Neutron Star Powered Nebulae: a New View on

Pulsar Wind Nebulae with the Fermi Gamma-ray Space

TelescopeJoshua Lande@joshualande

Please ask questions!!

Why do we do astronomy?

Nabta Playa 5th century BC

Liberal ArtsThe Trivium•grammar•logic•rhetoric

The Quadrivium•arithmetic•geometry•music•astronomy

Multiwavelenth astronomy

We can study astronomy across the electromagnetic spectrum

William Herschel 1800

Infrared Astronomy Radio-wave Astronomy

Karl Jansky 1933

ultraviolet - 1946

X-ray - 1949

Gamma-ray Astrophysics

Explorer XI

OSO-3

1972ApJ...177..341K

OSO-3: 621 gamma-rays

COS-B

SAS-2

Cos-B Skymap

EGRET

1988SSRv...49...69K

EGRET Sky Map

The Fermi Gamma-ray Space Telescope

The Fermi Gamma-ray Space Telescope

20 MeV to >300 GeV

The Large Area Telescope

TrackerLayers

Calorimeter Layers

Anti-Coincidence Detector (surrounding)

Large Area Telescope (LAT)Fermi Gamma-ray Space

Telescope

photon

positronelectron

Angular Resolution of the LAT

Blastoff!

The Gamma-ray Sky

Very High Energy Astrophysics

Very High Energy Astrophysics

The High Energy Stereoscopic System (H.E.S.S)

Fermi ~ 20 MeV to 300 GeV

Air Cherenkov Detectors ~100 GeV and ~30 TeV

Astrophysical Sources of Gamma-rays

Many sources of gamma-rays

The 2FGL Catalog

No association Possible association with SNR or PWNAGN Pulsar Globular clusterStarburst Gal PWN HMBGalaxy SNR Nova

Pulsars, Supernova Remnants, and PWNe are connected through a simple picture

Gaensler & Slane (2006)

Supernova are new stars that appear in the sky.

~,.

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~ L

|F

0 L~

0 c~o

0

Left: SN 1054 (Crab Nebula)

7 supernova visible by the human eye in ~2,000 years.

Right: SN 1572 (Tycho’s SN)

Pulsars are the remaining core of neutron Stars

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Pulsars have periodic emission

Pulsar Wind Nebula (PWN) are observed to surround pulsars

Energy Spectrum of the Crab Nebula

Radiation Processes in PWN

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Gamma-ray Observations

How to identify Gamma-ray Pulsars?

Vela

Pulsar Phase0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

Even

ts/B

in W

idth

0

0.2

0.4

0.6

0.8

1

610×

0.12 0.13 0.14

0.6

0.65

0.7

0.75

0.8

0.85

0.9

0.95

1

610×

0.54 0.56 0.58

0.6

0.7

0.8

0.9

1

610×

Pulsar light curve

Vela

Energy (GeV)−110 1 10

)−1

s−2

dN/d

E (e

rg c

m2 E

−1010

−910

Energy Band Fits

Maximum Llikelhood Model

Pulsar Energy Spectrum

Vela

117 Gamma-ray Pulsars in the Second Pulsar Catalog

Gamma-ray PWNCrab Nebula

Vela XAbdo et al 2010

Abdo et al 2010

Crab NebulaThe Astrophysical Journal, 749:26 (8pp), 2012 April 10 Buehler et al.

Pulsar phase0.2 0.4 0.6 0.8

Cou

nts

5000

10000

Pulsar phase0.2 0.4 0.6 0.8

Cou

nts

5000

10000

Figure 1. Phase profile of gamma rays above 70 MeV within 3! of the Crabpulsar for the first 33 months of Fermi observations (black histogram) andduring the 2011 April gamma-ray flare between MJD 55663.70 and 55671.02(black markers with error bars). The gray region indicates the adopted off-pulseinterval where the emission is dominated by the nebula. The flare phase profilehas been multiplied by a factor 59, such that the excess above the off-pulsecounts is the same as for the 33 months of observations. This demonstrates thatthe flare is a phase-independent flux increase.

of observations (MJD 54683–55664), excluding the 2011 Aprilflare.

Fluxes and spectra were obtained by maximizing the likeli-hood of source models using unbinned gtlike from the FermiScience Tools 9-23-01. The models included all sources in thesecond LAT source catalog within 20! of the Crab position(Abdo et al. 2011c) plus models for the Galactic and isotropicdiffuse emission (gal_2yearp7v6_v0, iso_p7v6source).The parameters left free to vary in the likelihood fit for33 month average spectra were the spectral parameters of theCrab, the normalization of the diffuse components, and a power-law spectral index for scaling the Galactic diffuse emissionmodel. For analysis on shorter timescales, only the isotropicdiffuse normalization was varied along with the Crab spectralproperties. All other parameters were fixed to the 33 month av-erage maximum likelihood values. The Sun was included in thesource model when it was within 20! of the Crab. The solarspectra during the two passages in front of the Crab were takenfrom Abdo et al. (2011b). The Moon was not included in thesource model as its gamma-ray contamination was found to benegligible for observations presented here.

We used the P7_V6_SOURCE instrument response functionswithout in-flight point-spread function corrections, selectingphoton events between 70 MeV and 300 GeV. Compared tothe more typical 100 MeV threshold, this choice leads toadditional systematic errors due to increased dispersion in thephoton energy reconstruction. The overall systematic flux erroris energy dependent: it amounts to 30% at 70 MeV and decreasesto 10% above 10 GeV (Rando et al. 2011). The dominant part ofthis systematic error is related to the overall flux normalization.It is caused by uncertainties in the effective area determinationand of the overall normalization of energy scale.

The stability of the LAT instrument over time was tested for alltimescales addressed in this paper using the Vela and Gemingapulsars, which are found to be stable in flux (Abdo et al. 2010b,

Figure 2. Spectral energy distribution for the Crab Nebula averaged over thefirst 33 months of Fermi observations. The axis on the right side indicates theisotropic luminosity. Also shown are data from COMPTEL in the soft gamma-ray band (Kuiper et al. 2001) and very high energy gamma-ray measurementsfrom Cherenkov telescopes (Aharonian et al. 2006; Zanin et al. 2011). Thedashed line shows the maximum likelihood model in the parameterizationdescribed in the text.

2010c). Their flux variations were <10%, yielding an upperlimit on the variations of the systematic errors with time. Amore detailed study of the systematic uncertainties is currentlybeing prepared within the LAT collaboration for publication.

The pulsar phase was assigned to the detected gamma raysbased on a high-time-resolution pulsar ephemeris. To obtainthe latter, we extracted 400 pulsar times of arrival (TOAs) fromLAT photons collected from MJD 54684 to 55668 with a typicaluncertainty of "100 µs (Ray et al. 2011). Using tempo2 (Hobbset al. 2006), we fitted a timing solution to these TOAs with atypical residual of 108 µs, or about 3 # 10$3 of the pulsarperiod. To obtain these white residuals, we modeled the pulsartiming noise using the method of Hobbs et al. (2004), with 20harmonically related sinusoidal terms. The ephemeris parameterfile, and the light curves and spectra shown in this paper arepublicly available online.14

3. TIME-AVERAGE ENERGY SPECTRA

The Crab appears to the LAT as a point source, even atthe highest photon energies. To separate nebular gamma-rayemission from that of the pulsar we apply a cut on the pulsarphase. The phased count rate of the pulsar with its double-peaked structure is shown in Figure 1. The pulsar dominatesthe phase-averaged gamma-ray flux, but its flux in the off-pulseinterval from 0.56 to 0.88 is negligible (Abdo et al. 2010a). It isin this interval that we measure the properties of the nebula.

The LAT detects the nebula in the energy range betweenthe high-energy end of the synchrotron and the low-energy endof the inverse-Compton components of the SED. The averagenebular spectrum measured during the first 33 months of Fermiobservations is shown in Figure 2. We fitted it as the sum ofsynchrotron and inverse-Compton components. The differentialphoton spectrum, !(E), of the synchrotron component wasparameterized with a power law

!S(E) = FS(!S $ 1)(100 MeV)1$!S

E$!S , (1)

14 http://www-glast.stanford.edu/pub_data/691/

2

1260 ABDO ET AL. Vol. 708

Figure 4. Counts maps (arbitrary units) presenting the pulsed (top row) and nebular (bottom row) emission, in three energy bands. Each panel spans 15! " 15! inequatorial coordinates and is centered on the pulsar radio position. Left: 100 MeV < E < 300 MeV; middle: 300 MeV < E < 1 GeV; right: E > 1 GeV.(A color version of this figure is available in the online journal.)

bars) and the overall errors (red error bars) are plotted for theFermi points. The EGRET spectral points are represented onthe same plot. As in the case of the spectrum of the Vela pulsar(Abdo et al. 2009a), derived using an earlier set of responsefunctions, Pass6_v1, markedly different from Pass6_v3 at lowenergies, the LAT spectral points at high energy indicate a lowerflux in comparison to EGRET. However, it can be noticed thatthe Fermi flux is higher than the EGRET flux, in the low energyband dominated by synchrotron radiation.

de Jager et al. (1996) found evidence in the EGRET data thatthe Crab synchrotron cut-off energy varied on timescales of theorder of a year. We do not see significant variation in eitherthe synchrotron or IC components in our more limited dataspan on timescales of 1, 2, or 4 months. As shown in Figure 5,a difference in flux is observed between EGRET and Fermi-LAT in the energy band dominated by synchrotron radiation aswell as at higher energies (above 1 GeV). Even if variabilityin the synchrotron tail could be expected between EGRET andLAT, the lifetimes of the electrons producing gamma-rays viaIC scattering are comparable to the remnant age, implying thatthe IC component should be steady in time. For these reasons,the flux change seen in the synchrotron component betweenEGRET and Fermi-LAT cannot be considered as significant.

The photon counts at high energy are too few for a significantcut-off or break to be seen in the flux distribution of the ICcomponent. No cut-off or break energy can be determined atlow energy for the synchrotron component using the LAT dataonly.

Energy [MeV]

210 310 410 510

]-1

s-2

.F [

erg

cm

2E

-1110

-1010

EGRET

Fermi

Figure 5. Spectral energy distribution of the Crab Nebula renormalized to thetotal phase interval. The fit of the synchrotron (purple dashed line) and IC (bluedash-dotted line) are represented separately with two power laws. The blackcurve is the best fit obtained with the sum of these two power laws. The LATspectral points are obtained using the model-independent maximum likelihoodmethod described in Section 4.2. The statistical errors are shown in black,while the red lines take into account both the statistical and systematic errors.Horizontal bars delimit the energy intervals. EGRET data points (Kuiper et al.2001) are shown for comparison (green stars).(A color version of this figure is available in the online journal.)

4.3. Spectral Analysis of the Pulsed Emission

Photons from both on- and off-pulse intervals are now con-sidered to analyze the pulsed emission. The spectral parameters

Abdo et al 2010 Abdo et al 2010

How do we know it is a PWN?

aharonian et al 2005

•PWN should have rising spectrum

•PWN can be extended

•Clear identification difficult:

•X-ray PWN often much smaller

•Pulsars can be offset

•other possible counterparts

•Pulsar energetics?

•PWN candidate vs clear detection?

•Energy dependent morphology

•Matching X-ray to Gamma-ray mormorphology?

L26 F. A. Aharonian et al.: The association of HESS J1825–137 with G 18.0–0.7

1. Introduction

PSR B1823–13 (also known as PSR J1826–1334) is a 101 msevolved pulsar with a spin-down age of T = 2.1 ! 104 years(Clifton et al. 1992) and in these properties very similar to theVela pulsar. It is located at a distance of d = 3.9 ± 0.4 kpc(Cordes & Lazio 2002) and ROSAT observations of this sourcewith limited photon statistics revealed a compact core, as wellas an extended di!use nebula of size "5# south-west of the pul-sar (Finley et al. 1998). High resolution XMM-Newton obser-vations of the pulsar region confirmed this asymmetric shapeand size of the di!use nebula, which was hence given the nameG 18.0–0.7 (Gaensler et al. 2003). For the compact core withextent RCN " 30## (CN: compact nebula) immediately sur-rounding the pulsar, a photon index of "CN = 1.6+0.1

$0.2 was mea-sured with a luminosity of LCN " 9d2

4 ! 1032 erg s$1 in the 0.5to 10 keV range for a distance of 4d4 kpc. The correspondingpulsar wind shock radius is Rs % 15## = 0.3d4 pc. The com-pact core is embedded in a region of extended di!use emissionwhich is clearly one-sided, revealing a structure south of thepulsar, with an extension of REN " 5#, (EN: extended nebula)whereas the "4# east-west extension is symmetric around thenorth-south axis. The spectrum of this extended component issofter with a photon index of "EN " 2.3, with a luminosity ofLEN = 3d2

4 ! 1033 erg s$1 for the 0.5 to 10 keV interval. Noassociated supernova remnant (SNR) has been identified yet.

At !-ray energies, PSR B1823–13 was proposedto power the close-by unidentified EGRET source3EG J1826$1302 (Nolan et al. 2003). TeV observationsof this pulsar by the Whipple and HEGRA Collaborationsresulted in only upper limits (Hall et al. 2003; Aharonian et al.2002), which are unconstraining with respect to HESS.

The region around PSR B1823–13 was observed as partof the survey of the Galactic plane with the HESS instru-ment (Aharonian et al. 2005a). In this survey, a source of veryhigh-energy (VHE) !-rays (HESS J1825–137) 11# south of thepulsar was discovered with a significance of 8.1". We note thatthe new VHE !-ray source is located within the 95% positionalconfidence level of the EGRET source 3EG J1826–1302 andcould therefore be related to this as of yet unidentified ob-ject. The High Energy Stereoscopic System (HESS) is an ar-ray of four imaging atmospheric Cherenkov telescopes locatedin the Khomas Highland of Namibia (Hinton 2004). It is de-signed for the observation of astrophysical sources in the en-ergy range from 100 GeV to several tens of TeV. The systemwas completed in December 2003 and has already provideda number of significant detections of galactic !-ray sources.These include the first detection of spatially extended emis-sion from a pulsar wind nebula (PWN) in very high-energy!-rays (Aharonian et al. 2005b). Each HESS telescope has amirror area of 107 m2 (Bernlohr et al. 2003) and the systemis run in a coincidence mode (Funk et al. 2004) requiring atleast two of the four telescopes to have triggered in each event.The HESS instrument has an energy threshold of &100 GeVat zenith, an angular resolution of "0.1' per event and a pointsource sensitivity of <2.0! 10$13 cm$2 s$1 (1% of the flux fromthe Crab Nebula) for a 5" detection in a 25 h observation.

-5

0

5

10

15

20

25

30

-14

-13.5

18h24m18h26m18h28m

PSR B1823-13

RA (hours)

)°Dec ( 3EG J1826-1302

PSF

HESS J1825-137

Fig. 1. Excess map of the region close to PSR B1823–13 (marked witha triangle) with uncorrelated bins. The best fit centroid of the !-rayexcess is shown with error bars. The black dotted circle shows thebest fit emission region size ("source) assuming a Gaussian brightnessprofile. The black contours denote the X-ray emission as detected byXMM-Newton. The 95% confidence region (dotted white line) for theposition of the unidentified EGRET source 3EG J1826–1302 is alsoshown. The system acceptance is uniform at the 20% level in a 0.6' ra-dius circle around HESS J1825–137.

2. HESS observations and results

The first HESS observations of this region occurred as part ofa systematic survey of the inner Galaxy from May to July 2004(with 4.2 h of exposure within 2' of HESS J1825$137).Evidence for a VHE !-ray signal in these data triggered re-observations from August to September 2004 (5.1 h). The meanzenith angle of the observations was 31' and the mean o!-set (#) of the source from the pointing direction of the systemwas 0.9'. The o!-axis sensitivity of the system derived fromMonte-Carlo simulations has been confirmed via observationsof the Crab Nebula (Aharonian et al. 2005c). The data set cor-responds to a total live-time of 8.4 h after application of runquality selection based on weather and hardware conditions.

The standard scheme for the reconstruction of events wasapplied to the data (see Aharonian et al. 2005d for details).Cuts on the scaled width and length of images (optimized on!-ray simulations and o!-source data) were used to suppressthe hadronic background. While in the standard scheme an im-age size cut of 80 photoelectrons (pe) was used to ensure wellreconstructed images, in the search for weak sources an addi-tional image size cut of 200 pe was applied to achieve optimumsensitivity. This cut reduces the background by a factor of 7 atthe expense of an increased analysis threshold of 420 GeV. Amodel of the field of view acceptance, derived from o!-sourceruns, is used to estimate the background. Figure 1 shows anuncorrelated excess count map of the 1.6' ! 1.6' region aroundHESS J1825–137. A clear and extended excess is observed to

Letter�to�the�Editor

Many TeV Pulsar Wind Nebula

•Many PWN detected at TeV energies

•Limited Background,

•Improved sensitivity

•No Pulsar signal

•32 TeV PWN

Harder at Gamma-ray energies

•Limited Angular Resolution

•Large Galactic Background

•Non-linear Detector response

•Emission could be from the pulsar.

•Crowded gamma-ray sky

How do we search for new gamma-ray emitting PWN?

Association with LAT-detected

Association with TeV PWN

Spatial Morphology

Extended Fermi Sources

You can study extended LAT sources using maximum-likelihood analysis

CHAPTER 4. MAXIMUM-LIKELIHOOD ANALYSIS OF LAT DATA 49

source model is time independent:

⌧(E 0, ~⌦0|�) =

Zd⌦F(E 0, ~⌦|�)

✓Zdt ✏(E 0, t, ~⌦)

◆PSF(~⌦0|E, ~⌦) (4.16)

This equation says that the counts expected by the LAT from a given model is the

product of the source’s flux with the e↵ective area and then convolved with the PSF.

Finally, we note that the PSF and e↵ective area are also functions of the conversion

type of the �-ray (front-entering or back-entering photons), and the azimuthal angle

of the �-ray. Equation 4.16 can be generalized to include these e↵ects.

4.5 Binned Maximum-Likelihood of LAT Data with

the Science Tools

We typically use a binned maximum-likelihood analysis to analyze LAT data. In this

analysis, �-rays are binned in position and energy (and sometimes also separately

into front-entering and back-entering events). The likelihood function comes from

the Poisson nature of the observed emission:

L =Y

j

✓kjj e�✓j

kj!. (4.17)

Here, j refers to a sum over position and energy bins, kj are the counts observed in

bin j, and ✓j are the model counts predicted in the same bin.

The model counts in bin j are computed by integrating the di↵erential model

counts over the bin:

✓ij =

Z

j

dE d⌦ dt ⌧(E, ~⌦, t|�i). (4.18)

Here, j represents the integral over the jth position/energy bin, i represents the ith

source, �i refers to the parameters defining the ith source, and ⌧(E, ~⌦, t|�i) is defined

CHAPTER 4. MAXIMUM-LIKELIHOOD ANALYSIS OF LAT DATA 47

In some situations, the spatial and spectral part of a source do not nicely decouple.

An example of this could be a spatially-extended SNR or PWNe which show a spectral

variation across the source, or equivalently show an energy-dependent morphology.

Katsuta et al. (2012) and Hewitt et al. (2012) have avoided this issue by dividing the

extended source into multiple non-overlapping extended source templates which are

each allowed to have a di↵erent spectra.

4.4 The LAT Instrument Response Functions

The performance of the LAT is quantified by its e↵ective area and its dispersion. The

e↵ective area represents the collection area of the LAT and the dispersion represents

the probability of misreconstructing the true parameters of the incident �-ray. The

e↵ective area ✏(E, t, ~⌦) is a function of energy, time, and solid angle (SA) and is

measured in units of cm2.

The dispersion is the probability of a photon with true energy E and incoming

direction ~⌦ at time t being reconstructed to have an energy E 0, an incoming direction~⌦0 at a time t0. The dispersion is written as P (E 0, t0, ~⌦0|E, t, ~⌦). It represents a

probability and is therefore normalized such that

Z Z ZdEd⌦dtP (E 0, t0, ~⌦0|E, t, ~⌦) = 1 (4.12)

Therefore, P (E 0, t0, ~⌦0|E, t, ~⌦) has units of 1/energy/SA/time

The convolution of the model a source with the IRFs produces the expected dif-

ferential counts (counts per unit energy/time/SA) that are reconstructed to have an

energy E 0 at a position ~⌦0 and at a time t0:

⌧(E 0, ~⌦0, t0|�) =

Z Z ZdE d⌦ dtF(E, t, ~⌦|�)✏(E, t, ~⌦)P (E 0, t0, ~⌦0|E, t, ~⌦) (4.13)

Here, this integral is performed over all energies, SAs, and times.

For LAT analysis, we conventionally make the simplifying assumption that the

CHAPTER 4. MAXIMUM-LIKELIHOOD ANALYSIS OF LAT DATA 49

source model is time independent:

⌧(E 0, ~⌦0|�) =

Zd⌦F(E 0, ~⌦|�)

✓Zdt ✏(E 0, t, ~⌦)

◆PSF(~⌦0|E, ~⌦) (4.16)

This equation says that the counts expected by the LAT from a given model is the

product of the source’s flux with the e↵ective area and then convolved with the PSF.

Finally, we note that the PSF and e↵ective area are also functions of the conversion

type of the �-ray (front-entering or back-entering photons), and the azimuthal angle

of the �-ray. Equation 4.16 can be generalized to include these e↵ects.

4.5 Binned Maximum-Likelihood of LAT Data with

the Science Tools

We typically use a binned maximum-likelihood analysis to analyze LAT data. In this

analysis, �-rays are binned in position and energy (and sometimes also separately

into front-entering and back-entering events). The likelihood function comes from

the Poisson nature of the observed emission:

L =Y

j

✓kjj e�✓j

kj!. (4.17)

Here, j refers to a sum over position and energy bins, kj are the counts observed in

bin j, and ✓j are the model counts predicted in the same bin.

The model counts in bin j are computed by integrating the di↵erential model

counts over the bin:

✓ij =

Z

j

dE d⌦ dt ⌧(E, ~⌦, t|�i). (4.18)

Here, j represents the integral over the jth position/energy bin, i represents the ith

source, �i refers to the parameters defining the ith source, and ⌧(E, ~⌦, t|�i) is defined

CHAPTER 5. ANALYSIS OF SPATIALLY EXTENDED LAT SOURCES 58

5.2.2 Extension Fitting

In pointlike, one can fit the position and extension of a source under the assumption

that the source model can be factorized: M(x, y, E) = S(x, y)⇥X(E), where S(x, y)

is the spatial distribution and X(E) is the spectral distribution. To fit an extended

source, pointlike convolves the extended source shape with the PSF (as a function of

energy) and uses the minuit library (James & Roos 1975) to maximize the likelihood

by simultaneously varying the position, extension, and spectrum of the source. As

will be described in Section 5.3.1, simultaneously fitting the position, extension, and

spectrum is important to maximize the statistical significance of the detection of the

extension of a source. To avoid projection e↵ects, the longitude and latitude of the

source are not directly fit but instead the displacement of the source in a reference

frame centered on the source.

The significance of the extension of a source can be calculated from the likelihood-

ratio test. The likelihood ratio defines the test statistic (TS) by comparing the like-

lihood of a simpler hypothesis to a more complicated one:

TS = 2 log(L(H1)/L(H0)), (5.1)

where H1 is the more complicated hypothesis and H0 the simpler one. For the case

of the extension test, we compare the likelihood when assuming the source has either

a point-like or spatially extended spatial model:

TSext = 2 log(Lext/Lps). (5.2)

pointlike calculates TSext by fitting a source first with a spatially extended model

and then as a point-like source. The interpretation of TSext in terms of a statistical

significance is discussed in Section 5.3.1.

For extended sources with an assumed radially-symmetric shape, we optimized

the calculation by performing one of the integrals analytically. The expected photon

CHAPTER 4. MAXIMUM-LIKELIHOOD ANALYSIS OF LAT DATA 44

4.2 Description of Maximum-Likelihood Analysis

The field of �-ray astrophysics has generally adopted maximum-likelihood analysis

to avoid the issues discussed in Section 4.1. The term likelihood was first introduced

by Fisher (1925). Maximum-likelihood was applied to astrophysical photon-counting

experiments by Cash (1979). Mattox et al. (1996) described the maximum-likelihood

analysis framework developed to analyze EGRET data.

In the formulation, one defines the likelihood, denoted L, as the probability of

obtaining the observed data given an assumed model:

L = P (data|model). (4.1)

Generally, a model of the sky is a function of a list of parameters that we denote as

�. The likelihood function can be written as:

L = L(�). (4.2)

In a maximum-likelihood analysis, one typically fits parameters of a model by maxi-

mizing the likelihood as a function of the parameters of the model.

�max = arg max�

L(�) (4.3)

Assuming that you have a good model for your data and that you understand the

distribution of the data, maximum-likelihood analysis can be used to very sensitively

test for new features in your model. This is because the likelihood function naturally

incorporates data with di↵erent significance levels.

Typically, a likelihood-ratio test (LRT) is used to determine the significance of a

new feature in a model. A common use case is searching for a new source or testing

for a spectral break. In a LRT, the likelihood under two hypothesis are compared. We

define H0 to be a background model and H1 to be a model including the background

and in addition a feature that is being tested for. Under the assumption that H0 is

nested within H1, we use Wilks’ theorem to compute the significance of the detection

0! 0.!1 0.!2 0.!3 0.!4 0.!5 0.!6Extension

10000

10200

10400

10600

10800

11000

11200Tes

tSta

tist

ic

(a)

102 103 104 105

Energy (MeV)

0

50

100

150

200

TS

ext

(b)

0.0 0.1 0.2 0.3 0.4 0.5!!2([deg]2)

101

102

103

Cou

nts

(c) Disk

Point

Counts

(d)

2!

3!

b

188!189!

l

0

500

1000

1500

2000

2500

3000

3500

count

s[d

eg]"

2

Extended Source IC 443

Search each source in 2FGL for extension

IC 443

Puppis A

W44

MSH15!52

W51C

W28

SMC

Gamma Cygni

Vela XCygnus Loop

Vela Jr.

LMC

RXJ1713.7!3946

HESS J1825!127

W30

Centarus A

New Extended Sources

0�

1�b

25�26�

l

0

25

50

75

100

125

150

175

200

225

count

s/[d

eg]2

HESS J1837-069

�1� 000

�0� 300

0� 000

0� 300

b

331� 300332� 000332� 300333� 000

l

0

30

60

90

120

150

180

210

240

270

count

s/[d

eg]2

HESS J1616−508

�1�

0�

1�

b

336�337�

l

0

30

60

90

120

150

180

210

240

270

count

s/[d

eg]2

HESS J1632-478

10!6

10!5

E2

dN

/dE

(MeV

cm!

2s!

1) (a) HESS J1616!508 (b) HESS J1614!518

LAT

H.E.S.S

104 105 106 107

Energy (MeV)

10!6

10!5

E2

dN

/dE

(MeV

cm!

2s!

1) (c) HESS J1632!478

104 105 106 107

Energy (MeV)

(d) HESS J1837!069

PWN Search in the Off-Peak

Search LAT-detected pulsars for PWN

0.0 0.2 0.4 0.6 0.8 1.00

100200300400500600700800

Cou

nts

0.0 0.2 0.4 0.6 0.8 1.00

100

200

300

400

0.0 0.2 0.4 0.6 0.8 1.00

50100150200250300350

Cou

nts

0.0 0.2 0.4 0.6 0.8 1.00

100

200

300

400

500

0.0 0.2 0.4 0.6 0.8 1.0Phase

0100200300400500600700

Cou

nts

0.0 0.2 0.4 0.6 0.8 1.0Phase

05

101520253035

We can define the off-peak region using a Bayesian Block decomposition of the pulsar light curve

Is it a pulsar or a PWN?6 Grondin et al.

Energy [MeV]310 410 510 610 710

]-1

s-2

dN

/dE

[erg

cm

2 E -1210

-1110

-1010

FIG. 3.— Spectral energy distribution of HESS J1825!137 in gamma-rays. The LAT spectral points (in red) are obtained using the maximum likelihoodmethod gtlike described in section 4.2 in 6 logarithmically-spaced energy bins. The statistical errors are shown in red, while the black lines take into account boththe statistical and systematic errors as discussed in section 4.2. The red solid line presents the result obtained by fitting a power-law to the data in the 1 – 100 GeVenergy range using a maximum likelihood fit. A 95 % C.L. upper limit is computed when the statistical significance is lower than 3 !. The H.E.S.S. results arerepresented in blue (Aharonian et al. 2006).

age of the pulsar, we fix the initial spin period at 10 ms andbraking index at 2.5, yielding an age of 26 kyr for the sys-tem. This simple injection spectrum slightly underestimatesthe LAT data but the overall fit is still reasonable. For thesource age of 26 kyr, we require a power-law index of 1.9,a cutoff at 57 TeV and a magnetic field of 4µG. The corre-sponding result is presented in Figure 4 (Top).Another option to fit the multi-wavelength data is adopting

the relativistic Maxwellian plus power-law tail electron spec-trum proposed by Spitkovsky (2008). For this injection spec-trum, we assume a bulk gamma-factor (!0) for the PWN windupstream of the termination shock. At the termination shockthe ambient pressure balances the wind pressure, fully ther-malizing the wind; in this case the downstream post-shockflow has ! = (!0 ! 1)/2. One could also interpret this asan effective temperature kT of mec2 (!0 ! 1)/2. Per thesimulations of Spitkovsky (2008), a power-law tail begins at7kT " 7/2mec2 !0, and suffers an exponential cutoff at somehigher energy. For our modeling we fix the power-law begin-ning at " 7kT , and allow kT , the power-law index, and theexponential cutoff to vary. The best fit, presented in Figure 4(Bottom), is obtained with kT = 0.14 TeV, corresponding toan upstream gamma-factor of 5.5 # 105, a magnetic field of3µG, a cutoff at 150 TeV and a power-law index of 2.3 closeto the value of" 2.5 proposed by Spitkovsky (2008). The rel-ativistic Maxwellian plus power lawmodel matches the multi-wavelength data and also directly probes the upstream pulsarwind via fitting of !0.HESS J1825!137 is detected at high significance by the

Fermi LAT, and demonstrates both morphological similarityand flux continuity with the H.E.S.S. regime. The LAT spec-tral index of 1.38 ± 0.12 ± 0.16 is consistent with both asimple power-law electron injection spectrum, as well as aMaxwellian plus power-law injection spectrum over a simplepower-law. A mean magnetic field of " 3! 4µG adequatelyfits the X-ray flux, and an age of " 26 kyr is consistent withthe data. A total of 5 # 1049 erg injected in the form of elec-trons by the pulsar is required to match the gamma-ray flux inthe nebula.

The Fermi LAT Collaboration acknowledges generous ongoing supportfrom a number of agencies and institutes that have supported both the de-velopment and the operation of the LAT as well as scientific data analysis.These include the National Aeronautics and Space Administration and theDepartment of Energy in the United States, the Commissariat a l’EnergieAtomique and the Centre National de la Recherche Scientifique / Institut Na-tional de Physique Nucleaire et de Physique des Particules in France, theAgenzia Spaziale Italiana, the Istituto Nazionale di Fisica Nucleare, and theIstituto Nazionale di Astrofisica in Italy, the Ministry of Education, Culture,Sports, Science and Technology (MEXT), High Energy Accelerator ResearchOrganization (KEK) and Japan Aerospace Exploration Agency (JAXA) inJapan, and the K. A. Wallenberg Foundation and the Swedish National SpaceBoard in Sweden. Additional support for science analysis during the opera-tions phase from the following agencies is also gratefully acknowledged: theInstituto Nazionale di Astrofisica in Italy and the Centre National d’EtudesSpatiales in France.The Nancay Radio Observatory is operated by the Paris Observatory, associ-ated with the French Centre National de la Recherche Scientifique (CNRS).The Lovell Telescope is owned and operated by the University of Manchesteras part of the Jodrell Bank Centre for Astrophysics with support from theScience and Technology Facilities Council of the United Kingdom.The Parkes radio telescope is part of the Australia Telescope which is fundedby the Commonwealth Government for operation as a National Facility man-aged by CSIRO. We thank our colleagues for their assistance with the radiotiming observations.

APPENDIX : DESCRIPTION OF SOURCELIKE

Sourcelike is a tool developed for performing morpholog-ical studies of spatially extended Fermi sources. Sourcelikeis an extension to pointfit (described in Abdo et al. 2010b),which was developed to efficiently create Test Statistic mapsand localize catalog sources with little sacrifice of precision.pointfit bins the sky in position and energy and increases ef-ficiency by scaling the spatial bin size with energy. Further-more, it uses a region of the sky centered on the source whoseradius is energy dependent: from 15! at 100 MeV to 3.5! at50 GeV. It was successfully used by and is described in the1FGL catalog (Abdo et al. 2010b). Sourcelike deviates frompointfit by fitting not the PSF but the PSF convolved with anassumed spatial shape. By independently fitting the flux ineach energy bin, Sourcelike performs an extension analysiswithout biasing the fit by assuming a spectral model. Sincethe PSF ranges a full two orders of magnitude in size over theenergy range of the instrument, this maximum likelihood ap-

– 37 –

Energy (MeV)210 310 410

]-1

s-2

dN

/dE

[erg

cm

2 E -1110

-1010

Energy (MeV)210 310 410

]-1

s-2

dN

/dE

[erg

cm

2 E

-1210

-1110

Energy (MeV)210 310 410

]-1

s-2

dN

/dE

[erg

cm

2 E

-1210

-1110

Fig. 2.— Spectral energy distributions of the off-pulse emission of J2021+4026 (top left),J2055+2539 (top right) and J2124!3358 (bottom), renormalized to the total phase interval. Sameconventions as for Figure 1.

4 Grondin et al.

FIG. 1.— Top: Fermi-LAT counts map above 10 GeV of the HESS J1825!137 region with side-length 5!, binned in square pixels of side length 0.05!.The map is smoothed with a Gaussian of ! = 0.35!. H.E.S.S. contours (Aharonian et al. 2006) are overlaid as gray solid lines. The position of the pulsarPSR J1826!1334 and of the close-by 1FGL sources are indicated with green and white squares respectively. LS 5039 is visible in the South-East at position(RA, Dec) = (276.56! , !14.85!). Bottom: Fermi-LAT Test Statistic (TS) map for events with energy larger than 10 GeV on a region of 2.5! side length. TheTS was evaluated by placing a point-source at the center of each pixel, Galactic diffuse emission and nearby sources being included in the background model.

the second represents our estimate of systematic effects asdiscussed below and is dominated by the uncertainties on theGalactic diffuse emission in the 1 – 5 GeV energy range. Withthe current statistics, neither indication of a spectral cut-off athigh energy nor significant emission below 1 GeV can be de-tected.Four different systematic uncertainties can affect the LAT

flux estimation : uncertainties on the Galactic diffuse back-ground, on the morphology of the LAT source, on the effec-tive area and on the energy dispersion. The fourth one is rel-atively small (! 10%) and has been neglected in this study.The main systematic at low energy is due to the uncertaintyin the Galactic diffuse emission since HESS J1825"137 islocated only 0.7! from the Galactic plane. Different ver-sions of the Galactic diffuse emission, generated by GAL-PROP (Strong et al. 2004), were used to estimate this error.The observed gamma-ray intensity of nearby source free re-

gions on the galactic plane is compared with the intensityexpected from the galactic diffuse models. The difference,namely the local departure from the best fit diffuse model, isfound to be ! 6% (Abdo et al. 2010e). By changing the nor-malization of the Galactic diffuse model artificially by ±6%,we estimate the systematic error on the integrated flux ofthe PWN to be 70% below 5 GeV, 34% between 5 and 10GeV, and <12% above 10 GeV. The second systematic is re-lated to the morphology of the LAT source. The fact that wedo not know the true gamma-ray morphology introduces an-other source of error that becomes significant when the sizeof the source is larger than the PSF, i.e above 600 MeV forthe case of HESS J1825"137. Different spatial shapes havebeen used to estimate this systematic error: a disk, a Gaus-sian distribution and the H.E.S.S. template. Our estimate ofthis uncertainty is #30% above 1 GeV. The third uncertainty,common to every source analyzed with the LAT data, is due

HESS J1825-137 (Grondin et al 2011)

PSR J2021+4026Ackermann et al 2010

HESS J1825-137 (Grondin et al 2011)

Spectral Shape:• Pulsars are cutoff• PWN rising spectrumMorphology• Pulsars are point sources• PWN could be extended

10�13

10�12

10�11

10�10

10�9

10�13

10�12

10�11

10�10E

2dN

/dE

(erg

cm�

2s�

1)

10�13

10�12

10�11

10�10

10�9

10�1 100 101 102

Energy (GeV)10�1 100 101 102

Energy (GeV)

We performed a spectral and spatial analysis of each off-peak region

Off-peak Sources

•116 pulsars tested

•34 significant sources

•9 are clearly pulsar emission

•4 are pulsar wind nebula

•1 new pulsar wind nebula

3C 58 is associated and

PSR J0205+6449

Coincident with SNR 3C 58 and

SN 1181

Search for TeV PWN

HESS J1303-613

�1�

0�

1�

b

26�27�28�

l

0

20

40

60

80

100

120

140

160

180

count

s/[d

eg]2

HESS J1841-055

�1�

0�

b

292�293�

l

0

10

20

30

40

50

60

70

80

90

count

s/[d

eg]2

HESS J1119-614 HESS J1356-645

0�

1�

b

313�314�

l

0

25

50

75

100

125

150

175

200

225co

unt

s/[d

eg]2

HESS J1420-607

PWN Detected by LAT

•Before Fermi, 1 PWN Detected (Crab)

•Now, 17 PWN candidates

•5 clearly associated with PWN

•12 have less certain identification.

PWN Population Study

102 103 104 105 106 107 108 109 1010 1011

⌧C [years]

1028

1029

1030

1031

1032

1033

1034

1035

1036

1037

1038

1039E

[erg

s�1]

LAT Detects PWN from young and highly-energetic pulsars

1034 1035 1036 1037 1038 1039

E

1032

1033

1034

1035

1036L

GeV The PWN

Luminosity is small compared to the pulsar’s spin-down energy

1033

1034

1035

1036

LG

eV(e

rgs�

1)

103 104 105

Age (yr)

100

101

102L

GeV

/LTeV

1035 1036 1037 1038 1039

E (erg s�1)

LGeV and LGeV/LTeV not correlated with age and spin-down energy

1031

1032

1033

1034

1035

1036

1037L

X(e

rgs�

1)

103 104 105

Age (yr)

10�2

10�1

100

101

102

103

104

LG

eV/L

X

1035 1036 1037 1038 1039

E (erg s�1)

LGeV/LX

correlates with the age and spin-down energy

The lifetime of gamma-ray emitting electrons is longer than of X-ray

emitting electrons.No. 1, 2009 EVOLUTION OF THE ! - AND X-RAY LUMINOSITIES OF PWNe 15

102 103 104 105

Time (yr)

0.01

0.10

1.00

Nor

mal

ized

num

ber o

f par

ticle

s

n !nX

tc!tcX 10-1

100

101

102

103

104

Rat

io n

! /n X

n! /nX

Figure 2. Time evolution of the number of particles radiating in VHE ! -rays, n! , and in X-rays, nX (solid lines), and of their ratio (dashed line). Pulsar birth is att = 0. Initial conditions for the pulsar spin-down luminosity are E0 = 1039 erg s!1 and tdec = 100 yr. Both curves are normalized to their maximum value. After theinitial rise, both particle populations reach a plateau. The fall begins at t greater than the cooling time, which is assumed to be tcX = 2.6 kyr for X-rays, tc! = 25 kyrfor ! -rays (for a magnetic field intensity B = 10 µG, and a Lorentz factor of ! -ray radiating electrons ! = 107).

is n = 3. As the braking indices inferred from the measurementof the period and its derivatives are significantly smaller than3 (Livingstone et al. 2007), we dealt with a generic n (see theAppendix), and found that the results derived from Equation (8)are unaffected by the choice of n.

Since it depends on E, also the particle injection rate Ndecreases in time. Therefore, the total number of particles

N "! t

0E(t #) dt # = E0 tdec

"t

t + tdec

#(9)

reaches a constant value N " E0 tdec for t $ tdec, and theparticle supply by the pulsar becomes negligible.

The electron energy distribution n(E, t) accounting for particleinjection and radiative losses evolves according to the kineticequation (e.g., Ginzburg & Syrovatskii 1964; Blumenthal &Gould 1970)

"n

"t= "

"E(nP ) + Q, (10)

where Q = Q(E, t) is the particle distribution injected perunit time, and P = P (E, t) is the radiated power per particlewith energy E. The normalization of n(E, t) is set by N via theinjection rate: N (t) =

$Q(E, t)dE.

At energies for which the radiative losses are negligible, thenumber of particles n(E, t) with energy E at time t has the sameprofile of the injected distribution Q(E) with a normalizationset by N. Therefore,

nu(E, t) "! t

0E(t #) dt # = E0 tdec

"t

t + tdec

#, (11)

where u stands for uncooled. As in Equation (9), a constantvalue nu(E, t) " E0 tdec is reached for t $ tdec.

The effect of the radiative losses is to limit the accumulation ofparticles at a given energy. After an energy-dependent coolingtime tc(E), the particles with initial energy E have radiated asignificant fraction of their energy (Chevalier 2000). Accountingfor pitch-angle averaged synchrotron and inverse Compton inthe Thomson regime energy losses, the cooling time can be

written as (Rybicki & Lightman 1979)

tc(E) = 9 m3ec

5

4 (1 + # ) e4 !E B2% 24.5 (1 + # )!1 ! !1

7 B!25 kyr,

(12)where !E = E/(mec

2) is the particle Lorentz factor, and# = Uph/UB , with Uph and UB the photon field and magneticfield energy densities, respectively (!E = !7 & 107, B = B5 &10!5 G). When the photon field is provided by the cosmic back-ground radiation (Uph = 0.26 eV cm!3), the synchrotron ra-diation is the main cooling process (# < 1) if B > 3 µG.This condition is generally fulfilled in PWNe as the equipar-tition magnetic field intensity ranges in B ' 1–100 µG.9Equation (12) shows that the cooling time of ! -ray radiatingparticles, trmc! , is one order of magnitude longer than that ofthe X-ray radiating particles, tcX , for example, for B = 10 µG,tc! ' 8–250 kyr and tcX ' 0.8–8 kyr. By comparing tc! and tcXwith the average characteristic ages of pulsars in TeV PWNe, the! -radiation is produced by long-lived electrons tracing the time-integrated evolution of the nebula, even up to the pulsar birth,whereas the X-ray emission is generated by younger electrons,injected in the last thousands of years.

Only the particles injected since the last tc(E) years willcontribute to n(E, t). Equation (11) is accordingly modified as

nc(E, t) "! t

t!tc

E(t #) dt # = E0 t2dec tc

(t ! tc + tdec) (t + tdec), (13)

where c stands for cooled. This implies nc(E, t) " E0 t2dec tct

!2

for t $ max(tc, tdec), and hence nc(E, t) " E tc usingEquation (8).

4. CONCLUSIONS

Equations (11) and (13) describe the time evolution of aparticle populations in two regimes, uncooled and cooled. Suchan evolution is exemplified in Figure 2 for the populations ofparticles producing ! -rays, n! , and X-rays, nX . After the initial

9 In radiation-dominated environment, like the Galactic Center, the inverseCompton can contribute to the cooling. In this case, the Klein–Nishina regimeshould be taken into account (Manolakou et al. 2007).

Mattana et al 2009

Conclusions

Acknowledgments

Stanford Physics

The LAT Collaboration

Big thanks to my defense committee!

The Funk Group

Thanks to my family!

Thanks to the administrators!

Finally, thanks for coming!

Questions?