasSystem in TeV γ-Strahlung im Jahr 2004 mit dem High Energy Stereoscopic Sys-tem (H.E.S.S.) erstmals detektiert wurde, gilt es als erste variable galaktische VHEQuelle.Die vorliegende Dissertation präsentiert VHE Daten des Systems PSR B1259 −63,gemessen in den Jahren 2005, 2006 b.z.w. vor und kurz nach dem Periastron imJahr 2007. Diese Daten erweitern das Wissen um die Lichtkurve dieses Objektesüber alle Phasen der Umlaufbahn. Die Lichtkurvendaten tragen zur Einschränkungmöglicher physikalischer Prozesse in dieser TeV Quelle bei.Es wurden Beobachtungen von VHE γ-Strahlung mit den H.E.S.S. Teleskopen, dieauf Grundlage der bildgebenden atmospherischen Cherenkov Technik funktionieren,durchgeführt. H.E.S.S. verfügt über eine Winkelauflösung von < 0.1 und eine En-ergieauflösung von < 20 %. Es wurden γ-Strahlungsereignisse in einem Energiebere-ich von 0.5− 70TeV gemessen. Aus diesen Daten wurden Energiespektren und eineLichtkurve mit monatlicher Zeitauflösung gewonnen.Von PSRB1259−63 wurde, unter Verwendung von 55 h Detektorzeit von April bisAugust 2007, VHE γ-Strahlung mit einer Gesamtsignifikanz von 9.5 Standardab-weichungen detektiert. Der monatliche Fluss an γ-Photonen wurde innerhalb derBeobachtungszeit vermessen was erstmals zu VHE Lichtkurvendaten noch weit vordem Periastron des Systems führte. Es wurde keine spektrale Variabilität auf einermonatlichen Zeitskala gefunden. Das differentielle Energiespektrum ist durch einPotenzgesetz mit einem Photonenindex von Γ = 2.8 ± 0.2stat ± 0.2sys und ein-er Flussnormalisierung von Φ0 = (1.1 ± 0.1stat ± 0.2sys) × 10−12TeV−1cm−2s−1

beschreibbar.PSRB1259−63 wurde auch in den Jahren 2005 und 2006 mit einer Messdauer vonjeweils 8.9 h und 7.5 h überwacht, weit weg vom Periastron. Hierbei war kein sig-nifikanter Überschuss an γ-Strahlung über Untergrund zu verzeichnen.PSRB1259−63 konnte als variable TeV γ-Strahlungsquelle bestätigt werden. Diezuverlässige Detektion von VHE Photonen, die bei einer wahren Anomalie des Pul-sarorbits von θ ≈ −0.35, also bereits ∼ 50 Tage vor dem Periastron, ausgesendetwurden, schliesst ein Szenario mit stellarer Scheibe als Zielmaterial für hadronis-che Wechselwirkungen als Hauptemissionsmechanismus eher aus. Zumindest wennman das derzeitige Wissen über Lage, Ausdehnung und Dichteprofil der Scheibe desPartnersterns berücksichtigt.Weiters konnten innerhalb einer phänomenologischen Studie, die die in dieser Arbeitpräsentierten TeV Daten zur Grundlage hatte, Hinweise gefunden werden, daß PSRB1259−63 ein periodischer VHE Strahler ist. Während der TeV Energiefluss eineFunktion des Abstandes Pulsar-Stern zu sein scheint, kann dieses Verhalten imRöntgenbereich nicht nachvollzogen werden. Darüber hinaus wurden Modellrech-nungen, die auf inverser Comptonstreuung (IC) von schockbeschleunigten Pulsar-windelektronen und UV-Photonen basieren, durchgeführt. Das dargestellte Modellberücksichtigt strahlungsfreie Verluste, die möglicherweise im Bereich, in dem derPulsarwind durch Sternenwinde und Materialausflüsse terminiert wird und Teilchenbis zu VHE beschleunigt werden, eine Rolle spielen. Die gefundenen Ergebnissezeigen ein eigentümliches nicht radiatives Kühlverhalten um den Periastron, das

die VHE Emission in PSRB1259−63 zu dominieren scheint. Die Unterschiede zwis-chen der γ-Strahlen- und Röntgenlichtkurve könnten ein Hinweis auf Synchrotron-strahlung als Ursache der Röntgenemission sein.

Schlagwörter:VHE Gamma-Strahlung, Gamma-Strahlungs-Astronomie - H.E.S.S., TeVBinärsysteme, Pulsare - PSRB1259−63

vi

Contents

1 Introduction 11.1 Astroparticle Physics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.2 γ-Ray Astronomy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

2 H.E.S.S. - The High Energy Stereoscopic System 72.1 The Imaging Air Cherenkov Technique . . . . . . . . . . . . . . . . . . . 82.2 The Telescope System . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112.3 Data Taking and Analysis . . . . . . . . . . . . . . . . . . . . . . . . . 16

3 TeV γ-Rays from Binary Systems 293.1 Non-Thermal Radiation Mechanisms . . . . . . . . . . . . . . . . . . . 31

3.1.1 IC Scattering, Bremsstrahlung and Synchrotron Radiation . . . . 313.1.2 π0 decay . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 353.1.3 Attenuation and radiating secondaries . . . . . . . . . . . . . . . 35

3.2 LS 5039 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 373.3 LSI+61-303 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 403.4 The Microquasar Cygnus X−1 . . . . . . . . . . . . . . . . . . . . . . . 41

4 The System PSRB1259−63/SS2883 474.1 System Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 474.2 Pulsars and Pulsar Winds . . . . . . . . . . . . . . . . . . . . . . . . . . 484.3 Be Stars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 514.4 Non-Thermal Radiation from PSRB1259−63 . . . . . . . . . . . . . . . 53

4.4.1 π0 decay . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 574.4.2 Non-Radiative Losses . . . . . . . . . . . . . . . . . . . . . . . . 584.4.3 Absorption . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

4.5 Radio observations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 634.6 X-Rays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

5 TeV Observations of PSRB1259−63 with H.E.S.S. 675.1 Measurements in 2004 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 675.2 Measurements in 2005, 2006 and 2007 . . . . . . . . . . . . . . . . . . . 67

5.2.1 Sensitivity Study for the 2007 Campaign . . . . . . . . . . . . . . 715.2.2 Observations and Analysis . . . . . . . . . . . . . . . . . . . . . 72

6 Model Studies 896.1 Hadronic Disc Scenario . . . . . . . . . . . . . . . . . . . . . . . . . . . 906.2 Inverse Compton TeV Flux . . . . . . . . . . . . . . . . . . . . . . . . . 95

6.2.1 Expected IC flux without adiabatic losses . . . . . . . . . . . . . 98

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Contents

6.2.2 Corrections due to non-radiative losses - the case of an asymmetriclightcurve . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98

6.2.3 Possible cooling profiles based on symmetric TeV emission . . . 103

7 Summary 111

Appendix 1151 Calculating θ(t) for a Kepler ellipse . . . . . . . . . . . . . . . . . . . . . 1152 Calculating the mean flux . . . . . . . . . . . . . . . . . . . . . . . . . . 116

2.1 Definition of the problem . . . . . . . . . . . . . . . . . . . . . . 1162.2 Monte Carlo Study . . . . . . . . . . . . . . . . . . . . . . . . . . 119

x

1 Introduction

The work presented in this thesis is embedded in the relatively new field of γ-ray as-tronomy which has its origins in astroparticle physics. Since the discovery of cosmicrays by the Austrian physicist Victor Franz Hess in 1912 the field astroparticle physicshas developed rapidly. However, even a century later, the origins of cosmic particles

Figure 1.1: Cosmic Ray observatory of the University of Innsbruck at the Hafelekar(“Station für Ultrastrahlungsforschung” 1931) as founded by Victor FranzHess (right) who discovered the cosmic radiation in 1912 during his balloonexperiments.

and photons hitting the earth atmosphere are still not fully understood. A variety ofcosmic accelerators have been suggested as explanation for the extremely high energiesof particles that are observed in the cosmic radiation.Amongst the various possible sources of very high energy (VHE) radiation discussedin the literature, i.e. supernova remnants, pulsars and plerions, active galactic nuclei(AGN) etc., are binary systems (also known as TeV binaries1) consisting of a massivestar and a compact companion object such as PSRB1259−63/SS2883 which will be thetopic of this work.Before discussing this system and the non thermal mechanisms connected to it in moredetail this chapter shall give a brief overview over the field of astroparticle physics andγ-ray astronomy.

11 TeV = 1012 eV = 1.602 · 10−7 J

1

1 Introduction

1.1 Astroparticle PhysicsAstroparticle physics can be understood as a science which combines problems fromastronomy and cosmology with aspects and techniques from elementary particle physics.Such different things as

• the nature and cosmological impact of dark matter

• cosmic neutrinos and their influence on the creation of the universe

• the origin of cosmic rays

• the reason for gamma ray bursts (GRB)

• the composition of the universe

• the decay of the proton

are current problems investigated in the field. In some respects astroparticle physicsworks at the interface between particle physics, astronomy/astrophysics and cosmology.The starting point of this science was the discovery and investigation of the cosmicradiation since Victor Franz Hess in 1912 (see Fig. 1.1). The cosmic radiation con-sists mainly of protons and light nuclei but also contains electrons (∼1% of galacticcosmic rays), positrons, γ-rays and essentially all chemical elements in ionized form.2The particle energies can be as high as a few 1019 eV at the so called GZK-cutoff be-yond which ultra high energy (UHE) particles get attenuated in the cosmic microwavebackground (CMB) through photo-disintegration or photo-production of pions. Theseextremely high energies lie beyond any technical accelerator ability on earth.3 The wayhow nature could possibly accelerate particles to such energies were a mystery for manyyears.4 Then in the late 1930ies Enrico Fermi came up with his mechanism for thecorresponding particle acceleration now known as first and second order Fermi acceler-ation. He suggested that particles can gain energy when being reflected magneticallyin plasma clouds [Fermi(1949)]. This is known as second order Fermi acceleration sincethe energy gain at randomly propagating magnetic mirrors is proportional to the mirrorvelocity squared β2

m. When being applied to astrophysical shocks the particles can un-dergo reflection on a magnetic mirror on both sides of the shock front again and again[Bell(1978)],[Blandford and Ostriker(1978)]. This scenario became known as first orderFermi acceleration (also diffusive shock acceleration), since the energy gain scales withβs = vs/c, where vs is the shock speed and c the speed of light. The repeated accelera-tion allows the particles to gain extremely high energies and also naturally leads to thetypical power law spectra observed.5 Although this mechanism alone is too inefficientdue to energy losses of the particles, it works if one assumes that the particles alreadyexceed thermal energies at the time of injection into the shock. Where the particles gaintheir initial energies is still unknown. This is known as injection problem.The fluxes of cosmic rays vary over orders of magnitudes and are a function of energy(see Fig. 1.2). For instance at an energy of ∼ 1015 eV there will be on average only289% of the nuclei are protons, 10% helium and 1% heavier elements.3The beam energy in LHC will be 7 TeV.4The highest energies are still a mystery today.5 dNdE∝ E−p where p ≥ 2, with N being the particle number and E the particle energy.

2

1.1 Astroparticle Physics

Figure 1.2: Cosmic ray spectrum of charged particles.

3

1 Introduction

one particle per year per square meter detectable. The detection techniques for cosmicrays are manifold and mainly depend on the necessary collection area of the detectordepending on the flux. At lower energies (MeV-TeV) air borne detectors such as balloonor satellite experiments with their moderate effective collection areas are sufficient. Be-yond energies of 100 TeV up to ultra high energies (> 1018 eV), ground based detectorswith collection areas orders of magnitudes higher than those seen in the mid energyregime are used.Since the charged particles of the cosmic radiation get deflected in galactic and in-tergalactic magnetic fields their origins remain unknown to us. This limitation is nottrue for γ-rays which keep their direction information while propagating. It is believedthat γ photons are produced by high energy particle populations thus allowing for anidentification of cosmic ray sources. High energy electrons and positrons can producesynchrotron light seen in radio and X-rays. VHE γ-rays could be either produced by in-verse compton scattering of electrons/positrons on low energy target photons (e.g. CMBor starlight) or by interacting multi TeV hadron populations producing neutral pionswhich decay into VHE photons. The investigation of γ-rays has therefore opened a newwindow in astronomy, namely γ-ray astronomy.

1.2 γ-Ray AstronomyThe common theory in astroparticle physics is that high energy particle populations suchas electrons/positrons and hadrons, e.g. protons, should produce VHE γ-rays. Thesephotons, in contrast to the particles, can be used as messengers of VHE sources sincethey remain undeflected by magnetic fields and travel straight to the observer.The history of γ-ray astronomy started when in 1961 the satellite Explorer XI detected22 cosmic photon events over a period of ∼23 days and the NASA satellite OSO-3 in1967 could identify several hard X-ray sources located in the Milky Way. These discov-eries were made in relatively low energy bands at the keV to MeV scale.6The fluxes of TeV photons in VHE sources are relatively small in comparison to sourcesfrom X-ray or optical astronomy. For instance we see ∼ 10−11 cm−2 s−1 photons above 1TeV from the Crab nebula, the standard candle in TeV astronomy. This means that theused detector systems or telescopes need a large enough collecting area to compensatefor the low fluxes. Such big effective areas are easier to be constructed in ground basedexperiments, since satellites or balloons are very limited in size. On the other handVHE photons are absorbed in the earth atmosphere which acts as a calorimeter on thecosmic radiation which produces showers of secondary particles, dissipating the primaryparticle’s energy. This is very important since life on earth would be hardly possible inan environment unprotected from cosmic rays. So a direct collection of γ-rays hittingearth is not possible from ground. However, it is possible to observe the secondaryshowers triggered by VHE photons via Cherenkov radiation. This radiation occurs forcharged particles propagating through a medium and exceeding the speed of light inthis medium. It is thus possible to indirectly observe γ-rays coming from VHE sources.This principle is used in Imaging Air Chernkov Telescopes (IACT) since the late 1980’s.Since the first detection of the Crab Nebula in TeV γ-rays by the Whipple Observa-tory (see Fig. 1.3) in 1989, more than 100 VHE sources have been detected by modern6Explorer XI operated above 50 MeV and OSO-3 from 7.7-210 keV.

4

1.2 γ-Ray Astronomy

IACTs such as H.E.S.S. and MAGIC thus establishing the field of VHE γ-ray astronomy.

Figure 1.3: The IACT Whipple de-tected the first TeV γ-ray source, the CrabNebula, in 1989

IACTs like Whipple and HEGRA showed thatpulsar wind nebulae such as the Crab Nebulaand AGN’s are cosmic accelerators of particlesto multi TeV energies. The H.E.S.S. experimentcould confirm supernova remnants as sources ofTeV photons (e.g. RXJ 1713-3946) as well as de-tect more exotic VHE sources such as starburstgalaxies (NGC 253), radio galaxies (M 87) and theinteraction of propagating cosmic rays with gasclouds in the galactic center. MAGIC finally wasable to detect pulsed VHE γ-ray emission fromthe Crab pulsar.Therefore γ-ray astronomy is a very fascinat-ing field with many questions still open suchas the nature of the spontaneous gamma raybursts (GRB) or possible decay of dark mat-ter.

The following thesis investigated TeV γ-rays coming from the binary system PSRB1259−63/SS2883 during observations in the years 2005-2007. This system representsan ideal laboratory to investigate the interactions between stellar matter outflows froma companion star and a pulsar wind, leading to shock acceleration of particles and sub-sequent non thermal emission. In fact the detection of PSRB1259−63 with H.E.S.S. in2004 established it as the first variable galactic VHE source.Chapter 2 presents the High Energy Stereoscopic System (H.E.S.S.) which is a Cheren-kov telescope system used to observe VHE γ-rays. The main part of this work is basedon data taken with the H.E.S.S. experiment.In Ch. 3 possible non thermal radiation mechanisms at work in TeV binaries which arealso relevant for other γ-ray sources are discussed. The known TeV binary sources areshortly introduced.In the next chapter (Ch. 4) the system PSRB1259−63 will be discussed. TeV, X-rayand radio data from previous observations will be presented here. Based on these data,several theoretical explanations for the non thermal emission seen in this system will bereviewed.The author’s own studies and analysis of H.E.S.S. data taken in the years 2005-07 arepresented in Ch. 5. The resulting implications on the corresponding theoretical modelsfollow in Ch. 6.A brief summary of the results of the work presented conclude this thesis in Ch. 7.

5

2 H.E.S.S. - The High Energy StereoscopicSystem

The High Energy Stereoscopic System H.E.S.S. is an array of four imaging air Cherenkovtelescopes arranged on a square of 120 m side length (Fig. 2.1). The system is located

Figure 2.1: (left) The H.E.S.S. telescope array. (right) Single H.E.S.S. telescope.

in the Khomas Highland in Namibia (2316′17′′ S1629′58′′ E) at an altitude of 1800mabove sea level. Each telescope has a spherical dish 13m in diameter, consisting of 380individual mirrors giving an overall reflective area of 107m2. Cherenkov radiation asgenerated in extended air showers is collected by the mirrors and focused onto a cameraconsisting of 960 photomultipliers with a pixel size of 0.16 resulting in a Field of View(FoV) of ∼ 5. Following a trigger criterion with respect to telescope multiplicity forcoincident operation, a shower image is recorded once at least two out of four telescopestrigger [Berge et al.(2007)]. Determination of shower parameters and consequent evalua-tion of the primary particle type, energy and direction is done using an image reconstruc-tion technique based on Hillas moments [Aharonian et al.(2006)]. The H.E.S.S. instru-ment has a trigger threshold for the photon energy around ∼ 100GeV for observationsat zenith given an optical mirror efficiency of > 80 % [H.E.S.S. Collaboration(2004)].Above this ideal threshold a point source at zenith with a photon flux of ∼1% of thatof the Crab nebula, i.e. < 2.0 × 10−13 cm−2 s−1, can be detected in a 25h observationat a significance level of 5σ.The following sections shall briefly explain the functionality of the array and give aninsight on how data are taken and analysed. Apart from the underlying physical princi-ples used in the imaging air Cherenkov technique the individual technical componentsof the system shall be presented.This chapter is only a rough overview about the H.E.S.S. experiment and the imagingair Cherenkov technique. For more details consult [Schlenker(2005)], [Beilicke(2005)],[Aharonian et al.(2006)], [Hillas(1985)], [Aharonian et al.(2004)], [Berge et al.(2007)].

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2 H.E.S.S. - The High Energy Stereoscopic System

2.1 The Imaging Air Cherenkov TechniqueH.E.S.S. is an Imaging Air Cherenkov Telescope (IACT) array that observes Cherenkovradiation produced in extended air showers. Such air showers are created in the interac-tions of cosmic rays and γ-rays hitting the earth atmosphere. After the first interactiona cascade of secondary particles evolves in the atmosphere and the incident energy isdissipated. As the secondary particles travel at a speed exceeding the phase velocity oflight in air cph, Cherenkov photons are created. This Cherenkov light can be used byIACTs in order to trace back the primary particle direction and energy.

Cherenkov Radiation

When a charged particle such as an electron moves through an insulator such as air witha velocity that exceeds the velocity of light in this medium then Cherenkov radiationoccurs. The charged particle disrupts the electrons in the atmosphere’s atoms which getpolarized. The atoms’ electron shells will relax back to equilibrium and the electronsstart radiating Cherenkov photons during this process. If the particle has a velocitysmaller than cph, neighbouring polarized and radiating atoms interfere destructivelyand no Cherenkov radiation is seen. However, if the particle is faster than light theradiation of neighboring atoms interferes constructively and forms a wavefront instead.The particle creates a Mach cone of Cherenkov light along its trajectory as schown inFig. 2.2.

Figure 2.2: Mach cone of Cherenkov light (blue) in air caused by a charged particle (red)exceeding the phase velocity of light cph in air [Horvath(2006)].

The cone’s angle θ is given by

cos(θ) = c

nv= 1nβ

, (2.1)

where v is the particle velocity and n the refractive index of air.

8

2.1 The Imaging Air Cherenkov Technique

For an electromagnetic shower in air the generated Cherenkov light shows (after absorp-tion effects in the atmosphere) a spectrum with an intensity maximum at λmax ≈ 300 nmwhich is also the wavelength where the H.E.S.S. cameras are sensitive.

Air Showers

Corresponding to the nature of the first interaction between a cosmic ray particle (orphoton) and an atom of the atmosphere there are two different types of air showers:1

• Electromagnetic showers are induced by photons (and electrons) that causepair production in the Coulomb field of an air atom via the electromagnetic force.The subsequent electron positron pair produces secondary Bremsstrahlung pho-tons that in turn undergo pair creation thus leading to an electromagnetic cascade(see Fig. 2.3 (left)). The energy loss dE per length dx for a Bremsstrahlung ra-diating electron/positron with incident energy E0 is proportional to its currentenergy E

Figure 2.3: (left) Electromagnetic air shower. (right) Monte Carlo simulated shower fora 100 GeV photon [Schmidt(2005)].(

dE

dx

)rad

= −Eρx0⇔ E(x) = E0e

− xρx0 (2.2)

where ρ is the density of the atmosphere and x0 represents the radiation length ing/cm2 [Kolanoski(WS 2005/06)]. Per radiation length x0 the number of particlesin the cascade double in each step until the mean particle energy reaches a criticalvalue Ecrit where pair production and Bremsstrahlung die out and ionisation losses

1In this work air showers from weak interactions such as the ones induced by e.g. neutrinos are notdiscussed since they do not occur at significant rates in the H.E.S.S. energy regime.

9


become dominant for charged particles. The maximal number of shower particlescan be estimated with Nmax ≈ E0/Ecrit, i.e. if the shower evolves over n radiationlengths x0 before dying out (Fig. 2.3 (right))2 then:

E0 = 2nEcrit ⇒ n ln 2 = ln E0Ecrit

. (2.3)

For electromagnetic showers in air Ecrit ≈ 84 MeV. The penetration depth ofthe shower maximum Lmax into the atmosphere is dependent on the positionof the first interaction and scales with the incident particle energy according toLmax ∝ lgE. Typically a shower triggered by a 1 TeV photon is absorbed at ahight of 10 km above sea level by the atmosphere. The secondary e+e− pairs inthe shower create ∼ 100 ph/m2 of Cherenkov photons in a light pool of radiusr ≈ 120 m on the ground.An IACT positioned within this Cherenkov light pool is able to record an imageof the shower projected onto the camera plane.

• InHadronic showers the incident particle is a proton or nucleus that scatters anair atom inelastically. The interaction force is thus the strong force leading to thecreation of secondary hadrons, i.e. baryons and mesons, and nuclear fission of airatoms. Around ∼90% of the secondaries are pions, kaons make up ∼10% of theshower particles (Fig. 2.4 (left)). The energy threshold for hadronic subcascades

Figure 2.4: (left) Hadronic air shower. (right) Monte Carlo simulated shower for a 100GeV proton [Schmidt(2005)].

is around 1 GeV.2For simplicity we assume here that x0 taken from Bremsstrahlung equals the radiation length for aγ photon xγ for pair production in air. Actually xγ = 9/7x0.

10

2.2 The Telescope System

The neutral pions decay electromagnetically into two photons,

π0 −→ γγ,

which in turn lead to electromagnetic subcascades. The charged pions producemuons and e+ and e− along with muon- and electron (anti)neutrinos via the decays

π+ −→ µ+νµ

π− −→ µ−νµ

µ+ −→ e+νµνe

µ− −→ e−νµνe

The muons, which have a life time of τrf = 2.2 · 10−6 s in the rest frame, can reachthe ground above energies of 10 GeV because of the relativistic time dilatationgiving a llife time in the laboratory frame of τlf = γ τrf.Due to the bigger transverse momentum of particles in hadronic showers and thefact that electromagnetic subcascades develop different from hadronic subcascades,hadronic showers show a broader and more diffuse morphology (Fig. 2.4 (right)).Cherenkov photons are mainly produced in the electromagnetic subcascades. Thisis an important discriminant for the γ/hadron separation in the data taken byIACTs. The radiation length X0,hd ≈ 90 g/cm2 in hadronic showers is almosttwice as big as for electromagnetic showers. Thus hadronic showers penetratedeeper into the earth atmosphere.

Shower Imaging and Parameterisation

If IACTs are hit by the light pool (Fig. 2.5 left) of an air schower they collect the Cher-enkov photons (there are ∼ 106 ph for a 1 TeV γ) with their reflectors and project themonto a camera. If the Cherenkov light hits the focal plane of the camera a projectedshower image is recorded (Fig. 2.5 bottom). In the camera image such a projection hasan elliptic shape for γ-ray like events (Fig. 2.5 right).Within the H.E.S.S. Heidelberg analysis software package the shower images are pa-

rameterised using an elliptic approximation computed with the Hillas second momentstechnique applied to the camera pixel intensity distribution [Hillas(1985)]. Using thesemoments one can infer the shower direction and extension as described in more detailin the next section (Sec. 2.3). According to this approach of the ellipse major axispoints towards the incident particle’s origin and the intensity of the image is a measurefor its energy. The image morphology and extension helps discriminating γ-rays frombackground events.


Each H.E.S.S. telescope consists of several components such as the camera, drive systemand mirror dish. There are as well central parts responsible for the whole array thatcoordinate the data read out of the 4 telescopes such as the central trigger and thecentral data acquisition (DAQ) system. These components shall be briefly introduced:

11


Figure 2.5: (left top) IACTs recording Cherenkov light from an air shower. (right top)Shower image from a γ-ray like event as seen in one of the H.E.S.S. cam-eras. (bottom) Schematic plot taken from [Schlenker(2005)] showing theprojection of a Cherenkov air shower into the telescope camera focal plane.

12


• The H.E.S.S. camera consists of 960 photomultiplier tubes (PMT). They arearranged in 60 drawers. The PMTs are operated with a supply voltage of 800-1000V. A matrix of light collecting Winston cones in front of the PMTs allows for alight collection efficiency of 75% of photons reflected from the mirrors. The PMTquantum efficiency lies between 20 − 30 % for light in the operating wavelengthrange λ ≈ 300− 700 nm. The PMTs comprise one trigger channel and two signalchannels. There is a high gain (HG) channel for high amplification in the rangeup to 200 photo electrons (p.e.) and a low gain (LG) for 15-1600 p.e. Each drawer(consisting of 16 PMTs) contains 3 temperature sensors, a local trigger card andreadout electronics that feed the PMT signal into an analogue ring sampler (ARS)with 128 bits where the data is stored for up to 70 ns. This is enough time tokeep the whole event information until a trigger decision has been made. The

Figure 2.6: (left) H.E.S.S. camera with lid opened and Winston cone matrix visible.(right) Drawer consisting of 16 PMTs with the single power supplies, 8-channel DAQ cards and control/interface card [Aharonian et al.(2004)].

ARS contents are read out, digitized and delivered to the central data acquisitionelectronics of the camera once a trigger signal is received. The signal amplitude issampled with a period of 1 ns and can be read out directly as a function of timein the so called Sampling Mode or in integrated form (default) in time windowsof 16 ns. Each drawer is fully independent and can be removed from the camerafor repairs. The high voltage (HV) of single PMTs can be turned off while datataking if e.g. a star is moving through the FoV.The camera also contains electronics for the voltage supply and a GPS receiverfor event timing synchronisation. The central trigger and the central DAQ areconnected to each camera by two optical fibers.From the camera center to the edges of the camera a gradient in acceptance isseen which has to be corrected in the data analysis when e.g. creating sky maps.The efficiency at which air showers are reconstructed varies with the position ofthe detection in the PMT array since there is a reduction in collected light fromshowers more offset from the camera axis. Figure 2.7 shows a slice through the mapof background counts taken from the 2007 PSRB1259−63 dataset. The numberof background events as a function of the galactic longitude illustrates the radialacceptance profile in the field of view (FoV) of the cameras.

13


Gal long.

-204 -202 -200 -198 -196 -194 -192 -190 -188 -186

co

un

ts

0

200

400

600

800

1000

1200

Figure 2.7: Background counts as a function of galactic longitude as recorded by theH.E.S.S. cameras. Shown is a slice through the background map of the 2007PSRB1259−63 data.

• The trigger system of the H.E.S.S. array consits of individual camera triggersand the central trigger system located in the control building of the H.E.S.S. site[Funk et al.(2004)]. For the trigger system, the camera PMT array is divided intooverlapping sectors of 8 × 8 pixels each. A camera trigger occurs if at least 3PMTs with a charge exceeding 5 p.e. have fired in one sector within a certain timewindow of a few ns. The camera trigger is sent to the central trigger via opticalfibre. The central trigger sends a signal to the triggering camera if at least twocameras have triggered within a certain time window3 and start the ARS read outof the camera PMTs. During read out the cameras are blocked for data taking.This system dead time amounts to up to 10% of the observation time.

• Mirrors and mirror dish of the H.E.S.S. telescopes are built in the Davis CottonDesign, i.e. the individual mirrors are arranged on a r = 15 m spherical dish. Themirrors themselves consist of glass with an aluminium layer and a silica coating.Their diameter d = 60 cm and focal length f = 15 m. The reflectivity equals≈ 80 % in the wavelength regime λ ≈ 300 − 600 nm. The mirrors are fixed on amechanical unit that features two electric motors that can move the mirrors foralignment.4 Control electronics for the mirrors as well as for the telescope drivesystem is located in an electronics hut attached to each telescope.

• There are two CCD cameras mounted onto the mirror dish.3The Cherenkov light has different optical paths to reach the single telescopes depending on the obser-vation zenith angle. Only for observations at zenith the light reaches all 4 telescopes approximatelyat the same time. The (mean) delay for photons reaching the telescopes is taken into account afterthe trigger.

4This is done only when mounting the mirror.

14


The LidCCD is located in the center of the dish in order to have the full cameraarray in the field of view. Pictures read out with the LidCCD are used in orderto measure the position of the camera with respect to the telescope structure as afunction of the zenith angle.The SkyCCD is located ≈ 4 m beside the telescope’s optical axis and features anoptical refractor with a focal length of 800 mm. It records images of the night skyto estimate the position of the telescope with respect to stars.

• The drive system is able to move the telescopes in azimuth (Az) and altitude(Alt) (coordinates) with the help of two servo-controlled AC motors to reach everypoint on the night sky. The maximum slewing velocity is ∼ 100min−1. The drivesystem is controlled via the central DAQ but can also be operated manually. Incase of a complete power failure which also would affect the computer control, abattery-backup together with battery-driven DC motors guarantee the safe man-ual park in of the telescopes into a camera shelter5.The telescopes themselves consist of a rigid steel structure that holds the mirrordish and the camera. It moves along steel rails that are fixed to a concrete foun-dation. The telescope’s orientation is controlled via angular transmitters that arefixed to the Alt/Az axis. Due to the weight of the camera and the steel structureitself the telescopes suffer from mechanical deformation depending on the Alt/Azorientation. These deformations are monitored with the help of the two CCDcameras and corrected with the help of a mechanical model. This Pointing modeldelivers a translation and rotation matrix that has to be applied to the cameracoordinate system to correct for relative changes of the camera position with re-spect to the mirror dish as well as to the fixed stars. The systematic pointingaccuracy for H.E.S.S. after these corrections is ∼ 6′′ for Right Ascension (RA) andDeclination (Dec) [Braun(2007)].

• The central data acquisition (DAQ) system monitors and controls the abovementioned telescope subsystems. The DAQ hardware consists of a computer clus-ter featuring ∼40 CPUs. The single machines are used as nodes for data processingor server machines, i.e. database-, storage- and domain-server. Two 1.4 TB RAID-systems (redundant array of independent disks) and two tape drives are used fordata storage. Media converters convert the signals from the telescopes from opti-cal signals (fiber) to electronic signals (copper cabels). The data stream betweenthe single machines is managed by several network switches. In the control roomdesktop computers are used for control and displaying purposes of the H.E.S.S. ar-ray.Concerning the DAQ software, the single systems such as e.g. the telescope cameraare registered as a set of processes in the DAQ framework. There are basically4 different process types every hardware component of the telescope is handledwith:

– A Controller process directly controls the hardware and reads out data whichis sent to a Receiver process.

– The Receiver performs the data processing and storage.5The park in position is located at Alt −35.5 below the telesope’s horizon.

15


– A Reader process requests data from the Receiver and makes it available asoutput, for instance on a display.

– The above processes for hardware and data handling are managed by a Man-ager process which itself is not involved in the data manipulation and trans-port.

Eevery process can be in 4 different states:– Safe: The process and its hardware are in a safe state (e.g. camera parked

in). No data taking is possible.– Ready The process and its hardware are configured and ready for data taking.– Running The process and its hardware are operating and data is taken.– Paused/Resumed The process and its hardware are pausing but data taking

can be resumed without reconfiguration.All subsystem processes (e.g. camera, drive system, CCDs, trigger a.s.o.) arecontrollable by the shift crew via graphical user interfaces (GUI) in the controlbuilding. Figure 2.8 shows a screenshot from the central DAQ array GUI whereall the processes and their states are listed.

A full description of the DAQ system lies beyond the scope of this thesis. The authorrefers to the description in [Schlenker(2005)] for further details especially concerningexplanations for the process handling, DAQ hardware, data flow and the control of thesingle H.E.S.S. run types (observation, calibration a.s.o.).

2.3 Data Taking and AnalysisThe H.E.S.S. data taking is organized in so called shifts of ∼3 week duration, separatedby ∼1 week of so called moontime, i.e. where no data taking is possible due to moonlightwhich would contaminate the observation of Cherenkov light.The H.E.S.S. system is controlled via the central data acquisition (DAQ) system whichperforms data read out and process control of system components such as the telescope’stracking system, the PMT cameras (including HV and Lid), the central trigger, datastorage, the weather station as well as networking connections to the 4 telescopes. Thedata taking itself is organzied in so called runs of 28 min duration (see Sec. 2.3). TheDAQ controls the data taking and stores the raw data to disk using the ROOT fileformat.6 An interim calibration of the data already allows for an anlysis on site.7 Aftereach shift the raw data are copied to tape and shipped to Europe.

Data Calibration

The starting point for the analysis of data from air showers as recorded with H.E.S.S. isthe number of p.e. in every pixel, i.e. PMT, making up the camera image. The Cherenkovlight collected in a PMT leads to a current of photo electrons which in turn is converted6http://root.cern.ch/drupal/7The calibrated datasets are written to a file format referred to as “data summary tapes” (DST).

16

2.3 Data Taking and Analysis

Figure 2.8: Central array GUI for the control of the single H.E.S.S. system processes.

17


by an analog to digital converter (ADC) into counts. Over the current range where thePMTs are operated in, the number of p.e.’s and ADC counts follow a linear relationship(Fig. 2.9). In order to determine this relationship, calibration runs have to be performed.

Figure 2.9: Operating range of linear behavior between photo electrons and ADC countsin the H.E.S.S. cameras [Aharonian et al.(2004)]

There are conversion coefficients (CC) for both High Gain (HG) and Low Gain (LG)channles in the camera. In H.E.S.S. such calibrations are performed roughly every 2days yielding also information about the PMT efficiency, signal timing profiles, electronicnoise in the cameras, the night sky background (NSB) due to e.g. scattered starlightand unusable pixels which have for instance to be switched off because of a star in theFoV:

• In an electronic pedestal run the PMT signals are read out randomly in orderto estimate the noise in the single pixels. During this calibration run the cameralid stays closed while the HV is on. Since the noise in a PMT is a function of thetemperature and the cameras become hotter during operation, the PMT signalsare also monitored during observation runs on a minute basis. As the lid then isopened these pedestals give also a measure for the NSB which broadens the noisedistribution (Fig. 2.10).

• The single photo electron (PE) run is performed with camera lid open and HVon but inside the camera hut in order to avoid contamination with NSB. An LEDin the hut radiates light pulses onto the camera at a rate of 70 Hz with an intensitysuch that on average there is 1 p.e. per PMT per event. This calibration run givesan ADC distribution that combines electronic noise with the single p.e. signal. Thenumber of p.e. seen in the PMT follows a poissonian distribution with a mean at1 p.e. The 1 p.e. distributions can be fitted to give the conversion coefficientsbetween 1 p.e. and ADC counts for each pixel. In Fig. 2.11 the ADC distributionfor a single PE run is shown. The first peak around ADC≈ −27 represents theelectronic noise. The second peak contains the distribution stemming from a single

18


Figure 2.10: Real data ADC distributions of pedestals for different levels of the NSB[Aharonian et al.(2004)]

p.e. superimposed on the noise and multiple p.e. events. The fit yields ADC≈ 80for the mean of the 1 p.e. distribution. Thus on average 1 p.e. = 80 ADC counts.

• Flatfielding is done similarly to the single PE calibration but with the LEDmounted in the center of the mirror dish and the camera lid opened thus allowingfor NSB. The 70 Hz pulses of the LED lie within a wavelength range of λ =390 − 420 nm and evenly illuminate the camera. Each pulse shows a duration of∼ 5 ns FWHM. The flatfielding is done in order to correct for differences in thesingle PMT efficiencies, i.e. to gain a flat camera field. These differences arisefrom the usual PMT component tolerances as well as from deviations among thesingle light collectors, i.e. Winston cones, in front of the PMTs.

• Muon rings in hadronic events are recorded to evaluate the reflectivity of themirrors which changes over time due to e.g. pollution and degredation of the mirrorcoating. Highly energetic muons can reach the ground and their Cherenkov lightforms rings in a single telescope (Fig. 2.12).

The expected photon distribution from muons can be modelled with a ring likemorphology which is adapted to the camera data using a χ2 fit. The mirror ormuon efficiency εµ = Np.e./Nγ can then be extracted from the ratio between mea-sured pixel intensities applying the usual conversion coefficients Np.e. and expectedCherenkov photons Nγ from the muon model. To evaluate Nγ, the muon energyhas to be inferred from the radius of the muon ring.

19


Figure 2.11: ADC distribution for a single PE run [Aharonian et al.(2004)]

Figure 2.12: Muon ring as seen in one of the H.E.S.S. cameras.

20


Data Analysis

Before being able to analyse the camera images a data reduction with respect to imagecleaning is applied. In order to get rid of the NSB and electronic noise in the images,only those pixels are kept which satisfy the so called tailcut, i.e., which recorded a signalcorresponding to at least 5 p.e. and which have a neighbour with a signal above 10 p.e.8After the tailcut the image can be parameterised calculating the second moments ofthe image intensity distribution. Following the approach suggested by Hillas et al.[Hillas(1985)] the corresponding parameters are then used to reconstruct the shower di-rection and energy: Length l, width ω, center of gravity cg, distance d between cameracenter and cg (see Fig. 2.13). Other parameters are the image size s, i.e. the accumu-

Figure 2.13: Parameterisation of shower images according to Hillas et al. [Hillas(1985)].Several camera images of the same shower are combined in stereoscopicobservations such as done with H.E.S.S.

lated pixel intensity and the total image pixel number np. While l points to the showerdirection, s is a measure of the particle energy.

After event parameterisation the event selection is applied. This means that aseries of cuts is applied in order to filter γ-ray like events from background:

• d must not exceed a certain value in order to avoid truncated shower images.

• s has to exceed a certain value as too dim events are hard to reconstruct.

• The telescope multyplicity n must satisfy n ≥ 2. This allows the shower directionreconstruction via intersection of multiple image axis and also gets rid of muonicbackground.

Some standard values for the above cut parameters are shown in Tab. 2.1. Combining8This is the criterion chosen for the so called standard cuts for southern sources std_0510_south.There are of course other configurations with more or less strict values.

21


Parameter Min Maxd 0 2s 80 p.e. ...

n 2 ...

Table 2.1: Values for local distance d, image size s (amplitude), and telescope multy-plicity n.

the information of several (at least two) telescopes yields the reconstructed direction ofthe γ-ray emitter. This principle of using Hillas moments in combination with stere-oscopy is shown in Fig. 2.13. When superimposing more than two shower images eachpair of major axis will usually intersect at a different point. Therefore the resultingreconstructed shower directions of each pair of images have to be weighted. Two imagesi, j are thus weighted according to

Wij = sin (φi − φj)(1si

+ 1sj

) (ωili

+ ωjlj

) (2.4)

where φ is the angle between the camera plane x-axis and the image ellipse major axis.The weight is chosen such that pairs with higher intersection angles as well as brighterimages with higher aspect ratio l/ω are favoured.

The energy reconstruction of the primary particle is done by comparing the im-age amplitude s = s(E, p, θ) which is a function of the particle energy E, the impactparameter p (between reconstructed shower axis and telescope) and zenith angle θ withexpectation values from Monte Carlo studies. For each telescope i it is thus possible toread Ei from a so called lookup table given s, p and θ. The reconstructed shower energyis then the mean of all Ei. The energy reconstruction is limited by the Poisson statisticsof the image intensity and the quality of the determination of p. H.E.S.S. has an energyresolution ∆E/E < 20 %.

The γ/hadron separation of recorded events separates unwanted hadronic eventswhich make up 99% of the recorded H.E.S.S. shower images from γ-ray like events.Cherenkov light in hadronic showers is mainly created in electromagnetic subcascades.For a given energy the shower thus looks broader and more diffuse. In order to usethis as a discriminant to the more homogeneous γ-ray events the mean scaled param-eter method is used for the parameters ω and l of the corresponding shower ellipse[Aharonian et al.(2006)]. According to this the measuerd value of of a given parameterp with expectation value < p > and scatter σp is scaled to give the scaled parameter

psc = p− < p >

σp. (2.5)

< p > and σp are functions of the shower energy, zenith angle and the impact parameter.As there are 4 H.E.S.S. telescopes the final parameter which is used for the analysis isthe so called mean reduced scaled parameter (MRSP). For a given scaled parameter psc,i

22


calculated for each telesope i = 1 . . . Ntel the MRSP is given by

pMRSP =∑tel

psc,i/Ntel. (2.6)

A comparison of the individual MRSPs with results taken from lookup tables of MonteCarlo simulated γ-ray and hadron showers allows for an efficient rejection of background.Figure 2.14 shows simulated distributions of the mean reduced scaled width (MRSW)parameter together with real data.

Figure 2.14: Monte Carlo generated MRSW values for proton showers (left) and γ-rays(right) in comparison to real data from background (left) and the Crabnebula (right) [Aharonian et al.(2006)].

From these distributions selection cuts for the MRSP can be chosen (see vertical lines)in order to reject hadronic showers.There are alternative methods for the analysis of Cherenkov data as e.g. described in[de Naurois(2005)]. For the analysis presented in this work the above discussed Hillasapproach was used.

Apart from the γ/hadron separation, the analysis of H.E.S.S. data also includes back-ground estimation to rule out false γ-like events and diffuse photons not originatingfrom the source observed. This can be done in different ways depending on whetherthe data is used to generate e.g. energy spectra or sky maps. In this work basically twoestimation methods were used [Berge et al.(2007)]:

• The reflected region background method uses background or OFF regions in theFoV which have the same offset from the camera center as the signal or ON region(Fig. 2.15 right). This makes the method independent of gradients in the cameraacceptance.9 The number of excess photons Nγ coming from the source is thuscalulated as

Nγ = NON − αNOFF (2.7)9If the acceptance is only a function of offset.

23


where NON and NOFF are ON and OFF counts, respectively, and α is the normalis-taion factor between ON and OFF regions, i.e. indirect proportional to the numberof OFF regions. For the reflected region background estimation observations have

Figure 2.15: (left) Background estimation using the ring model. The background istaken from a ring shaped OFF region around the ON region. (right)Reflected region background model. A number of circular OFF regionswith the same distance from the camera center as the ON region is chosen[Berge et al.(2007)].

to be carried out in the so called wobble mode, i.e. with the observation positionoffset from the target position. The wobble offset usually lies between 0.5 and0.7. The reflected region background model is used mainly for extracting photonspectra since no radial acceptance correction function for the data is needed.

• The ring background model is used for extracting sky maps from the source region.Here every bin of the 2D histogram representing the observed region uses a ringof bins around its position as OFF region (Fig. 2.15 left). Thus the correspondingmap showing the excess counts of γ-rays is correlated since every pixel is usedas ON and OFF region at the same time. For this approach α is approximatelythe ratio between the solid angle of the chosen background ring and the solidangle of the ON region. Typical values for α are α ∼= 1/7. For this method anacceptance correction has to be applied since the camera acceptance is decreasingwith increasing distance from the center.

Another quantity related to the rejection of background events is the angular or θ2-cut. This cut is applied to the squared angular distance of an event with respect tothe source position. The distribution of squared angular distances of photons comingfrom a point-like source such as the Crab nebula, typically follows the instrument’spoint spread function (PSF) as shown in Fig. 2.16. Depending on the cut configuration,

24


Figure 2.16: θ2-plot from γ-rays coming from the direction of the Crab nebula[Aharonian et al.(2006)]. After background subtraction the data followsthe instrument’s PSF (solid curve). The vertical lines indicate differentangular cuts on the data.

events above a certain angular distance (indicated by the vertical lines) are not countedas coming from the source position. In this work an angular cut of ∆θ2 = 0.0125 hasbeen used.The main goal of the analysis of VHE photons is to extract photon spectra, photonfluxes as a function of time (lightcurve) and TeV γ-ray sky maps from the source region.These results are the basis of any interpretation and understanding of a VHE emitter.This will be discussed in more deteail in Sec. 5.2.2.

Since in TeV astronomy the number of excess counts is marginal compared to e.g. opti-cal astronomy it is crucial to evaluate how significant the detection of γ-ray photons for agiven source is. The underlying statistics of ON and OFF counts is poissonian. The num-ber of excess photons is calculated according to Eq.(2.7). Li and Ma [Li and Ma(1983)]derived for the significance S of excess photons Nγ computed from ON and OFF counts

S =√

2NON · ln

[(α+ 1)α

· NON

NON +NOFF

]+NOFF ln

[(α+ 1)

(NOFF

NON +NOFF

)] 12.

(2.8)

A detection of a certain γ-ray source is considered to be firm once exceeding a significanceof ∼5 standard deviations.Equation 2.8 is derived using a maximum likelihood ratio method, testing the nullhypothesis E0 that there is no source, i.e. that the expectation value for excess photons

25


is < Nγ >= 0 having measured the values NON, NOFF. The parameter λ is defined as

λ = L (NON, NOFF|E0, < NB >c)L (NON, NOFF| < Nγ >,< NB >) , (2.9)

where L(X,P ) is the likelihood function, i.e. the probability for observation valuesX ocurring given parameters P . The maximum likelihood estimates for the photonbackground given E0 and given the existence of a photon source are < NB >c and< NB >, respectively. The parameter λ is thus the ratio between the probabilities tomeasure NON, NOFF if there is no source and if there is a source using estimates for theexpected background for either case and expected excess < Nγ > in case of the existenceof a source.It can be shown that the variable u2 = −2 lnλ follows a χ2 distribution with one degreeof freedom if the null hypothesis is fulfilled and u can be used as the significance of theobserved Nγ.

Systematics

There are a number of systematic uncertainties to be considered for the H.E.S.S. instru-ment. Systematic errors stated for the results in this work are taken from the studiesin [Aharonian et al.(2006)].The main influences for a bias in the air shower reconstruction with respect to thecorrect measurement of the photon energy, direction and subsequent quantities such asphoton flux and spectral index are

• The camera response due to varying PMT efficiencies and single p.e. response

• The optical response of the detector due to mirrors, Winston cones and shadowingeffects of the steel structure

• Influence of changing humidity, pressure and temperature of the atmosphere onthe interactions of photons and particles in air.

The various calibration methods discussed above account for these sources of systematicuncertainties with finite accuracy. Especially the atmospheric uncertainties are leastwell understood. A varying air density translates into changing hights of the showermaxima and thus light yield in the detector. The degree of absorption of Cherenkovphotons in the atmosphere is influenced by the humidity and amount of dust in theair. Atmospheric models are accounting for these effects. The atmosphere is constantlymonitored during data taking with respect to the relevant parameters. Changes in theatmospheric conditions become noticable in the trigger rate of the detector. Data takenunder a variable detector response due to atmospheric fluctuations are rejected and notused for the analysis.The systematic error on the absolute photon flux due to these uncertainties is roughlyestimated to be ∼20% (root mean square RMS). This number is taken from studieswith data from the Crab nebula. According to these studies the systematic errors inthe Monte Carlo simulations using models for shower interactions and the atmosphereaccount to 1% and 10%, respectively. The influence of broken pixels in the camera anda faulty energy reconstruction is estimated with an 5% error. Uncertainties in the live

26


time measurement give a roughly 1% error on the photon flux. Varying the selectioncuts in the analysis is used to estimate the systematic error there, yielding a ∼8%spread. Differences in the photon flux at the 1% level are seen when using differentbackground estimation methods, i.e. reflected region and ring model. The systematicinfluence of varying atmospheric conditions is taken from the run-by-run flux variabilityseen in the Crab data which accounts to 15%.Comparing the spectral indices from a power law fit to different datasets from the Crabnebula using different selection cuts and background estimation methods is used toestimate the systematic error on the photon index ∆Γ. The RMS of these influencesaccounts to ∆Γ = ±0.1. Including effects from varying the energy bin size in the photonspectra when fitting a power law finally gives ∆Γ = ±0.2 [Schlenker(2005)].

27

3 TeV γ-Rays from Binary Systems

This chapter is an introduction to the, for the astronomical community, relatively newclass of TeV γ-ray binaries. The initial intention to observe binary systems in VHE wasthe theoretical expectation that such systems could be VHE accelerators. This predic-tion was based on the fact that binaries are already known as non-thermal emitters inthe X-ray regime. Up to now ∼300 so called X-ray binaries are known.These systems consist of a massive star and a compact object such as a neutron star(NS) or a stellar black hole (BH). Depending on the mass of the stellar companion wedistinguish high mass X-ray binaries (HMXB) with a companion of spectral type O orB from low mass X-ray binaries (LMXB) with spectral type later than B (see Tab. 3.1).Non-thermal emission from such objects is believed to stem from particles acceleratedduring the accretion process of matter from the stellar donor onto the compact objector alternatively from acceleration in shocked wind zones between pulsar wind (PW)particles and stellar outflows (see Fig. 3.1 right panel).In the case of accretion driven non-thermal binary sources that additionally show jet-

Companion Black Hole (BH) Neutron Star (NS)High Mass Star HMXB HMXB

(Be, Blue Supergiant) MQ MQPulsar Plerion

Low Mass Star LMXB LMXB(spectral type MQ MQlater than B)

Table 3.1: Possible configurations of X-ray binary systems. HMXB = High Mass X-rayBinary, LMXB = Low Mass X-ray Binary, MQ = Microquasar. In configura-tions with a NS the spindown power E of the NS is an important parameter.Pulsars with a high E prevent the system from being accretion driven. As forPSRB1259−63 such binaries can emit non-thermal radiation in a plerionicshock scenario present in colliding winds between the star and the pulsar.

like structures in radio observations, where matter gets re-ejected along the rotation axisof the compact object, X-ray binaries are also known as microquasars (MQ). This namecomes from the fact that microquasars show similar physical properties as quasars, theirgalactic relatives, and are therefore suitable to study bigger scale active galactic nuclei(AGN) physics. In both systems a (stellar or galactic) BH accretes matter (from a donorstar in case of a microquasar). The accreted matter forms a disc around the BH beforefalling into it. The conversion of angular momentum of the infalling particles leads toheating of the accretion disc and subsequent X-ray/UV emission in MQs/AGNs. A partof the accreted matter gets re-ejected along ultrarelativistic jets that terminate in the socalled radio lobes (see Fig. 3.1 left panel). It is believed that e.g. in these jets particles

29


Figure 3.1: In a microquasar a compact object accretes matter from a donor star whichforms an accretion disc visible in X-rays. A fraction of the matter gets re-ejected along ultrarelativistic jets which terminate in the ambient interstellarmedium visible in radio. The jets are believed to be the sites of particleacceleration to VHE (pictures are taken from [Mirabel and Rodríguez(1998)]and [ESA/Hubble(2004)]).

30

3.1 Non-Thermal Radiation Mechanisms

are accelerated to VHE energies which can be seen in the emission of TeV γ-rays.Since PSRB1259−63 has been discovered in the VHE domain in 2004 by H.E.S.S. thenew source class of TeV γ-ray binaries has been established. Up to now 4 such sourceshave been detected in the VHE sky, all of them being known HMXB’s.1 Apart fromPSRB1259−63 these are LS 5039 [Aharonian(2006)], LS I+61-303 [Albert et al.(2008)]and Cygnus X-1 [Albert et al.(2007)].As for Cygnus X-1 which hosts a stellar BH and shows jet structures in radio mapsand therefore is a microquasar, the primary engine for accelerating particles to VHEenergies is driven by accretion of matter from the companion star falling onto the BH.The second possibility of efficient particle acceleration in the VHE regime mentionedabove is shock acceleration that takes place in the termination zone of colliding winds,where a pulsar wind (PW) meets outflow from a companion star. This scenario appliese.g. for PSRB1259−63 as the pulsar is too powerful for being accretion driven, i.e.only a small fraction (∼ 1%) of the spindown luminosity of L = 8 · 1035 erg s−1 is suf-ficient to generate a PW that prevents particles to fall onto the NS as demonstratedby [Tavani et al.(1997)]. For the moment PSRB1259−63 is the only TeV γ-ray binarywhere the case of a plerionic binary system is unambigeously proven. For LS I+61-303and LS5039 both scenarios are possible. These systems are microquasar candidates inthe sense that the nature of the compact object is not known and current mass estimatesallow for both a BH or NS. In case of a NS system the colliding wind model can not beruled out for the moment [Dubus(2006b)].Before discussing the individual known γ-ray binaries in detail some general remarks aremade about non-thermal radiation mechanisms as happening in most TeV sources com-prising VHE particle populations. The particular discussion of PSRB1259−63 followsin Ch. 4.


The generation of VHE radiation in sources such as binary systems can be traced backto multi TeV particle populations undergoing a number of different possible interac-tions with ambient radiation, matter and electromagnetic fields. The single interac-tion types are basically inverse compton (IC), bremsstrahlung and synchrotron radi-ation and shall be briefly explained below. Another scenario viable for VHE sourcesand also considered to be possible in binaries is the production of TeV photons inhadronic interactions. Other mechanisms such as photon attenuation and pair cas-cading will also be addressed. The below sections basically follow the reviews in[Blumenthal and Gould(1970)] and [Wilms(2008)] for the radiation mechanisms and thepaper in [Bosch-Ramon et al.(2008)] for radiating secondaries in TeV binaries.

3.1.1 IC Scattering, Bremsstrahlung and Synchrotron Radiation

The three most important VHE radiation mechanisms, namely inverse Compton scat-tering, bremsstrahlung and Synchrotron radiation, are all describable by the same fun-damental process where a very energetic electron scatters off a low energy photon.1Strictly speaking PSRB1259−63 is no HMXB as the definition of the latter also includes that thesystem is accretion driven.

31


The latter description is usually known as the IC process but also bremsstrahlung andsynchrotron radiation can be seen as IC scattering of virtual photons. In case of brems-strahlung (see Fig. 3.2) these photons constitute the Coulomb field of an atom or within a

Figure 3.2: Feynman graphs illustratingthe emission of a photon in thecoulomb field of a nucleus by aVHE electron [Brock(2006)].

plasma, for Synchrotron radiation it is themagnetic field that is made up by virtualphotons. The actual inverse Compton(IC) scattering is a quantum mechanicalprocess where the scattered light has to betreated with its particle nature, i.e. as pho-tons. Unlike the classical Thomson scatter-ing for lower non-relativistic energies wherethe wavelength of the scattered light doesnot change, the light is just deflected andsees a discrete change in phase, the IC ef-fect leads to a change in momentum and

energy of the scattered photon. The change in energy and subsequently in the photonwavelength is given by

E′ = E

1 + Emec2 (1− cos θ)

≈ E(

1− E

mec2 (1− cos θ))

(3.1)

λ′ − λ = E

mec(1− cos θ) (3.2)

Here E′ (E) and λ′ (λ) denote the photon energy and wavelength after (before) thescattering, respectively, as seen in the electron’s rest system. θ is the scattering angleand me the electron rest mass.In many VHE sources the IC effect is an important cooling process for electrons accel-erated beyond the TeV regime. Due to the VHE electrons in PWs it is also believed toplay a crucial role in PSRB1259−63 . The cross section σ for Compton scattering isenergy dependent and given in differential form by

dσ

dΩdE′ = 12r

20

(E′

E

)2 ( EE′

+ E′

E− sin2 θ

)δ

(E′ − E

1 + (E/mc2) (1− cos θ)

)(3.3)

where dσdΩdE′ is the differential cross section dσ for scattering into a solid angle dΩ and for

an energy intervall dE′ of the scattered photon as seen from the electron’s rest frame.r0 = e2

mec2 denotes the classical electron radius. The differential cross section showsan asymmetric behavior with respect to the scattering angle for energies E mec

2,the so called Klein-Nishina regime. Figure 3.3 (top) shows the angular dependence ofthe Compton differential cross section for different photon energies. For lower energiesthe symmetric Thomson formula holds. In the high energy Klein-Nishina regime thedifferential cross section as a function of scattering angle becomes asymmetric witha lower propability towards higher scattering angles. The energy distribution of thescattered photons in the laboratory system is shown in the bottom panel of the samefigure. It can be seen that depending on the incident photon energy, that the distribution

32


can be quite different in shape. In the figure the factor

Γε = 4εγ/mec2 (3.4)

describes the scattering domain, where ε is the incident photon energy in the laboratorysystem, me the electron’s rest mass and γ = (1− v2

c2 )−1/2 the Lorentz factor for electronsmoving with velocity v. For Γε 1 most photons are scattered in the low energy regime(Thomson regime) whereas the distribution peaks at high energies (E1 ≈ 1; E1 in unitsof the maximum possible scattered photon energy) for highly energetic photons, meaningthat most of the energy is converted within one scattering process. The timescale atwhich VHE electrons (and positrons) lose their energy via Comptonization, i.e. theircooling time, can be inferred from the energy loss rate dEic

dt of relativistic electronsmoving through an isotropic photon gas with a black body photon distribution n(ε) ascalculated in [Blumenthal and Gould(1970)]:

n(ε) =(π2(hc)3

)−1ε2/(eε/kT − 1) (3.5)

−dEicdt

∣∣∣∣Γε1

= πr02m2c5

∫n(ε)ε

(ln 4εγmc2 −

116

)dε (3.6)

Integration over Eqn. 3.6 gives

−dEicdt

= 16πr0

2 (mckT )2

h3

(ln 4γkT

mc2 −56 − 1.1472

)(3.7)

which can be used to calculate the cooling time tKN in the Klein-Nishina regime for agiven maximum electron energy Emax.

Bremsstrahlung is yet another important radiation mechanism in VHE astrophys-ics. It happens when charged particles are accelerated in a Coulomb field. An ultrarel-ativistic electron with energy Ee that is interacting with the Coulomb field of a nucleuswith charge number Z loses energy at a rate [Berestetskii et al.(1974)]

−dEbremsdt

= 4nzZ2αr2ecEe

(ln 2Eem2c4 −

13

), (3.8)

where α = e2/hc is the fine-structure constant and nz denotes the number density ofnuclei.2

Synchrotron radiation is the magnetic analogon to bremsstrahlung, i.e. it is theradiation emitted by relativistic electrons in a magnetic field3. From electrodynamics itis known that the radiation of an accelerated electron emits energy per unit time

−dEsyncdt

= 2e2

3c3 γ4(a2⊥ + γ2a2

‖

)(3.9)

where a⊥,‖ is the electron’s acceleration perpendicular and parallel to the magneticfield, respectively [Wilms(2008)]. Assuming no parallel acceleration we get only circular

2In Eq(3.8) interactions with the electrons from an atomic shell have been ignored.3For the non-relativistic case this radiation is known as cyclotron radiation.

33


Figure 3.3: (Top) Angular dependence of the Comptonization differential cross sectionfor different photon energies [Van Rooyen(2010)]. (Bottom) Normalizedphoton distribution in the laboratory system for IC scattering of electronsmoving through an isotropic photon gas for different factors of Γε (see text).E1 ∈ [0, 1] is the photon energy in units of the maximum possible photonenergy, i.e. ε′ = γmec

2Γε(1 + Γε)−1E1, where ε′ denotes the photon energyafter scattering. [Blumenthal and Gould(1970)].

34


motion along the field line and a⊥ = ωLγ−1v⊥ with ωL being the Larmor-frequency4.

In case of cirular motion the radiated energy becomes

−dEsyncdt

= 2e2

3c3 γ4 v

2⊥e

2B2

γ2m2ec

2 = 2β2γ2c · σT · UB · sin2 α (3.10)

for the electron scattering virtual photons from the magnetic field. UB = B2/8π isthe energy density of the B-field and σT = 8π

3 r20 is the Thomson-cross section. For an

isotropic velocity distribution integration over all electrons gives5

−dEsyncdt

= 4/3 · β2γ2c · σT · UB ∼ 1.6× 10−2eVs−1 ·(B2

8π

)(E

mec2

)2(3.11)

3.1.2 π0 decay

The π0-meson is a quantum mechanical superposition of the (anti-)up and (anti-)downquark combinations uu and dd: |π0〉 = 1√

2

(|uu〉 − |dd〉

). Its main decay mode (99%) is

into two γ’s via the electromagnetic force (see Fig. 3.4 left).Neutral pions could be produced in binary systems: Multiple TeV particle populations,as believed to be found in the relativistic jets of MQs (see Fig. 3.4 right) or in PW shockzones, can interact with hadronic target material. In a PW driven binary source sucha target can be the dense wind of a stellar companion or in a MQ the jet itself. TheVHE particles in MQ jets can also interact with ambient X-ray photons stemming fromsynchrotron radiation from particles accelerated in the black hole’s accretion disc. Inall such cases one expects the production of pions and subsequently the emission of TeVphotons.

3.1.3 Attenuation and radiating secondaries

Once VHE photons have been created in binaries in one of the above mentioned processesthey also very likely can suffer an early disappearance through absorption in ambientdense photon fields. According to [Kirk et al.(1999)] and [Dubus(2006b)] VHE photonsgenerated in binary systems such as PSRB1259−63 can be absorbed via pair productionγγ −→ e+e− in the photon field of a stellar companion. If this is the case for a significantfraction of TeV photons then e+e−-pair cascades would be the result which in turn wouldtransfer the absorbed emission power to lower photon energies observable in other wavebands.The differential absorption opacity dτ due to photons of energy ε seen by a γ-ray ofenergy E is given by

dτ = nεσγγ(1− cosψ)dεdΩdr (3.12)

where nε is the photon radiation density in cm−3 erg−1 sr−1, σγγ is the photon-photoninteraction cross-section, ψ the angle at which the photon trajetories intersect, dΩ is thesolid angle element of a surface emitting the soft target photons and dr denotes the lineelement along the γ-ray trajetory. Figure 3.5 illustrates this for a binary system such4Note that numerically the Larmor-frequency νL = ωL/2π = 2.8MHz (B/1G).5Note that the average pitch angle is 〈sin2 α〉 = 1

4π

∫ 4π0 sin2 αdΩ = 1

4π

∫ 2π0 dφ

∫ π0 sin2 α sinαdα = 2

3 .

35


Figure 3.4: (left) Feynman diagram for the decay of a neutral pion into two photons.(right) Ultrarelativistic jet of ejected particles from a microquasar blackhole. In such jets hadronic interactions could lead to the production ofneutral pions that decay into VHE γ’s [IIHE Bruxelles(2007)].

as PSRB1259−63. The interaction cross-section σγγ only depends on the parameter

s = εE

2m2ec

4 (1− cosψ). (3.13)

Pair creation will occur for s > 1.However, for sufficiently small magnetic fields present in binaries, pair cascading could

Figure 3.5: Sketch defining angles and distances in a binary system [Kirk et al.(1999)].

also partly come up for attenuation losses, as secondary electrons from the cascade areable to produce TeV photons via inverse Compton (IC) scattering and therefore mak-ing the source again more transparent for this energyband [Bosch-Ramon et al.(2008)].The latter scenario is certainly dependent on the separation distance D of the two bi-nary companions as the B-field scales with 1

D . Above a critical value for the B-field

36

3.2 LS 5039

[Khangulyan et al.(2008a)] of

Bc = 10(

L∗7 · 1038 erg/s

) 12(R

R∗

)−1G, (3.14)

where L∗ and R∗ are the star’s luminosity and radius, respectively, and R denotes thedistance between the star and the γ-ray absorption point, pair cascading for photonenergies above ∼ 1 TeV is largely suppressed due to dominating synchrotron radiationof electrons. Taking into account estimates for the magnetic field strengths of the orderof kG near OB-type stars and their winds, this is likely to be the case.

3.2 LS 5039LS 5039 comprises a compact object that orbits a O6.5V star on a mildly eccentric(e = 0.35) orbit with a period of 3.9 days. Identified as massive binary X-ray systemin 1997 [Motch et al.(1997)], that also shows a faint radio signature [Marti et al.(1998)]with resolved mildly relativistic bipolar radio jets originating from a central core[Paredes et al.(2000)], it has been classified as a microquasar. However, the bipolar jetstructure could also be mimicked by cometary tails as proposed in [Dubus(2006b)] andrecently observed in the similar northern object LS I+61 303 [Albert et al.(2008)]. Thesystem has been discovered in the TeV regime by H.E.S.S. during the 2004 galacticplane scan [Aharonian(2005)]. A follow up campaign in 2005 yielded an overall datasetof 69.2 h of observations, establishing the variable nature of the flux and spectral evolu-tion of this γ-ray source [Aharonian(2006)]. A total of 1969 γ photons with a significanceof 40 standard deviations were obtained from the data using an analysis method de-scribed in [de Naurois(2006)]. The corresponding excess of VHE photons was found tobe coincident with the VLBA radio position of LS 5039.Decomposition of the run-wise (28min bins) VHE flux data above 1TeV obtained fromthe H.E.S.S. observations into its frequency components by means of a Lomb-Scargle[Scargle(1982)] periodogram yields a significant peak at a period of 3.9078±0.0015 days.This is fully consistent with the optical period found in [Casares et al.(2005)].The run-wise lightcurve as a function of orbital phase φ is shown in Fig. 3.6. The VHEflux of γ-rays ≥ 1TeV follows an almost sinusoidal behavior with the emission maximumbeing at φ ≈ 0.7 which roughly coincides with the inferior conjunction of the system,i.e. the position in which the compact object aligns with the lign of sight between thestar and the observer.The data also revealed a modulation in the differential energy spectrum of VHE pho-tons (see Fig. 3.6). This is expected when considering the variable environment ofthe system, i.e. changing magnetic field strengths, target photon densities and rela-tive position of the two system constituents with respect to the line of sight. Dividingthe data into two broad phase intervals, one centered at inferior conjunction (INFC,0.45 < φ ≤ 0.9) and one at superior conjunction (SUPC, 0.9 < φ ≤ 0.45), i.e. withthe compact object in front/behind the star, respectively, with respect to the observer,yields two distinct spectral shapes corresponding to the high and low flux states in thesystem. The INFC spectrum (high state) is well described by a power law with photonindex Γ = 1.85± 0.06stat± 0.1syst and an exponential cutoff at Eexp = 8.7± 2.0TeV. TheINFC spectral behavior (low state), however, follows a pure power law with a rather

37


Figure 3.6: (upper panel) Differential energy spectrum of VHE photons stemming fromLS 5039. The dataset has been divided into two phase bands correspondingto the high flux state around inferior conjunction (INFC) as well as low fluxstate centered at superior conjunction (SUPC). The shaded regions depictthe 1σ confidence intervals of the according fits to the data. The spectrumclearly hardens around inferior conjunction between 200GeV and a few TeV.(lower panel) Run-wise integrated photon flux above 1TeV from LS 5039 asa function of orbital phase, measured by H.E.S.S. between 2004 and 2005.Each run has a duration of ∼ 28min. The vertical blue lines denote themaximum and minimum in the binary separation distance at periastron andapastron respectively. Accordingly, the vertical dashed red lines representinferior and superior conjunction, i.e. the alignment of the star and thecompact object with respect to the line of sight [Aharonian(2006)].

38

3.2 LS 5039

Figure 3.7: (Top panel) Spectral indices of a pure power law fit to VHE photons from LS5039 below 5TeV for phase intervals ∆φ = 0.1. (Bottom panel) Flux nor-malisation at 1 TeV for the same fits and phase binning [Aharonian(2006)].

steep index of Γ = 2.53 ± 0.06stat ± 0.1syst ranging from 200GeV up to ∼ 20TeV. Atthe corresponding edges of this energy range the γ-ray spectrum seems to be almostinvariable, while the maximum in modulation occurs around ∼ 5TeV. Moreover, acomparison of all power law fits to the data divided into phase bins of width 0.1 showsa strong anti-correlation between the photon index Γ and the flux state. This has beendone for photons below 5TeV to omit effects stemming from the spectral cutoff duringhigh state. According to this, the spectrum becomes harder in the high flux state andsofter in the low state (see Fig. 3.7).The modulation in the VHE γ-ray flux indicates that the emission zone lies relativelyclose, i.e. within a radius of ∼ 1AU to the stellar companion. At such distances, variableabsorption of γ-rays in the dense stellar photon field is expected due to the productionof e+e−-pairs [Dubus(2006b)]. In the light of a pure absorption scenario, a maximumin spectral modulation is expected around 300GeV with a hardening of the spectrumtowards the low flux state. This, however, is in contrast to the observations. This sug-

39


Figure 3.8: VHE γ-ray flux above E > 400GeV from LSI+61-303 in units of10−12 cm−2 s−1 as a function of orbital phase as measured by MAGIC in 2006(red points) and 2008 (black points) [Albert et al.(2008)]. The lightcurve isclearly variable.

gests more complicated scenarios for the generation of VHE radiation in this system,accounting e.g. for modulations in acceleration and cooling time scales, variations inthe stellar photon field density and magnetic field strength along the compact object’sorbit [Khangulyan et al.(2008b)].Time dependent accretion rates in case of a microquasar scenario should also be takeninto account [Romero et al.(2007)].

3.3 LSI+61-303

The system LSI+61-303 is in many respects similar to PSRB1259−63 as it also com-prises a Be star as massive partner to the as of yet unidentified compact object (NS orBH). Located in the northern sky at a distance of ∼ 2 kpc, just like PSRB1259−63 itfeatures a highly eccentric orbit (e = 0.72 ± 15) but has a much faster orbital periodof τ = 26.5 d. Variability in lightcurves throughout all wavebands from radio, infraredover opical to X-rays has been found for this system. It has been first detected in TeVγ-rays by the MAGIC collaboration in 2006 showing a variable flux on timescales ofdays with a peak intensity near apastron at orbital phases φ ∼ 0.656 (see Fig. 3.8)[Albert et al.(2008)]. The integrated flux above 400GeV around the peak emission, i.e.between φ = 0.6 and 0.7, is (7.9 ± 0.9stat ± 2.4syst) × 10−12 cm−2 s−1. A Lomb-Scargleperiodogram of the lightcurve yields an orbital period of 26.8 ± 0.2 d compatible withthe periods seen in the optical, radio and X-ray band (Fig. 3.9). This indicates thatthe VHE flux modulation in this system is strongly connected to the trajectory of thecompact object. Moreover, the peak emission in X-rays seems to coincide with the max-imum of the TeV γ-ray flux.The differential energy spectrum of VHE γ-rays from LSI+61-303 is well described by asimple power law with a photon index of Γ ∼ 2.6. There is no sign for spectral variabilitywhen comparing the spectra from different phase bins, i.e. 0.5 < φ < 0.6, 0.6 < φ < 0.76By definition the periastron is set to φ = 0.23 ± 0.02 for this system. This is because the orbitalephemeris of LSI+61-303 is defined with respect to radio outbursts and these do not occur at φ = 0.

40

3.4 The Microquasar Cygnus X−1

in 2008 and the overall spectrum as measured in 2006, as shown in Fig. 3.9.Tests for intra-night-variability showed a constant flux level on timescales down to

30min. The regular radio outbursts every orbital cycle with a two-sided, seemingly pre-cessing jet morphology have led some authors to the conclusion that LSI+61-303 couldbe a microquasar and the emission seen from it accretion driven[Bosch-Ramon et al.(2006)]. However, the lack of evidence for the existence of an accre-tion disc and the complex as well as variable morphology of the jet-like radio structuresfavor a pulsar wind scenario comparable to the case of PSRB1259−63 (Sec. 4). In aPW scenario the jet-like structures seen in the radio data of LSI+61-303 (Fig. 3.10 toppanel) can be interpreted as not stemming from a microquasar jet but as the trail ofa shocked PW that is directed away from the companion star [Dubus(2006a)]. A sim-ilar model presented in [Nerronov(2008)] therefore suggests that LSI+61-303 could bea downsized version of PSRB1259−63 where the maximum of the γ-ray excess appearsaround apastron for the simple reason that for closer separation distances the generatedTeV photons suffer attenuation due to absorption in the denser stellar photon field (see3.10 bottom panel).


Cygnus X-1 is a HMXB system located at a distance of ∼2.2 kpc. It consists of a stellarBH of 21 ± 8MÀ and a supergiant companion star of spectral type O9.7 Iab with amass of 40 ± 10MÀ. The BH orbits its companion almost on a circle (e ≈ 0.06) inτ = 5.6 d. The system is thought to be inclined between 25 − 65 with respect to theobserver. Since Cygnus X-1 unambigously features a BH, it is so far the only knownaccreting binary system that has been detected in the TeV regime. As measurementswith VLBA7 show a one sided elongated morphology (15 mas in length) in the radiomap during the system’s hard state, Cygnus X-1 can be considered as microquasar. Thejet seems to be collimated with an opening angle < 2 and consists of highly relativisticmatter (v ≥ 0.6 c). The jet terminates in the ambient medium and forms a ringlikeradio structure of 5 pc in diameter.X-Ray measurements show the typical signs of accretion which can be seen as high/softand low/hard states in the spectra, respectively, depending on the accretion rate. Thismeans that the X-ray emission is high in flux with a soft spectral index whenever theBH is accreting and on the other hand shows a hard spectrum in the low state. Thehigh energy (HE) measurements as carried out by experiments such as COMPTEL andINTEGRAL show a non-thermal component. The hard X-ray emission from CygnusX-1 is believed to be produced in the IC scattering of soft star photons by thermalelectrons which could be located in a corona or at the base of the microquasar jet. Inaddition a thermal soft component is believed to stem from the accretion disc.A strong sign for accretion going on in the system are the observed fast variations atthe ∼ms scale in the 3-30 keV band with a change of a factor of 3-30 in flux. Similardramatic flux variations are also seen in the ∼ks regime for 15-300 keV. So Cygnus X-1 isreckoned to be a system where energy is dissipated in a radiatively inefficient relativisticjet where also TeV γ-ray emission could occur.

7Very Long Baseline Array, http://www.vlba.nrao.edu/

41


Figure 3.9: (top) Differential energy spectra dFdE for the phase bins 0.5 < φ < 0.6

(green) and 0.6 < φ < 0.7 (red) obtained during the 2008 MAGIC campaignas well as the overall 2006 data (dashed blue) where a significant excessin TeV γ-rays from LSI+61-303 has been measured. The spectra are allwell described by simple power laws and are all compatible with each otherwithin the errors given, i.e. no spectral variability can be found. (bottom)Lomb-Scargle periodogram for the lightcurve of LSI+61-303 (upper panel).From this a peak frequencyof 0.0377d−1 corresponding to an orbital periodof 26.8±0.2 d can be found in the VHE daily flux. Simultaneous backgrounddata is also shown (middle panel). The subtraction of a pure sinusoidal atthe extracted orbital frequency from the periodogram (yellow line) as wellas a sinusoidal together with a Gaussian wave form (blue line) is shown inthe lower panel [Albert et al.(2008)].

42


Figure 3.10: (top) Radio contours of the system LS I+61-303 as a function of orbitalphase (not to scale!). (bottom) Model for LS I+61-303 as a downsizedversion of PSRB1259−63 . In this scenario TeV photons can only escapethe stellar radiation field around apastron where the separation distancebetween pulsar and star is sufficiently large [Nerronov(2008)].

43


Figure 3.11: Photon fluxes from Cygnus X-1 in units of the flux from theCrab nebula as seen in differ-ent wavebands measured simulta-neously with MAGIC, Swift andRXTE (top down). A flare in theflux data seen with all three instru-ments is indicated by the verticalred line [Albert et al.(2007)].

When the VHE γ-ray telescopeMAGIC observed this target in2006 for 46.2 h no steady TeV γ-ray emission could be measured[Albert et al.(2007)]. However, on2006-09-24 during a period of ∼80minutes containing a simultaneoushard X-ray flare seen by SWIFT andRXTE the system was active in VHEphotons. In this time slot MAGIC de-tected Cygnus X-1 with a significanceof 4.9σ (4.1σ post trials) showing aphoton spectrum following a simplepower law (see Fig. 3.12). The peak inthe TeV emission occured right at therising edge of the first X-ray peak seenby Swift (see Fig. 3.11). On the otherhand, the next night there was no sig-nificant TeV emission seen while an-other soft X-ray peak was seen. Thissuggests that soft/hard X-rays couldbe produced in different regions of thesystem and that hard X-rays and γ-rays are linked, possibly by the rel-ativistic jet. In such a picture thehard X-rays could be produced at thebase of the jet whereas the γ-rayswould be generated in the interac-tion of the jet with the stellar wind.The time scales of the correspondingemission prcesses would be differentand therefore explain the slight shiftbetween the X-ray and γ-ray peak.The γ-ray peak occured at an orbitalphase of 0.91 where the BH is behindthe star with respect to the observer.This actually is the moment where theopacity for TeV γ-rays should be thehighest due to pair production in thedense photon field of the star. TheVHE data therefore suggest that theγ-ray source in Cygnus X-1 is far awayfrom the compact object which wouldfit to the senario of the jets interact-ing with the stellar wind as the sourcefor VHE emission.

44


Figure 3.12: Energy spectrum of the γ-ray events measured from Cygnus X-1 on 2006-09-24 (blue points). The data can be described by a simple power law asindicated in the plot. Also shown are the upper limits (black bars) for theoverall observation of 46.2 h livetime which yielded no significant detectionof Cygnus X-1 in TeV γ-rays.

45

4 The System PSRB1259−63/SS2883

Since the discovery of PSRB1259−63 in radio in 1992 by Johnston et al. this objecthas been a constant target for various experiments ranging from radio wavelengths (see[Johnston et al.(1992)] and [Johnston et al.(1999)]) to X-ray measurements (see e.g.[Greiner et al.(1995)],[Hirayama et al.(1999)],[Nicastro et al.(1999)],[Shaw et al.(2004)][Chernyakova et al.(2006)]) up to TeV energies covered by IACT experiments such asH.E.S.S. and CANGOROO (see [Aharonian et al.(2005a)] and [Kawachi et al.(2004)]).This chapter will introduce the various system parameters of this binary and discussbriefly the physical mechanisms which may lead to non thermal emission. After thediscussion of radio and X-Ray data for this object Ch. 5 will present the VHE data forPSRB1259−63.

4.1 System Outline

The system PSRB1259−63/SS2883 consists of a 48 ms pulsar that orbits a massiveBe2-type star on an eccentric orbit with a period of 3.4 years (see Tab. 4.1)[Tavani et al.(1997)]. The massive companion of several solar masses features a hetero-geneous wind with different densities and velocity profiles at the polar and equatorialregions. The denser and slower circumstellar wind forms a disc, presumably slightly in-clined to the pulsar’s orbit (see Fig. 4.1). Such a tilted disc could account for the eclipseof the pulsed radio signal 12 days prior to and 14 days after periastron as reported in[Johnston et al.(1999)].

Parameter ValueEccentricity, e 0.87

Orbital Period, Porb [d] 1273Compact Object Neutron Star (NS)

Pulsar Period, P [ms] 47.7P = dP

dt 2.27579 · 10−15

Spin-down age, τ [yr] 3 · 105

Spin-down luminosity, L[erg s−1] 8 · 1035

Magnetic field, B [G] 3 · 1011

Companion Star Be2Temperature [K] 2.4 · 104

Mass [MÀ] 10

Table 4.1: System parameters of the plerionic binary PSRB1259−63/SS2883.

The two zone stellar wind introduces further complications for the modelling as cor-responding interaction mechanisms crucially depend on which stellar wind region is

47


θ

Figure 4.1: 3D model sketch of PSRB1259−63. The pulsar size (indicated by the sphereon the blue trajectory) is exaggerated by orders of magnitude. The greenweb depicts the circumstellar disc of the Be star. According to observationaldata from various energy bands, the pulsar orbit seems to be inclined withrespect to the circumstellar disc by an angle δ as well as tilted with respectto the line of intersection between disc and semiminor axis of the ecliptic byan angle ω. In this plot δ equals 20 and ω was chosen with 6. The redlines indicate the definition of the true anomaly θ which is the angle betweenperiastron and the pulsar position as seen from the companion star.

encountered by the pulsar wind (PW) particles. Before discussing the PW interactionsin detail, the general properties of the two companions shall be presented.

4.2 Pulsars and Pulsar Winds

A pulsar is a rapidly rotating neutron star that has formed from a supernova explosionending the evolution of a star with a mass 1.44MÀ < MStar < 3MÀ. The mass bound-aries correspond to the Chandrasekhar limit for the quantum mechanical degeneracypressure built up by the electrons in an atom and the Tolman-Oppenheimer-Volkofflimit, respectively. The latter being the Chandrasekhar analogy for matter entirely con-sisting of neutrons, which also can be described by a cold degenerate fermion gas.Since the discovery of pulsars in 1967 by J. Bell and A. Hewish1 their exact physicalproperties have remained unknown. It is known, however, that pulsars are the sourceof periodic signals in various energy bands on timescales from ms to s. Moreover itis believed that these pulsars are the origin of relativistic particle winds which play acrucial role for the system discussed in this thesis.

1On the 28th of November 1967 Jocelyn Bell and her doctoral adviser Antony Hewish discovered thepulsating radiosignal from PSR B1919+21.

48

4.2 Pulsars and Pulsar Winds

Figure 4.2: (left) Generic pulsar model showing the lightcylinder and the different zonesin the magnetosphere. (right) Generation of leptonic wind particles at thepulsar surface. Both figures are taken from [Lorimer and Kramer(2004)].

Many sophisticated pulsar models exist. This chapter shall give a rough overview of thebasic ingredients of models for pulsars and pulsar winds (PW). The following sectionbasically follows the review in [Gaensler and Slane(2006)].

A Basic Pulsar Model

When a star collapses to form a pulsar, the magnetic field of the star also contracts andbecomes denser and therefore stronger. Pulsars carry the strongest magnetic fields in theknown universe. The magnetic field is typically of the order of 1012 − 1013G, in generalnot aligned with respect to the pulsar’s rotation axis and forced to co-rotate with thespinning object. This co-rotation of high magnetic fields is believed to be responsiblefor the radiation seen from the pulsar. In a naive model, the pulsar behaves like a dipolthat radiates away electromagnetic energy through the rotating B-field originating atthe magnetic polar caps (see fig. 4.2 left). This generates a so called lighthouse effect,i.e. the direction at which the radiation is emitted moves around the rotation axis.This mechanism is the reason for the periodic radio signals, pulsars have been identifiedwith in the first place. Apart from the pure electromagnetic radiation the pulsar alsois believed to emit a strong wind of ultrarelativistic particles, most likely electrons andpositrons. The physical mechanisms for such a PW are explained later in this section.The energy source for all sorts of emissions seen from a pulsar is the rotational kineticenergy Erot which is dissipated over time as spin down luminosity

E = −dErotdt

= 4π2IP

P 3 (4.1)

49


where P is the pulsar’s period, P = dP/dt and I the neutron star’s moment of inertia.I has a typical value of ∼ 1045 g cm2 and the range for E lies between 1028 erg s−1 and1039 erg s−1. Measuring P and P from the observed time dependent repetition rate ofradio pulses allows for a rough estimate of the age of the pulsar. If one assumes that thepulsar initially had a (birth) period of P0 and that its spin-down in angular frequencyω = 2πP follows ω = −kωn with breaking index n 6= 1 and some constant k then itsage is given by

τ = P

(n− 1)P

[1−

(P0P

)n−1]. (4.2)

For P0 P Eq. 4.2 yields the so called characteristic pulsar age τc = P/(n− 1)/P . Atthe beginning of a pulsar’s evolution it starts with an initial spin-down luminosity E0.Assuming n being constant, the time evolution of E reads

E(t) = E0

(1 + t

τ0

)− (n+1)(n−1)

(4.3)

withτ0 = P0

(n− 1)P0= 2τcn− 1 − t, (4.4)

as initial spin-down time scale. This implies that the pulsar has an almost constantenergy output until it reaches the age τ0 and subsequently shows the approximate timedependence E ∝ t−(n+1)/(n−1). The energy emitted feeds a population of energeticeletrons and positrons which generate the PW. In analogy to Eq.4.3, the spin-downperiod reads

P = P

(1 + t

τ0

)1/(n−1). (4.5)

In the traditional magnetic dipole model the magnetosphere of a rapidly rotating neu-tronstar is divided into several zones (see Fig. 4.2). The light cylinder is the surface onwhich a co-rotating object would move with the speed of light. The cylinder radius isdefined as RLC = c/ω where ω is the angular velocity. Inside the cylinder the magne-tized plasma surrounding the pulsar is dominated by magnetic energy and the field linesco-rotate like a rigid body. Since the lines emerging around the polar caps are crossingthe light cylinder they do not close2.The charged particles forming the PW are believed to stem from charge separated gapseither near the pulsar surface around the polar caps where they (electrons) have beentorn out by the strong electromagnetic forces present there or from outer regions limitedby the light cylinder (see fig. 4.2 left). The created particles are immediately acceler-ated to ultrarelativistic energies within the strong electromagnetic fields. The electricpotential for a rotating magnetic field in case of an aligned rotator can be as high as

∆Φ = Bω2R3NS

2c ≈ 6× 1012(

B

1012 G

)(RNS10 km

)3 ( P1 s

)−2V, (4.6)

2Which strictly speaking is violating Maxwellian electrodynamics.

50

4.3 Be Stars

where RNS is the neutron star radius and

B = 3.2× 1019(PP )12 G (4.7)

is the equatorial surface magnetic field strength calculated for a dipole magnetic fieldwhere P is given in seconds.3 While moving in the curved polar B-field the acceleratedelectrons emit photons. These photons in turn feed a pair production mechanism viainteraction with the magnetic field and lower energy photons (Fig. 4.2 right) thereforecreating more electrons/positrons replacing particles that are lost due to centrifugalwinds.Basically in all models the PW which leaves the pulsar magnetosphere is dominatedby the Poynting flux FPF = − c

4π∫S(E × B)dA with only small contributions from the

particle kinetic energy flux FParticle. However, the magnetization parameter σ which isdefined as

σ = FPF

FParticle= B2

4πργc2 , (4.8)

where ρ and γ are the particle mass density and Lorentz factor, respectively, typi-cally requires values below σ < 0.01 in order to explain the observed high synchrotronluminosities in relation to the spin-down power of pulsars. So somehow the PW’s mag-netization must change dramatically from being magnetically dominated with σ ≈ 104

to kinetically dominated with σ < 0.01 between the light cylinder and the position of thewind termination shock where PWs get shocked by ambient media. Before this shockthe wind particles suffer no radiative losses since the magnetic field is moving with thewind effectively causing no Lorentz forces on the trajectories of the particles. At theshock, however, the particles are accelerated and the magnetic field lines are not frozenin the wind rest frame any longer. The particles thus start radiating synchrotron lightin the B-field forming a PW nebula (PWN) such as the one seen in the Crab nebula(Fig. 4.3). A corresponding mechanism that would explain this transition behavior inmagnetization remains up to now unknown.

4.3 Be Stars

Be stars are a subclass of the spectral class B which stands for extremely luminousand blue stars. The lower case e stands for forbidden hydrogen emission lines of thespectra of this object. Be stars are usually quite massive (10 − 20MÀ) and feature astellar disc due to rapid rotation. This disc is thought to be responsible for opticallinear polarization and prominent infrared (IR) radiation through the scattering of starlight in the disc ([Lamers et al.(1998)]) as well as emission from free-bound and free-free radiation. Moreover Hα lines are seen from such a circumstellar disc. From thewavelength dependence of the IR excess the mass loss rate can be derived. For Be starsthis is of the order of 1-2× 10−7MÀ/yr. From Be stars bound in X-ray binary systemsit is known that apart from the dense low velocity equatorial wind, i.e. the disc, there isalso a less dense but high velocity polar wind which leads to resonance lines in the UV

3Equation 4.7 is retrieved from equating Eq (4.1) with the Larmor formula for magnetic dipole radiationPrad = 2/3c3 (BR3

NS sinα)2 (4π2/P 2)2, where α is the inclination angle of the B-field with respect

to the rotation axis.

51


Figure 4.3: X-Ray image from the Crab nebular obtained by the CHANDRA sattelite.

regime. The two wind zones show different velocity profiles of the underlying plasmapopulations as can be seen in Fig. 4.4. The velocity distribution within the disc canusually be described by:

v(r) = v0

(r

RÀ

)m(4.9)

with m = n− 2 and 3 < n < 3.75. Whereas the polar wind velocity function reads as

v(r) = v0 + (v∞ − v0)(

1− RÀr

)β(4.10)

where v∞ is the terminal velocity, v0 = 0.01v∞ and β = 1. The wind velocities withinthe dense disc can be deduced from fluxes in X-ray outbursts in these systems andrange between 150 and 600 km s−1 ([Waters et al.(1988)]). The particle density profilefor such discs follows a power law of the form

N(R) = N0

(RÀR

)n(4.11)

where N0 is the particle density at the star surface, R and RÀ are the distance from andthe radius of the star, respectively, and n < 1 for R < 3RÀ. The scaling hight of Be stardiscs is thought to be of the order of h > 0.5RÀ. Monte Carlo simulations suggest thatdiscs with a particle disribution profile following N ∼ R−n where n = f(R) and n ∼ 0.5at R = RÀ could be responsible for the near-UV spectropolarimetry of Be stars.

52

4.4 Non-Thermal Radiation from PSRB1259−63

Figure 4.4: Velocity profile for polar (dotted line) and equatorial (solid line) wind regionsfor a typical Be-star as e.g. X Per. A big difference in the acceleration ratebetween the two zones is noticable [Waters et al.(1988)].


Coming back to PSRB1259−63, the mechanisms which are responsible for the genera-tion of VHE radiation in such a binary system shall be discussed in more detail.This section basically follows the publications in [Khangulyan(2006)], [Dubus(2006b)]and [Neronov and Chernyakova(2007)] in case of IC and π0-decay as well as the papersin [Dubus(2006c)] and [Kirk et al.(1999)] for pair production and absorption in TeV bi-naries and [Khangulyan(2006)] in case of adiabatic cooling.The general idea for the generation of a multiple TeV particle population within PSRB1259−63 capable of producing VHE photons is acceleration at the shock region be-tween PW and the stellar companion wind. At the standoff point where the two windsmeet, the cold ultrarelativistic PW gets shocked by the stellar outflow and the PW par-ticles are isotropized and accelerated to TeV energies (see Fig. 4.5). These particles canin case of electrons be cooled via IC scattering of UV star photons, radiate synchrotronor bremsstrahlung light in the various energy bands. If a certain fraction of PW particlesconsitsts of hadrons also hadronic mechanisms can lead to electromagnetic emission inconnection with the stellar disc as discussed in Sec. 4.4.1.In [Khangulyan(2006)] for TeV electrons in PSRB1259−63 , tKN , the cooling time for

53


Figure 4.5: Simulation of a shocked PW. One can see the cometary like tailof particles trailing away from the shock region close to the pulsar[van der Swaluw et al.(2003)].

IC scattering in the Klein-Nishina regime, is approximatetly given by

tKN ≈ 7× 103ω−10 E0.7

1TeV s (4.12)

with ω0 being the target photon energy density at the shock standoff point in erg/cm3

and E1TeV denoting the photon energy in units of 1 TeV. In case of PSRB1259−63 themaximum electron injection energy Emax is determined by the size of the emissionregion, i.e. the size of the termination shock between the PW and the stellar outflowdue to particle escape as well as by the timescale for synchrotron cooling tsync which isthe dominant cooling mechanism for higher values of γ = 1/

√1− (v/c)2. The range of

the γ-factor itself depends on the injection spectrum of electrons in the shock region andis of course determined by the initial γ of the PW. The maximum value γmax dependson the acceleration timescale tacc which can be estimated by using the gyroradius ofan electron (i.e. this radius should not exceed the size of the shock region in order toprevent particles escaping from it) [Dubus(2006b)]:

tacc ≈γme

eB(4.13)

According to this γmax is determined by the prerequisite that tacc < tsync such thatparticles are accelerated before being cooled via synchrotron radiation. The synchrotroncooling timescale is given by4

tsync = 94m3ec

5

e4γ

1B2 (4.14)

4This follows from integrating Eq(3.11) considering dE/dt = mc2dγ/dt.

54


In [Dubus(2006b)] the interplay in the system PSRB1259−63 between the above men-tioned timescales has been modelled. Depending essentially only on 3 parameters,namely the magnetization of the PW σ, the size of the shock region Rs and thus thebinary separation ds and last but not least the pulsar luminosity E, these timescaleschange with these quantities. When computing the according total inverse coolingtimescale t−1

rad = t−1sync + t−1

KN using parameters suitable for a comparable system likeLS 5039 as a function of the γ-factor one finds the behavior shown in fig. 4.7. It canbe seen that the radiation timescale drops dramatically once synchrotron cooling is thedominant mechanism. For LS 5039 this happens to be above γs ≈ 2 × 106. The localminimum around γKN = mec2

hν ≈ 6 × 104 denotes the transition between the Thomsonand the Klein-Nishina regime below which IC dominates over synchrotron cooling.5 In[Neronov and Chernyakova(2007)] the spectral energy distribution (SED) from radio toγ-rays of PSRB1259−63 has been modelled using only IC and synchrotron contribu-tions (see Fig. 4.6). A spectral break around 1 MeV had to be introduced in order toaccount for the EGRET upper limits in the soft γ-ray regime. This translates into abreak around 100 MeV in the electron injection spectrum, roughly coincident with theCoulomb break energy ECoul expected from Coulomb losses that electrons will sufferin the dense stellar disc. The radio emission is modelled as synchrotron radiation fromelectrons trailing away from the shock after having undergone IC scattering and there-fore having produced X-ray and γ-ray emission. The drawback of a pure IC scenario

Figure 4.6: Model SED showing IC and synchrotron contributions for PSRB1259−63 to-gether with real data from various energy bands (radio to TeV)[Neronov and Chernyakova(2007)].

is the expectation of the maximum flux in TeV photons near periastron which clearly

5Assuming a photon energy of 2.8kT∗ ≈ 9 eV for the peak in the blackbody spectrum of the staraccording to Wien’s displacement law.

55


defies the data (compare Fig. 4.9 and Fig 4.10).Bremsstrahlung from shocked PW electrons during the disc passage could, according

Figure 4.7: Radiation timescales at the standoff point of a hypothetical PW shock inLS 5039 as computed in [Dubus(2006b)]. Solid lines indicate the radiationtimescales at periastron (black) and apastron (grey), respectively. The con-stant dashed lines represent the respective escape timescales tesc. AboveγS = 2× 106 synchrotron radiation is the dominant cooling mechanism. Forlower values of γ the cooling is IC dominated. The local minimum in thecooling curve is located at γ = 6× 104 corresponding to the transition fromthe Klein-Nishina to the Thomson regime.

to [Chernyakova et al.(2006)] and [Neronov and Chernyakova(2007)], also be responsi-ble for non thermal emission in the keV to TeV regime. The (energy independent)bremsstrahlung loss time,

tbrems = 104[

ndisc1011 cm−3

]−1s (4.15)

with a typical density ndisc ∼ 1010 − 1011 cm−3 of the slow equatorial stellar wind, is ofthe order of the proton-proton interaction time [Neronov and Chernyakova(2007)]. If thePW consisted of protons, the TeV emission could as well stem from neutral pion decay(see next section). tbrems is of the order of the IC cooling time for TeV electrons (compare

56


Figure 4.8: (left) Contributions of IC and bremsstrahlung fluxes to the overall γ-ray emission together with measurements from COMPTEL, EGRET andH.E.S.S. (right) Spectral Energy Distribution for PSRB1259−63 producedin pp-interactions from pion decay. The VHE γ-ray emission in this modelcomes from decaying π0’s while the radio to X-ray excess represents syn-chrotron and IC emission from secondary electrons/positrons, respectively[Neronov and Chernyakova(2007)].

Eq. 4.12). This means that bremsstrahlung could contribute a significant fraction to theoverall VHE emission (see Fig. 4.8). If one estimates the timescale of particles in thePW with velocity vPW escaping the shock region beyond the binary separation distanceR to be of the order tescp ∼ R/vPW , the fraction of the power of relativistic electronsLe converted into (bremsstrahlung) γ-rays is approximately Lγ/Le ≈ tescp/tbrems ∼10%

[ndisc/1011 cm−3]. Enhanced bremsstrahlung photon flux could also naturally come

up for the observed decrease in VHE photons at periastron since the pulsar could beleaving the equatorial wind at this epoch assuming a misaligned disc. The spectralbreak seen in the model SED at some 100 MeV can be justified by ionisation losses ofelectrons below 350 MeV which start dominating over the bremsstrahlung losses.

4.4.1 π0 decayIf the PW contains a significant fraction of protons and/or ions there is yet anotherpossibility for the conversion of PW power into VHE photons. The production of π0-mesons and their electromagnetic decay into two gammas is a scenario able to accountfor VHE emission in hadronic PW interactions. Protons with energies from GeV to TeVcan lose their energy when interacting with protons in the stellar wind. Naturally theinteraction rate between protons will peak when the pulsar passes the dense circumstellardisc. According to [Neronov and Chernyakova(2007)] the interaction time in this caseis

tpp = 1.6× 104[ndisc/1011 cm−3

]−1s (4.16)

Just like in the case of bremsstrahlung one can compare tescp to the pp interaction timetpp and find that ∼ 10 % of the PW power can be converted into secondary particles, suchas π-mesons and subsequently γ-rays from π0-decay, neutrinos, electrons and positrons.π0’s will carry away about 1

3 of the overall energy transfer in pp interactions. This in

57


turn means that π0-decay is less efficient than bremsstrahlung in terms of conversioninto VHE γ-rays:

Lγ/Lp ≈ 0.3 tescp/tbrems ∼ 3 %[ndisc/1011 cm−3

](4.17)

However this figure could be by far higher as the exact fraction of protons/ions in thePW is unknown. With a significantly higher hadronic PW content the γ-ray emissiondue to pp interactions could easily outshine the bremsstrahlung’s contribution.Figure 4.8 (right panel) shows the overall spectral energy distribution (SED) fromradio to TeV γ-rays in PSRB1259−63 for a purely hadronic model as calulated in[Neronov and Chernyakova(2007)]. Here the TeV flux stems from decaying π0’s whilethe radio and X-ray flux can be accounted for by radiating secondary electrons/positronsthat are naturally generated in the pion decay chain:

π+ −→ µ+ + νµ

µ+ −→ e+ + νµ + νµ

π− −→ µ− + νµ

µ− −→ e− + νµ + νµ

In this picture the radio flux is synchrotron radiation from the secondary electrons/positrons. At higher energies the latter also can do IC scattering on the stellar photonsand cause the X-ray emission seen in the data.

4.4.2 Non-Radiative LossesTo the above mentioned radiative mechanisms we find competing processes such as adia-batic cooling or particle escape losses from the shock region. Apart from the accelerationrate of primary particles, the magnetisation of the PW and the magnetic field conditionsat the standoff point, adiabatic expansion of the shock region and escaping electronsare the most important free parameters influencing the emission of VHE photons withinPSRB1259−63.The termination shock in PSRB1259−63 is supposedly a complicated region which al-lows for particles to escape and for adiabatic cooling due to a change in size. Thesetwo non-radiative energy loss mechanisms are not necessarily connected. For instancefast diffusing electrons can carry away energy from the emission region without sufferingany adiabatical losses. According to [Khangulyan(2006)] the time tescp for particles toescape can be quite short, i.e. tescp ≈ R/(c/3) which yields 103 s for periastron and 104 sduring apastron. The time for adiabatic losses tad ≈ d/v can be even much shorter sincethe characteristic shock radius d R and v can reach relativistic speeds. Here v is thevelocity at which the emission region expands. The exact calculation of non-radiativelosses is very complicated and has so far not been attempted. This is due to the manyparameters involved in the dymanics of the shock region influencing and causing bothparticle escape and adiabatic cooling. However it is possible to infer the degree of suchcontributions to the overall energy budget by studying the real flux data delivered byH.E.S.S. Figure 4.9 (top) shows the flux in 1 TeV photons measured in 2004 as a func-tion of time together with a simulated reference lightcurve (see Sec. 6.2) from which

58


the time profile of non-radiative cooling can be phenomenologically deduced. From thisapproach it becomes clear that the timescale for adiabatic losses tad drops dramaticallyaround periastron to ∼ 100 s in order to match the steep decrease in TeV photon fluxseen in the data. A natural explanation for this could be the smaller size of the shockregion near periastron. The region which is filled with relativistically accelerated PWparticles should be denser for smaller separation distances. This effect should becomeeven stronger for periods where the pulsar passes through the dense stellar disc and theemission region becomes compressed even further. Further away from periastron thefraction in adiabatic losses decreases significantely, however, with tad still being shorterthan the radiative time scales (∼ 104 s) throughout the whole orbit (see Fig. 4.9 (bot-tom)). The fact that adiabatic losses seem to dominate over radiative losses at all orbitalphases and energies is also responsible for the electron acceleration spectrum remainingunchanged even if radiative losses (IC, Synchrotron) are different for the various energybands and orbital epochs.

4.4.3 Absorption

Neglecting particle escape and adiabatic losses (see Sec. 4.4.2) the (anisotropic) energyflux of scattered IC photons EFE , with FE = E dN

dE , at a given energy E corrected forabsorption due to pair cascading reads

EFE = E2

d2

(dNs

dΩdEdt + dNIC

dΩdEdt

)e−τ (4.18)

where d is the distance to the emission region, dNs/dΩdEdt and dNIC/dΩdEdt denotethe rate of synchrotron and IC photons per steradian per second per energy interval,respectively. Equation 4.18 does not account for the significant drop in photon fluxaround periastron which is presumably due to adiabatic losses.VHE losses in PSRB1259−63 due to pair cascading become noticable above 50GeVas the threshold for the γ-ray energy E is roughly 45GeV × 2/(1 − cosψ) for an as-sumed monochromatic target photon field with a photon energy of ≈ 5.8 eV (comparewith Eq. 3.13).6 This is depicted in Fig. 4.10 where the model energy spectrum andlightcurve is plotted comparing emission including pair production with the case of noabsorption due to cascading: The solid line was calculated for a magnetic field B = 3.2Gincluding photon-photon absporption and pair cascading. The dotted line shows the in-trinsic emission not accounting for pair production. The dashed line in the top panelshows the IC Compton emission for B = 0.32G such that the injection rate was rescaledto give the same synchrotron flux as for the high B-field. The model lightcurve in thelower panel shows a significant asymmetry in flux for 100 GeV and 1 TeV photons withrespect to periastron. The fact that fluxes prior to periastron are systematically strongerin the model calculation in [Kirk et al.(1999)] can be explained with the inclination ofthe system’s orbit with respect to the observer meaning slightly higher scattering anglesψ before periastron and therefore enhanced energy transfer to the scattered photon. Themaximum energy transfer for the case of a head-on collision would happen at aroundperiastron when the pulsar is almost behind the star. However, this is also the pointwhere the optical depth in the star’s photon field is largest along the line of sight and6For the definition of ψ and other quantities used in this section compare with Sec. 3.1.3 and Fig. 3.5.

59


Figure 4.9: (top) H.E.S.S. data of 1 TeV photons emitted from PSRB1259−63 in2004 together with a simulated reference lightcurve. The time profile ofnon-radiative energy losses is shown in the upper right panel. (bottom)Energy loss (in units of the electrons’ γ-factor) of 1 TeV electrons inPSRB1259−63 as a function of the separation distance measured as fractionof the distance at periastron [Khangulyan(2006)].

60


Figure 4.10: Model energy spectrum 12 days prior to periastron (top) and lightcurve(bottom) for PSRB1259−63 as calculated in [Kirk et al.(1999)]. The datapoints (*) shown are ASCA and OSSE detections whereas the upper limits(arrows) were measured by COMPTEL and EGRET.

61


IC photons are absorbed. This in turn should reduce the flux just before periastron (seesolid line in Fig. 4.10 (lower panel)).

However, as shown in [Dubus(2006c)], absorption can not be fully responsible for theprominent reduction in TeV photon flux around periastron in PSRB1259−63. Assumingthe γ-rays being emitted at the pulsar position with a simple power law of the formdN/dE ∝ E−2.8 (H.E.S.S. observed a power law with a photon index of 2.8 in 2007)and calculating only absorption due to pair production gives the lightcurve shown inFig. 4.11. It can be seen that the maximum absorption with 40% of the photons being

Figure 4.11: Integrated photon flux above 380 GeV from PSRB1259−63 as measured byH.E.S.S. in 2004. The flux is normalized to its maximum at 10−7 m−2 s−1.The solid line is a model lightcurve including only absorption due to paircreation as calculated in [Dubus(2006c)]. A power law with a constantphoton index of 2.8 was assumed for the emission spectrum. Obviouslyabsorption does not play a key role for the significant variability of the TeVemission around periastron.

absorbed occurs slightly before periastron. The approximate flux minimum as suggestedby the H.E.S.S. data seems to come slightly later. It is clear that other mechanismsmust be at work in order to account for the observed variability which seems to be anintrinsic feature of the emission mechanism.

62

4.5 Radio observations

4.5 Radio observationsIn 1992 PSRB1259−63 was observed for the first time at radio wavelengths usingthe 64m Parks radio telescope which operates at frequencies at 600 and 1520 MHz[Johnston et al.(1992)]. From these observations the nature of the binary compact objectcould be clarified and various system parameters (see Tab. 4.1) were deduced from theradio signal. The clearly pulsed radio signal was identified to originate from a NS,showing a crab like puls profile. Moreover the pulsed radio signal from the NS showeda variable character in intensity with a complete disappearance of the signal at 430MHz. This has been taken as a hint for the pulsar propagating into the circumstellardisc (see Fig. 4.12). The unpulsed component of the radio emission is strongest aroundperiastron and qualitatively in agreement with the behavior seen in other wavebands(Fig. 5.3). Since the observations in 1992 PSRB1259−63 has been monitored andreobserved throughout the following periastron passages, confirming the conclusions ofthe initial measurements.The origin of the unpulsed radio emission in PSRB1259−63 is likely to be synchrotronradiation from cooled electrons trailing the shock region after having undergone ICscattering.

4.6 X-RaysX-ray measurements as carried out by ROSAT [Greiner et al.(1995)], BeppoSAX[Nicastro et al.(1999)], ASCA [Hirayama et al.(1999)], INTEGRAL [Shaw et al.(2004)]and XMM Newton [Chernyakova et al.(2006)] of PSR B 1259−63 showed unpulsed andnon-thermal radiation from a source variable in flux and spectral index. The X-rayluminosity LX evolves significantly in intensity towards periastron. Starting at LX ∼1033erg s−1 it peaks at LX ∼ 20 × 1033erg s−1 some 10 days prior to periastron. Theluminosity roughly stays constant at this level over periastron with receding intensityafter the passage. This behavior is traced by the development in the spectral indexof the X-ray emission as well as by the radio flux [Neronov and Chernyakova(2007)](Fig. 5.3& 4.13).

As origin of the X-ray emission several mechanisms have been sugessted (see e.g. ref-erences [Neronov and Chernyakova(2007)], [Khangulyan(2006)], [Kirk et al.(1999)],[Dubus(2006a)]). In an IC dominated picture photons in this energy band most likelystem from synchrotron radiation of the shock accelerated electrons in the magnetic fieldat the standoff point. Upstream of the shock the magnetic field of the PW moves withthe particles and therefore prevents radiation. In a hadronic disc scenario where theinteraction of the PW with the stellar disc generates pions, X-rays could also come fromradiating secondaries generated in the decay chains of π±-mesons.

63


Figure 4.12: (top) Mean PSRB1259−63 puls profile as seen at the radio frequencies660 and 1520 MHz. (bottom) Pulsed radio flux as a function of time[Johnston et al.(1992)].

64

4.6 X-Rays

Figure 4.13: Evolution of the X-ray photon index Γ as a function of the true anomalyθ (lower panel) along with the X-ray flux around periastron as measuredduring the years 1994, 1997 and 2004 with different detectors (upper panel)[Chernyakova et al.(2006)].

65

5 TeV Observations of PSRB1259−63 withH.E.S.S.

In this chapter observational VHE data that has been collected from PSRB1259−63in the first H.E.S.S. campaign in 2004 will be reviewed. After this the analysis of datataken by H.E.S.S. during the years 2005-2007 will be presented.

5.1 Measurements in 2004First observations of PSRB1259−63 in the TeV regime have been carried out by H.E.S.S.during the 2004 periastron passage [Aharonian et al.(2005a)]. A clear signal of γ-raysat a significance level of 13σ was detected. The photon flux with an average level of5 % of that of the Crab nebula was measured to be variable at timescales of days, whichmade the system the first variable galactic TeV source in the history of γ-ray astronomy.The differential energy spectrum of γ-rays followed a simple power law of the form

dN

dE= Φ0 ·

(E

1 TeV

)−Γ(5.1)

with Γ = 2.7±0.2stat±0.2sys and Φ0 = 1.3±0.1stat±0.3sys×10−12TeV−1cm−2s−1. Themonthly spectra that were measured for the observation periods March, April and June2004 showed no spectral variability with respect to the photon index Γ (see Fig. 5.1).Slightly offset by 0.6 to the north of the target position, another γ-ray source wasdetected. This source, HESS J1303-631, is an up to now unidentified VHE source,i.e. there are no counterparts to this source in other wavebands known.The integrated flux of VHE photons above an energy threshold of 380GeV around the2004 periastron passage is shown in Fig. 5.2. It shows the flux level on a night by nightbasis. As can be seen the flux is variable on timescales of days, corresponding to aχ2-probability of 1.2 × 10−7 for a constant flux. Its shape shows two features of risingand decreasing flux, asymmetric with respect to periastron. This peculiar shape gaverise to speculations about the TeV source in PSRB1259−63 being closely connectedto the pulsar interacting with the disc as also the other wavebands seem to trace theoverall behavior in increasing and receeding flux that can be seen in the VHE regime (seeFig. 5.3). This hypothesis also lead to the deduction of spacial parameters of the disc ofSS2883 such as location and thickness along the pulsar orbit [Chernyakova et al.(2006)].

5.2 Measurements in 2005, 2006 and 2007The successful detection of PSRB1259−63 in 2004 led to follow-up observations of thissource in the years 2005 and 2006 in order to monitor the VHE emitter during periods ofpresumed quiescence. The H.E.S.S. campaign during the 2004 periastron mainly covered

67

5 TeV Observations of PSRB1259−63 with H.E.S.S.

Figure 5.1: (top) Significance skymap for the PSRB1259−63 field of view (FoV) for45 h of data (live time) taken in 2004. A clear signal at 13σ can beseen from the target direction. The other source in the FoV, 0.6 to thenorth of PSRB1259−63 is the unidentified TeV γ-ray emitter HESS J1303-631. (bottom) Overall differential energy spectrum for PSRB1259−63 asobtained from the 2004 H.E.S.S. campaign. The spectrum is well de-scribed by a simple power law with Γ = 2.7 ± 0.2stat ± 0.2sys and Φ0 =1.3± 0.1stat ± 0.3sys × 10−12TeV−1cm−2s−1 [Aharonian et al.(2005a)].

68

5.2 Measurements in 2005, 2006 and 2007

Figure 5.2: Integrated daily flux above 380GeV of VHE photons from the sourcePSRB1259−63 as measured by the H.E.S.S. experiment around the 2004 pe-riastron. The vertical dashed line indicates periastron. On the upper panelthe unpulsed radio flux from the same observation period is shown. Thetime period around periastron, where the pulsed radio signal was eclipsedpresumably by the dense stellar disc, is depicted by a horizontal arrow[Aharonian et al.(2005a)].

69


Figure 5.3: Multiwavelength data of PSRB1259−63 as taken from 1994-2004: (Upperpanel) X-Ray data gathered by experiments ASCA, Beppo-SAX and-XMMNewton. (Middle panel) TeV data taken by H.E.S.S. during the 2004 peri-astron. (Lower panel) Radio data taken from 1994-2004. The grey shadedarea denotes the presumed location of the disc as concluded from the TeVand X-Ray data in [Chernyakova et al.(2006)].

70


orbital phases after the passage. The next periastron took place on the 27th of July2007 and the visibility of PSRB1259−63 for the H.E.S.S. telescopes for this time of theyear implied that the majority of observations of a second periastron campaign in theTeV regime would cover orbital phases before the passage (Fig. 5.4). A sensitivity studyfor the instrument estimating the exposures needed for a re-detection of the sourcefor the expected zenith angle band was performed (see Fig. 5.5). According to thisan observation campaign of 60h of data taking on PSRB1259−63 with H.E.S.S. wasproposed and scheduled for the period April to August 2007.

5.2.1 Sensitivity Study for the 2007 CampaignThe sensitivity of an IACT is defined as the amount of exposure time T that is neededto detect a source of certain strength, at a given zenith angle (ZA) θ and at a definedsignificance level, e.g. ∼ 5σ. The sensitivity of the H.E.S.S. instrument is a function ofθ, the photon energy E and the offset ω of the projected source position with respect tothe camera center. For observations at a given ZA the exposure time can be computedfrom the photon excess Nγ and the exposure integral δexp

Nγ(T,E, θ, ω) = Φ0 · T∫ (

E

E0

)−ΓA(E, θ, ω)dE︸︷︷︸

:=δexp

, (5.2)

where Φ0 represents the flux normalisation at normalisation energy E0 and Γ is thespectral index assuming a source whose energy spectrum follows a power law. Theeffective collection area of the detector A(E, θ, ω) is a measure of the probability of anincident photon hitting the detector to be detected. It is defined as

A(E, θ, ω) = 2π∫ ∞

0P (E, θ, ω,R)RdR (5.3)

where P is the probability of an incident photon to be detected and R is the impactdistance of the corresponding shower with respect to the telescope array center. Inpractice Eq. 5.3 is simplified to

A(E, θ, ω) = R20π lim

N→∞

n(E, θ, ω)N(E, θ, ω) , (5.4)

where R0 denotes the impact distance from the array center at which the probability ofshower detection is still not negligible, N is the number of simulated γ-rays hitting thetelescope and n the number of triggered photons.The excess in photons is basically a function of time Nγ = Nγ(t) and can be computedaccording to Eq. 2.7 from the ON and OFF rate in the detector. The significance for agiven excess according to Li&Ma [Li and Ma(1983)] is given in Eq. 2.8. Using Eq. 2.8the necessary exposure time T can be extracted. Assuming a certain source strength bychoosing values for Φ0 and Γ, respectively, to compute S(t = T ) from Eq. 5.2 the onlyquantity which has to be known in addition is the background or OFF rate for the ZAband investigated. For the study presented here the OFF rate was taken from real OFFsource data, gathered at the corresponding ZAs.The visibility for PSRB1259−63 in 2007 is shown in Fig. 5.4 and Tab. 5.1. According to

71


this the sensitivity of H.E.S.S. was computed for a ZA of 45 in the way described above.From real data an OFF rate of 275 ph/h and α = 0.2 was extracted. Equation 5.2 yields7.0 ph/h, assuming Φ0 = 0.5× 10−12 TeV−1 cm−2 s−1 corresponding to the average fluxnormalisation of PSRB1259−63 at 1 TeV measured in 2004. Using these quantities withEq. 2.8 gives the sensitivity evolution depicted in Fig. 5.5 along with the cumulative pho-ton excess as a function of time. According to this PSRB1259−63 should be detectableat the 5σ-level after 50h of exposure time. The visibility of PSRB1259−63 around the2007 periastron for θ < 45 as a function of the Modified Julian Date (MJD) is shownin Fig. 5.6. The green shaded boxes depict the visibility time slots below 45 ZA forPSRB1259−63 in 2007. According to this 5 observation periods from April to August2007 were defined. The proposed observation time for each slot as well as the exposuretime eventually taken is also given below each box. The 2007 visibility time slots arereflected with respect to periastron (τ = 0 d) as empty boxes and overlayed with thedaily TeV flux from 2004 for illustration.

Figure 5.4: Visibility for PSRB1259−63 in 2007. Yellow bands denote moon light in-tervals. The source altitude is colour coded.

5.2.2 Observations and AnalysisThe dataset presented here is obtained from 8.6 h (8.3h livetime), 7.5 h (6.9h livetime)and 54h (52h livetime) of exposures taken in 2005, 2006 and from April to August2007, respectively, around the nominal source position of PSRB1259−63. Table 5.2summarizes the dates and livetimes for the dataset used here. The data were taken

72


Figure 5.5: (left) Expected development of detection significance for PSRB1259−63 ata zenith angle of 45 assuming a flux normalisation at 1 TeV of Φ0 = 0.5×10−12 TeV−1 cm−2 s−1 as seen for orbital phases far from periastron (∼ τ −40d) in Fig. 4.9. (right) Expected cumulative photon excess as a functionof time t for the same conditions.

Time [days relative to periastron]

-100 -50 0 50 100

]-1

s-2

F(>

380 G

eV

) [m

-0.04

-0.02

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

-610×

August

-/5.3 h

April

10/5.3 h

May

20/14.6 h

June

30/15.5 h

July

15/14.4 h

PSR B1259-63

2004

Figure 5.6: Visibility time slots for the 2007 H.E.S.S. campaign on PSRB1259−63 belowZAs θ < 45. For a detailed description see the text.

73


Table 5.1: Total time of visibility above altitudes of 25, 35, 40, 45 and 49 ofPSRB1259−63 from January to August 2007.

Month > 25 > 35 > 40 > 45 > 49in 2007 [h] [h] [h] [h] [h]1 61.8 41.9 30.4 17.0 1.52 88.8 69.0 58.3 45.5 15.23 119.1 97.2 76.8 50.8 14.94 126.9 96.9 75.3 49.9 14.95 106.4 86.5 74.4 50.0 15.16 83.6 63.6 52.9 40.0 15.27 58.5 38.2 27.3 14.2 0.38 32.5 11.5 1.8 0.0 0.0

in wobble-mode, i.e. with the pointing position slightly offset from the target position.Due to the radial acceptance profile of the detector this mode allows a simple simul-taneous background estimation using the Reflected-Region method (see Sec. 2.3). Forthe observation campaign in 2007 this technique has been applied only with respect toRight Ascension (RA) at an offset of 0.7 so as not to interfere with a second sourcein the FoV HESS J1303−631 [Aharonian et al.(2005b)] which is located ∼ 0.6 to thenorth of PSRB1259−63 . The 2007 observations were carried out at ZAs ranging from40.6 to 62.7. The mean ZA is 44 leading to an analysis energy threshold of 620 GeV.The datasets from 2005 and 2006 contain exposures taken during the H.E.S.S. galacticplane scan and dedicated observation runs on HESS J1303−631 with a positive offset of0.7 in declination (DEC). This leads to wobble offsets with respect to the position ofPSRB1259−63 for the analysis presented here both in RA and DEC, ranging between0.5 and 1.9.1 The mean ZAs for these observations were 44.1 in 2005 and 47.1 in2006. The usual quality criteria with respect to weather conditions and fully functionalarray hardware are applied to the data [Aharonian et al.(2006)].

Detection

The Hillas analysis was applied, incorporating so-called standard cuts on image quality(image amplitude 80 p.e.) and an angular cut of θ2 < 0.0125 deg2 for θ defined as angulardistance between the position of a γ-ray-like event in the FoV and the nominal targetposition. In order to measure the hadronic background in the FoV simultaneously,the Reflected-Region background model was used. Using this technique, the level ofOFF events is taken from regions within the same FoV which are located at the samedistance with respect to the camera center as the ON region in order to account forthe radial acceptance of the detector. OFF regions that overlap with a circular regionof radius 0.45 at the position of HESS J1303−631 were omitted in the backgroundcalculation. A correction due to degredation of the mirrors with respect to the initial80% reflectivity has been taken into account as described in [Aharonian et al.(2006)].This standard H.E.S.S. point source analysis for the 2007 dataset resulted in a clear

1Higher wobble offsets (> 0.9) additionally increase the energy threshold due to the radial acceptanceprofile of the camera.

74


RA

13h20m 13h10m 13h00m 12h50m

-65

-64

-63

-62

-4

-2

0

2

4

6

8

10

12

14

De

c[d

eg

]

]σ

Sig

nif

ica

nc

e[

HESS J1303-631

PSR B1259-63

H.E.S.S.2007May-August

Figure 5.7: Correlated significance map for the PSRB1259−63 FoV from the obser-vation period from May to August 2007. There is a clear signal in TeVγ-rays visible from the target direction. The white cross indicates thenominal position of PSRB1259−63. The extended source to the north isHESS J1303−631[Aharonian et al.(2005b)].

75


excess of 450 photons from the direction of PSRB1259−63 resulting in a statisticalsignificance of 9.5 standard deviations for this detection (see Table 5.2). Figure 5.7shows the correlated significance map from the observation period from May to August2007 for the PSRB1259−63 FoV using the Ring Background model with a correlationradius of 0.5 as described in [Berge et al.(2007)]. A fit of the signal with a templategiven by the shape of the point spread function of the instrument yields (J2000) RA13h2m41s± 6sstat, DEC −6349′1′′± 41′′stat for the excess center position. This is withinerrors compatible with the nominal position of PSRB1259−63 [Wang et al.(2004)] andthe TeV signal detected in 2004 [Aharonian et al.(2005a)].The analysis of the 2005 and 2006 datasets showed no significant excess (Table 5.2).

A calculation of upper limits at the 99% confidence level according to[Feldman and Cousins(1998)] on the integrated photon flux above 1TeV yields 7.1 ×10−13 cm−2 s−1 and 7.0× 10−13 cm−2 s−1 for these measurements, respectively.A crosscheck analysis which is based on a semi-analytical model approach for air show-

ers in order to predict the expected intensity in each pixel of the camera as describedin [de Naurois(2005)] was also performed using an independent analysis and reconstruc-tion chain. This method has a similar signal efficiency but superior background rejectioncompared to the Hillas analysis. On the other hand, the Hillas analysis is more robustagainst systematic errors. Therefore, throughout this work the Hillas analysis methodis used.

Energy Spectra

A spectral analysis of the detected excess events from within the ON region for thewhole 2007 dataset using the Hillas analysis shows that the differential energy spectrumof the collected photons as a function of particle energy follows a simple power lawas given in Eq.(5.1), with flux normalisation at 1TeV Φ0 = (1.1 ± 0.1stat ± 0.2sys) ×10−12 TeV−1 cm−2 s−1 and photon index Γ = 2.8 ± 0.2stat ± 0.2sys (see Fig. 5.8). Thespectral parameters from a power law fit to the monthly data taken during the obser-vation periods in May, June and July 2007 are shown in Tab. 5.3. All spectra were welldescribed by a power law as shown by the reduced χ2 values. Even though there are nosignificant changes in photon index among the individual darkness periods from May toJuly, the possibility of spectral hardening towards periastron indicated when comparinge.g. Γ and Φ0 between May and June in Tab.5.3 (see also Fig. 5.9) was investigated. The1σ and 2σ error contours of the correlated parameters Γ and Φ0 taken from the powerlaw fit to the monthly spectra are shown in Fig. 5.9, showing no significant evidence forspectral variability.

Lightcurve

The integral VHE flux of photons F (> 1TeV) above an energy of 1TeV has been calcu-lated by integrating Eq. (5.1) above this threshold, assuming an average photon indexof Γ = 2.8 taken from the overall spectrum (Fig. 5.8). The flux normalisation Φ0 hasbeen determined using Eq.(5.2).There was no significant excess in TeV γ-rays in 2005, 2006 and during the first ex-posures in 2007 taken in April (τ = −104 d; τ = 0 d being the periastron passage)which re-confirms the variable character of this source as already established from the

76


Energy (TeV)1 10

210

]-1

s-2

cm

-1d

N/d

E [

TeV

-1810

-1710

-1610

-1510

-1410

-1310

-1210

-1110

PSR B1259-63April-August 2007

H.E.S.S.

Figure 5.8: Differential energy spectrum dN/dE for γ-rays taken from within the 0.112ON region around the target postion of PSRB1259−63 extracted from 52.5 hof (livetime) data taken between April and August 2007. The line is a fitto a power law which yields a flux normalisation Φ0 = (1.1 ± 0.1stat ±0.2sys)× 10−12TeV−1cm−2s−1 and photon index Γ = 2.8± 0.2stat ± 0.2sys.The integral flux for all γ-rays above 1TeV is F (> 1TeV) = (6.1±0.7stat)×10−13 cm−2 s−1.

77


Energy (TeV)1 10

210

]-1

s-2

cm

-1d

N/d

E [

Te

V

-1810

-1710

-1610

-1510

-1410

-1310

-1210

-1110

May

June

July

PSR B1259-63May-July 2007

H.E.S.S.

]-1

s-2

cm-1

[TeV0

Φ

-1210

Γ

-5

-4.5

-4

-3.5

-3

-2.5

-2

Figure 5.9: (top) Differential energy spectra dN/dE of PSRB1259−63 for the monthlydarkness periods May, June and July 2007. For the data subsets taken inApril and August, no spectra could be derived due to insufficient statistics.(bottom) 1σ and 2σ error contours for the correlated parameters Φ0 and Γof a power law fit to the spectra for the observation periods in May, Juneand July.

78


H.E.S.S. data from the year 2004. In 2007 the total integrated photon flux above1TeV is (6.1 ± 0.7stat) × 10−13 cm−2 s−1 corresponding to 2.7% of that of the Crabnebula above the same threshold. This translates into a mean energy flux of the VHEemission of FE(E > 1TeV) ≈ 2 × 10−12 erg cm−2 s−1 implying a γ-ray luminosity ofLγ ≈ 6× 1032 erg s−1 at a distance of 1.5 kpc. This luminosity is ∼ 0.1 % of the pulsarspin-down power. The average flux levels for each observation period in 2007 are shownin the monthly lightcurve in Fig. 5.11. As shown in Table 5.2 the emission of TeVphotons from PSRB1259−63 with a significant signal (> 5σ) seen with both analysesstarted in June 2007, i.e. ∼ 50 days prior to the periastron passage (τ = −50d). Fit-ting the overall runwise flux data in 2007 with a constant leads to a goodness of fit ofχ2/ndf = 135.3

118 corresponding to a probability of Pχ2 = 13 %. A fit with a constant tothe monthly lightcurve (April-August 2007) leads to a goodness of fit of χ2/ndf = 15.7

4corresponding to a probability of Pχ2 = 3×10−3. This significant decrease in fit qualitywhen choosing a coarser, i.e. monthly, binning implies a variable character of the fluxduring the given period just like the fit to the monthly data would suggest.This also becomes obvious by the outcome of a Kolmogorov-Smirnov(KS) test[Kolmogorov(1933)], which is more sensitive to trends, contrary to the classical χ2-test.The test variable t and probability PKS to get t ≤ tc, where tc is a critical value for t,are defined in the following way:

t =√n ·max |Fn(x)− Φ(x)| (5.5)

PKS = 1− 2∞∑k=1

(−1)k−1 · exp(−2k2t2c) (5.6)

Fn(x) = number of xi ≤ xn

(5.7)

Here n is the number of data points, Fn is the cumulative distribution constructed fromthe data and Φ represents the expected theoretical cumulative distribution. The criticalvalue tc is usually chosen to give PKS ≤ 5% for a positive test result, i.e. compatiblewith the null-hypothesis. The test has been applied to the deviations from a constantlightcurve. It is testing whether the cumulative probability distribution function Fn ex-tracted from the deviations of the lightcurve from the fit with a constant agrees with theintegrated Gaussian F as expected for normally distributed deviations. The compati-bility of the error weighted residuals of the monthly flux with a Gaussian distributionaround the average flux level was rejected with a test probability PKS of 14 %. That ofthe nightly fluxes failed the test at the 87 % level (see Fig. 5.10).The combination of the monthly integrated fluxes presented in Fig. 5.11 with the daily

lightcurve as extracted from the 2004 H.E.S.S. campaign [Aharonian et al.(2005a)] to-gether with the measurements from 2005 and 2006 in a single plot is shown in Fig. 5.12.In this representation the flux is shown as a function of the true anomaly2 (lower axis)and orbital phase3 (upper axis), respectively. It can be seen that the overall flux levelin 2007 is comparable to that measured in 2004, while they correspond to different or-2The true anomaly θ ∈ [−0.5, 0.5] is the angle between periastron and the current position of an objectalong a Keplerian orbit as seen from the focal point at the position of the companion object.

3The orbital phase or mean anomaly of a Kepler orbit is defined as φ = E − e sinE where e is theeccentricity and E is the eccentric anomaly defined as sinE = y/b for a point (x, y) satisfying theknown equation x2

a2 + y2

b2 = 1. In this work φ is scaled to φ ∈ [−0.5, 0.5].

79


x

-2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2

Fn

(x)/

Ph

i(x

)

0

0.2

0.4

0.6

0.8

1 KS Test Probability P = 87 %

Fn - culmulative test prob dist

Phi - integrated gaussian

Kolmogorov Smirnov Test

Figure 5.10: Culmulative test probability distribution for the deviations of the nightlyPSRB1259−63 fluxes from a constant flux (red) in comparison to the in-tegrated Gaussian behavior as expected for fluctuations around a constant(green). The two distributions are significantly different according to aKolmogorov-Smirnov test.

80


Time MJD

54200 54220 54240 54260 54280 54300 54320

]-1

s

-2F

(>1T

eV

) [

cm

-0.5

0

0.5

1

1.5

2

-1210×

April May June July August

PSR B1259-63

H.E.S.S.

Figure 5.11: Integrated photon flux above 1TeV for the individual H.E.S.S. observa-tion periods from April to August 2007. The red vertical line indicatesthe periastron passage. There was no significant γ-ray emission fromPSRB1259−63 detected in the April pointings whereas the photon flux be-came notable at the 3σ-level from ∼ 75 days prior to periastron onwards.A fit with a constant to the monthly data gives Pχ2 = 3× 10−3.

81


bital phases. Between the datasets of 2004 and 2007 there is only a marginal overlap inorbital phase. The exposures taken in July and August 2007 each overlap with a singlenight of observations of the 2004 campaign (at a true anomaly θ = −0.17 and θ = 0.20,respectively). The corresponding fluxes are not significantely deviating from each other(1.8 and 0.6 standard deviations, respectively). However, the 2007 measurements sufferfrom low statistics. It is not possible at present to test directly whether the source showsorbit-to-orbit variability. More overlapping data would be desirable.However, the lightcurve is observed to be symmetric with respect to periastron althoughthis can not easily be seen in Fig. 5.12. There the two humps appear to exhibit a differ-ent shape with the pre-periastron hump being broader. This wrong impression is dueto the different time binning used for the 2004 and 2007 data. The high degree in sym-metry of the lightcurve with respect to periastron becomes noticable when overlayingpre and post perisatron fluxes. This is shown in Fig. 5.13 where the energy fluxes at 1TeV of PSRB1259−63 are shown as a function of the binary separation distance. Thereis a clear correlation between pre and post periastron data measured in the years 2004and 2007 by H.E.S.S. This indicates basically two things: i) the TeV flux is a functionof the binary separation only. ii) the system shows indications of periodicity.

82

5.2Measurem

entsin

2005,2006and

2007

Table 5.2: Datasets for the H.E.S.S. campaigns on PSRB1259−63/SS2883 in 2005, 2006 and 2007. Shown are the days relative toperiastron τ , the true anomaly θ, the orbital phase (mean anomaly) φ, the livetime t, the number of ON and OFF eventsNON , NOFF , the background normalisation α and the number of excess photons Nγ for the Hillas type analysis for eachobservation period. The significances S according to [Li and Ma(1983)] are shown for both analysis techniques, as outlinedin the text.

Period τ/[d] θ φ t/[h] NON NOFF α Nγ SHillas∗/[σ] SModel

∗∗/[σ]

2005 386 0.47 0.31 8.3 347 6909 0.047 22.7 1.2 1.22006 −454 −0.48 −0.37 6.9 271 3201 0.079 18.0 1.1 0.5

2007April −104 −0.40 −0.084 5.3 205 2571 0.074 15.8 1.1 2.9May −74 −0.38 −0.060 14.6 623 7280 0.074 84.4 3.4 5.8June −46 −0.35 −0.037 15.5 843 8373 0.073 228.8 8.4 9.3July −17 −0.25 −0.014 14.4 575 6238 0.077 96.4 4.1 7.4August 9 0.17 0.007 3.2 124 1383 0.073 22.9 2.1 0.9

2007 Total 52.5 2353 25633 0.074 448.7 9.5 13.2∗ Standard H.E.S.S. analysis based on Hillas moments.∗∗ H.E.S.S. semi-analytical model analysis used as cross check.

83


Table 5.3: Spectral parameters for a power law fit to the monthly H.E.S.S. data. For theperiods April and August 2007, no spectrum could be obtained due to lowstatistics: Mean Modified Julian Date MJD, ∆+−

MJD time interval to last/firstmeasurement, days relative to periastron τ , true anomaly θ, orbital phase(mean anomaly) φ, Photon index Γ, flux normalisation Φ0, mean energyflux FE and γ-ray luminosity Lγ above 1TeV ∗, χ2 per number of degrees offreedom χ2

ndf and probability Pχ2 for the fit are shown. Shown are statisticalerrors only.

Period MJD ∆+MJD

∆−MJD

τ θ φ Φ0

[d] [d] [d] [10−12 TeV−1 cm−2 s−1]

2004 53104.4 1.3±0.1

2007May 54235.1 5.7 6.3 -74 -0.38 -0.060 0.7±0.2June 54263.1 5.7 8.3 -46 -0.35 -0.037 1.5±0.2July 54291.9 8.0 7.1 -17 -0.25 -0.014 1.3±0.4

Total∗∗ 54262.5 1.1±0.1

Period Γ FE Lγ χ2/ndf Pχ2

[10−12 erg cm−2 s−1] [1032 erg s−1]

2004 2.7±0.2 3.0±0.9 8±2 2.3/5 0.81

2007May 2.6±0.5 1.4±0.4 4±1 2.374/3 0.50June 3.8±0.5 3.0±0.4 8±1 1.352/3 0.72July 2.7±0.3 2.5±0.6 7±2 1.294/3 0.73

Total∗∗ 2.8±0.2 2.2±0.6 6±2 4.678/5 0.46∗ Monthly values for FE and Lγ in 2007 have been computed assuming a fixed photon index of Γ = 2.8.∗∗ Entire H.E.S.S. dataset from April to August 2007.

84

5.2Measurem

entsin

2005,2006and

2007

θTrue Anomaly

-0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5

]-1

s-2

F(>

1 T

eV

) [c

m

-0.5

0

0.5

1

1.5

2

2.5

-1210×

2004 daily

2005/2006

2007 monthly

φPhase -0.1 0.10.01-0.01 0

PSR B1259-63

H.E.S.S.

Figure 5.12: VHE integrated flux from PSRB1259−63 above 1TeV as a function of the true anomaly. The corresponding orbitalphases (mean anomaly) are shown on the upper horizontal axis. The red vertical line indicates the periastron passage.Shown are data from the years 2004 to 2007: The black points are the daily fluxes as measured in 2004. Green emptytriangles show the overall flux levels as seen in 2005 and 2006. Blue filled squares represent the monthly fluxes takenfrom the campaign in 2007.

85


r [m]100 200 300 400 500 600

910×

-1s

-2, eV

cm

dE

dN

2E

0

1

2

3

4

5

6

Figure 5.13: Energy fluxes of 1 TeV photons from PSRB1259−63 as a function ofthe binary separation distance. The measurements were carried out byH.E.S.S. during the 2004 (black dots - fluxes using a bin width of 2days) and 2007 (red empty squares - monthly fluxes) periastron passage,respectively.

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6 Model Studies

As other VHE sources, the production of VHE gamma-rays in binaries requires a popu-lation of charged particles with multi-TeV energies. One possibility is shock accelerationwithin the termination zone of colliding winds [Maraschi and Treves(1981)],[Tavani et al.(1994)], [Tavani et al.(1997)], [Bogovalov(2007)] which applies for PSR B1259−63/SS2883 when the PW is shocked by the stellar wind.The various physical mechanisms that are discussed with respect to the subsequentgeneration of TeV γ-radiation lead to a variety of models attempting to describe theobservational data. The peculiar shape of the lightcurve of this VHE photon emit-ter allows for different interpretations, focussing either on leptonic IC scenarios, oralternatively, hadronic interactions. IC scattering may take place where ultrarelativis-tic electrons/positrons accelerated at the termination shock of the cold pulsar wind,where the particle flow compresses, hit UV photons from the companion star. Had-ronic scenarios emphasize the role of the outflow of SS2883 and the circumstellar discwhose dense material could be a target for efficient hadronic interactions while the pul-sar crosses the disc shortly before and after the periastron. The stellar disc seems tobe an ideal reservoir for target material interacting with the PW that could carry aconsiderable fraction of hadronic particles like ions. Predictions depend sensitively onparameters like the disc’s density, thickness, extension and orientation with respect tothe pulsar orbit. Currently the knowledge about these quantities is limited and de-pends on model interpretations of available data measured in the radio to X-Ray bandsas discussed in [Johnston et al.(1994)], [Johnston et al.(1996)], [Johnston et al.(2005)],[Melatos et al.(1995)], [Tavani et al.(1997)], [Bogomazov(2005)]. According to thesestu- dies the disc appears to be inclined by an angle δ in the range of 10−40 comparedto the pulsar ecliptic. Moreover the vanishing of the pulsed radio signal between 16 daysbefore and 15 days after periastron [Johnston et al.(2005)] accounts for the asymmetricposition of the line of intersection of the disc with the orbital plane with respect to theorbital semimajor axis. In [Chernyakova et al.(2006)], the disc position is inferred fromthe H.E.S.S. 2004 data by assuming that the peak VHE emission corresponds to orbitalphases of maximum circumstellar density. According to this, the disc intersects the pul-sar orbit at a true anomaly of θ = −0.197 and θ = 0.303, respectively ( θ ∈ [−0.5, 0.5]),with respect to periastron and covers the pulsar orbit over an angular band of ∼ 18.5(∆θ = 0.05).In the IC scenario many parameters contribute to the complexity of the problem. Theoverall system geometry significantly influences predictions for the VHE emission asshown by [Kirk et al.(1999)]. The IC cross section varies with orbital phase as the an-gle between the line of sight and the vector connecting the stars changes. Also themagnetic field strength B is a function of the separation r of the two objects due tochanging magneto hydrodynamic conditions at the PW shock where the field lines fromthe wind get compressed [Tavani et al.(1997)],[Kirk et al.(1999)]. The B-field shouldbecome stronger towards periastron, resulting in faster synchrotron losses. This in turn

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6 Model Studies

implies a shift in the ratio of radiation timescales, affecting the efficiency of IC coolingfor VHE electrons in the Klein-Nishina regime and hence the TeV photon index. More-over non-radiative cooling mechanisms such as adiabatic expansion of the shock regionor particle escape can be important effects as demonstrated by [Khangulyan(2006)]. In[Bogovalov(2007)] it was pointed out that the interaction of pulsar and stellar windsleads to relativistic motion of matter at the termination shock. The correspondingDoppler factor with respect to the line of sight will strongly depend on the posi-tion of the pulsar along its orbit causing modulations of the non-thermal radiationof electrons. Finally, [Bednarek(1997)], [Sierpowska-Bartosik and Bednarek(2008)] and[Bosch-Ramon et al.(2008)] have discussed the possibility of radiating secondaries stem-ming from pair cascades forming close to the star where the photon field density is highenough.The following chapter summarizes the two most prominent approaches from the theoryof VHE γ-rays from PSRB1259−63, i.e. the hadronic disc scenario and the leptonicIC model. The presented theoretical methods and models employing different physicalexplanations for the varying flux of the system are the basis for the model calcula-tions performed in this thesis following the work in [Neronov and Chernyakova(2007)],[Khangulyan(2006)] and [Hnatic(2007)]. The goal is to test predictions with up to dateexperimental results and develop the models further.

6.1 Hadronic Disc Scenario

As outlined in [Chernyakova(2005)] and [Neronov and Chernyakova(2007)] the rise andvice versa the fall of the flux level throughout all frequency bands (Fig. 5.3) prior to andshortly after periastron, leads to the hypothesis that the stellar disc featured by SS2883might play a crucial role especially in the TeV regime. The basic idea is that the densedisc material acts as target for the ultrarelativistic pulsar wind for hadronic interactionswhenever the pulsar plunges into the stellar disc. According to this, π0-mesons arecreated at a significant rate and subsequently decaying into TeV photons. Thus the TeVemission should correlate with the disc’s density profile, i.e. the denser the disc regionthe pulsar passes through the higher the interaction rate with the pulsar wind and thusthe higher the flux level seen in VHE photons.Following the work of [Neronov and Chernyakova(2007)] it is thus assumed that the TeVflux FTeV correlates with the disc density profile ρ, i.e. FTeV ∝ ρ. As parameter for thepulsar position the true anomaly θ is used. The time dependence of the true anomaly,θ(t), is computed from the Keplerian orbit of the pulsar, as detailed in Appendix 1. Thetrue anomaly θ(t) together with the mean anomaly (phase) φ(t) are shown in Fig. 6.1for the system PSRB1259−63.The integrated flux above 1 TeV coming from the system during periastron passage asa function of θ is plotted (see Fig. 5.12). A significant rise and fall of the flux level isidentified with entrance and exit of the pulsar into and from the disc, respectively. Byassuming the TeV flux as being a tracer of the disc’s density profile (with a Gaussianshape), extension, i.e. opening angle, and location of the disc with respect to the pulsarorbit can be retrieved by fitting the lightcurve with a Gaussian. The fit to the 2004

90


time [d]

-600 -400 -200 0 200 400 600

[-0

.5,0

.5]

∈an

gle

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

θtrue anomaly

φmean anomaly

Figure 6.1: True anomaly, phase and angle with respect to the observer inPSRB1259−63 as a function of orbital time.

91

6 Model Studies

True Anomaly

-0.4 -0.35 -0.3 -0.25 -0.2 -0.15 -0.1

]-1

s-2

F(>

1 T

eV

) [c

m

-0.5

0

0.5

1

1.5

2

2.5

-1210×

PSR B1259-63

H.E.S.S.2004 daily

2007 monthly

Figure 6.2: Fit of the 2004 flux measurements above 1 TeV (black dots) with a Gaussianfollowing Fig. 4 in [Chernyakova et al.(2006)] in order to determine the lo-cation of the circumstellar disc. Also shown are the fluxes measured in 2007(blue squares).

92


H.E.S.S. data with a Gaussian of the form

F (θ) ∼ exp(−(θ − θdisc)2

2∆θ2disc

)(6.1)

is shown in Fig. 6.2. In this plot fluxes measured after periastron passage have beenshifted with respect to periastron by 0.5 in true anomaly and added to the pre-periastronphase. This is based on the assumption that the position of the second crossing shouldbe shifted by 180 relative to the first entrance of the pulsar into the disc. Note, however,that in this approach it has not been considered that the binary separation is different forthe corresponding pulsar positions when being shifted by 0.5, translating into differentdensities in the stellar disc.The location of the peak of the Gaussian is identified as the centre of the disc intersectingthe orbital plane and ∆θ2

disc as its thickness. The following values for these parametersare retained from the fit1:

θdisc = −0.195± 0.003∆θdisc = 0.040± 0.003.

(6.2)

Using only the daily flux data from 2004 gives a χ2-probability of Pχ2 = 0.22 indicatingthat the hadronic disc model indeed is a good description for the TeV flux seen forthis period. However, when including the 2007 data, the fit probability dramaticallyreduces to Pχ2 = 2 ·10−11. It is obvious in Fig. 6.2 that the pre-periastron data taken in2007 (blue dots) significantly deviate from a simple Gaussian disc density profile. Thisbecomes even more obvious if the locations of the pulsar along its trajectory for thesingle observation periods in 2007 are compared with the location of the disc as shownin Fig. 6.3. According to this the excess in June (Table 5.2), corresponding to 47 daysprior to periastron passage, occurs at unexpectedly small values for the true anomalyof θ ≈ −0.35 (≈ −50 off the expected disc density maximum). No matter how thedisc is oriented, the TeV emission occurs far off the disc as such discs typically do notextend further than ∼20 stellar radii. This could either indicate a more complicated discstructure (e.g. inhomogenious density profile featuring clumps of matter) or disfavor thedisc as being solely responsible for the TeV flux in a hadronic scenario and thereforesupporting the idea of a leptonic Inverse Compton model. As mentioned in Sec. 4.3,Be stars do also feature a faster, less dense polar wind component which can extendmuch further out than the dense circumstellar disc wind. This wind still could explainthe observed TeV emission in PSRB1259−63 in terms of hadronic interactions but thehadronic circumstellar disc scenario as the only explanation for VHE γ-rays from thissystem seems to be ruled out by the 2007 data.

1Note that the results in [Chernyakova(2005)] for the disc parameters were θ∗disc = 109.1 and ∆θ∗disc =18.5 respectively, using 2004 data only. In the convention used throughout this work this correspondsto θ∗disc = −0.197 and ∆θ∗disc = 0.051. The differences to the results presented here are presumablydue to systematics in the code solving the Kepler problem which is sensitive to numerical precisionfor small values of the true anomaly. Moreover, the different minimization strategies pursued byROOT while fitting can lead to different results if there exist local minima.

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6 Model Studies

θ

08/07: θ=0.17

07/07: θ=−0.25

06/07: θ=−0.35

05/07: θ=−0.38

04/07: θ=−0.40

Figure 6.3: Top view model sketch for the PSRB1259−63 orbit. The black dot repre-sents SS2882 and the circumstellar disc is depicted in green. The pulsar sizeis exaggerated by a huge factor. The circumstellar disc is assumed to beextended out to 20 stellar radii RÀ, as typical for Be stars. The mean pulsarpositions for the individual H.E.S.S. observation periods in 2007 are shownalong the orbital trajectory as stars together with the corresponding dateand the true anomaly θ (definition indicated by red thin lines). The smallerstars indicate the pulsar position of each period’s first and last measurement,respectively. The positive excess of TeV photons in June 2007 at an orbitalposition of θ ≈ −0.35 seems to have occurred far outside the estimated disccrossing phase.

94

6.2 Inverse Compton TeV Flux


Alternatively, the TeV γ-ray flux from PSRB1259−63 could originate from InverseCompton (IC) scattering of UV photons from the companion star by ultrarelativis-tic pulsar wind electrons, accelerated at the shock front between the leptonic wind andthe stellar outflow [Khangulyan(2006)].According to the current theory of pulsar winds, a rapidly rotating neutron star losesits rotational power via the generation of a leptonic wind that carries away kinetic andelectromagnetic energy at a rate of the so called spin down luminosity L = Erot (seeSec 4.2). A considerable fraction of this wind could also consist of hadrons as discussedin the previous section. For the rest of this section we assume the PW to consist purelyfrom electrons (here the term electron also includes positrons). The ratio between elec-tromagnetic and kinetic energy flux is typically much smaller than 1 [Bogovalov(2007)].This means that the bulk of the rotational loss energy is transformed to kinetic en-ergy of the ultrarelativistic electrons and positrons. This wind is considered to be cold,i.e. there is only little or no unordered motion of the particles. As the magnetic fieldlines from the pulsar propagate with the wind particles, the B-field is frozen withinthe reference frame of the moving particles. This is due to the very high conductivityof the wind plasma causing the magnetic field lines to be “dragged” with the chargedparticles. This is the reason for the lack of any sign of radiative cooling via synchrotronradiation of the leptons while freely propagating. If however the cold ultrarelativisticwind encounters a radiation field, e.g. UV photons from a nearby star (or even photonsfrom the Cosmic Microwave Background (CMB) for sufficiently energetic particles), thiswind can produce X-rays and γ-rays and become visible for various instruments. In thecase of PSRB1259−63 the pulsar wind could in addition be terminated by the densestellar outflow forming a shock region in which the wind particles are accelerated to veryhigh energies. Moreover the wind becomes isotropized when being shocked. A contactdiscontinuity, i.e. a transition layer across which there is no particle transport, betweenthe wind and the stellar equatorial outflow is built up along the line of balanced rampressures2, separating the two media from each other and forming a bow like shockregion surrounding the pulsar (see Fig. 6.4).

In order to account for the lightcurve data as measured by H.E.S.S. in terms of the ICscenario, the interplay of several phase dependent parameters has to be studied carefully.The flux of upscattered TeV photons not only depends on the scattering angle ψ withrespect to the line of sight but also on the cross section σ (which is a function of theelectron γ-factor, the seed photon energy ε and the resulting VHE photon energy Eγ),the photon energy distribution of the stellar radiation field nph(ε), the electron energydistribution3 ne(t, γ), magnetic field conditions at the shock and the influence of non-radiative cooling processes such as e.g. adiabatic losses and particle escape. Integration

2Ram pressure is the pressure which occurs when for instance a body moves through a fluid leading toa drag force acting on the body.

3ne(t, γ) denotes the number of electrons per energy γ (in units of mec2)

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6 Model Studies

Figure 6.4: Schematic plot of the shock region as shown in [Bogovalov(2007)]. The thickred lines represent termination shock. The thin blue line corresponds to thecontact discontinuity.

over these quantities yields the IC γ-ray flux as a function of the pulsar epoch tp:(dN(tp)dtdEγdS

)IC

=(R∗r

)2

︸︷︷︸scales stellar photon density

c

4πD2

∫γne(tp, γ,Ω)×

∫εnph(ε)dσ(γ, ε, Eγ , ψ)

dEγdΩ (1− cosψ) dεdγ,

(6.3)

with dσ(γ,ε,Eγ ,ψ)dEγdΩ being the differential cross section for IC scattering at electron energy

γ and photon energy ε under the angle ψ (Fig. 3.5) producing a VHE photon of energyEγ.4 The solid angle element dΩ = dS/D2, with dS being the detector area elementand D the distance between pulsar and observer.5In order to evaluate the VHE flux from Eq(6.3) first ne = ne(t, γ) has to be computed.This is done by solving the differential equation accounting for all possible energy lossesof the injected VHE electrons such as synchrotron radiation, IC losses and adiabaticcooling. First the case for radiative losses only (IC and synchrotron) is treated. Afterthis the theoretical result obtained from Eq(6.3) is compared with the H.E.S.S. dataand subsequently the adiabatic loss rate is inferred from the discrepancy between themodel curve and the data.

Calculating the Electron Distribution Function

According to Ginzburg and Syrovatskii [Ginzburg and Syrovatskii(1964)], the electrondistribution function (EDF) ne(t, γ), i.e. the number of electrons per energy (in units4Note that all energies in Eq(6.3) are given in units of mec

2.5The factor 1

4π in Eq(6.3) accounts for isotropically distributed electrons.

96


of mec2) interval, as a function of time t and γ, is described by a partial differential

equation of the form:

∂ne(t, γ)∂t

+ ∂γne(t, γ)∂γ

+ ne(t, γ)Tesc

= Q(t, γ), (6.4)

where γ is the lepton energy loss rate and the source term Q(t, γ) denotes the incidentacceleration rate of injected electrons from the pulsar wind. Tesc represents the escapetime for particles from the acceleration site. The terms on the l.h.s. of Eq(6.4) describethe differential changes in the EDF due to the electron energy losses caused by radiation,expansion and particle escape. The spectrum of accelerated electrons at the shock is,according to shock acceleration theory, assumed as a simple power law with an energycutoff at Ee,max

Q(t, γ) = Aγ−αe− γmc2Ee,max . (6.5)

A is the normalisation coefficient, i.e. the total acceleration power, determined by thefraction of PW particles transferred to VHE injection particles. The escape time be-comes important for times comparable to the acceleration time tacc, i.e. the time it takesto accelerate particles up to very high energies in the shock region. A simple estimatefor the corresponding time interval, which is a function of the magnetic field B(r), whichitself depends on the binary separation r, is given as

tacc ≈ ηRLc, (6.6)

where RL = mcγ/eB(r) is the Larmor radius for leptons and η = (c/Vs)2 characterizesthe acceleration rate. Vs denotes the plasma velocity in the shock. The lepton energyloss rate γ (in units of mec

2) due to e.g. synchrotron radiation (syn), IC cooling (ic)and adiabatic losses (ad) can be written as

γ = γsyn + γic + γad. (6.7)

The general solution to (6.4) can be written as

ne(γ, t) = 1|γ|

∫ γmax

γQ(t, γ′)e

−τ(γ,γ′)Tesc dγ′ (6.8)

where

t =∫ γmax

γ

dγ′

|γ′|

and τ(γ, γ′) =∫ γ′

γ

dγ′′

|γ′′ |,

with initial condition ne(γ, t = 0) = 0 [Hnatic(2007)]. Equation (6.8) describes the EDFof electrons after acceleration in the shock region. Here Tesc, Ee,max and γ as well astacc are parameters that influence the final shape of the EDF. In order to match theH.E.S.S. data these quantities can be used as free parameters within reasonable physicalboundaries. For the subsequent calculations no escape term for injected electrons has

97

6 Model Studies

been considered (Tesc −→∞) thus yielding

ne(γ, t) = 1|γ|

∫ γmax

γQ(t, γ′)dγ′. (6.9)

For an electron moving through a Planck photon field as provided by a companion starwith temperature T the energy loss via IC scattering dE/dt = mec

2 ˙γic in the Klein-Nishina regime is given in Eq(3.7).

6.2.1 Expected IC flux without adiabatic losses

Knowing ne(t, γ) the integration in Eq(6.3) can be performed. For the moment γad isset to γad = 0 in Eq(6.7) and only radiative cooling of the shock accelerated electronsis taken into account. This ansatz gives the loss free IC flux, where all the electronenergy losses are radiative. Numerical evaluation of Eq(6.3) using a Planck photonspectrum for nph(ε, T ) (see Eq(3.5)), Eq(6.9) for the EDF ne(t, γ) as well as the standardexpression for the cross section σ for deep Klein-Nishina IC scattering as calculated in[Blumenthal and Gould(1970)] (see Eq(3.3)) adapted to the orbital parameters of PSRB1259−63 yields the flux of 1 TeV photons coming from PSR B1259−63 as a functionof time as shown in Fig. 6.5 around periastron. In this calculation the normalisation Ain Eq(6.5) was taken from the condition that the conversion efficiency of PW particlesfor being transferred to the injection spectrum in the shock is FL = 0.1, thus

LFLmec2 =

∫ γmax

γminγQ(γ)dγ =⇒ A = LFL

c2me log (γmax/γmin) ,

where L is the total luminosity of the pulsar (see Tab. 4.1). The minimum and maximumelectron energies were chosen as Ee,min = 1 GeV and Ee,max = 10 TeV, respectively. Theindex α in Eq(6.5) was set to α = 2.The theoretical lightcurve of expected IC photons is comparable to that computed

in [Kirk et al.(1999)] (see Fig. 4.10). The occurence of a weak maximum just beforeperiastron is a result of the anisotropy of IC scattering. The computed lightcurve isconstant within a factor of two throughout the entire orbital period in contrast tothe observed H.E.S.S. fluxes. In conclusion, such a radiative scenario, not taking intoaccount any other (non-radiative) cooling mechanisms, can not explain the observedTeV emission.

6.2.2 Corrections due to non-radiative losses - the case of an asymmetriclightcurve

The above observation supports the model proposed in [Khangulyan(2006)] in whichnon-radiative cooling mechanisms such as adiabatic cooling through expansion of theemission region as well as the escape of injected VHE particles are responsible for thesudden drop in TeV photons near the periastron passage.As an analytical calculation of such non-radiative losses is highly complex due to themany degrees of freedom of the system it was suggested to infer the non-radiative coolingrate from the data itself by adopting a reference lightcurve. Using data taken in 2004(black dots) only, Khangulyan et al. [Khangulyan(2006)] used an arbitrary reference

98


time, days

-80 -60 -40 -20 0 20 40 60 80

-1s

-2, eV

cm

dE

dN

2E

-110

1

10

Figure 6.5: IC flux of 1 TeV photons as a function of time to the periastron passage asexpected from PSRB1259−63 evaluating Eq(6.3) numerically. Also shownare the H.E.S.S. data taken in 2004 (black) and 2007 (red).

curve of the formF (x) = a|x|αe−β|x| + b, (6.10)

where x can denote any orbital parameter (symmetric with respect to x = 0) suchas time τ , true anomaly θ or the binary separation distance r. They assumed thephoton flux to evolve asymmetric as a function of orbital time with respect to periastron.Different values for the amplitudes apre and apost in Eq(6.10) for the pre- and post-periastron part of the lightcurve, respectively, were used. Thus the lightcurve showstwo “humps” with different maxima. Equation (6.10) is shown in Fig.6.6 (blue dottedline). In order to adapt the expected TeV energy flux as depicted in Fig. 6.5 to thementioned reference curve non-radiative losses have to be introduced. This is done byapplying correcting cooling coefficients to the electron injection spectrum. Extractingthese from the reference lightcurve one can achieve a better agreement between themodel lightcurve and the data. The time profile for the cooling coefficients inferredfrom Eq(6.6) as done by Khangulyan et al. is shown in Fig. 4.9 and was discussedin Sec. 4.4.2. However, the parameters for the reference lightcurve used in 2004 werechosen arbitrarily in [Khangulyan(2006)], i.e. not stemming from a fit to the data. Bothasymmetry of the lightcurve with respect to periastron and a very high amplitude inthe pre-periastron photon flux were arbitrary assumptions.In this section, therefore, an adapted lightcurve is used for this study, i.e. a best fitmodel curve, including the results from the data taken in 2007. A best fit curve treatingthe pre-periastron data separately from the post-periastron data is shown in Fig. 6.6in green (dashed). Both sides of the model curve with respect to periastron follow the

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6 Model Studies

time_inter, days

-100 -50 0 50 100

-1s

-2, eV

cm

dE

dN

2E

-0.5

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

Figure 6.6: Arbitrary reference light curve for 1 TeV photons fromPSRB1259−63 around periastron as used in [Khangulyan(2006)] (bluedotted) as well as the best fit model lightcurve (green dashed) to theH.E.S.S. data from 2004 (black dots) and 2007 (red dots).

100


form

F (x) = |x|αeβ|x|−δ + 0.25 (6.11)

which is equivalent to Eq(6.10). A fit yields the parameters

αpre = 0.47± 0.39 (6.12)βpre = −0.030± 0.013δpre = 0.41± 0.86Pχ2 = 0.05

for the pre-periastron curve and

αpost = 5.2± 5.0 (6.13)βpost = −0.16± 0.17δpost = 12.4± 11.2Pχ2 = 0.08

for the post-periastron part. The fit quality, quantified by Pχ2 , is marginally acceptablefor both parts of the lightcurve.Using the above parameters for the reference lightcurve given in Eq(6.11), the result-ing time profile of cooling coefficients changes in comparison to Fig. 4.9 as depictedin Fig. 6.7. The main difference to the adiabatic energy loss time profile extractedin [Khangulyan(2006)], where only the pre-periastron part of the reference curve wasused to infer the cooling coefficients, is its asymmetry and a steep and dramatic rise inadiabatic losses towards periastron.6 The asymmetric character of the reference curvetranslates into different cooling timescales for the pre- and post-periastron epochs, re-spectively. This can be justified in two ways. That non-radiative losses should increasedramatically around periastron can be explained by a change in size of the emissionregion as a function of orbital phase. The nearer the pulsar gets to the star the smallerthe shock region should be resulting in an increase of adiabatic losses with a mini-mum cooling time of ∼110 s at periastron, comparabel to the peak value shown inFig. 4.9. The influence of the asymmetrically located stellar disc as well as polar windcould lead to significant deviations from a smooth symmetric cooling profile since thecompression of the shock should be even higher within the dense equatorial wind. Asconcluded from radio observations the pulsar indeed crosses the disc for the first timewhen being closer to periastron than at the second crossing after the periastron passage[Johnston et al.(1992)].A second contribution to asymmetry is the fact that both the IC cross section and theeffective optical depth τ Eq(3.12) in the dense stellar photon field are maximal just be-fore periastron due to the specific alignment of the system with respect to the observer(Fig. 3.5). If one interpretes attenuation due to pair creation as an “adiabatic” loss inthe TeV band since the absorbed energy is translated radiatively to lower bands andnot visible any longer at VHE, this energy loss should be also contained in the cooling

6Strictly speaking the profile in Fig. 6.7 is not a smooth function and shows a jump at τ = 0. It istherefore an unphysical description for the cooling behavior at periastron.

101

6 Model Studies

time, days

-100 -50 0 50 100

-1ad

iab

ati

c c

oeff

icie

nt,

s

-410

-310

-210

Figure 6.7: Cooling coefficients for non-radiative processes taking place inPSRB1259−63 around periastron as a function of time (with respectto periastron τ = 0) as inferred from the best fit reference lightcurve inFig. 6.6 (green dashed).

102


profile in Fig. 6.7.Introducing the non-radiative cooling corrections as inferred from the reference curveEq(6.11) to the overall energy losses, Eq(6.7) yields a different EDF ne(γ, t) in Eq(6.9).The energy distributions of VHE electrons that are losing energy in the shock regionalso via particle escape and adiabtic cooling are thus shown in Fig. 6.8 for the pre- andpost-periastron epoch. Interestingly, the post-periastron epoch shows a slightly higherrequired non-radiative cooling rate with characteristic time Tcool ∼ 5 · 103 s than thepre-periastron phase far from the passage. This results in a more efficient cooling ofelectrons 100 days after periastron in comparison to 30 days post-periastron as can beseen when comparing the top and lower panels in Fig. 6.8. A possible reason for thiscould be the geometrical asymmetry of the emission region which could be e.g. of theform of a bow shock with respect to the alignment of the system as seen from earth.In this case the required cooling coefficients would not only account for non-radiativecooling in the strict sense but also for non-isotropic effects in the acceleration processeshappening in the shock.Inserting the above non-radiatively cooled electron distributions ne(γ, t) into Eq(6.3)and calculating the flux of γ-ray photons of various energies yields the model lightcurvesshown in Fig. 6.9. A comparison of the H.E.S.S. data from 2007 and 2004 with theexpected energy flux suggested by the model discussed above shows an overall goodqualitative agreement. However, especially in the post-periastron epoch, the flux isunderestimated. The reason for this could either be an overestimation of the adiabat-ical cooling profile for post-periastron data or a harder electron injection spectrum inEq(6.5).Nevertheless, the assumption that non-radiative cooling processes especially around pe-riastron play a key role in connection with the TeV emission seen from PSR B1259−63seems plausible in the light of the results of this study.

6.2.3 Possible cooling profiles based on symmetric TeV emission

The study of an asymmetric lightcurve presented above yields results for the predictionof TeV photons from PSR B1259−63 describing the peculiar drop at periastron withreasonable accuracy. In comparison to the analysis in [Khangulyan(2006)] the furtherdevelopment of the model was based on three new ingredients:

. the 2007 dataset,

. a reference lightcurve based on a Pχ2 fit, resulting in

. an asymmetric cooling profile for PSRB1259−63.

However, as discussed in Sec. 5.2.2, the VHE flux seen from PSRB1259−63 shows sym-metry with respect to periastron. So the above analysis was redone assuming botha symmetric lightcurve and symmetric cooling profile. In this section three differentpossible symmetric cooling profiles are compared. But first of all a phenomenologi-cal discussion of the PSRB1259−63 lightcurve both in the γ-ray and X-ray band ispresented.

103

6 Model Studies

[eV]eE

910

1010

1110

1210

1310

) γ

n(

3γ

4610

4710

4810

4910

5010

5110

= 0τ

= 15τ

= 30τ

= 100τ

[eV]eE

1010

1110

1210

1310

) γ

n(

3γ

4610

4710

4810

4910

5010

5110 = 0τ

= 15τ

= 30τ

= 100τ

Figure 6.8: Electron distribution (EDF) at the emission region in PSRB1259−63 in-cluding non-radiative losses for different orbital phases τ (in days) fromperiastron for the pre- (top panel) and post-periastron (lower panel) epoch.

104


time, days

-100 -50 0 50 100

-1s

-2, eV

cm

dE

dN

2E

-110

1

10

1 TeV

500 GeV

100 GeV

10 GeV

Figure 6.9: Model lightcurves for energy fluxes of 10 GeV, 100 GeV, 500 GeV and 1 TeVphotons from PSRB1259−63 around periastron including IC and adiabaticcooling as well as particle escape of VHE electrons from the emission region.The red and black dots show the H.E.S.S. energy fluxes at 1 TeV as recordedin 2007 and 2004, respectively.

105

6 Model Studies

The lightcurve of PSRB1259−63 as seen in X-rays and γ-rays

While γ-ray binaries such as LS 5039 and LSI+61 303 have been observed over severalorbits and thus could be confirmed as periodical VHE emitters [Aharonian(2006)],[Albert et al.(2009)] this was not possible for PSRB1259−63 so far because of the ratherlong orbital period of 3.4 years. The overlap between the H.E.S.S. datasets of 2004 and2007 is marginal and thus inconclusive in this regard (see Fig. 5.12). It was thus upto now unknown whether the TeV lightcurve of this object shows periodicity. Onlyindirect evidence for PSRB1259−63 being a periodical VHE emitter as following fromthe discussion of Fig. 5.13 in Sec. 5.2.2 can be claimed. According to this the TeV fluxin PSRB1259−63 is a function of the binary separation distance r of the system.In X-rays, however, such a behavior can not be seen. In Fig. 6.10 X-ray data in the

1−10 keV band from ASCA [Kaspi et al.(1994)], Beppo-Sax , XMM Newton[Chernyakova et al.(2006)] and Suzaku [Uchiyama et al.(2009)] from the last periastronpassages since 1994 are shown again as a function of the binary separation r. Here the

r [m]0 200 400 600 800 1000 1200 1400

910×

-1s

-2 e

rg c

m-1

2 [

1-1

0 k

eV

], 1

0X

F

-1210

-1110

-1010

Figure 6.10: X-ray fluxes in the 1−10 keV band from pre-periastron (black dots) andpost-periastron (red empty squares) phases measured in the years 1994,1997, 2004 and 2007 as a function of the binary separation distance r.

picture is different from the symmetric lightcurve seen in the VHE regime. It seems thatfor r > 200 ·106 km pre- and post-periastron phases are separated by almost one order ofmagnitude in flux since there is a steep drop in the pre-periastron part of the lightcurve(black dots). Interestingly, this point of broken symmetry in the X-ray lightcurve iscoincident with an increase in the TeV flux by a factor of ∼ 3 (compare Fig. 5.13). Theclear discripancies between the X-ray and the γ-ray lightcurves presented here indicate

106


that the physical mechanisms responsible for the corresponding non-thermal emissionare different in nature for both regimes.

Three different cooling profiles

In this study, three different symmetric time profiles for the non-radiative cooling coef-ficients as shown in Fig. 6.11 were used in order to account for the γ-ray flux variabilityin PSRB1259−63 as measured by H.E.S.S. Using these non-radiative loss profiles for

time, days-100 -50 0 50 100

-1ad

iab

ati

c c

oeff

icie

nt,

s

-410

-310

-210

Figure 6.11: Three different symmetric cooling profiles for non-radiative processes tak-ing place in PSRB1259−63 around periastron as a function of time (withrespect to periastron τ = 0) in order to account for the combinedH.E.S.S. datasets shown in Fig. 5.13.

γad = γad(t) in Eq(6.7), Eq(6.4) is solved for the EDF ne(t, γ). Thus calculations of theIC energy flux using the newly computed EDFs give the predictions shown in Fig. 6.12.Comparing Fig. 5.13 and Fig. 6.12 it seems that there is a peculiar “dip” in the TeV emis-sion around r ≈ 200 · 106 km that is best reproduced when assuming a non-monotonicloss rate as depicted by the black solid curve in Fig. 6.11. Using a monotonic and thusless complicated cooling function such as the green dash dotted profile gives a marginaloverall agreement with the H.E.S.S. data and fails to describe the reduced photon fluxesseen at θ ≈ ±90.In general (and especially in case of an IC scenario), the VHE flux from a binary systemis not expected to be symmetric with respect to the periastron passage. Indeed, thecorresponding symmetric orbital phases have to be characterized by different γ-γopacities and scattering angles with respect to the line of sight. Thus, either the change

107

6 Model Studies

[deg]θ

-100 -50 0 50 100

-1s

-2, eV

cm

dE

dN

2E

1

10

Figure 6.12: Predicted energy fluxes of 1 TeV photons from PSRB1259−63 corre-sponding to the three different non-radiative loss profiles as shown inFig. 6.11 compared to the 2004 (black dots) and 2007 (red empty squares)H.E.S.S. data.

108


in the γ-γ opacity is almost perfectly compensated by the orbital dependence of the γ-rayproduction mechanism, or the observed symmetry of the flux level indicates (i) a negli-gibly small absorption of the γ-rays and (ii) a γ-ray production mechanism, which has aweak dependence on the orbital phase. This would require the IC scattering to proceeddeep in the Klein-Nishina regime, where the IC crossection σic changes only marginallyover a large range of scattering angles. The latter favours a higher temperature of thestar in the system, as is suggested by [Negueruela et al.(2009), in preparation]. On theother hand, the luminosity of the star cannot strongly exceed the value suggested by[Johnston et al.(1992)] because of enhancement of the γ-γ absorption. To explain thevariability of the observed flux as a function of the separation distance the introductionof non-radiative (adiabatical) losses, which dominate in PSRB1259−63 over the wholeorbital period (see Fig. 4 in [Khangulyan(2006)]), is reasonable. Moreover, the observedlightcurve with a number of humps and dips suggests a rather complicated dependenceof the non-radiative losses on the separation distance. In particular, one may expect theadiabatic loss rate to have a peak close to periastron together with two smaller peakslocated at orbital positions characterized by a true anomaly of θ ≈ ±90. Those smallerpeaks may be linked to the impact of the stellar disc, although the corresponding ori-entation of the disc is not supported by radio observations [Bogomazov(2005)].The fact that the symmetry seen in the TeV lightcurve is not reflected in the 1-10 keVband, requires additional assumptions on the orbital phase dependence of the magneticfield. Although any detailed discussion of the ratio of TeV and X-ray fluxes requiresrather accurate calculations and goes beyond the scope of this work, a qualitative expla-nation for a sharp increase of the X-ray flux before periastron passage may be suggested:In frameworks of the dominant non-radiative losses, a decrease of the IC flux by a factorof 3 should be caused by an equivalent enhancement of the non-radiative losses. Thismay be reached with an increase of the ram pressure in the stellar outflow, so that thePW termination shock moves closer to the pulsar (roughly by a factor of 3). This wouldnot significantly change the density of the target photons (assuming the shock is locatedclose to the pulsar), but should lead to a significant increase of the magnetic field inthe production region (again by a factor of 3). Thus, it is indeed natural to expect anincrease of the synchrontron flux by one order of magnitude. On the other hand, it hasto be noted that the overall orbital behavior of the X-ray flux cannot be explained bymeans of these simple arguments. Although the H.E.S.S. data are not yet significantenough to be conclusive regarding the existence of two dips in the TeV lightcurve, thesymmetry of this feature in the VHE regime with respect to periastron and the corre-lation with a significant rise of the X-ray emission at the same separation distance areremarkable. It could be well explained by a non-monotonic adiabatic cooling profile,tracing a change in the size of the shock region and magnetic field strength, inducede.g. by stellar matter outflows of increased density such as the stellar disc.

109

7 Summary

The second H.E.S.S. campaign on the binary system PSRB1259−63/SS2883 around pe-riastron in 2007 (−0.08 < φ < 0.01) yielded VHE data for the first time covering earlypre-periastron orbital phases commencing ∼ 110 days before the passage. Measurementsin 2005 (φ = 0.31) and 2006 (φ = −0.37) covering orbital phases near apastron for thefirst time showed no significant flux of γ-rays from this source leading to an upper limitof 7 × 10−13 cm−2 s−1 for the integrated photon flux above 1TeV at the respective or-bital positions. As expected the source showed a significant excess (9.5σ) of TeV γ-raysin 2007 after 3.4 years of quiescence. Spectral features as well as the variable sourcecharacter known from exposures in 2004 were confirmed. The mean energy flux of thesource was measured to be FE(E > 1TeV) ≈ 2×10−12 erg cm−2 s−1 corresponding to anintegrated flux in VHE photons above 1TeV of about 2.7% of that of the Crab nebula.The overall lightcurve including also data taken in 2004 shows two ’humps’ located atphases φ ≈ −0.08 . . . − 0.004 and φ ≈ 0.009 . . . 0.08 with peak emissions of significantphoton excesses at φ ≈ −0.007 and φ ≈ 0.017, respectively. This differs from the trendin the VHE flux vs. φ seen in the VHE binary LSI+61 303, which has a moderate-length period and which exhibits VHE emission over a wide range of orbital phasesφ ≈ 0.225 . . . 0.625 and a peak at φ ≈ 0.325 . . . 0.425 [Albert et al.(2009)].1 However,LSI+61 303 is a much more compact system than PSRB1259−63: the compact object inLSI+61 303 is always at a distance from its Be companion that is smaller than or equalto the orbital separation at periastron passage in PSRB1259−63. The early onset of theVHE emission in PSRB1259−63 with respect to the pulsar’s orbital phase (φ ≈ −0.04)occurs much further away from the Be star. This presents difficulties for a pure hadronicdisc scenario taking into account positional parameters for the circumstellar disc. Thus,models which associate the TeV emission in PSRB1259−63 with the pulsar crossing thedisc are clearly challenged by the H.E.S.S. data presented in this work.The VHE lightcurve of PSRB1259−63 shows a high degree of symmetry between preand post periastron fluxes when viewed as function of the binary separation r. Sincethe H.E.S.S. data include both pre and post periastron orbital phases taken during dif-ferent campaigns in the years 2004 and 2007 this γ-ray source can be classified as beingperiodical.One possible reason for the VHE photon flux in PSRB1259−63 being a function of rcould be that in the Klein-Nishina regime the IC crossection σic changes only marginallyover a large range of scattering angles combined with the fact that adiabtical lossesare indeed dominant in PSRB1259−63 over the whole orbital period (see Fig. 4 in[Khangulyan(2006)]). The fact that the symmetry seen in the TeV lightcurve is notreflected in the 1-10 keV band indicates that X-rays are produced by a mechanismdifferent from IC. Synchrotron radiation in combination with a complex orbital phasedependence of the B-field could account for the significant deviations between pre and1 Here phases are quoted subtracting the presently defined periastron phase at φ∗ = 0.275[Aragona et al.(2009)]

111

7 Summary

post periastron fluxes seen in X-rays above a separation distance between the two objectsof r ≈ 200 · 106 km. The coincidence between the significant rise in the pre periastronX-ray flux by a factor ∼10 and drop in TeV emission (factor ∼3) at the same separa-tion distance could also be attributed to a compression of the shock region when thepulsar comes closer to the star. If, for instance, the stellar disc leads to a sudden in-crease of the PW ram pressure, VHE particles could escape the compressed shock regionwhile a compression of the B-field would be noticable in enhanced synchrotron emission.Such a scenario would naturally account for the two dips in the TeV lightcurve aroundθ ≈ ±90.Although the H.E.S.S. data are not yet significant enough to be conclusive regardingthe existence of two dips in the TeV lightcurve, the symmetry of this feature in the VHEregime with respect to periastron and the correlation with a significant rise of the X-rayemission at the same separation distance are remarkable. It could be explained by anon monotonic adiabatic cooling profile, tracing a change in the size of the shock regionand magnetic field strength induced by stellar matter outflows of increased density suchas the Be star disc.PSRB1259−63 remains a fascinating TeV binary system featuring complex PW dy-namics with many questions still open. More sensitive observations in the VHE regimeusing future observatories that would allow for phase resolved spectra on time scales ofdays, will contribute to a better understanding of this source.

112

Appendix

1 Calculating θ(t) for a Kepler ellipse

From Kepler’s first law it is known that the motion of a celestial body around a massivecompanion as in the case of PSRB1259−63 can be described by an ellipse. The semimajor axis of this ellipse is given by

a = GM

2|E| (1)

E being the system’s overall energy, M the mass of the massive companion and G thegravitational constant. In cartesian coordinates the elliptical trajectory of the pulsarreads

(x, y) = (r cos θ, r sin θ) (2)

with r = p

1 + e cos θ (3)

and L = r2θ (4)

Retrieving from this r = −(L2

p )r/r3 for the acceleration and comparing with the equa-tion of motion

r = −GM rr3 (5)

yields for the parameter

p = L2

GM. (6)

Energy conservation for a Keplerian motion yields

E = r2

2 + L2

2r2 + V (r) (7)

Writing (7) in terms of r = dr/dt and using the fact that p = a(1− e2), one finds2

dt

dr= r√

2|E|(−r2 + 2ar − a2(1− e2))(8)

Integrating over r, while using the ansatz a − r = ae cos Ψ, r = a(1 − cos Ψ), dr =ae sin ΨdΨ yields3

t = T

2π (Ψ− e sin Ψ), (9)

2Introducing a and e with the help of (1) and (6) respectively.3Note that we have used Kepler’s 3. law here.

115

Appendix

where T is the orbital period. Equation (9) is the so called Keppler Equation. Ψ isalso known as eccentric anomaly. In order to get r as a function of time via r =a(1− e cos Ψ(t)) a representation of Ψ with respect to t has to be found. The functionΨ = Ψ(t) is retrieved from the transzendental Eq(9) using Newton’s Method4 for thezeros of

f(Ψ) = Ψ− e sin Ψ− 2πtT

, i.e (10)

Ψn+1 = Ψn −f(Ψ)f ′(Ψ) =

e(sin Ψn −Ψn cos Ψn) + 2πtT

1− e cos Ψn(11)

The subsequent knowledge of Ψ = Ψ(t) gives r(t). The temporal behavior of the trueanomaly θ(t) of the Kepler ellipse is conducted, considering the equation for the pulsartrajectory (2):

r(t) = a(1− e cos Ψ(t))

cos θ(t) = cos Ψ(t)− e1− e cos Ψ(t) (12)

2 Calculating the mean fluxIn the course of this thesis and the work with the PSRB1259−63 H.E.S.S. data takenin 2007 a number of systematic/methodological effects when computing “mean” photonfluxes from a variable source have been encountered. Especially a suitable estimatorfor the mean of a varying parameter such as the flux of a transient emitter had to befound. The following chapter shall summarize the systematic studies and their resultsconcerning different approaches to calculate mean photon fluxes from the data.

2.1 Definition of the problem

Integrated photon fluxes F (E > Eth) above an energy threshold Eth are computedintegrating Eq(5.1), i.e.

F (E > Eth) = Φ0

∫Eth

(E

E0

)−ΓdE, (13)

In Eq(13) a standard powerlaw source with constant photon index Γ is assumed. Theflux normalisation Φ0 is retrieved from Eq(5.2)

Nγ(E > Eth) =∫ ∞Eth

dNγ

dEdE = TΦ0

∫ ∞Eth

(E

E0

)−ΓA(E, θ)dE︸︷︷︸

:=δexp

,

since the source shows a photon excess of Nγ above an energy threshold of Eth afterthe observation (live)time T recorded with a detector with effective area A(E, θ). The4The zero of a function f(x) near a starting value x0 is approximated by the successive subtractionxi − xt,i where (xt,i, 0) denotes the point of intersection of the tangent in f(x) with the x-axis, i.e.xi+1 = xi − f(xi)

f ′(xi) .

116

2 Calculating the mean flux

exposure integral is denoted by δexp. The product Tδexp is the exposure.Usually integrated fluxes are computed for different time intervals such as for single“runs”, i.e. pointings of ∼ 28min duration in case of H.E.S.S., observation nights or evenwhole observation periods such as months. Integrated fluxes are based on measurementsthat have finite accuracy and therefore come with errors, i.e. ususally the 1σ confidenceintervall, i.e. ∆Frun,i = σi for the measurement.If “runwise” fluxes Frun,i for a single observation night have been measured one methodto calculate the flux for the whole night Fnight is to compute the ’weighted mean’ (WM)of the runwise fluxes, i.e.

Fnight =

∑iFrun,iσ2i∑

i1σ2i

(14)

∆F 2night = 1∑

i1σ2i

.

Another possibility is the direct evaluation of Eqs(13)& (5.2) using the accumulatedphoton excess Nγ and exposure of the whole night, from now on called the ’sum ofexcesses over sum of exposures (SESE)’ method. To first order one might expect thatboth methods yield the same result for the mean photon flux, i.e.∑

iFrun,iσ2i∑

i1σ2i

≈ ΣiNγ,i(E > Eth)ΣiTiδexp,i

∫Eth

(E

E0

)−ΓdE. (15)

Due to low statistics in the corresponding time bins a time averaged Γ may be used forthe calculation of the single fluxes F .However, the two sides in Eq(15) are not necessarily equivalent and show significantdifferences at least for a weak and/or variable source such as PSRB1259−63 whenusing the errors ∆Fi on the flux as weights according to

σi = ∆Fi = 12 (∆Fup,i + ∆Fdown,i) , (16)

where ∆Fup,i and ∆Fdown,i are errors up and down on the flux. Equations (13)& (5.2)then yield upper and lower bounds on the flux normalisation Φ0, finally resulting in theerror on the flux since Γ = const.As shown in Tab1 and Fig1, the weighted means using Eq(14) of photon fluxes of differ-ent time binnings using the whole PSRB1259−63 2007 H.E.S.S. dataset give significantlydifferent results for the mean flux. It appears that the finer the time binning the morethe weigthed mean deviates from the overall flux computed according to Eqs(13)& (5.2).All single fluxes in each time binning (runwise, nightly, monthly, overall) were computedalso using Eqs(13)& (5.2). The reason for the significant difference between the twoestimators WM Eq(14) and SESE Eqs(13)& (5.2) for the mean flux of a variable γ-ray source such as PSRB1259−63 is the implicit assumption of measuring a constantquantity when using the WM. Usually when measuring a physical quantity (such ase.g. the electrical conductivity ρ of a material or the temperature T in a room) thecorresponding quantity is basically constant throughout the measurement. The WM of

117

Appendix

Runwise Nightly Monthly Total

4.0± 0.6 5.0± 0.6 5.7± 0.6 6.0± 0.6

Table 1: Overall integrated photon fluxes F (E > 1TeV) [10−13 cm−2 s−1] ofPSRB1259−63 in 2007 above 1 TeV using the weighted means of fluxes withdifferent time binning. The single fluxes in the different representations, i.e.runwise, nightly and monthly, were calculated using Eqs(13)& (5.2).

Time MJD

54200 54220 54240 54260 54280 54300 54320

]-1

s

-2F

(>1T

eV

) [

cm

-0.5

0

0.5

1

1.5

2

-1210×

April May June July August

Figure 1: Comparison of the weighted mean of the runwise PSRB1259−63 2007H.E.S.S. data (green squares) depicted by the red dashed line with theweighted mean taken from monthly fluxes (black squares) as shown by theblack dashed-dotted line. Runwise as well as monthly fluxes were calculatedusing the accumulated photon excess in each time bin, i.e. Eqs(13)& (5.2).

single measurements that all fluctuate around a true constant value is thus an appro-priate estimator for the quantity to be measured as long as the underlying statisticsfeatures a symmetric probability density function (pdf), something which is not true forPSRB1259−63. In case of PSRB1259−63 the mean photon flux is not equivalent to thevalue of a best fit constant as the source is variable. The measured single fluxes such asrunwise fluxes do not fluctuate around a true value < F > following e.g. a gaussian pdfp(F ) ∝ exp

(−1

2

(F−<F>

σ

)2)

such that

< F >=∫Fp(F )dF. (17)

Thus the WM of the single fluxes is not the mean photon flux but rather the best fit tothe data assuming a constant source.

118


2.2 Monte Carlo StudyIn order to test the behavior and bias of the two above mean flux estimators, i.e. the WMusing the σi as weights and the SESE-method with respect to different parameters suchas source variability, flux level and distribution of exposures in the data, a toy MonteCarlo was used, generating fluxes fluctuating (where the underlying ON and OFF countsfollow Poisson statistics) around different given model lightcurves. For this simulationa point-like source using a Θ2-cut of ∆Θ = 0.0125 was assumed. A background photonOFF-rate as function of the zenith angle θ, i.e. NOff(θ) = 100 cos θ/ cos 20 events h−1,as shown in Fig2 was used. To test for different degrees of variability four types of model

[deg]θ

0 10 20 30 40 50 60

-1co

un

ts h

60

70

80

90

100

Figure 2: Off rate in events per hour as a function of the zenith angle θ in degrees usedfor the generation of fluxes from different model sources.

lightcurves were used:

• constant

• weakly variable

• highly variable

• PSRB1259−63 like lightcurve in a linear approximation of the data taken in 2007.

The used lightcurves are shown in normalized form in Fig3. For each given modellightcurve using flux normalisations from 1 to 100 % of the flux of the Crab nebula,120 runs of 25 min livetime data were generated using the standard Heidelberg cutconfiguration (std_0510_south) [Aharonian et al.(2006)]. The true mean flux for everysimulated lightcurve according to Eq(13) is known a priori since the flux normalisationΦ0 and the photon index Γ are parameters chosen in the simulation.

119

Appendix

time

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

no

rm

ali

ze

d f

lux

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

time

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

no

rm

ali

ze

d f

lux

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

2.2

time

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

no

rm

ali

ze

d f

lux

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

time

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

no

rm

ali

ze

d f

lux

0.4

0.6

0.8

1

1.2

1.4

1.6

Figure 3: Lightcurves used in the Monte Carlo simulation: (top left) constant (top right)highly variable (bottom left) mildly variable (bottom right) PSRB1259−63-like. Both flux and time are normalized to unity in these plots.

120


From these Monte Carlo data the overall mean flux was estimated using both the WMand the SESE-method.As the used weight for the WM-method is not an a priori fixed quantity, different weight-ings were used in an experimental approach. The color code for the used estimators forthe mean flux from the Monte Carlo generated runwise fluxes in the following plots isas follows:

. (red) SESE Eqs(13)& (5.2)

. (blue) WM from runwise fluxes using as weight σi,run = ∆Fi,run

. (cyan) WM from runwise fluxes using the somewhat empirical weightσi = (Tiδexp,i)−1/4

. (black) WM of monthly fluxes using as weight σi,mon = ∆Fi,mon. The usedmonthly fluxes were calculated using the SESE-method.

The influence of the distribution of exposures in the simulated dataset was tested byusing once uncorrelated exposures, i.e. with no correlation to the run number, and onceintroducing to the data a correlation between the run number and exposure as shownin Fig4.

run

20 40 60 80 100 120

exposure

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

910×

run

20 40 60 80 100 120

exposure

0.6

0.8

1

1.2

1.4

1.6

1.8

2

910×

Figure 4: Exposure as a function of the run number as used in the simulation: (left)uncorrelated (right) (anti-)correlated.

Results

The relative deviations ∆FF for the mean flux Fest computed according to the above

mentioned methods from the true mean flux Ftru, i.e.

∆FF

= Fest − FtruFtru

, (18)

121

Appendix

as a function of Ftru (given in % of the flux from the Crab nebula) were computed forthe lightcurve types in Fig3. The results are shown in Figs5 to 9.

Constant Lightcurve:

. There is a significant deviation for the WM of runwise fluxes (blue) from the truemean flux for lower flux levels. The deviation equals ∼15% at a flux level of 1%Crab (see Fig5).

Flux (>1 TeV) [% Crab]1 10

210

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∆

-0.5

-0.4

-0.3

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-0

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expδ TΣ N /ΣSESE,

run F∆ = σWM runwise,

mon F∆ = σWM monthly,

41-

expδ TΣ = σWM

Figure 5: Relative deviations of estimated mean fluxes from the true mean flux simulat-ing a constant lightcurve using uncorrelated exposures in the data. See textfor the color code.

Variable Lightcurve:

. The deviation of the WM from the true mean becomes worse for variable sources.The deviation is especially bad for higher fluxes (see Fig6). In this regard thedegree of variability and the lightcurve shape influence the bias significantly. Thisbecomes clear when e.g. comparing monthly flux biases (black) to those comingfrom runwise data (blue) for the highly and mildly variable model lightcurve asshown in Fig6.

. For variable lighcurves the exposure distribution has an influence on the estima-tors used (see Fig7). For datasets with exposures (anti-)correlated with the runnumber, i.e. in time, also the SESE-method (red) shows a bias.

. Inverting the correlation between exposure and run number (time) (compare Fig8left and Fig4 right) inverts the sign of the bias of the SESE-method (compare redline in Fig7 left and Fig8 right).

. The WM estimator using exposure weighting (cyan), i.e. σi = (Tiδexp,i)−1/4, is onaverage the most stable estimator used in this study.

122



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expδ TΣ = σWM

Figure 6: Relative deviations of estimated mean fluxes from the true mean flux sim-ulating a highly (left)/mildly (right) variable lightcurve using uncorrelatedexposures in the data. See text for the color code.


210

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-0

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41-

expδ TΣ = σWM

Figure 7: Relative deviations of estimated mean fluxes from the true mean flux simu-lating a highly (left)/mildly (right) variable lightcurve using (anti-)correlatedexposures in the data. See text for the color code.

123

Appendix

run

20 40 60 80 100 120

exposure

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

910×


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41-

expδ TΣ = σWM

Figure 8: (left) Correlated exposure distribution. (right) Deviations of the estimatedmean flux from the true flux for the highly variable lightcurve using correlatedexposures.

The case of PSRB1259−63

. For a lightcurve similar to what was measured from PSRB1259−63 in 2007 a biasfor the WM of ∼10% at the 3% Crab level is seen5 in case of an uncorrelated ex-posure distribution. This is well within the systematic error given for H.E.S.S. fluxmeasuerements of about ∼20%. Moreover, throughout this thesis only mean fluxesusing the SESE method were used which according to Fig9 (red line in left plot)shows no deviations in case of uncorrelated exposures (approximately true for theH.E.S.S. dataset) and a bias of ∼13% for strong time correlations in exposure(Fig9 red line in right plot).

Interpretation

The above bias behavior of the various estimators with respect to the overall true fluxcan be interpreted and partly explained as follows:

. It is clear that the concept of the WM-method is only applicable to constant quan-tities and has to fail once a measured quantity is variable within the time apertureof its measurement. In case of a variable quantity the single measurements actuallydo not fluctuate around a given mean following a normal distribution. For weakersources the underlying pdf is not even symmetric since ON and OFF counts followa Poisson distribution (see next point).

. The circumstance that there are also deviations down for the WM of fluxes of aconstant model lightcurve in particular at lower flux levels (Fig5) is explained bythe fact that downward fluctuations get a higher weight in the WM method than

5The overall flux level of the H.E.S.S. dataset for the PSRB1259−63 observations in 2007 was 2.7%of that of the Crab nebula.

124



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expδ TΣ = σWM

Figure 9: Relative deviations of estimated mean fluxes from the true mean flux sim-ulating a PSRB1259−63 like lightcurve using uncorrelated (left) and (anti-)correlated (right) exposures in the data. See text for the color code.

upward fluctuations since the used weights are 1σ2iand σi ∝

√NOn,i + α2NOff,i and

higher fluxes therefore mean higher absolute errors.

. There is also a bias in the SESE approach once having time correlated exposuredistributions in the data of a variable lightcurve. The reason for this becomesclear once one interprets SESE mean fluxes as being exposure weighted . Thisbecomes noticeable once the flux is not constant for a given time interval andintrinsically varying photon excesses get weighted differently according to increas-ing/decreasing exposures (Figs7&8).

. The WM using σi = (Tiδexp,i)−1/4 as weight (cyan) was the best estimator. Thereason for this is that this weight partly reverts the effect discussed above, i.e. theweighting effect of a correlated exposure distribution on variable fluxes in theSESE method is weakend by a weight indirectly proportional to the exposure.

Conclusion

• In general the WM is not equal to the true mean of a quantity. In case of aquantity variable in time the WM, using the measurement errors as weights, is thebest fit to the data assuming a constant as nullhypothesis.

• Thus the WM is not at all a good estimator for mean fluxes of single measurementsboth for low flux levels and variable lightcurves when using the errors on the fluxas weights.

• Datasets including strong correlations between the observation exposure and timeshould be treated with care as the corresponding fluxes calulated according toEqs(13)& (5.2) will contain a bias.

• It should be noted that it is desirable to look for corrections of the effects discussedabove and to find a bias-free estimator for weak and/or variable photon fluxes.

125

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• As the analysis in this thesis using data from the weak and mildly variable sourcePSRB1259−63 was not affected beyond the typical systematic error margins, theSESE-method seemed to be a sufficiently reliable estimator and such studies havenot been carried out as they would have gone beyond the scope of this work.

126

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http://astro.uni-tuebingen.de/~wilms/teach/radproc/

List of Figures

1.1 Hafelekar Observatory . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Cosmic ray spectrum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31.3 Whipple telescope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

2.1 H.E.S.S. array . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72.2 Cherenkov cone . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82.3 Electromagnetic shower . . . . . . . . . . . . . . . . . . . . . . . . . . . 92.4 Hadronic shower . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102.5 IACT technique . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122.6 H.E.S.S. camera . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132.7 Camera acceptance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142.8 Central array GUI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172.9 Camera response curve . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182.10 Camera Pedestals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192.11 Single PE calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202.12 Muon ring . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202.13 Stereoscopy and Hillas moments . . . . . . . . . . . . . . . . . . . . . . 212.14 Mean reduced scaled width . . . . . . . . . . . . . . . . . . . . . . . . . 232.15 Background models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 242.16 Angular distance event distribution . . . . . . . . . . . . . . . . . . . . . 25

3.1 Microquasar . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 303.2 IC Feynman graphs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 323.3 Inverse Compton Effect . . . . . . . . . . . . . . . . . . . . . . . . . . . 343.4 Hadronic jet interactions . . . . . . . . . . . . . . . . . . . . . . . . . . . 363.5 Sketch defining angles and distances in a binary system . . . . . . . . . 363.6 LS 5039 energy spectrum and photon flux . . . . . . . . . . . . . . . . . 383.7 LS 5039 spectral index and flux normalisation . . . . . . . . . . . . . . . 393.8 LSI+61-303 lightcurve . . . . . . . . . . . . . . . . . . . . . . . . . . . . 403.9 LSI+61-303 spectrum and LS-periodogram . . . . . . . . . . . . . . . . 423.10 LS I+61-303 radio contours and plerionic model . . . . . . . . . . . . . . 433.11 Cygnus X-1 MWL lightcurve . . . . . . . . . . . . . . . . . . . . . . . . 443.12 Cygnus X-1 energy spectrum . . . . . . . . . . . . . . . . . . . . . . . . 45

4.1 PSRB1259−63 model sketch . . . . . . . . . . . . . . . . . . . . . . . . 484.2 Pulsar . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 494.3 Crab Nebula . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 524.4 Be star winds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 534.5 Pulsar wind shock . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 544.6 PSRB1259−63 SED I . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

137

List of Figures

4.7 Radiation timescales . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 564.8 PSRB1259−63 SED II . . . . . . . . . . . . . . . . . . . . . . . . . . . . 574.9 Cooling profile . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 604.10 Model spectrum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 614.11 PSRB1259−63 2004 lightcurve . . . . . . . . . . . . . . . . . . . . . . . 624.12 PSRB1259−63 radio profile . . . . . . . . . . . . . . . . . . . . . . . . . 644.13 X-ray photon index and flux . . . . . . . . . . . . . . . . . . . . . . . . . 65

5.1 Skymap and Spectrum . . . . . . . . . . . . . . . . . . . . . . . . . . . . 685.2 2004 Lightcurve . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 695.3 PSRB1259−63 in radio to VHE . . . . . . . . . . . . . . . . . . . . . . . 705.4 Visibility for PSRB1259−63 . . . . . . . . . . . . . . . . . . . . . . . . . 725.5 H.E.S.S. sensitivity for PSRB1259−63 . . . . . . . . . . . . . . . . . . . 735.6 Visibility time slots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 735.7 Correlated significance map . . . . . . . . . . . . . . . . . . . . . . . . . 755.8 Differential energy spectrum . . . . . . . . . . . . . . . . . . . . . . . . . 775.9 Monthly spectra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 785.10 Kolmogorov-Smirnov test . . . . . . . . . . . . . . . . . . . . . . . . . . 805.11 PSRB1259−63 lightcurve 2007 . . . . . . . . . . . . . . . . . . . . . . . 815.12 Integrated flux vs. θ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 855.13 1 TeV photons vs. r . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86

6.1 PSRB1259−63 orbital angles . . . . . . . . . . . . . . . . . . . . . . . . 916.2 Disc density profile fit . . . . . . . . . . . . . . . . . . . . . . . . . . . . 926.3 Pulsar phases during H.E.S.S. observations . . . . . . . . . . . . . . . . 946.4 Pulsar wind shock . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 966.5 IC flux in PSRB1259−63 . . . . . . . . . . . . . . . . . . . . . . . . . . 996.6 Refernce Curves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1006.7 Asymmetric cooling profile . . . . . . . . . . . . . . . . . . . . . . . . . 1026.8 Electron distribution function . . . . . . . . . . . . . . . . . . . . . . . . 1046.9 Model lightcurves for asymmetric cooling . . . . . . . . . . . . . . . . . 1056.10 PSRB1259−63 in the 1−10 keV band . . . . . . . . . . . . . . . . . . . 1066.11 PSRB1259−63 symmetric cooling profiles . . . . . . . . . . . . . . . . . 1076.12 Model lightcurves for symmetric cooling . . . . . . . . . . . . . . . . . . 108

1 PSRB1259−63 mean photon flux in 2007 . . . . . . . . . . . . . . . . . 1182 Off rate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1193 Lightcurve shapes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1204 Exposure distributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1215 Relative deviations, constant lightcurve, uncorrelated exposure . . . . . 1226 Relative deviations, variable lightcurve, uncorrelated exposure . . . . . . 1237 Relative deviations, variable lightcurve, (anti-)correlated exposure . . . 1238 Relative deviations, correlated exposure, variable lightcurve . . . . . . . 1249 Relative deviations, PSRB1259−63-like lightcurve . . . . . . . . . . . . 125

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List of Tables

2.1 std_0510_south cuts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

3.1 X-ray binary configurations . . . . . . . . . . . . . . . . . . . . . . . . . 29

4.1 PSRB1259−63 parameters . . . . . . . . . . . . . . . . . . . . . . . . . 47

5.1 Zenith angle visibility . . . . . . . . . . . . . . . . . . . . . . . . . . . . 745.2 PSRB1259−63 Dataset . . . . . . . . . . . . . . . . . . . . . . . . . . . 835.3 PSRB1259−63 Spectral Parameters . . . . . . . . . . . . . . . . . . . . 84

1 PSRB1259−63 mean photon flux in 2007 . . . . . . . . . . . . . . . . . 118

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Selbständigkeitserklärung

Berlin am 7.10.2009

Ich, Matthias Kerschhaggl, bestätige hiermit, daß ich vorliegende Arbeit selbständigund ohne unerlaubte fremde Hilfe verfasst habe. Ferner erkläre ich mich mit der Aus-lage dieser Arbeit in der Universitätsbibliothek der Humboldt Universität zu Berlin füreinverstanden.

gez. Matthias Kerschhaggl

141

the tev gamma-ray binary psr b1259-63€¦ · doctor rerum naturalium (dr. rer. nat.) im fach...

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