magnetic fields of cool stars from near-infrared...
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ACTAUNIVERSITATIS
UPSALIENSISUPPSALA
2020
Digital Comprehensive Summaries of Uppsala Dissertationsfrom the Faculty of Science and Technology 1927
Magnetic fields of cool stars fromnear-infrared spectropolarimetry
ALEXIS LAVAIL
ISSN 1651-6214ISBN 978-91-513-0930-9urn:nbn:se:uu:diva-406608
Dissertation presented at Uppsala University to be publicly examined in Polhemsalen, Ångströmlaboratoriet, Lägerhyddsvägen 1, Uppsala, Tuesday, 26 May 2020 at 09:15 forthe degree of Doctor of Philosophy. The examination will be conducted in English. Faculty examiner: Jeff Valenti (Space Telescope Science Institute).
Online defence: https://uu-se.zoom.us/j/414848524
AbstractLavail, A. 2020. Magnetic fields of cool stars from near-infrared spectropolarimetry. Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology 1927. 54 pp. Uppsala: Acta Universitatis Upsaliensis. ISBN 978-91-513-0930-9.
Magnetic fields rule many physical processes in and around stars throughout their lifetime. All cool stars possess a magnetic field, likely generated by dynamo processes. In order to properly understand the evolution of cool stars, we need to understand their magnetism. Stellar magnetic fields can be directly observed through the imprint of the Zeeman effect in intensity and polarized spectra. In intensity spectra (Stokes I), spectral lines are broadened or split into several components by the magnetic field. Modelling this effect in high-resolution spectra allows us to determine the average unsigned magnetic field strength over the stellar surface. The magnetic field also induces circular (Stokes V) and linear polarization (Stokes QU) in spectral lines, according to its orientation. These polarization signals can be used to map the large-scale magnetic field at the surface of the star using tomographic techniques such as Zeeman Doppler imaging (ZDI).
In this thesis, we investigated pre-main-sequence T Tauri stars and the active M dwarf AD Leo with the goal to understand their magnetic fields. We modelled the Zeeman broadening in high-resolution near-infrared spectra of low-mass and intermediate-mass T Tauri stars and derived their mean magnetic field strengths. In intermediate-mass T Tauri stars, we only found fields weaker than 2-3 kG. However, we found that low-mass T Tauri stars can have a wide range of magnetic field strength from relatively weak fields of 1.5 kG to fields as strong as 4.4 kG, and that their field strengths do not correlate with stellar parameters. Our observations of the M dwarf AD Leo led to the first detection of linear polarization in the spectral lines of an M dwarf. We also discovered that its Stokes V profiles, which were constant over many years, had changed in our observations. We mapped its global magnetic field using ZDI and found that it became concentrated into smaller areas on the stellar surface. Finally, we analyzed Stokes IV observations of the spectroscopic binary V1878 Ori. Both components of this system are intermediate-mass T Tauri stars with very similar properties. We determined stellar parameters by studying orbital motion of the components and comparing their disentangled spectra to theoretical models. We then mapped the global magnetic fields of the two stars simultaneously using ZDI. We found that their magnetic fields have radically different geometries and different strengths.
Keywords: stars: magnetic field, stars: pre-main-sequence, stars: late-type, techniques: spectroscopic, techniques: polarimetric
Alexis Lavail, Department of Physics and Astronomy, Observational Astronomy, 516, Uppsala University, SE-751 20 Uppsala, Sweden.
© Alexis Lavail 2020
ISSN 1651-6214ISBN 978-91-513-0930-9urn:nbn:se:uu:diva-406608 (http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-406608)
We are an impossibility in an impossible universe.—Ray Bradbury
List of papers
This thesis is based on the following papers, which are referred to in the textby their Roman numerals.
I Lavail, A., Kochukhov, O., Hussain, G.A.J., Alecian, E., Herczeg G.J.,and Johns-Krull C. (2017)Magnetic fields of intermediate mass T Tauri StarsAstronomy & Astrophysics, 608, A77
II Lavail, A., Kochukhov, O., and Hussain, G.A.J. (2019)Characterising the surface magnetic fields of T Tauri stars withhigh-resolution near-infrared spectroscopyAstronomy & Astrophysics, 630, A99
III Lavail, A., Kochukhov, O., and Wade, G.A. (2018)A sudden change of the global magnetic field of the active M dwarf ADLeo revealed by full Stokes spectropolarimetric observationsMonthly Notices of the Royal Astronomical Society, 479, 4836
IV Lavail, A., Kochukhov, K., Hussain, G.A.J., Argiroffi, C., Alecian, E.,Morin, J., and the BinaMIcS collaboration (2020)The large-scale magnetic field of the eccentric pre-main-sequencebinary system V1878 OriSubmitted to Monthly Notices of the Royal Astronomical Society
Reprints were made with permission from the publishers.
List of papers not included in the thesis
The following are publications to which I have contributed but that are not in-cluded in this thesis.
1. Kochukhov, O. and Lavail, A. (2017)The Global and Small-scale Magnetic Fields of Fully Convective, RapidlySpinning M Dwarf Pair GJ65 A and BThe Astrophysical Journal, 835, 1, L4
2. Piskunov, E., Stempels, E., Lavail, A. et al. (2018)A unique infrared spectropolarimetric unit for CRIRES+Proceedings of the SPIE, 10702, 1070234
Contents
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2 Stellar magnetic fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112.1 Magnetic fields in early stellar evolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112.2 Magnetic fields across the H–R diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142.3 Stellar multiplicity and magnetism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
3 Direct observations of stellar magnetic fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173.1 The Zeeman effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173.2 Stokes parameter formalism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203.3 Calculation of stellar Stokes parameter spectra . . . . . . . . . . . . . . . . . . . . . . . . . . . 203.4 Zeeman broadening . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223.5 Zeeman Doppler Imaging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
4 Summary of papers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 294.1 Paper I . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 294.2 Paper II . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 334.3 Paper III . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 354.4 Paper IV . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
5 Summary and outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
6 Contribution to the included papers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
7 Summary in other languages . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 467.1 Svensk sammanfattning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 467.2 Résumé en français . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
8 Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
1. Introduction
Since magnetic fields were first observed in the Sun (Hale 1908), they havebeen detected and measured in a plethora of stars, from pre-main-sequence(PMS) stars to the late stages of stellar evolution, from low-mass to massivestars, and from cool to hot stars (Donati & Landstreet 2009). Moreover, itis now understood that invoking magnetic fields is needed to understand howstars evolve. Magnetic fields are required to properly describe many stellarcharacteristics and processes including – but not limited to – stellar formation,rotation, accretion, activity, flares, and winds. Last but not least, the influenceof stellar magnetic fields extends far beyond the stellar surface. It can reachall the way to planets orbiting their host star. In this respect, magnetic fieldscan strongly impact the habitability of exoplanets, and influence the type oflife that could thrive on these worlds.
The magnetic field of our nearest star, the Sun, is now studied in minute de-tails and at all times. Dedicated observatories both on the ground and in spacespatially resolve the solar disk and acquire high-quality observations at a highcadence. Even then, we do not have today a complete understanding of the dy-namo processes which are believed to generate and maintain solar magnetism(Charbonneau 2010). Additionally, studying the Sun provides us with data forjust one set of stellar parameters and only one moment in a stellar lifetime. It isnot enough to observe the Sun in order to obtain a thorough understanding ofstellar magnetic fields and of the mechanisms that generate them. Through thestudy of other stars, both Sun-like and with different parameters (for instanceage, effective temperature, mass and internal structure), our understanding ofstellar magnetism can be greatly improved. The goal of this thesis is to studythe magnetic fields of cool stars, and supply observational constraints that canultimately help providing a clear picture of the physical processes generatingmagnetic fields in the Sun and in other stars (Brun & Browning 2017). Suchobservational studies are needed to understand how cool-star magnetic fieldswork and guide modelling efforts. In this thesis, we are focussing on PMSstars and M dwarfs, as their magnetic fields are not well understood today.
Unlike for the Sun, we cannot spatially resolve the surface of the vast ma-jority of stars with direct imaging, even with the largest telescopes or interfer-ometers available today. Nonetheless, from spectroscopy we can recover themean unsigned magnetic field as well as a rough distribution of magnetic fieldstrengths. Furthermore, tomographic methods were developed to reconstructthe topology of the large-scale stellar magnetic field from spectropolarimet-ric time-resolved data. The articles presented in this thesis make use of these
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methods to characterize the magnetic fields of young T Tauri stars (Paper I,Paper II, and Paper IV) and of the active M dwarf AD Leo (Paper III).
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2. Stellar magnetic fields
2.1 The importance of magnetic fields in early stellarevolution
In the early stages of stellar evolution, magnetic fields play an immense role,starting with star formation. Stars are born from the collapse of dense fila-mentary molecular clouds. Competing forces are at play there, including self-gravity which is pulling material within the cloud as well as resisting forcesincluding pressure. If gravity overcomes the resisting pressure forces – andpotentially the complex actions of turbulence and magnetic fields – then thecontraction towards a protostar surrounded by a protostellar disk begins. Themolecular clouds are initially permeated with magnetic fields which becomeincorporated into the protostar and its surrounding disk. The presence of mag-netic fields can also provide resistance against the collapse of the molecularcloud and hence impede or delay star formation and even affect the multi-plicity of the emerging protostars (Boss & Keiser 2013; Körtgen & Banerjee2015).
The protostar continues accreting material from its surrounding disk, andthis process is thought to be greatly affected by the magnetic field. Materialfrom the disk migrates inwards towards the protostar until it reaches a pointwhere the protostellar magnetosphere has disrupted the inner disk. There, thematerial can be funneled out of the disk by the magnetic field lines and fall intothe star at free-fall velocities, producing hot continuum radiation. A simplifieddepiction of this mechanism is shown in Fig. 2.1, and a more detailed picturecan be obtained from recent 3D magnetohydrodynamics studies (Kurosawa& Romanova 2013; Romanova & Owocki 2015). The material accreted ontothe star brings angular momentum with it. Without a mechanism to removeangular momentum from the star, it could spin up towards break-up veloci-ties (Hartmann & Stauffer 1989). However, such fast rotation rates are notobserved in young stars. They tend to be slow rotators with rotation periodscommonly in the 1–10 days range (see Bouvier 2013, for a review of observa-tional studies of stellar rotation). It is believed that magnetic fields are drivingthe mechanisms which slow down stellar spin at this stage. In this context,the process of "magnetic braking" has been invoked (Koenigl 1991). It oper-ates by locking the stellar magnetic field lines into the disk thus transferringangular momentum from the protostar to the disk. The magnetic field is alsothought to be responsible for launching bipolar outflows and jets, which alsoshed angular momentum from the protostar and disk ensemble (Gerrard et al.2019; Pudritz & Ray 2019, and references therein).
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Figure 2.1. A simplified and not to scale sketch of magnetospheric accretion
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-1
0
1
2
3.53.63.73.83.9
log
10(L
/L)
log10(Teff/K)
0.2 M
0.5 M
1 M
1.5 M
2 M3 M4 M5 M
Figure 2.2. Pre-main-sequence H–R diagram. Mass tracks from the Yale-PotsdamStellar Isochrones (Spada et al. 2017) are plotted in grey thin lines until the zero agemain-sequence (ZAMS, dark thick line). The dashed line marks the boundary betweenfully convective regime (on its right) and partially convective regime (on its left).
At this point, the protostar is deeply embedded in a cloud of dust and gas,and the escaping radiation is dominantly in the far infrared and millimeterwavelength domain. This makes observations of these stars very challengingin the optical domain, and gives an advantage to observations at longer wave-lengths. When the collapse is over, the protostar crosses the stellar birthline.It eventually becomes a visible star on the PMS.
The evolution of stars on the PMS can be visualized using the Hertzsprung–Russell diagram (H–R diagram) in which the luminosity of a star L is plottedagainst its effective temperature Teff. Throughout their life, stars follow trackson this diagram, which primarily depend on their initial mass.
The stars with the lowest mass are fully convective stars on the birthline.From there, they contract due to gravitation and stay fully convective through-out. They reach the main-sequence when their core attains a sufficient temper-ature to initiate hydrogen burning. On the H–R diagram, these stars follow adownwards vertical track, the so-called Hayashi track (Hayashi 1961). Theireffective temperature stays roughly constant while their radius and hence theirluminosity decrease. This is illustrated by e.g the 0.2 M� track in Fig. 2.2.Low- and intermediate-mass PMS stars also start by following a Hayashi track.However, they eventually develop a radiative core, at which point they switchto a horizontal Henyey track (Henyey et al. 1955). It leads them to the main-
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sequence when hydrogen starts burning in their core. This is illustrated bye.g the 1 M� track in Fig. 2.2, in which the dashed line marks the boundaryat which stars develop a radiative core. After the PMS stage, stars continuetheir evolution and reside most of their lifetime on the main-sequence. Theyeventually evolve off the main-sequence towards their ultimate fate during thelate stages of stellar evolution.
2.2 Magnetic fields across the H–R diagramStellar magnetic fields were first directly detected on our own star, the Sun,over a hundred years ago. Hale (1908) acquired polarized solar spectra whileplacing the instrument slit over sunspots. The presence of a strong magneticfield was identified (≈ 3 kG) through the signature of the then newly discov-ered Zeeman effect (explained in Sect. 3.1). Subsequently, magnetic fieldswere discovered on hot chemically peculiar stars through the pioneering workof Babcock (1947), and then eventually on more exotic stars such as rotatingneutron stars and white dwarfs (Hewish et al. 1968; Gold 1968; Kemp et al.1970). Eventually, Robinson et al. (1980) obtained the first direct detectionof a magnetic field at the surface of two cool stars. Since then, ever morecapable instrumentation was developed and computational power increasedtremendously. We have been able to routinely study stellar magnetic fields andobtain a fair coverage of the Hertzsprung-Russell diagram (Donati & Land-street 2009). We now know that across the stellar zoo, magnetic fields varyextremely in strengths and topologies, occur at widely different rates, and areperhaps generated (or maintained) by different mechanisms.
Cool stars – stars with an effective temperature Teff lower than roughly 7000K – are the most numerous stars in the universe. Also, they all exhibit a mag-netic field. These fields range from relatively simple dipolar fields to extremelycomplex fields with many small-scale structures (Reiners 2012). They evolveon timescales that can vary from hours or days to decades. The best-studiedcool star, the Sun, shows complex and evolving magnetic structures on its sur-face. Its magnetic field follows a nearly-periodic 22-year cycle, which consistsof two consecutive 11-year activity cycles separated by a flip of the global fieldpolarity. During the activity cycles, the number of sunspots, their area, and lat-itude at which they emerge vary dramatically. The total solar irradiance, themagnetic field itself, the radio flux at 10.7 cm, and the occurence rates of flaresand coronal mass ejections follow the same cycle (Hathaway 2015).
In contrast, only a small fraction of hot stars exhibits an observable mag-netic field. Their magnetic field tends to be simple (often mostly a tilteddipole), and stable over at least several decades. This difference betweenthe magnetic field of cool and hot stars reflects the difference in their interiorstructure. While the coolest stars are fully convective, warmer stars develop aradiative core surrounded by a convective envelope. The radiative zone grows
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with increasing temperature until a convective core develops, surrounded by aradiative zone.
The magnetic fields of cool stars are believed to be actively generated andmaintained through dynamo processes (Parker 1955). In the Sun and similarstars, the magnetic field is likely generated by the interplay between convec-tive motions and differential rotation (the so-called α −Ω dynamo). It is alsopresumed that the strong shear present at the thin interface layer between theconvective and radiative zones (the tachocline) plays an essential role (Char-bonneau 2010). It is interesting to note that even though the Sun is the starstudied in most detail, there is no complete theory today than can explain itsmagnetism satisfactorily.
In cooler and fully convective stars, there is by definition no tachocline,meaning that the dynamo processes could be different than in the Sun, eventhough this is debated (Wright & Drake 2016). No model can reproduce ade-quately all observed characteristics of magnetic fields in fully convective stars.However, a dynamo powered only by convective motion – the so-called α2 dy-namo – can reproduce some of its characteristics (Yadav et al. 2015). Also,recent simulations from Emeriau-Viard & Brun (2017) modelling dynamos inPMS stars with different extents of convection zone – from fully to partiallyconvective and thus going from α2 dominated to α −Ω dominated regimes– also seem to yield results which reproduce some of the trends observed inPMS stars magnetic fields.
Large surveys targeting hot stars detect magnetic fields in only a small frac-tion of them. Less than 10% of A/B-type stars are found to be magnetic (Poweret al. 2007; Sikora et al. 2019), and these stars show chemical peculiarities(Ap/Bp stars), while around 7% of O-stars are magnetic (Grunhut et al. 2017).However, weak magnetic fields were detected on the A-type star Vega and onAm-type stars including Sirius (Lignières et al. 2009; Petit et al. 2010, 2011;Blazère et al. 2016a,b, 2020). This suggests that weak undetected magneticfields could be present in many other A-type stars.
Both the occurrence rates of the magnetic fields and their nature vary greatlybetween cool and hot stars. The magnetic fields of hot stars are generally sim-ple. Typically, the topology is predominantly a dipole that is tilted from therotation axis. The fields are stable on timescales up to decades. These char-acteristics of hot-star magnetism seem to indicate that there are no physicalprocesses modifying or generating magnetic fields on short time scales insidethese stars. Rather, it is a so-called "fossil field", a relic of the field acquiredby the star at early evolutionary phases, perhaps from the molecular cloud inwhich the star formed (Neiner et al. 2015).
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2.3 Stellar multiplicity and magnetismBinary and multiple stars are excellent laboratories to study stellar physicsin general. They contain stars born at the same epoch and from the samematerial. In the context of stellar magnetic field studies, studying binaries canallow disentangling the effect of stellar parameters from the initial conditionswhen the stars are formed. It is also particularly interesting to study the impactof magnetic field on binarity, and vice versa. In close binary for instance, tidalinteractions, which influence the rotation rates of the components, could havea significant impact on the magnetic field generation as well. Furthermore, themagnetospheres of the two stars can also interact with each other. In this case,magnetic reconnection phenomena can occur and drive stellar activity.
Until recently, the magnetism of binary stars had barely been investigated.The situation changed with the BinaMIcS (Binarity and Magnetic Interactionsin various classes of Stars) large programme using the ESPaDOnS and Narvalspectropolarimeters respectively mounted at the the Canada-France-Hawaiitelescope and the télescope Bernard Lyot (Alecian et al. 2015). The goal ofBinaMIcS is to study in details the magnetic fields of stars in close-binary andimprove our understanding of the interplay between stellar magnetism and bi-narity. The rationale of the large programme was to observe various typesof close binary stars (from cool to hot stars) with the high-resolution opticalspectropolarimeter ESPaDOnS. The data can then be used to map the globalmagnetic fields of the stars using Zeeman Doppler imaging, and model magne-tospheric structures. Key science goals that BinaMIcS attempts to investigateinclude assessing the impact of magnetism on stellar formation, the effect oftidally-induced flows on magnetic fields, and magnetospheric binary compo-nent interactions on stellar activity.
The spectra of double-lined spectroscopic binary, which contain informa-tion from the two components, are both a blessing and a curse. While theycontain twice the information than spectra of single star would yield, they canbe very challenging to interpret due to their composite nature. The spectraneed to be disentangled in order to extract individual spectra for each compo-nent. The fact that we acquire time-series of intensity and polarized spectra inthis programme actually facilitates the disentangling. We can use the fact thatthe two stars experience a variable Doppler-shift throughout the orbit. Assum-ing that the spectrum of each star is constant through the orbit, we can extracta mean spectrum for each star using spectrum disentangling codes.
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3. Direct observations of stellar magneticfields
There are several ways to detect or characterize magnetic fields in stellar light.First, there are indirect methods. These methods rely on characterizing a phe-nomenon triggered, driven, or influenced by the magnetic field. One proxy formagnetic activity is the chromospheric heating. It can be traced by analyzingthe Ca II H and K emission lines (Schrijver et al. 1989), as well as the Hα line(Reiners & Basri 2010). Another indirect method is to analyze the photomet-ric variability of stellar light curves – which we now have plenty of thanks tospace missions such as CoRoT and Kepler. A periodic dimming or brigtheningin the light curve can be associated to the presence of dark spots and/or faculaeon the stellar surface, and these are thought to be caused by magnetic fields.These features on the stellar surface can also be studied with high-resolutionspectra (Sect. 3.5) and imaged directly with interferometric techniques, albeitfor a small number of stars (Roettenbacher et al. 2016). Other proxies trac-ing magnetic fields include flares (Pettersen 1989; Davenport 2016), X-ray(Pevtsov et al. 2003) and radio emissions (Güdel 2002). These proxies are use-ful to obtain an insight on the magnetic field, and some can be applied to largesamples of stars. However, they only give indirect estimates of the magneticfield characteristics through the use of empirical relations. Therefore, theycannot replace direct measurements, which provide first-hand information onthe stellar magnetic field.
Luckily for an observer, surface magnetic field in stars leaves a direct im-print in the stellar spectra via the Zeeman effect.
3.1 The Zeeman effectSpectral lines result from the emission or absorption of a photon by an atom, ora molecule. This corresponds to a transition of the atom or molecule from oneenergy level to another. The energy difference between the initial and final lev-els will determine the wavelength of the resulting spectral line. If a magneticfield is present, the energy of both the initial and final level will be perturbed.Specifically, a level with the total angular momentum quantum number J splitsinto 2J+1 levels. Each of these levels has a different magnetic quantum num-ber M. This is schematically shown in Fig. 3.1. Dipole transitions betweenthese levels follow the selection rule ΔM =−1, 0, or +1.
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no magnetic field magnetic field
σ σπ
1s
2p
spectral lines
transitions
energy levels
a) b)
Figure 3.1. Schematic illustration of the Zeeman splitting and polarization in a spectralline.
In the simple case of normal Zeeman splitting – as first discovered by PieterZeeman – the spectral line splits into a triplet. The triplet consists of the so-called π-component, which is not shifted with regards to the unperturbed line,and of the two σ -components: one red- and one blue-shifted. The wavelengthseparation ΔλB between the central π-component and the side σ -componentsis proportional to the strength of the magnetic field B, the unperturbed wave-length λ0 and follows the relation
ΔλB = 4.67×10−13geffλ 20 B (3.1)
with B expressed in G, λ in Å, and where geff (unitless) is the so-called ef-fective Landé factor (Landi Degl’Innocenti & Landolfi 2004). The effectiveLandé factor geff describes the magnetic sensitivity of a given spectral line.Typically, geff varies between 0 – for magnetically insensitive lines which arenot affected by the presence of magnetic field – to values typically up to 3 forvery magnetically sensitive spectral lines. For some transitions, geff values canalso be negative.
In the general case, spectral lines follow the so-called anomalous Zeemansplitting, where there can be multiple π- and σ -components. Equation 3.1is still valid, but the meaning of ΔλB is now the wavelength separation be-tween the centre-of-gravity of the red-shifted σ -component and the unper-turbed wavelength λ0.
From Equation 3.1, it is clear that for a given spectral resolution, it is easierto detect magnetic fields at longer wavelength and from magnetically sensitivespectral lines with high geff values. The Zeeman splitting of a magneticallysensitive line in the near-infrared is illustrated in Fig. 3.2.
The splitting of spectral lines into π- and σ -components is not the only ob-servable consequence of the Zeeman effect. The π- and σ -components alsobecome polarized and exhibit distinct polarization signals. The observed polar-ization depends on the angle between the magnetic field vector and the line ofsight. If the line of sight is parallel to the magnetic field vector (what we call alongitudinal field), the π-component is not observable. The σ -components are
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Figure 3.2. This figure shows synthetic stellar spectra computed for the parameters ofthe T Tauri star TW Hya studied in Paper II, around the magnetically sensitive Ti I lineat 22311 Å. The spectra are computed assuming that the stellar surface is covered witha uniform radial magnetic field, with a magnetic field strengths of 0, 1, and 2 kG.
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Figure 3.3. Illustration of the Stokes parameter definitions. The observer is facing theradiation source.
circularly polarized in opposite directions, clockwise and counterclockwise. Ifthe line of sight is perpendicular to the magnetic field vector (transverse field),then both σ - and π-components are observed to be linearly polarized, in or-thogonal directions. This is schematically illustrated in the right-hand panelof Fig. 3.1.
3.2 Stokes parameter formalismTo quantify the relative contribution of light in different polarization states, anecessary step to characterize stellar magnetic field through the Zeeman effect,we use a common formalism to describe the polarization state of the light: thefour Stokes parameters I, Q, U , and V . Stokes I represents the total intensity,and is what is commonly acquired with astronomical instruments equippedwith regular optics, such as imaging cameras or spectrographs. With polariza-tion optics, the other Stokes parameters become accessible. Stokes Q is thedifference between the light polarized along two orthogonal reference axes onthe sky. Stokes U is a similar difference in a reference frame rotated by 45◦.Stokes V is the difference of the clockwise and counterclockwise circular po-larization, as illustrated in Fig. 3.3. This formalism is very convenient, as thefour Stokes parameters can be easily accessed when observing with the typeof spectropolarimeters in use today.
3.3 Calculation of stellar Stokes parameter spectraThe work presented in this thesis is based upon the comparison of observedand synthetic stellar spectra, in either one or several of the four Stokes pa-rameters. This section describes the methodology that we used to computehigh-resolution synthetic Stokes parameter spectra. In essence we are solv-ing the polarized radiative transfer (PRT) equation in the stellar atmosphere.The star’s atmosphere is considered to be in hydrostatic equilibrium and weuse one-dimensional plane-parallel stellar model atmospheres. Moreover, thelocal thermodynamical equilibrium is assumed throughout our computations.
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We also assume the magnetic field strength and orientation to be independenton height in the stellar atmosphere, which is the usual assumption in stellarmagnetism studies. Finally, we solve the PRT equation, using different ap-proaches when we compute the Stokes I spectra used in Papers I and II andwhen we compute the Stokes IQUV profiles in Paper III and Paper IV.
For the analysis in Papers I and II, we used the SYNMAST code (Kochukhov2007) to compute high-resolution Stokes I stellar spectra emerging from amagnetized atmosphere (Stokes QUV spectra are also computed by the code).The inputs to the code are (a) a line list extracted from the VALD database(Ryabchikova et al. 2015) for appropriate effective temperature and surfacegravity, and (b) a model atmosphere which we took from the MARCS grid(Gustafsson et al. 2008). First, the equation of state solver included in SYNMASTcalculates the ionization and molecular equilibrium and partition functions areinterpolated for atoms and molecules (Piskunov & Valenti 2017). Opacitiesare computed for each layers of the 1-D model atmosphere and the PRT equa-tion is then solved numerically for a given local magnetic field vector and anumber of limb angles on the stellar surface. The algorithm used to solvethe PRT equation is a modification of the Diagonal Element Lambda Operatorsolver (de la Cruz Rodríguez & Piskunov 2013). The computation makes useof adaptive grids (both for the distribution of layers in the atmosphere and forwavelength points) in order to obtain accurate line profiles. Finally, the localspectra are combined and disk-integrated to simulate stellar spectra.
For Paper III and Paper IV, we needed to produce synthetic Stokes IQUVprofiles in order to model observations in the context of global magnetic fieldmapping. Instead of computing Stokes profiles by solving the PRT equationnumerically, we used the Unno-Rachkovsky solution. Under the assumptionof a Milne-Eddington model atmosphere, it provides analytical local StokesIQUV profiles for a given local magnetic field vector (Landi Degl’Innocenti &Landolfi 2004, Chapter 9.8). In both papers, the parameters of the analyticalline profiles were adjusted to reproduce the disk-integrated Stokes I profiles,while the Stokes V profiles were used in the modelling of the field geometry. InPaper III, additionally, we used two extra line parameters: the Stokes I and Vfilling factors fI and fV in order to reproduce the observed profiles, followingprevious ZDI studies of active M dwarfs (Morin et al. 2008). Physically, thefI parameter is the fraction of each surface element covered by magnetic field,and fV is the fraction producing a net circular polarisation. The local StokesIV profiles are then given by
I = fI × IUR(B/ fV )+(1− fI)× I0,
V = fV ×VUR(B/ fV ),(3.2)
where IUR and VUR are the Stokes IV local profiles from the Unno-Rachkovskysolution, I0 is the local Stokes I profile computed without magnetic field, andB is the local magnetic field vector. Using these two filling factors is neededin order to match both the broadening of the observed Stokes I and V profiles
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(which depends on the total field present) as well as the amplitude of the StokesV profiles which depends on the field component left after cancellation ofopposite polarities (traced by fV ).
3.4 Zeeman line broadening in stellar intensity spectraAs detailed in Sect. 3.1, magnetic field splits spectral lines into multiple com-ponents. The wavelength separation between the components depends on thestrength of the magnetic field, the effective Landé factor of the line, and thesquare of the wavelength of the spectral line. In practice, measuring stellarmagnetic fields from the Zeeman broadening or splitting of spectral lines en-tails discriminating between the broadening caused by the magnetic field andall the other processes affecting the shape of the spectral lines under study.Indeed the spectral line shape and strength depend on the stellar parametersTeff and logg, individual element abundances, and are also affected by othersources of broadening such as instrumental, rotational, micro- and macrotur-bulent broadening.
The study of Zeeman broadening is based on comparing the observed spec-trum with synthetic spectra. As Zeeman broadening is not very sensitive tothe orientation of the field and its topology, it is common to assume a purelyradial magnetic field. Although we cannot recover the detailed topology ofthe magnetic field, we can still assess different models specifying the mag-netic field strength distribution at the surface of the star. Typically, the star isdivided into different regions that are covered with uniform magnetic fields.The free parameters are the surface fraction of each region, and the magneticfield strengths. For instance, in the case of a simple model with one non-magnetic region and one region covering a fraction f of the stellar surfacewith a magnetic field B, the resulting synthetic spectrum I is computed withthe linear combination:
I = f × IB +(1− f )× I0 (3.3)
where IB and I0 are the synthetic spectra corresponding to, respectively, a uni-form, radial magnetic field B, and no magnetic field. Equation 3.3 can begeneralized to two or more magnetic components, each having its own f andB. Models using several components with fixed magnetic field strengths of 0,2, 4, and 6 kG have also been repeatedly used in the literature (Johns-Krull2007; Yang et al. 2008; Yang & Johns-Krull 2011).
An important aspect in this type of analysis is to choose the level of com-plexity of the model describing the partitioning of the stellar magnetic fieldstrength distribution. Ideally, the complexity of the model should be selectedaccording to the information contained in the observed spectrum. This is whyin Paper I, we used two different models, the simplest model correctly re-producing the observations for most stars, and switching to a more complex
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0
2
46
8
10
2
0
2
4 0 6
42
0 0
2
46
8
etc ....
Figure 3.4. Illustration of our approach in paper II describing the distribution of thesurface magnetic field with progressively more complex models. The values in eachpie chart are magnetic field strengths in kG.
model for the rest of the sample. We developed the methodology further in Pa-per II, in which more complex models were clearly needed to accomodate thestronger observed magnetic fields. In this work, we used Bayesian statisticsto devise an approach that lets the data select the complexity of the magneticfield model through the use of an information criterion (Bayesian InformationCriterion; BIC). We started modelling the data with a simple model containingtwo components, 0 and 2 kG. We then successively added components to themodels with field strengths of 4, 6, 8, 10, 12, and ultimately 14 kG, fittingthe data at each step. In order to avoid overfitting the data using unnecessarystrong magnetic field, we selected the model which yields the lowest value ofthe BIC. This criterion effectively penalizes extra parameters if they do notsignificantly improve the fit to the data. This approach worked best for thesample of stars studied in Paper II, and provided excellent results for a widerange of magnetic field strengths.
3.5 Zeeman Doppler ImagingStellar spectra are extremely rich in information about the stellar atmosphere.The strength, shape, and position of spectral lines provide the observer with in-formation on the effective temperature, surface gravity, elemental abundances,radial velocity of the star, projected rotation rate, turbulence, and magneticfield. But that is not all, spectral lines can also be used to map features on thestellar surface.
The shape of a spectral line is affected by the stellar rotation. Photonscoming from the central meridian on the stellar disk, with no velocity projectedon the line of sight, will suffer no red- or blueshifting with regards to thecentral wavelength of the spectral line in the rest frame of the star. However,the stellar surface is moving away from the observer on one limb, and towardsthe observer on the other, thus redshifting or blueshifting photons emitted therethrough the Doppler effect. If a spot is present on the stellar surface, it leavesan imprint in the spectral line. From its wavelength shift with regards to theline centre, the spot’s longitude can be inferred. This is illustrated in the left-hand side subplots of Fig. 3.5. The latitude position of the spot is however
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Figure 3.5. Sketch explaining the principle of Doppler imaging. The presence ofa spot on the stellar surface produces a distortion on the spectral line profile. Thedistortion is shifted in wavelength according to the position of the spot relative to thedisk centre. Subplots a) and b) show the resulting disk-integrated line profiles forspots characterized by a decrease of local continuum brightness (low temperature spot)and an increase of local equivalent width (high element abundance spot). Subplot c)displays a dynamic spectrum (the evolution of the residual spectral line profile as afunction of rotational phase). The profiles are computed with four cool spots on thesurface at different latitudes: −30, 0, +30, and +60 degrees. This shows that spectraldistortions corresponding to spots at different latitudes exhibit different behavioursin the time-series observations. Adapted with permission from Kochukhov (2016).Copyright: Springer International Publishing Switzerland 2016
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degenerate and cannot be obtained from a single observation. Nonetheless,the latitude degeneracy can be lifted if a time-series of observations coveringdifferent phases of the stellar rotation is obtained. As is depicted in the right-hand side subplot of Fig. 3.5, features at different latitudes have a differentbehaviour in the spectral time-series. This means that, by studying time-seriesof intensity spectra, we can reconstruct star spot maps. This forms the basis ofthe Doppler imaging methodology (Kochukhov 2016).
This method can be applied to map temperature or chemical abundance onstellar surfaces. An extension of this inversion technique to Stokes parameters– Zeeman Doppler imaging (ZDI; Brown et al. 1991; Piskunov & Kochukhov2002) method – makes use of the Zeeman effect (described in Sect. 3.1) toreconstruct the surface magnetic field topology. Magnetic features on the sur-face produce a signature in polarized spectra through the Zeeman effect, asshown in Fig. 3.6. These signatures can also be related to magnetic spot posi-tions on the stellar surface, with longitude coming from the wavelength shiftand latitude reconstructed from the evolution of the features in time-series ob-servations. In contrast to Doppler imaging, which reconstructs a scalar mapfrom Stokes I time-series, ZDI recovers a vector map (radial, meridional, andazimuthal components of the field) from a time-series of Stokes profiles.
As can be seen from Fig. 3.6, different components of the magnetic fieldinduce different circular polarization signals. Radial fields produce strongStokes V signatures, which are strongest when magnetic spot is located at diskcentre, and the signatures do not change sign as the star rotates. Azimuthalfields have a relatively strong Stokes V signature too. However, they behavevery differently from radial field signatures, as they are weakest and switchsign at disk centre. This means that the radial and azimuthal components ofthe magnetic field can be disentangled. Meridional fields, on the other hand,have weak Stokes V signatures, and are hence difficult to recover from StokesV data alone.
Application of ZDI to cool stars is not straightforward. Indeed, the typicalamplitude of polarization signatures caused by magnetic fields in the spectraof cool stars is low. Typically, the amplitude of a cool-star polarization signalin Stokes V is in the range of 10−3–10−4 of the unpolarized continuum. Thisis, in most cases, too weak to be detected in individual spectral lines. The lin-ear polarization in Stokes QU is usually an order of magnitude weaker than thecircular polarization signal. To overcome this problem, multi-line techniqueswere developed to combine the information from a large number of spectralline profiles into one single mean profile with a greater signal-to-noise ratio.The most commonly used multi-line technique is the least-squares deconvo-lution (LSD, Donati et al. 1997; Kochukhov et al. 2010). LSD effectivelycombines all selected spectral lines assuming that they are scaled version ofa unique profile. In practice that means that the observed spectrum is consid-ered to be a convolution of a mean profile with a line mask, which containsinformation on the wavelength, depth, and effective Landé factor of each line
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a)
b)
c)
Figure 3.6. This figure shows Stokes V polarization signatures of a magnetic spot onthe stellar surface for three rotation phases. Different rows show the different signaturesfor magnetic spots with a (a) radial, (b) meridional, or (c) azimutal field. Adapted withpermission from Kochukhov (2016). Copyright: Springer International PublishingSwitzerland 2016
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in the spectrum. The resulting LSD profiles can then be used to reliably detectweak magnetic fields and as an input to ZDI. In the context of magnetic fieldstudies of cool stars, the linear polarization signatures are extremely weak andusually not observed. With the exception of the RS CVn star II Peg, studiedin all four Stokes parameters by Rosén et al. (2015), all ZDI mapping of coolstars has been performed with only Stokes V data.
The signature of the magnetic field in the intensity spectrum depends ona scalar (the norm of the magnetic field vector). It is not sensitive to weakmagnetic fields (B � 1 kG) in stellar spectra due to the competition of non-magnetic broadening mechanisms, but the signatures of magnetic fields withopposite polarities do not cancel. Polarization signatures are much more sen-sitive to weak magnetic field, as there is simply no polarization signal if themagnetic field is null. However, the polarization signal arising through theZeeman effect in the Stokes QUV spectra depends on both the magnitude andorientation of the magnetic field vector. This means that polarization diag-nostics suffer from cancellation of signals corresponding to magnetic fieldsof opposite polarities. For this reason, reconstruction of the magnetic fieldtopology from Stokes V or, to a lesser extent, QUV misses out small-scalestructures and can recover only the large-scale component of the field. A sub-stantial fraction of the magnetic energy is therefore missing from the ZDIinversion. Magnetic field strengths obtained from ZDI are always weaker thanthe strengths derived from Stokes I Zeeman broadening, the latter tracing bothglobal and small-scale fields.
In this thesis, we used the ZDI inversion code InversLSD (Kochukhov et al.2014) to reconstruct magnetic maps of the active M dwarf AD Leo from StokesV data (Paper III). We also used its adaptation to binary stars InversLSDBto map the brigthness and magnetic field of the PMS double-lined binaryV1878 Ori (Paper IV).
In both cases, the procedure adopted for the inversion is the following:1. Divide the stellar surface(s) into a grid of surface elements of roughly
equal area;2. Pre-compute a grid of local fiducial line profiles through the analytical
Unno-Rachkovsky formulae. The mean central wavelength and effectiveLandé factor were computed from the LSD line mask and the line wasassumed to split as a Zeeman triplet.
3. For a given set of initial parameters describing the surface magnetic field,the actual local LSD profiles are computed by interpolation within thepre-computed grid of LSD profiles;
4. The disk-integrated LSD profiles are computed and compared to obser-vations. In the case of Paper IV, the LSD profiles are composite profilesfrom the two stellar components;
5. The field distribution is iteratively updated and the best-fitting solutionis found using a modified Levenberg-Marquardt algorithm (Piskunov &Kochukhov 2002).
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The magnetic field components (radial, meridional, azimuthal) are describedwith a spherical harmonic (SH) expansion (Donati et al. 2006b; Kochukhovet al. 2014). This allows an easier characterization of the field (for example,a measurement of the poloidal vs toroidal, axisymmetric vs non-axisymmetricfield components) than reconstructing the field pixel by pixel.
A ZDI inversion is an ill-posed inverse problem (Hadamard 1902). Thismeans that there is no unique and stable solution, even if one could obtain anoiseless dataset with a full phase coverage, as different magnetic topologiescan produce the same signature in Stokes V . Solution of an ill-posed problemrequires introducing a regularization function that will favour the "simplest"solution that fits the data. Commonly used types of regularizations in ZDIinversions are:
• The maximum entropy method (MEM, Brown et al. 1991) which selectsthe solution minimizing the deviation of each pixel from the mean value.MEM is not optimal for reconstructing large-scale fields, which do notobviously take a default value. For instance, MEM has difficulties re-covering a simple large-scale field such as a dipole covering the entirestar;
• Tikhonov regularization which minimizes the local horizontal gradientsin the map and hence favours smoother solutions (Tikhonov & Arsenin1977; Piskunov & Kochukhov 2002);
• If a SH expansion is used to describe the field, one can use a penaltyfunction given by the sum of magnetic energy in each SH componentweighted by a factor that increases with the spherical harmonic degree �(Morin et al. 2008; Kochukhov et al. 2014). This regularization favourssimpler global field configurations and limits the contribution of anycomplex structures that are unecessary in the fit.
Notwithstanding the choice of regularization, ZDI with Stokes V alone onlyrecovers large-scale magnetic fields, and is unable to recover a substantial partof the magnetic flux that cancels out – typically in the case of neighbouring lo-cal fields with opposite polarities. However, by comparing the mean magneticfield value obtained from ZDI with the field strength obtained from Zeemanbroadening, one can estimate the fraction of the magnetic field "missing" inthe ZDI inversions.
Rosén et al. (2015) show that for II Peg, inversions using four Stokes pa-rameters unveil more complex and stronger magnetic fields than recoveredwith Stokes V only. Additionally, in Stokes V inversions, the radial and merid-ional fields are difficult to disentangle at lower latitudes, and the meridionalfield is generally not reliably recovered over parts of the stellar surface (Rosén& Kochukhov 2012). In any case, ZDI – even with Stokes V only – is aformidable tool that allows to derive a useful model of the large-scale mag-netic field topology, albeit with the limitations mentioned above.
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4. Summary of papers
4.1 Paper IMagnetic fields of intermediate-mass T Tauri stars
In Paper I, we present results from the magnetic field study of intermediate-mass T Tauri stars (IMTTS) through the modelling of Zeeman broadening innear-infrared high-resolution CRIRES spectra. IMTTS are pre-main-sequencestars with a mass 1M� < M < 4M�. These stars later become Herbig Ae/Bestars, and eventually A/B type stars when on the main-sequence. The magneticfields of A/B type stars have been extensively studied and only a small frac-tion (less than 10%) show a strong field (Power et al. 2007; Sikora et al. 2019).This field tends to be simple and stable over at least several decades. It is the-orized that these fields have been acquired from a previous evolutionary stage,and are hence called "fossil fields" (Neiner et al. 2015). The magnetic fieldsof Herbig Ae/Be stars – which are the precursors to A/B type stars – werealso investigated thoroughly in a large spectropolarimetric survey. The resultsindicated that Herbig Ae/Be and A/B type stars have similar magnetic char-acteristics, and that a similar fraction of these stars exhibits a strong, simple,and stable field (Alecian et al. 2013). These results suggest that the magneticfields of those stars was generated at an even earlier evolutionary phase, whenthese stars were IMTTS.
Therefore, we studied IMTTS in order to characterize their magnetic fields.We acquired high-resolution near-infrared spectra of five IMTTS and one low-mass T Tauri star with the high-resolution CRIRES spectrograph (Käufl et al.2004) mounted at one of the 8-m unit telescopes of the Very Large Telescopeobservatory. Due to the design of the CRIRES spectrograph, each observa-tion yields a very narrow part of the near-infrared spectrum, covering onlya handful of spectral lines. We observed every star twice, first with a spec-trograph setting covering magnetically sensitive Fe I line around 1565 nm,and another time to record magnetically insensitive CO lines around 2308 nm.Our reduced and normalized spectra in the two wavelength settings are shownin Fig. 4.1. We used the magnetically insensitive lines to characterize non-magnetic broadening, which in our case was limited to determination of therotational Doppler broadening parameter ve sin i as we adopted fixed valuesof the micro- and macro-turbulent velocities vmic = 2 kms−1 and vmac = 0kms−1.
We then generated a grid of synthetic stellar spectra with variable magneticfield modulus 〈B〉 and ve sin i. Ultimately, we found the value of 〈B〉 and ve sin i
29
Figure 4.1. Normalized observed CRIRES spectra in the H and K bands (respectivelyleft- and right-hand side subplots).
30
0.7
0.8
0.9
1
No
rm
ali
ze
d i
nte
ns
ity
15622
Wavelength (Å)
15648 15662
Figure 4.2. Observed spectrum of the star CHXR 28 around the three magneticallysensitive spectral lines used in the analysis (blue histogram), overplotted with the bestmagnetic fit (thick black line) and the corresponding non-magnetic synthetic spectrum(thin grey line).
that gives the best fit to the magnetically sensitive spectral lines through χ2
fitting. Assuming a radial magnetic field of uniform strength covering theentire stellar surface provided a good fit for four out of six stars in the sample.For the two other stars, we assumed that the radial uniform field covers onlya fraction of the surface, and that the rest of the surface is non-magnetic. Asan example, the best-fit to the spectrum of the star CHXR 28 is depicted inFig. 4.2.
There is a partial degeneracy between the magnetic field modulus 〈B〉 andthe rotational broadening ve sin i: both broaden spectral lines. Therefore, weallowed ve sin i to vary during our analysis. Whenever possible, we took intoaccount the confidence intervals previously constrained using the magneti-cally insensitive CO lines. This permitted to obtain robust error estimates onthe magnetic field modulus, which take into account the uncertainties on theve sin i determination. We also carried out our analysis separately with spectrallines of different magnetic sensitivities. We found that while formally compat-ible, the results from mildly sensitive lines are systematically different withrespect to the results from the most magnetically sensitive line.
Our measurements indicate that we find magnetic fields with strengths be-tween roughly 1 and 2 kG, and we do not detect very strong magnetic fields(> 3 kG) that are known to be present in low-mass T Tauri stars (Yang et al.2008; Yang & Johns-Krull 2011). The magnetic field values for the stars in thesample are presented on a H–R diagram together with the results from Paper IIin Fig. 4.3.
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Figure 4.3. PMS H–R diagram showing the near-infrared Zeeman broadening magneticfield measurements of T Tauri stars. Results from Paper I are indicated by filled bluecircles (the dark and light blue indicate respectively the results from the highly- andmildly-sensitive spectral lines), the yellow circles display the results from Paper II, andlight grey circles show results from the literature (Sokal et al. 2020, and referencestherein). The radius of the circles is proportional to 〈B〉2 as indicated in the key atthe bottom left. To put these results in the stellar evolution context, the zero ageMain-Sequence (ZAMS) is overplotted with the dashed blue line, the limit betweenthe fully and partially convective interiors is shown with the dotted yellow curve, andevolutionary tracks for different masses are plotted in grey lines.
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4.2 Paper IICharacterising the surface magnetic fields of T Tauri stars withhigh-resolution near-infrared spectroscopy
In Paper II, we studied the magnetic fields of eight low-mass T Tauri stars,following a similar approach as the one described in Paper I (Sect. 4.1). Weobtained high-resolution near-infrared spectra with the CRIRES instrument,using two wavelength settings. We observed the same magnetically insensi-tive CO lines around 2308 nm as in Paper I to constraint non-magnetic broad-ening. However, instead of observing the magnetically sensitive Fe I linesaround 1565 nm, we chose a set of strong Ti I and Na I lines around 2220 nm.These are more suitable for magnetic field measurements for cooler effectivetemperatures. We observed all but one star repeatedly in order to investigatenight-to-night variability of the magnetic field. Also, five stars in the samplewere previously studied using Zeeman Doppler imaging, allowing us to deter-mine the fraction of the magnetic field recovered from spectropolarimetry.
The simple magnetic field strength distribution models used in Paper I couldnot accomodate the strong magnetic fields clearly needed to reproduce thespectral lines shapes in this stellar sample. We therefore used more complexmodels. We also developed a Bayesian data-driven framework that lets theinformation contained in the data select the complexity of the magnetic fieldmodel. Specifically, we compared the results of four models:
• Model 1: A fraction f of the star is covered with a magnetic field B, therest of the surface is non-magnetic. The mean magnetic field modulus is〈B〉= B f .
• Model 2: Magnetic fields B1 and B2 cover fractions f1 and f2 of thestellar surface, the remainder is non-magnetic. 〈B〉= B1 f1 +B2 f2.
• Model 3: Fixed magnetic field strength values of 2, 4, and 6 kG coverfractions f1, f2, f3 of the stellar surface while the rest of the surface isnon-magnetic. 〈B〉= 2 f1 +4 f2 +6 f3 kG.
• Model 4: A generalization of Model 3 with fixed magnetic field strengthvalues of 2, 4, 6, 8, 10, 12, and 14 kG. However, the maximum mag-netic field value allowed in the model is selected through the use of theBayesian information criterion (BIC), which essentially limits the num-ber of free parameters if they do not substantially improve the fit to thedata. Limiting the maximum magnetic field in the model using the BICallows us to always use an adequate model without overfitting the data.
Parameters of Models 1–2 were determined with a grid-search in the freeparameter space. Markov chain Monte Carlo (MCMC) methods were em-ployed to perform the model parameter inference for Models 3–4. We foundthat Model 4 performs best, and provides excellent results for the full range ofmagnetic field strengths. Our observations and the best-fitting synthetic spec-tra using Model 4 are shown in Fig. 4.4. We measured 〈B〉 values ranging from1.5 to 4.4 kG. These results are presented in an H–R diagram together with the
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Figure 4.4. Observed spectra around the four spectral lines used in the analysis (blackhistogram) together with the best magnetic fit (orange solid line) and the correspondingnon-magnetic synthetic spectrum (grey solid line). The spectra for different stars areoffset vertically.
results from Paper I in Fig. 4.3. We did not detect large night-to-night fieldstrength variability, with a mean peak-to-peak deviation of 0.3 kG and meanpeak-to-average deviation of 0.1 kG. These results suggest that the small-scalemagnetic field is distributed homogeneously over the stellar surface. We werealso able to compare our results with the average magnetic field recoveredfrom ZDI mapping of the same stars. We find that ZDI recovers between 42%and 2% of the field that is measured using Zeeman broadening. Higher val-ues are seemingly recovered for poloidal axisymmetric global field geometriesthan for toroidal non-axisymmetric fields.
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Figure 4.5. The upper panel shows Stokes V LSD profiles of AD Leo for each epochbetween 2006 and 2016 as well as unpublished profiles from observations in 2019.The epochs are indicated above each subplot. The lower panel shows individual 2016Stokes I spectra (coloured lines, bottom) overplotted with the average 2006–2012Stokes I spectrum (thick black line, bottom) individual 2016 Stokes V spectra (middle),average 2006–2012 Stokes V spectrum (black line, top) overplotted with the average2016 Stokes V spectrum (bright orange, top). All Stokes V spectra in this figure aremagnified by a factor of 10 and shifted vertically.
4.3 Paper IIIA sudden change of the global magnetic field of the active M dwarf ADLeo revealed by full Stokes spectropolarimetric observations
In Paper III, we presented the first full Stokes spectropolarimetric observationsof an active M dwarf – AD Leo (GJ 388) – and the mapping of its large-scalemagnetic field through Zeeman Doppler imaging using circular polarization.
We obtained high-SNR high-resolution full Stokes spectropolarimetric ob-servation of the active M dwarf AD Leo between February and April 2016with the ESPaDOnS spectropolarimeter (Donati 2003; Donati et al. 2006a)mounted at the 3.6-m Canada-France-Hawaii Telescope (CFHT). The circularpolarization signatures are clearly visible in individual spectral lines, as shownin the bottom subplot of Fig. 4.5. We computed Stokes IQUV LSD profilesby combining around 1400 atomic lines between 450 and 985 nm. The time-series of our LSD profiles is presented in Fig. 4.6.
We obtained the first detection of linear polarization signatures in the spec-tral lines of an active M dwarf, with definite detections for three out of six
35
Figure 4.6. Time-series of the Stokes IQUV LSD profiles of AD Leo computed fromour observations. The LSD profiles are shifted vertically and sorted according to theirrotation cycle (indicated over Stokes I LSD profiles) increasing upwards.
36
Stokes Q profiles and two out of six Stokes U profiles, and marginal detectionsfor one Stokes Q profile and three Stokes U profiles. The median amplitudeof Stokes QU profiles is 13 weaker than the median amplitude of Stokes Vprofiles. For a handful of cool stars for which Zeeman Stokes QU signatureswere detected, these signatures were found to be 5–10 weaker than Stokes Vprofiles (Kochukhov et al. 2011; Rosén et al. 2015). The fact that linear po-larization profiles are weaker than expected in AD Leo could be a sign thatits magnetic field has many small-scale structures. Indeed, observations of Apstars showed that a contribution of small-scale structures to the global mag-netic field geometries decreases the amplitude of linear polarization profiles(Kochukhov et al. 2004; Rusomarov et al. 2018).
The Stokes V LSD profiles of AD Leo were essentially constant duringall previous spectropolarimetric observations spanning 2006–2012. Yet, wenoticed that our profiles from 2016 were significantly different, as can be seenin the upper panel of Fig. 4.5. The LSD profiles from 2016 are broader andhave a weaker amplitude. The change in the shape of the Stokes V profiles canalso be seen in individual spectral lines, as shown in the lower panel of Fig. 4.5.This rules out that what we observe is an artefact of the LSD procedure.
To investigate the change in the surface magnetic field that explains thechange in the Stokes V profiles, we used ZDI to map the large-scale mag-netic field with the 2012 and 2016 datasets. The ZDI was carried out withthe InversLSD code (Kochukhov et al. 2014), which describes the magneticfield components using a spherical harmonic expansion, and we adopted amaximum angular degree �max = 10. We adopted the stellar parameters de-termined in the previous spectropolarimetric study of AD Leo by Morin et al.(2008): ve sin i = 3 kms−1, inclination angle i = 20◦, and a rotation periodProt = 2.2399 days.
The surface magnetic field maps and the fits to the observed Stokes V LSDprofiles are displayed in Fig. 4.7. We observe a quantitative change of thelarge-scale magnetic field. The topology of the field is mostly unchanged andstill predominantly dipolar, but the magnetic energy decreased by about 20%.Also, the Stokes V filling factor had to be significantly lowered from 13% to7% in order to fit the data. This means that while the field is globally weaker,it is concentrated in smaller area so that local magnetic fields actually becomestronger.
We managed to obtain further Stokes IV observations of AD Leo in 2019using the same instrument: ESPaDOnS at the CFHT. The Stokes V LSD pro-files from this latest observing campaign, unpublished so far, are presented inthe right-hand side subplot of Fig. 4.5. The profiles seem to have regainedsome amplitude, but have not recovered to the amplitude levels of 2006–2012.
In this paper, we detected for the first time evidence that active M dwarfswith a predominantly dipolar and axisymmetric large-scale field can undergosecular transformation of their field topology – which is not predicted by the-
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Figure 4.7. ZDI maps of the large-scale magnetic field of AD Leo reconstructed fromthe 2012 and 2016 datasets – respectively a) and b) panels – shown with the fits (redline) to the observed Stokes V LSD profiles (black histogram). The maps are flattenedpolar projections which show the stellar surface down to −30◦ latitude, the thick blackline represents the equator, and the dotted lines represent the +30◦ and +60◦ latitudes.The side bars show the correspondence between the colour table and magnetic fieldstrength in kG.
oretical dynamo models. We also strongly advocate for long-term spectropo-larimetric monitoring of M dwarfs in order to investigate this phenomenon.
4.4 Paper IVThe large-scale magnetic field of the eccentric pre-main-sequencebinary system V1878 Ori
In Paper IV, we investigated global magnetic field properties of the PMS binarysystem V1878 Ori. This system is a double-lined spectroscopic binary with aneccentric orbit in which both components are intermediate-mass T Tauri starswith nearly equal masses and luminosities. The system was observed as partof the BinaMIcS large program (Alecian et al. 2015), which aims at studyingthe magnetic field of binary stars. We obtained time-resolved optical spec-tropolarimetric observations in Stokes IV parameters using the ESPaDOnSspectropolarimeter at the Canada-France-Hawaii Telescope. ComplementaryX-ray observations of the system at periastron and outside periastron were
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also acquired with the XMM-Newton satellite. These X-ray observations donot detect signs of X-ray emission enhancement at periastron, which suggeststhat possible magnetospheric interaction at periastron did not affect coronalactivity.
We computed Stokes IV LSD profiles for each observation in our time-series combining around 5300 atomic spectral lines. Circular polarizationis clearly detected in the LSD composite profiles, for both components andthroughout the orbit. We applied our spectral disentangling code to the StokesI LSD profiles and measured radial velocities (RV) for the two components.Combining our RV measurements with literature values, we could refine theorbital parameters for this system. Using the refined orbital solution, we thenapplied a spectral disentangling procedure to the observed intensity spectra,and recovered average intensity spectra for each component over a large frac-tion of the optical domain. These spectra were then used to determine atmo-spheric parameters of both components (Teff, logg, ve sin i, vmic, and overallmetallicity) through spectrum synthesis modelling.
Finally, we carried out the mapping of the brightness and magnetic fielddistributions at the surfaces of both stars using the Zeeman Doppler imagingtechnique applied to the observed composite Stokes IV LSD profiles. As partof this analysis, we derived individual rotational periods of both components.The recovered brigthness and magnetic field maps are presented in Fig. 4.8and the observed LSD profiles as well as the computed profiles are shown inFig. 4.9. We find that despite their very similar stellar parameters, V1878 OriA and B posses a strikingly different global magnetic field. On the one hand,the magnetic field of the primary is mostly poloidal and non-axisymmetricwith a mean field strength of 180 G. On the other hand, the field of the sec-ondary is predominantly toroidal and axisymmetric with a mean field strengthof 320 G. This is the first ZDI study of a binary intermediate-mass T Tauri starsystem.
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Brightness Brightness
Radial field Radial field
Meridional field Meridional field
Azimuthal field Azimuthal field
0.8
1.0
1.2
-0.2
-0.1
0.0
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kG
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V1878 Ori A V1878 Ori B
Figure 4.8. ZDI maps of the brigthness distribution and large-scale magnetic field ofV1878 Ori A and B (respectively left and right column). The maps are equal-areaHammer-Aitoff projections. The central meridian corresponds to 180◦ longitude, orrotational phase 0.5, with the longitude increasing from left to right. The colour barson the right-hand side link the colour table to the brightness and the strength of themagnetic field in kG.
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Figure 4.9. Observed (black symbols) and computed (solid orange lines) Stokes IVLSD profiles of V1878 Ori shifted vertically according to the orbital phase. The blackdashed line in the Stokes I panel shows the effect of removing brightness spots. Therotational phases of the primary and the secondary components are indicated on theleft- and right-hand side of the plot, respectively.
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5. Summary and outlook
The last two decades have seen a great progress in the study of stellar mag-netism thanks to new instrumentation (optical spectropolarimeters) and ad-vanced tomographic techniques. In this thesis, we made use of both in or-der to measure and characterise the magnetic fields of cool stars. We pro-vided new observational constraints for low-mass as well as for intermediate-mass T Tauri stars. We did so using both Zeeman broadening modelling innear-infrared spectra and Zeeman Doppler imaging using optical spectropo-larimetry. We developed a methodology for Zeeman broadening measure-ments which provides reliable results for a wide range of field strengths, ac-comodating strong fields without overfitting the data. We also detected thefirst Zeeman linear polarization signals in the spectral lines of an M dwarf(AD Leo), and observed a sudden and unexpected transformation of the globalmagnetic field of that star, where the surface magnetic field seemed to becomeconcentrated on smaller scale. Finally, we mapped the magnetic field at thesurface of the binary IMTTS system V1878 Ori. We found that the two com-ponents, albeit having similar stellar parameters, harbour radically differentglobal magnetic fields.
Our magnetic field observations helped covering uncharted regions of thePMS H-R diagram and investigated evolution of cool-star magnetism in thetime-domain. These observations will hopefully prove useful for constrainingdynamo models and discriminating between different scenarios for the evolu-tion of stellar magnetic fields.
Many facets of the magnetic fields of cool stars and PMS stars in particularare still not fully understood. How exactly are the magnetic fields generatedand at which stage do hot stars acquire their fossil magnetic fields? Is there acommon type of dynamo harboured in all cool stars? Which cool stars expe-rience magnetic cycles and why? Naturally, more observations are needed toanswer these questions. Particularly, monitoring targets during years and evendecades is necessary for tracking secular evolution of stellar magnetic fieldsas well as magnetic cycles.
Luckily, the future seems bright. The next generation of instruments willprovide exquisite data for studies of cool-star magnetism. High-resolutionnear-infrared spectropolarimeters such as SPIRou at the 3.6-m Canada-France-Hawaii Telescope (already in operation) and CRIRES+ at ESO’s 8-m VeryLarge Telescope (currently being tested at the telescope), are indeed unmatchedinstruments for the study of cool stars and their magnetic fields. First, coolstars and particularly pre-main-sequence stars – which might be shrouded by
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dust – are much brighter and therefore easier to observe in the near-infraredthan in the optical. This mean that we will be able to analyse high-resolutionintensity and polarization spectra of fainter and younger stars than today, forinstance Class I stars, and even brown dwarfs. It will therefore become possi-ble to study more cool stars using ZDI with four-Stokes parameters, which canunveil more details of the magnetic field topology. Additionally, it will now be-come feasible to routinely perform Zeeman broadening analysis and ZeemanDoppler Imaging consistently on the same datasets. This will give us a morecomplete picture of the stellar magnetism, with information on both small- andlarge-scale magnetic components simultaneously. The coming years will cer-tainly bring many answers when it comes to cool-star magnetic fields, as wellas many new questions.
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6. Contribution to the included papers
Paper ILavail, A., Kochukhov, O., Hussain, G.A.J., Alecian, E., Herczeg G.J., andJohns-Krull C. (2017)Magnetic fields of intermediate mass T Tauri StarsAstronomy & Astrophysics, 608, A77
The co-authors (PI Gaitee Hussain) wrote the observing proposal and the datawere reduced by Gregory Herczeg. The scope of the project was developedin collaboration with Oleg Kochukhov and Gaitee Hussain. I developed themethodology together with Oleg Kochukhov, wrote the analysis code based onspectrum synthesis software from Oleg Kochukhov, and performed the analy-sis of the data (refinement of oscillator strength values, ve sin i determination,and Zeeman broadening modelling) as well as the interpretation of the results.I led the writing of the paper with input from co-authors. The writing of Sect.2 (Observations and data reduction) was led by Gregory Herczeg.
Paper IILavail, A., Kochukhov, O., and Hussain, G.A.J. (2019)Characterising the surface magnetic fields of T Tauri stars with high-resolutionnear-infrared spectroscopyAstronomy & Astrophysics, 630, A99
The co-authors (PI Oleg Kochukhov) wrote the observing proposal. The spec-tra were reduced by an automatic pipeline, and I completed the data reductionwith modelling and removal of telluric absorption, improvement of the wave-length solution, and continuum normalization. Using an approach based onthe work from Paper I, I performed the analysis (ve sin i determination andZeeman broadening modeling) improving the methods with the implementa-tion of additional magnetic components and the use of Bayesian statistics andMarkov chain Monte-Carlo methods. I led the writing of the paper with inputfrom co-authors.
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Paper IIILavail, A., Kochukhov, O., and Wade, G.A. (2018)A sudden change of the global magnetic field of the active M dwarf AD Leorevealed by full Stokes spectropolarimetric observationsMonthly Notices of the Royal Astronomical Society, 479, 4836
I led the writing of the observing proposal and defined the scope of project incollaboration with the co-authors. I performed the analysis of the data (least-squares deconvolution, estimation of the mean longitudinal magnetic field, andZeeman Doppler imaging) using codes developed by Oleg Kochukhov. I ledthe writing of the paper with input from co-authors.
Paper IVLavail, A., Kochukhov, K., Hussain, G.A.J., Argiroffi, C., Alecian, E., Morin,J., and the BinaMIcS collaboration (2020)The large-scale magnetic field of the eccentric pre-main-sequence binary sys-tem V1878 OriSubmitted to Monthly Notices of the Royal Astronomical Society
The co-authors (PI Evelyne Alecian) acquired the data. I performed the anal-ysis (least-squares deconvolution, spectrum disentangling, refinement of theorbital solution, spectrum synthesis, Zeeman Doppler imaging) using codesdeveloped by Oleg Kochukhov and collaborators. The X-ray analysis was per-formed by Costanza Argiroffi, who also wrote the corresponding section ofthe paper. I led the writing of the rest of the paper with input from co-authors.
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7. Summary in other languages
7.1 Svensk sammanfattningMagnetfält spelar en viktig roll under stjärnors livstid. De påverkar många pro-cesser, speciellt när stjärnorna är unga. Magnetfält kan t.ex bromsa stjärnorsrotation, påverka tillflödet av material från omgivningen och driva stjärnvindaroch utflöden. Om vi vill förstå hur stjärnor utvecklas måste vi därför förstå hurderas magnetfält fungerar.
Det finns indirekta sätt att påvisa magnetfält, men det bästa tillvägagångssät-tet är naturligtvis direkta observationer. Magnetfält är “osynliga” men de läm-nar ett avtryck i det ljus som stjärnan avger genom hur de påverkar atomeroch joner i stjärnans atmosfär, genom den så kallade Zeemaneffekten. Mag-netfältets inverkan på atomerna leder till att spektrallinjerna breddas i ob-serverade stjärnspektra, särskilt vid infraröda våglängder. Vi kan modelleraZeemanbreddningen och från detta uppskatta den genomsnittliga magnetfält-styrkan över stjärnans yta. Utöver breddning så ger delar magnetfältet ävenupp spektrallinjerna i polariserade komponenter (linjärt, cirkulärt polariseratljus), och utvecklingen av dessa kan modelleras under en stjärnas rotationför att kartlägga magnetfältets geometriska beteende över ytan. Denna metodkallas “Zeeman Doppler Imaging” (ZDI) och används för att kartlägga detstorskaliga magnetfältet (eftersom effekter av småskaliga fält tenderar att taut varandra i polarisationssignalerna). Zeemanbreddning inkluderar däremotockså det småskaliga fältet, vilket vanligtvis har den högsta fältstyrkan i svalastjärnor.
Vi modellerade Zeemanbreddningen i spektrallinjer av 14 T Tauri-stjärnormed låga till mellanhöga massor för att se hur magnetiska fältet utvecklasmed massan. Vi upptäckte att T Tauri-stjärnor med mellanhöga massor somobserverades inte har särskilt starka magnetfält (svagare än 2-3 kG). Å andrasidan kan T Tauri-stjärnor med låga massor ha både svaga och starka fält (upptill mer än 4 kG), och magnetfältets styrka verkar inte vara en enkel funktion avstjärnornas egenskaper. Vi visade också att det genomsnittliga magnetfältet fördessa stjärnor inte varierar väsentligt under de få upprepade observationernasom vi gjorde för varje stjärna. Detta antyder att fältet är ganska väl förde-lat över stjärnornas yta. Slutligen kan vi också visa att fältstyrkor beskrivnaav ZDI är låga jämfört med det totala magnetfältet som mäts med Zeeman-breddning (2-42 procent). Denna skillnad beror på fältets komplexitet.
Vi observerade också den välstuderade, aktiva M-dvärgen AD Leo. Vigjorde spektropolarimetriska observationer av stjärnan i både cirkulär och lin-jär polarisering, och gjorde den första detektionen av linjär polarisering i spek-trallinjer av en M-dvärg. Vi upptäckte också att de cirkulärt polariserade
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spektra, som vid tidigare observationer mellan 2006 till 2012 varit statiska,förändrades i våra observationer från 2016 Vi gjorde ZDI-modellering av ob-servationerna av de cirkulärt polariserade spektra för att kartlägga stjärnfältetsmagnetfält och förstå vilken förändring i magnetfält som ledde till förändrin-gen i data. Fältets geometri hade inte förändrats mycket, utan var fortfarandei princip en dipol. Vi fann dock att fältet hade koncentrerats till en mindredel av ytan. Denna ganska snabba förändring kan inte förklaras av nuvarandeteoretiska modeller för magnetfält i stjärnor.
Slutligen observerade vi det spektroskopiskt binära stjärnsystemet V1878Ori. Båda stjärnorna i detta system är T Tauri-stjärnor med mellanhöga mas-sor och liknande egenskaper. Vi fick en tidsserie av cirkulärt polariseradeobservationer av detta system, och detekterade cirkulära polarisationssignaleri båda stjärnorna i samtliga observationer. Med hjälp av vår spektrumavskiljn-ingskod kunde vi mäta radialhastigheterna för de två stjärnorna och förbättraomloppsparametrarna. Spektrum för de individuella stjärnorna kunde såledesextraheras och användas för att bestämma stjärnparametrarna för både denprimära och den sekundära stjärnan. Slutligen applicerade vi ZDI först på in-tensiteten, och sedan de cirkulärt polariserade data för att kartlägga ljusstyrkanoch magnetfältet på ytan av varje stjärna. Trots att stjärnorna är väldigt lika, såtyder våra observationer på att de har helt olika magnetfält. Den primära stjär-nan i systemet har etthuvudsakligen poloidalt och icke-axymmetriskt fält. Fäl-tet i sekundärstjärnan är huvudsakligen toroidalt och axymmetriskt. Styrkanav magnetfältet i den primära stjärnan är ungefär hälften så starkt som det iden sekundära stjärnan,
Under de kommande åren kommer ny instrumentering att göra det möjligtatt förbättra studier av svala stjärnors magnetfält ytterligare. Högupplöstaspektropolarimetrar som mäter vid när-infraröda våglängder, t.ex. CRIRES+och SPIRou, kommer att möjliggöra observationer av ljussvagare och yngrestjärnor, samt göra det möjligt att tillämpa både Zeemanbreddnings- och ZDI-metoder samtidigt på samma data.
7.2 Résumé en françaisLes champs magnétiques jouent un rôle essentiel pendant toute la vie d’uneétoile. Ils influencent beaucoup de processus physiques, particulièrement quandles étoiles sont jeunes. Les champs magnétiques peuvent, par exemple, freinerla rotation des étoiles, influencer la manière dont les étoiles accrètent de lamatière, voire même générer des vents ainsi que des éruptions stellaires. Enrésumé, pour comprendre l’évolution des étoiles, il faut connaitre leur champmagnétique.
Plusieurs méthodes permettent d’étudier indirectement les champs magné-tiques stellaires. Néanmoins, les observations directes fournissent les meilleursrésultats. Les champs magnétiques sont en eux-mêmes invisibles. Cepen-
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dant, ils laissent une empreinte visible dans la lumière nous provenant desétoiles. C’est ce que l’on appelle l’effet Zeeman. Cet effet produit un élargisse-ment des raies spectrales (l’élargissement Zeeman), particulièrement dans lalumière proche infrarouge. En modélisant cet élargissement, il est possibled’estimer l’intensité du champ magnétique moyenné sur la surface stellaire.De plus, le champ magnétique induit aussi la polarisation des raies spectrales.En modélisant l’évolution de la polarisation des raies spectrales au cours dela rotation de l’étoile, nous pouvons cartographier son champ magnétique.Cette méthode, appelée imagerie Zeeman Doppler (« Zeeman Doppler imag-ing », ou ZDI en anglais) cartographie les grandes échelles spatiales du champmagnétique, car les signaux provenant de petites structures sur la surface onttendance à s’annuler. A contrario, l’élargissement des raies Zeeman mesurel’intégralité de l’intensité du champ magnétique, qui provient majoritairementdes structures à petite échelle pour les étoiles froides. C’est pour cela que lesdeux méthodes sont complémentaires.
Dans cette thèse, nous avons d’abord modélisé l’élargissement Zeemandes raies spectrales pour 14 étoiles T Tauri (jeunes étoiles) peu massives etde masse intermédiaire. Nous avons découvert que les étoiles T Tauri demasse intermédiaire de notre échantillon ont un champ magnétique relative-ment faible (c’est-à-dire d’une intensité moyenne inférieure à 2-3 kG). Enrevanche, l’intensité du champ magnétique des étoiles T Tauri de faible massevarie beaucoup entre les étoiles et peut atteindre jusqu’à 4,4 kG dans notreéchantillon. De plus, elle n’est pas corrélée avec les paramètres stellaires.Nous avons aussi observé que l’intensité du champ magnétique ne variait pasde manière significative d’une nuit à l’autre, suggérant que le champ magné-tique est réparti plutôt uniformément sur la surface stellaire. Finalement, nousavons montré que la méthode d’imagerie Zeeman Doppler ne mesure qu’unefraction (entre 2 et 42 % pour notre échantillon) du champ magnétique total etque cette fraction dépend de la complexité du champ magnétique.
Nous avons aussi observé l’étoile AD Leo, une naine M dont le champ mag-nétique a déjà été étudié en détail, en spectropolarimétrie circulaire et linéaire.Pour le première fois, nous avons détecté des signaux de polarisation linéairedans les raies spectrales d’une étoile naine M. Nous avons aussi découvert queles signaux en polarisation circulaire, qui étaient constants dans toutes les ob-servations précédentes entre 2006 et 2012, avaient soudainement changé lorsde nos observations de 2016. Nous avons cartographié le champ magnétiquede l’étoile à l’aide de l’imagerie Zeeman Doppler afin d’interpréter ce change-ment dans les observations. Alors que la géométrie du champ magnétique n’apas changé de manière significative, nous avons trouvé que le champ s’est con-centré sur des zones plus petites à la surface de l’étoile. Cette transformationassez soudaine n’est pas expliquée par les modèles de champs magnétiquesstellaires.
Finalement, nous avons aussi étudié l’étoile binaire V1878 Ori. Les deuxétoiles du système sont des étoiles T Tauri de masse intermédiaire avec des
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caractéristiques similaires. Nous avons obtenu une série d’observations spec-tropolarimétriques de ce système en polarisation circulaire, et nous avonsclairement détecté un signal provenant des deux étoiles pour toutes les ob-servations. À l’aide de notre code de « démêlage » de spectres, nous avonspu mesurer les vitesses radiales des deux étoiles afin d’affiner les paramètresorbitaux du système binaire. Nous avons ainsi pu démêler les spectres et ex-traire un spectre individuel pour chacune des deux étoiles, que nous avonsutilisé pour déterminer leurs paramètres stellaires. Enfin, nous avons utilisél’imagerie Zeeman Doppler pour cartographier la distribution de luminosité etle champ magnétique à la surface des deux étoiles. De manière surprenante,nous avons découvert que leur champ magnétique est radicalement différent.Le champ magnétique de l’étoile primaire est majoritairement poloïdal et non-axisymétrique alors que le champ de l’étoile secondaire est majoritairementtoroïdal et axisymétrique. L’intensité du champ magnétique de l’étoile pri-maire est aussi environ deux fois faible que celle de la secondaire.
Le futur s’annonce prometteur : de nouveaux instruments vont nous permet-tre d’améliorer notre compréhension des champs magnétiques stellaires. Desspectropolarimètres infrarouges à haute résolution installés sur des grands téle-scopes comme SPIRou au Canada-France-Hawaii Telescope ou CRIRES+ auVery Large Telescope vont rendre possible l’observation d’étoiles moins bril-lantes et plus jeunes. En outre, ils vont permettre d’utiliser à la fois la méthoded’élargissement Zeeman et l’imagerie Zeeman Doppler sur les mêmes jeux dedonnées.
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8. Acknowledgements
If you are reading this thesis today, it is thanks to a long list of people.First, I would like to thank my supervisors: Oleg Kochukhov, Nikolai
Piskunov, and Gaitee Hussain. You have all been fantastic, always presentto help and offer guidance, advice, and amazing expertise, no matter how busyyou were. Oleg, I cannot count how many times I came to you completelyconfused, and left enlightened. I count myself extremely lucky to have hadyou as my supervisor, and I am very grateful. Nik, I learned so much withyou, both through the many science discussions but of course also through allthe stories, anecdotes, and the emergency trips to Garching. Thanks for every-thing ! Gaitee, it has been a great time working with you at ESO. I’m gratefulthat you gave me these opportunities to come to Garching and work together.We’ve had many great discussions throughout this PhD, in person or remotely,and you’ve always contributed with many great ideas. Thank you so much.
I would like to thank all the colleagues in the astronomy division in Uppsalaas well. On top of the good atmosphere, there were countless nice and mem-orable fikas, lunch break discussions, astropubs, wine tastings, beer brewing,pub quizzes, movie watching, boat building, and even surströmming eating. Iam also very grateful to the work-saving colleagues from IT and administra-tion, it was great working and sharing a corridor with you all.
I’d particularly like to give a big thanks to the PhD student and post-docgroup with whom I spent a lot of great times these past years. I feel we’vebuilt up a nice group together with a positive and supportive atmosphere, andthis is amazing. Very very special thanks to: Christian for being the best andmost supportive office mate (no competition possible), James (I can’t give youjustice in a sentence, you are all round amazing; witty, steam-trainy, funny,and kind); Jon (Paddus blesses you), Lisa (for the fully-Stoked humour andkindness), Luka (always bringing the positive vibrations - no quantum joke),Samuel (untiring organizer of social events), Sara L. (for the great trips andeventful hikes together in various places), Sofie (grand beer and meme master),and Thomas M. (for the great brewing times and all the nice chats in general).
I also had the chance to meet many kind and inspiring astronomers in con-ferences, workshops, visits, and online: thanks to you all. Merci StéphaneUdry and Julien Morin for hosting me in beautiful Genève and Montpellierfor a little while.
To the Flogsta/Stenhagen/CEMUS/SRC sustainable hippies (particularlyAntonin, Guy, Mel, Pauline, and Sanna): a billion thanks for being awesome,and for the struggle to make Uppsala and its university a bit more sustainable!
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To the Allis climbing crew: our sessions have been (and will hopefully stay)amazing times.
Forgetting the great team in Garching would be criminal: thank you Adrien(orange boi), Anna, Annagrazia, amazing Annalisa, Anne-Laure, Angela, Be-linda, Bitten, Carlo, Darshan, Emin (mountain-goat), Giannina, Johanna, Julián,Sandra, Suhail, pizza-master Taïssir, and Tyler; for the always-disastrous hikes,beers, bretzels, pizze, astrokinos, and whatnot. Thanks to you all, my stay inBavaria has been amazing. I’d like to thank the CRIRES+ colleagues too, notonly in Garching but also in Firenze, Göttingen (oh Göttingen, thanks Ulf forall the great chats and discussions), and Tautenburg.
J’aimerai finalement remercier du fond du coeur toute la famille (Lavail &Dauriach), mi hermanita, et mes parents. Si j’écris cette thèse aujourd’hui:c’est bien grâce à vous ! À tou-te-s les potes – du Sud et d’ailleurs – vous êtesles meilleur-es. La distance nous sépare, mais c’est toujours un tel plaisir dese retrouver. Et enfin à Alice: merci infiniment pour ton soutien, ta présence,et ton aide, sans toi je n’y serai jamais arrivé. Merci d’être toi, et pour toutesces aventures ensemble. Je t’aime.
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Acta Universitatis UpsaliensisDigital Comprehensive Summaries of Uppsala Dissertationsfrom the Faculty of Science and Technology 1927
Editor: The Dean of the Faculty of Science and Technology
A doctoral dissertation from the Faculty of Science andTechnology, Uppsala University, is usually a summary of anumber of papers. A few copies of the complete dissertationare kept at major Swedish research libraries, while thesummary alone is distributed internationally throughthe series Digital Comprehensive Summaries of UppsalaDissertations from the Faculty of Science and Technology.(Prior to January, 2005, the series was published under thetitle “Comprehensive Summaries of Uppsala Dissertationsfrom the Faculty of Science and Technology”.)
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