Exploring the magnetic topologies of cool stars
J. Morin, J.-F. Donati, P. Petit, L. Albert, M. Auriere, R. Cabanac, C. Catala, X. Delfosse, B. Dintrans, R. Fares, T. Forveille, T. Gastine, M. Jardine, R. Konstantinova-Antova, J. Lanoux, F. Lignieres, A. Morgenthaler, F. Paletou, J.C. Ramirez Velez, S.K. Solanki, S. Theado, V. Van Grootel
aa r X i v : . [ a s t r o - ph . S R ] S e p Physics of Sun and Star SpotsProceedings IAU Symposium No. 273, 2011D.P. Choudhary & K.G. Strassmeier, eds. c (cid:13) Exploring the magnetic topologiesof cool stars
J. Morin , , J.-F. Donati , P. Petit , L. Albert , M. Auri`ere ,R. Cabanac , C. Catala , X. Delfosse , B. Dintrans , R. Fares ,T. Forveille , T. Gastine , M. Jardine , R. Konstantinova-Antova ,J. Lanoux , F. Ligni`eres , A. Morgenthaler , F. Paletou ,J.C. Ramirez Velez , S.K. Solanki , S. Th´eado , V. Van Grootel Dublin Institute for Advanced Studies, 31 Fitzwilliam Place, Dublin 2, Irelandemail: [email protected] LATT, Universit´e de Toulouse, CNRS, 14 Av. E. Belin, 31400 Toulouse, France CFHT, 65-1238 Mamalahoa Hwy, Kamuela HI 96743, USA LESIA, Observatoire de Paris-Meudon, 92195 Meudon, France LAOG, UMR5571 CNRS, Universit´e Joseph Fourier, BP 53, 38041 Grenoble, France Institute of Astronomy, Bulgarian Academy of Sciences, 72 Tsarigradsko shose, Sofia, Bulgaria School of Physics and Astronomy, University of St Andrews, St Andrews, Scotland KY16 9SS Centre d’Etude Spatiale des Rayonnements, Universit´e de Toulouse, CNRS, France Max-Planck Institut f¨ur Sonnensystemforschung, Katlenburg-Lindau, Germany
Abstract.
Magnetic fields of cool stars can be directly investigated through the study of theZeeman effect on photospheric spectral lines using several approaches. With spectroscopic mea-surement in unpolarised light, the total magnetic flux averaged over the stellar disc can bederived but very little information on the field geometry is available. Spectropolarimetry pro-vides a complementary information on the large-scale magnetic topology. With Zeeman-DopplerImaging (ZDI), this information can be retrieved to produce a map of the vector magnetic fieldat the surface of the star, and in particular to assess the relative importance of the poloidal andtoroidal components as well as the degree of axisymmetry of the field distribution.The development of high-performance spectropolarimeters associated with multi-lines tech-niques and ZDI allows us to explore magnetic topologies throughout the Hertzsprung-Russeldiagram, on stars spanning a wide range of mass, age and rotation period. These observationsbring novel constraints on magnetic field generation by dynamo effect in cool stars. In particu-lar, the study of solar twins brings new insight on the impact of rotation on the solar dynamo,whereas the detection of strong and stable dipolar magnetic fields on fully convective starsquestions the precise role of the tachocline in this process.
Keywords. stars: low-mass, brown dwarfs, stars: magnetic fields, stars: activity, stars: rotation,techniques: spectroscopic, techniques: polarimetric
1. Context: stellar dynamos
Magnetic field is a key parameter to understand stellar formation and evolution. Incool stars, it powers activity phenomena that are observed across a large part of theelectromagnetic spectrum and a wide range of timescales. Since the early XX th century,the cyclic solar magnetic field has been thought to be constantly regenerated againstohmic dissipation by a magnetohydrodynamical process: the dynamo. Although the so-lar dynamo is still far from being fully understood, the basic concepts, as exposed byParker (1955) in his α Ω dynamo model are rather simple: (i) an initially poloidal mag-1 J. Morin, J.-F. Donati, P. Petit et al.netic field is converted into a stronger toroidal one by differential rotation, (ii) a poloidalfield component is regenerated from the toroidal field by a second mechanism, such asthe α effect. Two decades ago, helioseismology revealed the existence of the tachocline(e.g., Spiegel & Zahn 1992), a thin layer of strong shear located at the interface betweenthe inner radiative zone and the convective envelope. Since then, many theoretical andnumerical studies have stressed the crucial role of the tachocline in the solar dynamo,being the place where large-scale toroidal fields can be stored and strongly amplified(e.g., Charbonneau & MacGregor 1997).Partly convective cool stars possess an internal structure similar to that of the Sun,i.e. an inner radiative zone and an outer convective envelope supposedly separated bya tachocline. Hence, it is generally assumed that their magnetic fields — as revealedby activity or direct measurements — are generated by a solar-like dynamo. However,some cool partly-convective stars strongly differ from the Sun, either in depth of theirconvective zone or rotation rate, and the impact of these differences on their dynamo ismostly unknown. On the other hand, main sequence stars less massive than ∼ .
35 M ⊙ ( ∼ M3) are fully convective (e.g., Chabrier & Baraffe 1997) and therefore do not possessa tachocline. If the tachocline is indeed an essential part of the solar dynamo, magneticfield generation in these fully convective objects must rely on different physical processes.
2. Magnetic field measurement and modelling
Direct measurements of stellar magnetic fields rely on the properties of the Zeemaneffect. Two complementary methods are successfully applied to cool stars. By measuringZeeman broadening of photospheric spectral lines it is possible to assess the magneticflux averaged over the visible stellar disc (e.g., Saar 1988). This method is thereforeable to probe magnetic fields regardless of their complexity but provides virtually noinformation about the field geometry. On its part, the analysis of Zeeman polarisationin spectral lines provides information on the vector properties (i.e. strength, orientationand polarity). However, as neighboring magnetic regions of opposite polarities resultin polarised signatures of opposite sign that cancel each other when integrating overthe stellar disc, spectropolarimetry can only detect the large-scale component of stellarmagnetic fields.Polarized signatures in spectral lines of cools active stars have a small amplitude,making their measurement a hard task. Two advances have brought a large number of coolstars within reach of spectropolarimetric measurements. First, multi-line techniques (suchas LSD, Donati et al. 1997) extract the polarimetric information from a large numberof photospheric lines resulting in a S/N multiplex gain that can reach as high as severaltens when thousands of lines are used. Secondly, the new generation spectropolarimetersESPaDOnS and NARVAL (see Donati 2003) feature a high overall efficiency and coverthe full optical domain allowing to take full advantage of multi-line techniques.Thanks to ( i ) the sensitivity of the Zeeman effect to field lines orientation ( ii ) rotationalmodulation and ( iii ) Doppler effect, the temporal evolution of polarised signatures instellar lines strongly characterizes the parent magnetic topology. Thus, from a time-series of circularly polarised spectra sampling the stellar rotation cycle, Zeeman-DopplerImaging can perform a maximum entropy reconstruction of the vector magnetic fielddistribution at the surface of the star (Semel 1989, Donati & Brown 1997). Although theresulting magnetic map has a better resolution for high v sin i values, this technique isalso successfully applied to slow rotators (e.g., Morin et al. 2008b). For high S/N dataspanning several stellar rotations, differential rotation can also be constrained (e.g., Petitet al. 2002). agnetic topologies of cool stars Figure 1.
Rotational dependence of the mean reconstructed magnetic flux (green line), and ofthe fraction of magnetic energy stored in the poloidal field component (red line).
3. Solar twins
We selected a sample of 4 nearby dwarfs with stellar parameters as close as possibleto the solar ones, except for the rotation period (see Petit et al. 2008). In particular,their internal structure is expected to be very similar to the Sun’s. We aim at studyingthe effect of rotation alone on the solar dynamo. For each star, a set of ∼
10 pairs ofunpolarised and circularly polarised spectra was collected with NARVAL, from which wecan map the surface magnetic field and to precisely determine the rotation period.The first conclusion of this study is that the shorter the rotation period, the stronger isthe large-scale magnetic field (see Fig. 1, green line). For the 2 slow rotators ( P rot =22.7and 20.5 d), the magnetic maps reconstructed by ZDI are dominated by low order mul-tipole modes, this is reminiscent of the solar global magnetic field. The fast rotators( P rot =12.3 and 8.8 d) mainly feature a strong belt of toroidal field roughly encirclingthe pole, similar to the magnetic topologies of very active cool stars (e.g., Donati et al.2003). The transition from an almost purely poloidal magnetic field to a strongly toroidalone, is apparently due to rotation, with a P rot threshold located between 12 and 20 d(see Fig. 1). These observations are in agreement with recent MHD simulations of solar-type stars where dynamo action produces mostly toroidal magnetic topologies, featuringstrong belts throughout the bulk of the convective envelope for Ω = 3 Ω ⊙ (Brown et al.2010, although the simulation domain does not encompass the stellar surface).From our unpolarised spectra we measure the Ca ii activity, and find that the R ′ HK ( B mean )relation follows a power-law with an exponent of 0.32. This is significantly different fromthe solar relation (established from observations of the quiet Sun and active regions)which has an exponent of 0.6 (e.g., Schrijver et al. 1989). As the chromospheric flux isalso sensitive to spatial scales smaller than those contributing to the polarimetric signal,this apparent discrepancy suggests that a larger fraction of the total magnetic energylies in the large-scale component as rotation increases.The stars we have observed are expected to exhibit magnetic cycles and associatedevolution of their topology. Chromospheric activity monitoring exists for two stars of our J. Morin, J.-F. Donati, P. Petit et al.sample (e.g., Hall et al. 2007), showing in particular that our slowest rotator ( P rot =22.7 d)undergoes an activity cycle of 7 yr, and that we observed it in a high activity state. Thepredominantly quadrupolar magnetic topology we reconstruct is indeed reminiscent ofthe Sun’s topology close to solar maximum (Sanderson et al. 2003). On the fastest rotator( P rot =8.8 d) we observe strong year-to-year evolution: between 2007 and 2008 the polarityof the main ring of azimuthal field had its polarity reversed, and between 2008 and 2009the fraction of magnetic energy stored in poloidal field dramatically increased (see Petitet al. 2009). These rapid changes suggest a short cycle, and therefore a correlation: fasterrotation would imply shorter activity cycles. Spectropolarimetric observations of therapid rotator τ Boo ( P rot =3.3 d) by Fares et al. (2009) have also revealed two polarityreversals of the poloidal field component in two years, although in this case the higherstellar mass ( M ⋆ =1.3 M ⊙ ) and the close-in orbiting giant planet may also play a role.
4. Fully convective stars
Following the first detection in polarised light of a large-scale magnetic field on a fullyconvective star by Donati et al. (2006), we have carried out the first spectropolarimetricsurvey of a sample M dwarfs lying on both sides of the fully convective boundary (0 . 75 M ⊙ ) and spanning a wide range of periods (0 . < P rot < . a ) M dwarfs more massive than ∼ . ⊙ (partly convective) exhibit magnetic topolo-gies with a strong toroidal component, even dominant in some cases; the poloidal com-ponent is strongly non-axisymmetric. For most of these stars, we can measure surfacedifferential rotation, values are between 60 and 120 mrad d − (i.e. between once andtwice the solar rate approximately), and the topologies evolve beyond recognition on atimescale of a few months. These properties are reminiscent of the observations of moremassive (G and K) active stars (e.g., Donati et al. 2003).( b ) Stars with masses between ∼ ⊙ (close the fully convective limit) hostmuch stronger large-scale magnetic field with radically different topologies: almost purelypoloidal, generally nearly axisymmetric, always close to a dipole more or less tilted withrespect to the rotation axis. These topologies are observed to be stable on timescales ofseveral years, and differential rotation (when measurable) is of the order or a tenth ofthe solar rate. Our findings are in partial agreement with the recent numerical study byBrowning (2008). Similarly, we observe that fully convective stars can generate strong andlong-lived large-scale magnetic fields featuring a strong axisymmetric component, thatare able to quench differential rotation. But we observe almost purely poloidal surfacemagnetic fields, whereas in the simulation the axisymmetric component of the field ismainly toroidal (although the simulation does not encompass the stellar surface).( c ) Below ∼ ⊙ , we observe 2 different categories of magnetic fields: either a verystrong dipole (similar to group b above) or a much weaker field generally featuring a sig-nificant non-axisymmetric component, and in some cases a toroidal one. Strong temporal agnetic topologies of cool stars Figure 2. Properties of the magnetic topologies of our sample of M dwarfs (plus GJ 490 B,Phan-Bao et al. 2009) as a function of rotation period and mass. Larger symbols indicate strongerfields, symbol shapes depict the degree of axisymmetry of the reconstructed magnetic field (fromdecagons for purely axisymmetric to sharp stars for purely non axisymmetric), and colours thefield configuration (from blue for purely toroidal to red for purely poloidal). Solid lines representcontours of constant Rossby number Ro = 0 . . 01. The theoreticalfull-convection limit ( M ⋆ ∼ . 35 M ⊙ ) is plotted as a horizontal dashed line, and the approximatelimits of the three stellar groups discussed in the text are represented as horizontal solid lines. variability is also observed on some objects of this second category. However stars in bothcategories have similar stellar parameters and cannot be separated in the mass-rotationdiagram. This unexpected observation is not yet understood, and may be explained inseveral different ways: for instance, another parameter than mass and rotation period(such as age) may be relevant, two dynamo modes may be possible or stars may switchbetween two states in this mass range, etc. J. Morin, J.-F. Donati, P. Petit et al. 5. Conclusions and future work Taking advantage of recent developments in spectropolarimetric instrumentation andanalysis techniques, it is nowadays possible to study dynamo action across the wholecool stars regime. We focus here on two projects: solar twins and fully convective Mdwarfs. Both studies have already provided dynamo theorists with novel observationalconstraints, and have also raised new questions on the impact of magnetic fields and theirtopology on e.g., stellar spindown, structure, and chromospheric and coronal activity.Our understanding of stellar dynamos also benefits from spectropolarimetric studiestargeting other objects than cool main sequence stars. 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