Surface magnetism of cool stars
O. Kochukhov, P. Petit, K.G. Strassmeier, T.A. Carroll, R. Fares, C.P. Folsom, S.V. Jeffers, H. Korhonen, J.D. Monnier, J. Morin, L. Rosen, R.M. Roettenbacher, D. Shulyak
AAstronomische Nachrichten, 13 December 2016
Surface magnetism of cool stars
O. Kochukhov ,(cid:63) P. Petit , , K. G. Strassmeier , T. A. Carroll , R. Fares , C. P. Folsom , , S. V. Je ff ers ,H. Korhonen , J. D. Monnier J. Morin , L. Ros´en , R. M. Roettenbacher , , and D. Shulyak Department of Physics and Astronomy, Uppsala University, SE 75120 Uppsala, Sweden Universit´e de Toulouse, UPS-OMP, IRAP, F-31400 Toulouse, France CNRS, Institut de Recherche en Astrophysique et Plan´etologie, 14 Avenue Edouard Belin, F-31400 Toulouse, France Leibniz Institute for Astrophysics Potsdam (AIP), An der Sternwarte 16, 14482 Potsdam, Germany INAF, Osservatorio Astrofisico di Catania, Via Santa Sofia, 78, I-95123 Catania, Italy Institut f¨ur Astrophysik, Georg-August-Universit¨at G¨ottingen, Friedrich-Hund Platz, D-37077 G¨ottingen, Germany Niels Bohr Institute, University of Copenhagen, Juliane Maries vej 30, DK-2100 Copenhagen, Denmark Department of Astronomy, University of Michigan, Ann Arbor, Michigan 48109, USA LUPM, Universit´e de Montpellier, CNRS, Place Eug`ene Bataillon, F-34095 Montpellier, France Department of Astronomy, Stockholm University, SE-106 91 Stockholm, SwedenReceived XXXX, accepted XXXXPublished online XXXX
Key words stars: activity – stars: late-type – stars: low-mass – stars: magnetic field – starspotsMagnetic fields are essential ingredients of many physical processes in the interiors and envelopes of cool stars. Yet theirdirect detection and characterisation is notoriously di ffi cult, requiring high-quality observations and advanced analysistechniques. Significant progress has been recently achieved by several types of direct magnetic field studies on the surfacesof cool active stars. In particular, complementary techniques of the field topology mapping with polarisation data andtotal magnetic flux measurements from intensity spectra have been systematically applied to di ff erent classes of activestars leading to interesting and occasionally controversial results. In this paper we summarise the current status of directmagnetic field studies of cool stars, and investigations of surface inhomogeneities caused by the field, based on the materialpresented at the Cool Stars 19 splinter session. Copyright line will be provided by the publisher
Magnetism is an important, yet incompletely characterizedand poorly understood, ingredient of stellar physics. Mag-netic fields are playing a key role in stellar evolution, in-cluding accretion processes in young stars, angular momen-tum loss, internal mixing. The fields of cool stars governdynamic, energetic phenomena on stellar surfaces and sig-nificantly influence the stellar environments, including plan-etary systems. Understanding, for example, the cyclic be-havior of cool star magnetic fields is critical for assessingpossible impact of the solar variability on the terrestrial cli-mate and exoplanet habitability.An analysis of the Zeeman e ff ect in spectral lines is theonly source of direct information about the strengths andtopologies of stellar magnetic fields. During recent yearssignificant progress has been made by magnetic broaden-ing and Zeeman-Doppler imaging (ZDI) studies of coolstars. On the one hand, more physically refined and nu-merically sophisticated analysis techniques were developed.The number of objects studied with these methods has in-creased significantly. This allowed establishing the presenceof magnetic fields in essentially all classes of cool stars and (cid:63) Corresponding author: [email protected] revealing unexpected trends with stellar parameters. More-over, long-term monitoring of a handful of sun-like starsyielded first direct observations of magnetic cycles. At thesame time, some puzzling discrepancies between results ofapplications of di ff erent diagnostic methods have been iden-tified, suggesting that certain aspects of modern observa-tions are not fully understood or even misinterpreted.The splinter session “Surface Magnetism of Cool Stars”at the Cool Stars 19 conference has provided a compre-hensive overview of recent results of the direct studies ofmagnetic fields in cool stars. A special emphasis was givento the discussion of reliability and consistency of di ff erentmagnetic indicators and to the comparison of the results ob-tained by di ff erent research groups. In this paper we sum-marise some of the new results presented at this session. Westart with a discussion of limitations of the widely used to-mographic field topology reconstruction method (Sect. 2).Two independent tests of magnetic inversions are presentedfor the simulated Sun-as-a-star spectropolarimetric observa-tions (Sect. 2.1 and 2.2), allowing a realistic assessment ofthe degree of field complexity that can be recovered frommodern observational data. We then present results of in-terferometric imaging of dark star spots on the surfaces ofcool active stars (Sect. 3) and summarise new findings of the Copyright line will be provided by the publisher a r X i v : . [ a s t r o - ph . S R ] D ec O. Kochukhov et al.: Surface magnetism of cool stars magnetic field studies of solar-type stars (Sect. 4), youngcool stars (Sect. 5), and low-mass stars (Sect. 6). The sum-mary and conclusions are given in Sect. 7.
Zeeman-Doppler Imaging (ZDI) is a powerful technique tomap stellar magnetic fields. It has provided (and continuesto provide) a wealth of information on stellar large-scalemagnetic surface field distributions in the last decades (see,for a review, Donati & Landstreet 2009; Fares 2014).Spectral lines, if formed in the presence of magneticfields, are polarised. Studying the polarisation of these linessheds light on the strength of the magnetic field. Zeeman-Doppler Imaging often uses a set of circular polarisationprofiles collected over one or several stellar rotations, andconverts these profiles into a magnetic map of the stellarphotosphere. This tomographic imaging procedure is ill-posed, a regularisation method, such as Maximum Entropy(Brown et al. 1991; Hussain et al. 2000), Tikhonov regular-isation (Piskunov & Kochukhov 2002) or an iterative reg-ularisation method like the Landweber iteration (Carroll etal. 2012), is needed to get a unique magnetic map. In coolstars, the signature of linear polarisation is very small andhardly detected, it is only very recently that detections oflinear polarisation were made (see Sect. 2.3). Thus, it isnot possible to use linear polarisation for every object, andthe mapping consists mainly of inverting circular polarisa-tion profiles. We note here that even for circular polarisationin cool stars, a multi-line technique (e.g. Least-Square De-convolution or LSD, Donati et al. 1997; Kochukhov et. al.2010 or multi-line SVD reconstruction, Carroll et al. 2012)should be used in order to detect a polarisation signature;the polarisation level in single lines is usually within theobservational noise.ZDI su ff ers from several intrinsic limitations. Small-scale fields on the stellar surface are not resolved, strongfields in dark spots are suppressed by their low surfacebrightness, signatures of small-scale features can cancel outin some field geometries. In polarised light these featuresare often missed, especially when using circular polarisa-tion only. The work presented here aims at testing the conse-quences of these limitations for reliability of reconstructedlarge-scale magnetic maps. / SDOmagnetograms
The Solar Dynamics Observatory (SDO, Pesnell et al. 2012)and the Helioseismic and Magnetic Imager (HMI, Schouet al. 2012) on its board observe the Sun with high ca-dence. They deliver high-resolution images in which thesmall-scale field is well resolved. Continuum images, mag-netograms and dopplergrams are publicly available. Using solar data to test ZDI allows us to assess the ef-fects of small-scale field and its evolution, dark spots, andfield geometries on the reconstructed map. Solar HMI / SDOdata contain the information we need, both spatial wise andtime wise. The Sun, however, is not the best candidate forZDI. It is a slow rotator, and it is seen nearly equator on.When a star is observed equator on, it is not possible toattribute a feature to the northern or southern hemisphere,which causes a mirroring e ff ect in the reconstructed map.To avoid this a ff ect, we choose an epoch with the highestinclination of the Sun’s rotation axis relative to the ecliptic.To perform ZDI, we developed a technique to producesynthetic intensity and circular polarisation profiles of theSun-as-a-star, similar to the profiles we collect using stel-lar spectropolarimeters. A solar intensity profile for one ro-tation phase is calculated based on the observed intensityand the Doppler maps, taking into account the brightness ofeach pixel and its velocity. In order to calculate the circu-lar polarisation profile, we use both the calculated intensityprofile and the observed magnetogram, and assume a weak-field approximation. To make the synthetic profiles as real-istic as possible, we added synthetic noise to the profiles,with signal-to-noise ratios similar to those obtained for so-lar like stars observed with the ESPaDOnS and NARVALspectropolarimeters (Marsden et al. 2014).We then calculated one intensity and circular polarisa-tion profile per day for the Sun over one solar Carrington ro-tation. We used these profiles as input data for our ZDI codeand reconstructed a large-scale magnetic map. The code weused is the ZDI code described in Donati et al. (2006); themagnetic field is represented using a spherical harmonicsexpansion and Maximum Entropy is used as a regularisa-tion method.In order to assess the reliability of the resulting mag-netic map, we compared it with the HMI synoptic map forthe same Carrington rotation. Synoptic maps are high reso-lution maps, i.e. having high orders of spherical harmonics.We thus filtered the high order spherical harmonics (small-scale field) from the synoptic map, and kept the low orderspherical harmonics (large-scale field) to compare to thelarge-scale ZDI magnetic map. The ZDI map shows simi-lar features as the filtered synoptic map. In particular, thenegative and positive field regions are reconstructed fairlywell (see Fig. 1).In order to asses quantitatively the similarities betweenthe maps, we calculated, for each bin of longitude, the meanmagnetic density by averaging the magnetic field for all lat-itudes. Our result shows similar magnetic density per longi-tude bin for the reconstructed map and the synoptic filteredmap, with a longitude lag of about 5 degrees.The results presented here show that the ZDI radialfield is fairly well reconstructed when comparing a ZDI re-constructed map to an observed synoptic map. Small-scalefield, adopted from the HMI / SDO data to calculate the cir-cular polarisation profiles fed into the ZDI inversion, doesnot seem to a ff ect the reconstructed large-scale magnetic Copyright line will be provided by the publisher sna header will be provided by the publisher 3
Fig. 1
Left: the reconstructed ZDI magnetic map of the Sun, right: the filtered HMI Synoptic map (down to the samespherical harmonics as the ZDI map). The maps show similar configurations (note a di ff erence in the colour scale betweenthe two maps). Fig. 4
Disk-integrated Stokes V profiles resulting fromthe original map (solid line) shown in Fig. 2, and from thelarge-scale, (cid:96) max = i ff ect of such evolutionon the reconstructed maps will also be addressed in a futurework. Slow rotating stars can be mapped with ZDI techniques aswell as moderate or rapidly rotating stars can. However,slow rotation limits the spatial resolution down to a degreethat we used to call the large-scale field. Although it seemsthat we all know what is meant when we ascribe a surfacefield to its large-scale component, it is not quite apparentwhat its physical realism is nor its relation to the underlyinggenerator (i.e. dynamo) of these fields.To get an idea about the relation between a detailedmagnetic surface distribution and its large-scale counter-part we utilised solar SOLIS / VSM synoptic vector magne-tograms of Carrington rotation (CR 2117) from Gosain et al.(2013), to obtain the radial, meridional, and azimuthal com-ponent of the vector magnetic field with a surface resolution
Fig. 5
Relative magnetic energy content (solid line) andlongitudinal magnetic flux (dashed line) over maximum de-gree ( (cid:96) max ). With increasing values of (cid:96) max the energy con-tent of the reconstructed maps slowly rises to the valueof the original map. The longitudinal magnetic flux onthe other hand, which is responsible for the appearance ofthe disk-integrated Stokes V signal, increases much morerapidly to the value of the original map.of 1 ◦ by 1 ◦ , see Fig. 2. This high-resolution magnetogram isthen implemented in the ZDI / DI code iMap (Carroll et al.2012) to compute the Sun-as-a-star Stokes profiles for vari-ous rotation phases.To obtain the so called large-scale field of the solar mag-netogram CR2117, we decomposed the synoptic map usinga spherical harmonic decomposition. We reconstructed theindividual field vector maps by restricting the reconstructionto an angular degree of (cid:96) ≤
5, see Fig. 3. We used this re-construction to calculate again the Sun-as-a-star Stokes pro-files with the forward module of the inversion code iMap .The two sets of Stokes I and V profiles calculated fromthe original high resolution map and from the low-order (orlarge-scale) reconstruction are almost identical for all rota-tion phases. Fig. 4 demonstrates this for one phase angle.In fact, a test ZDI inversion with these profiles – assumingsolar parameters – yields a ZDI map which has striking sim-ilarity with the low-order reconstruction, just like the one inFig. 1. The reason for the similarity between the Stokes V profiles of the original high-resolution map and its large-scale reconstruction can readily be understood by realising Copyright line will be provided by the publisher
O. Kochukhov et al.: Surface magnetism of cool stars
Fig. 2
Orthographic plot of the high resolution solar synoptic magnetogram (CR 2117). The distribution of the radialfield is shown for di ff erent rotation phases. The surface resolution is 1 ◦ by 1 ◦ . The field strength is saturated at 100 G.However, peak values reach up to 1300 G. Fig. 3
Orthographic plot of the reconstructed large-scale solar magnetogram (CR 2117). Again the distribution of theradial field is shown for di ff erent rotation phases. This map is computed by restricting the spherical harmonic reconstructionto (cid:96) ≤
5. The maximum field strength here is 6.8 G.that the longitudinal magnetic flux to the observer is almostthe same for both maps, and thus the disk-integrated Stokes V profiles are the same. One can see this from Fig. 5, wherein dashed lines the relative amount of longitudinal magneticflux generated by the reconstructed maps is shown, for in-creasing maximum spherical harmonic degree (cid:96) max of thereconstructed maps. The solid line represents the relativemagnetic energy content as a function of (cid:96) max . These twocurves highlight the odd relation between the detailed mag-netogram and its large-scale counterpart: while both gener-ate the same observable signature already for low (cid:96) max num-bers (see the steep increase of the dashed curve), they bothhave a vastly di ff erent energy content (slow rise of the solidcurve). For (cid:96) max = Magnetic fields strongly influence stellar and planetary evo-lution. It is therefore important to reconstruct the mag-netic fields as accurately as possible. The magnetic fields ofcool stars are, in general, complex, evolving and relativelyweak. Historical cool star magnetic field studies are madeby assuming a homogeneous surface temperature, (constantStokes I ), and by only using circular polarisation, (Stokes V ), since that is usually the only type of detectable polari-sation signal. However, ZDI studies have shown that usingonly Stokes V is not optimal (e.g. Donati & Brown 1997;Kochukhov & Piskunov 2002; Ros´en & Kochukhov 2012).If a cool spot coincides with a magnetic feature, whichis typical for sunspots, the spot geometry and positionsare poorly reconstructed and the magnetic field strength isseverely underestimated if only Stokes V is used to map themagnetic field (Ros´en & Kochukhov 2012). If temperatureinhomogeneities are ignored, the low amplitude of the po-larisation profiles, caused by a lower local intensity, can bemisinterpreted as a weak magnetic field. Indeed, it was alsoshown that the quality of the magnetic mapping is improvedif Stokes I is included in the reconstruction process in orderto simultaneously derive the temperature distribution (Car-roll et al. 2012; Ros´en & Kochukhov 2012). Copyright line will be provided by the publisher sna header will be provided by the publisher 5
Fig. 6
Results of the Stokes IV (upper row) and Stokes IQUV (lower row) ZDI inversions for the RS CVn star II Peg(Ros´en et al. 2015). The star is shown at four rotational phases, with the magnetic field lines rendered with the potentialfield extrapolation using the radial field map reconstructed from observations. The open and closed magnetic field linesare shown with di ff erent colour. The spherical map corresponds to the radial surface magnetic field distribution. Notice theincrease of small-scale fields in the IQUV reconstruction compared to the IV reconstruction.There are also other limitations to Stokes V and Stokes IV mapping. The same set of Stokes V profiles can corre-spond to di ff erent magnetic field configurations since Stokes V is not sensitive to the azimuth angle of the field. It canalso lead to crosstalk, especially between radial and merid-ional field components (Donati & Brown 1997; Kochukhov& Piskunov 2002; Ros´en & Kochukhov 2012). If Stokes QU parameters are included in the reconstruction, the fieldstrength is increased for all components, especially for themeridional component, and there is almost no crosstalk(Ros´en & Kochukhov 2012).However, linear polarisation has only been detected in afew cool stars (Kochukhov et al. 2011; Ros´en et al. 2013)and only for one cool star, II Peg, has the detected linearpolarisation signatures been su ffi cient for magnetic imag-ing. Two sets of observations were obtained for II Peg andthese were used to reconstruct the surface temperature andmagnetic field of a cool star using Stokes IQUV for the firsttime (Ros´en et al. 2015). To enable comparison with usualZDI studies, reference temperature and magnetic field mapswere also derived from the same sets of observations, butonly using Stokes IV .It is preferable to use individual lines instead of LSDprofiles when doing ZDI since many individual lines withwell known line parameters can be used. Clear distortionsdue to temperature inhomogeneities could be seen in indi-vidual lines in the Stokes I spectra but no clear polarisationsignatures were seen in the Stokes QU spectra of II Peg. Inorder to derive magnetic field maps, the LSD Stokes V QU profiles had to be used. The common methodology for ZDIusing LSD profiles is to apply the single-line approxima-tion, i.e. treat the LSD profile as a single spectral line withsome assigned mean line parameters (e.g. Marsden et al.2011; Kochukhov et al. 2013; Hussain et al. 2016). It hasbeen shown that this approach is appropriate for Stokes V ifthe magnetic field is weak, ≤ QU (Kochukhov et al. 2010). A new ZDI methodology de-scribed by Kochukhov et al. (2014) was therefore applied.A table of local synthetic LSD profiles corresponding todi ff erent magnetic field strengths, orientations, limb anglesand temperatures were pre-calculated with the full polarisedspectrum synthesis using the same line mask as was used toderive the LSD profiles of the observations. The observedLSD Stokes V QU profiles were then compared directly tothe synthetic LSD Stokes
V QU profiles meaning no as-sumptions about the behaviour of the LSD profiles had to bemade. The final temperature and magnetic field maps werederived by combining individual-line temperature mappingwith LSD profile magnetic field mapping.The results show discrepancies between the Stokes IV solution and the Stokes IQUV solution for both sets of ob-servations. The fit between the model profiles and observedprofiles was equally good for Stokes IV , independently ifStokes QU were also included in the inversion. However,the corresponding LSD Stokes QU model profiles from theStokes IV inversions do not at all agree with the observedLSD Stokes QU profiles. At the same time, the fit to theStokes QU profiles is good when Stokes QU are modelled. Copyright line will be provided by the publisher
O. Kochukhov et al.: Surface magnetism of cool stars
The di ff erence is also seen in the resulting magnetic fieldmaps of II Peg (see Fig. 6). The magnetic field is 2.1–3.5times stronger on average when Stokes QU are incorporatedin the inversion compared to using only Stokes IV . Since aspherical harmonic decomposition of the magnetic field isused, the complexity of the field can also be compared. Themagnetic energy contained in (cid:96) = − IV are used. Even if the total energy is largerin the Stokes IQUV case, the amount of energy in each (cid:96) islarger in the Stokes IV case for (cid:96) = − (cid:96) = − IQUV case is only 35% of the energy of the dipolecomponent in the corresponding Stokes IV inversion. Themagnetic energy seems to be systematically shifted towardhigher (cid:96) when all four Stokes parameters are used comparedto only Stokes IV . This implies that Stokes V can be fittedequally well by very di ff erent magnetic field configurations,and that Stokes V is not sensitive to complex, high- (cid:96) mag-netic field structures, in agreement with the discussion inSect. 2.2.The extended magnetic field topology of II Peg was alsoinvestigated using the potential source surface extrapolationmethod (Jardine et al. 2002). The results (see Fig. 6) showedthere were more open field lines in the Stokes IV magneticmap and that the magnetic energy at the source surface wasalso 2.5–5.3 times higher compared to the Stokes IQUV case. This implies that the magnetosphere of II Peg is morecompact in the Stokes
IQUV inversion. This finding has im-portant implications for the stellar wind models and angularmomentum loss.
For decades observations of spots on stars other than the Sunhave been obtained through indirect means, both by usingphotometry and from high-resolution spectra with Dopplerimaging techniques (see Strassmeier 2009 for a review).From the beginning of the starspot studies, it has been an as-piration for many to directly image starspots, and until veryrecently the Sun was the only star on which cool, dynamo-created starspots had been directly imaged.Unfortunately, stars appear spatially very small fromEarth and are only seen as point sources by our single-aperture telescopes. The largest stars with dynamo-createdcool spots have angular sizes of θ ∼ / near-infrared interferom-etry. Wittkowski et al. (2002) investigated the possibility ofusing VLTI for studying starspots. The first attempt usingAMBER at VLT was carried out by Korhonen et al. (2010). Fig. 7
Interferometric image of ζ And obtained with theSURFING code. Data were obtained in September 2013using the MIRC beam combiner at the CHARA Array.Adapted by permission from Macmillan Publishers Ltd: Na-ture. Roettenbacher et al. 2016, Nature, 533, 217, copyright2016.Unfortunately, the longest baseline (140m) and the short-est wavelength ( H -band) currently available at VLTI do notallow for resolving features on active stars.The breakthrough in directly imaging starspots is onlypossible with the Georgia State University’s Center forHigh-Angular Resolution Astronomy (CHARA) Array (tenBrummelaar et al. 2005) and the Michigan InfraRed Com-biner (MIRC, Monnier et al. 2004). The CHARA Array isan interferometric facility located on Mt. Wilson in Cali-fornia consisting of six 1-meter telescopes and has base-lines ranging from 30 to 330 meters. The CHARA Ar-ray can achieve angular resolutions between 0.2 mas ( V -band) and 0.7 mas ( K -band). MIRC is the only instrumentat the CHARA Array that can combine light from all thesix telescopes, allowing for robust interferometric imaging( H -band). MIRC has been very successful in studying dis-torted fast rotators (e.g., Monnier et al. 2007), interactingbinaries (Zhao et al. 2008), the mysterious eclipse of (cid:15) Au-rigae (Kloppenborg et al. 2010), and components of binarystars up to the flux ratio of 370 ±
40 (Roettenbacher et al.2015).The capabilities of MIRC and the CHARA Array haveinitiated the giant leap forward in directly imaging starspots.Recently, Roettenbacher et al. (2016) published two inter-ferometric images of the K-giant primary of a RS CVn bi-nary ζ Andromedae. With data from 2011 and 2013, bothimages were obtained from six-telescope CHARA / MIRCobservations spanning the star’s rotation period ( P rot = .
77 days). In order to perform image reconstruction onthis unique data set, the code SURFING (SURFace imag-ING; Monnier in prep.) was written. SURFING makes aglobal model of the star for an entire rotation – the almostnightly observations within one observing run are com-bined into one surface map, analogous to what is done inDoppler imaging. This results in increased surface resolu-tion of 0.025 mas per pixel.The interferometric images of ζ And show clear coolareas on the surface, as shown in Fig. 7. In both epochs,a prominent polar spot is present, as has also been ob-
Copyright line will be provided by the publisher sna header will be provided by the publisher 7 served in the previous Doppler images (e.g., Korhonen etal. 2010). Additionally, the maps show lower latitude fea-tures that are seen to change significantly between 2011 and2013. In 2011, the lower latitude cool regions are predom-inantly located on the Northern hemisphere, and in 2013,they are on the Southern hemisphere. This indicates inter-esting symmetry breaking in the North-South location of thespots on ζ And. Only very weak symmetry breaking is seenin the locations of sunspots (e.g., Hathaway 2015). Interest-ingly, there are indications that during the low solar activityperiod of 1660–1774, during the so-called Maunder mini-mum, the solar activity would have shown strong symmetrybreaking with spots only on the Southern hemisphere (Ribes& Nesme-Ribes 1993). Whether this could hint at interest-ing similarities between the dynamos operating during thegrand minima of solar activity and the very active stars like ζ And is an open topic. In any case, the observed symme-try breaking implies di ff erent dynamo operation in ζ Andthan in the Sun. However, more data are needed before wecan confirm that this symmetry breaking is a persistent phe-nomenon.The recent results clearly show that near-infrared inter-ferometry is a new, exciting tool for imaging and studyingstellar surface features. It provides the most reliable infor-mation on the exact hemisphere on which the spots reside,and can lead to further studies of stellar magnetic struc-tures that were not possible with the previously used in-direct methods. At present, interferometric imaging is re-stricted to only the brightest and closest stars due to lim-itations in angular resolution, but the method does not re-quire large projected surface rotations, like Doppler imag-ing does. This opens up new targets that have not been ap-proachable with Doppler imaging. With present technology,only a small number of spotted targets can be imaged withhigh enough resolution to reveal discrete spots; however, alarger sample imaged for surface asymmetries as opposedto details can be used to break the hemisphere degeneraciesof Doppler imaging results.
The long-term monitoring of magnetic activity, and in par-ticular the detection of magnetic cycles, in solar-type starsprovides an important insight into the mechanisms of dy-namo generation and magnetic field amplification. Mag-netic cycles in solar-type stars are most commonly investi-gated using proxies of magnetic activity such as the S-index(Ca II H&K) used in the Mount Wilson long-term monitor-ing of chromospheric activity (Wilson 1978; Duncan et al.1991; Baliunas et al. 1995). The results of this monitoringshow that solar-type stars exhibit di ff erent levels of activityvariation, irregular activity variations in fast rotating youngstars, cyclic activity in comparatively older slowly rotatingsolar-type stars and Maunder minimum-like flat activity.While the proxies of magnetic activity are reliable indi-cators of magnetic activity, they do not give an indication of Fig. 8
The temporal variation of (cid:15)
Eridani’s magneticfield topology as a function of its S-index cycle. The sym-bol shape indicates the axisymmetry of the field (non-axisymmetric by pointed star shape and axisymmetric bydecagon), the colour of the symbol indicates the proportionof poloidal (red) and toroidal (blue) components of the fieldand the symbol size indicates the magnetic field strength.
Fig. 9
Surface averaged magnetic field measurements ob-tained for (cid:15)
Eridani by Lehmann et al. (2015) from Zeemanbroadening of Stokes I spectra. The solid line indicates asine-fit using a period of ≈ (cid:15) Eridani ( v sin i = . − , pe-riod = = (cid:15) Eridani’s large-scale magnetic field geom-
Copyright line will be provided by the publisher
O. Kochukhov et al.: Surface magnetism of cool stars etry has been reconstructed in Je ff ers et al. (2014) over 6observational epochs (2007–2013).The results of this long-term monitoring are summarisedin Fig. 8 where the geometry of the large-scale mag-netic field is indicated by the symbol shape and size. For (cid:15) Eridani, the magnetic field geometry is quite variable ontimescales of less than a year. The geometry of the fieldvaries from poloidal to toroidal over similar timescales,though there is no evidence of any cyclic behaviour. In ad-dition to these results there are additional observations se-cured in 2014 (at activity minimum) and 2015 (on the ap-proach to activity maximum) and a further analysis of thesedata will show if there is any possible cyclic behaviour of (cid:15)
Eridani’s large-scale magnetic field.It is instructive to compare results of the spectropolari-metric modelling with the measurements of total magneticflux from Stokes I . Such measurements, based on principalcomponent analysis of high and low Land´e-factor Stokes I line-profiles, were presented for (cid:15) Eridani by Lehmannet al. (2015). Clear short-term variations of the surface av-eraged magnetic field of up to few tens Gauss were de-tected together with evidence for a three-year cycle (seeFig. 9). Over time, the grand average surface-field densitywas (cid:104) B (cid:105) = ±
47 G. The overall trend of these results alsofits with the contemporaneous S -index measurements fromMetcalfe et al. (2013). On the other hand, the field densitiesreconstructed in the ZDI Stokes V images of Je ff ers et al.(2014) were at most ±
40 G for the radial and the azimuthalcomponent and about half of that for the meridional com-ponent with a total surface average of at most 20 G (valuesranged between 10 ± ± ff er-ent than the approximately 186 G from Zeeman broadeninganalysis and indicates that our respective measuring tech-niques in Stokes V and Stokes I either suppress or enhancesome of the field aspects. Young solar mass stars undergo a large structural evolutionas they traverse the pre-main sequence. These stars begintheir life fully convective, then develop radiative cores asthey leave the Hyashi track. Young stars in this mass rangealso undergo a significant evolution in their rotation rate.Early on the pre-main sequence, the stars are strongly in-teracting with their circumstellar disks, and this interactionregulates their rotation rate. Eventually the star decouplesfrom its disk, but the star is still on the pre-main sequenceand contracting, therefore the rotation rate of the star in-creases. These stars also have magnetised stellar winds,and lose angular momentum through the interaction of theirmagnetic field and wind. This spin-down is a slow process,thus it only significantly impacts rotation rates after a starhas reached the main sequence (e.g. Irwin et al. 2007; Gal-let & Bouvier 2013, 2015).The magnetic fields of these stars are expected to begenerated by dynamos, most likely through an α - Ω dynamo that depends on both rotation and convection. Thus both thestructural evolution and the rotational evolution should havea strong impact on stellar magnetic fields. Additionally, stel-lar spin-down is controlled by the stellar magnetic field, thusan understanding of these magnetic fields is critical for un-derstanding rotational evolution.The direct detection of magnetic fields in young fast ro-tating stars has been achieved through spectropolarimetricobservations, detecting the signature of the Zeeman e ff ectin the polarised spectrum of these stars. Zeeman broad-ening measurements from total intensity spectra are use-ful for slower rotating lower mass stars (e.g. Saar 1996;Reiners et al. 2009), but so far these more rapidly rotatingstars are challenging targets for that technique. The spec-tropolarimetric observations discussed here are from theESPaDOnS instrument at the Canada-France-Hawaii Tele-scope in Hawaii, the Narval instrument at the T´elescopeBernard Lyot in France, and the HARPSpol instrument atthe ESO 3.6m telescope in La Silla, Chile.A few large surveys of magnetic properties of youngsolar-like stars have been conducted, or currently are inprogress. The MaPP (Magnetic Protostars and Planets; Do-nati et al. 2008, 2011) project focused on classical TTauri stars (cTTS). The MaTYSSE (Magnetic Topologiesof Young Stars and the Survival of massive close-in Ex-oplanets; Donati et al. 2014, 2015) project is currently inprogress, extending this work to weak-liked T Tauri stars(wTTS). In the framework of the Toupies project (TOwardsUnderstanding the sPIn Evolution of Stars; PI J. Bouvier),Folsom et al. (2016, and in prep.) focused on magneticfields of older pre-main sequence and young main sequencestars, after most of the structural evolution is complete butspanning the strong rotational evolution of these stars. TheToupies project focused on stars in known open clusters orstellar associations to provide reasonably accurate ages. TheBCool project (Marsden et al. 2014; Petit et al in prep.) fo-cused mostly on older field stars that have spun down signif-icantly, but provides a good comparison for cool stars thatare no longer young. These projects all use time series ofcircularly polarised (Stokes V ) spectra as input for ZDI toreconstruct the strength and geometry of the large-scale stel-lar magnetic field. This methodology has some limitations,most notably small scale magnetic features are below theresolution of the technique and cancel out, leaving them un-detected. However, this is the only method that provides ge-ometric information, and it is the large scale magnetic fieldthat controls the stellar wind and angular momentum loss.Using results from these large projects, and some stud-ies of individual stars, Vidotto et al. (2014) found a cleartrend of the average large-scale radial magnetic field de-creasing with stellar rotation period, as well as Rossby num-ber and age. A number of trends are well established withmagnetic activity proxies, such as the X-ray activity Rossbynumber relation. And a similar trend in Zeeman broaden-ing measurements with Rossby number was found for M-dwarfs (e.g. Reiners et al. 2009). However, until recently Copyright line will be provided by the publisher sna header will be provided by the publisher 9 < B > ( G ) Toupies (ZAMS)BCoolMaPP (T Tauri)MaTYSSE (wTTS)
Fig. 10
Average large-scale magnetic field strength fromZDI as a function of stellar age. Data from the Toupies,MaPP, MaTYSSE, and BCool projects are presented here.such trends had not been established for large-scale mag-netic fields.A similar set of results were found by Folsom et al.(2016), who focused on stars with a narrower range ofmasses, closer to solar, and with more well determined ages.They found a continuous decrease in the average (unsigned)magnetic field strength from ZDI with increasing age, ap-proximately following a power law. This spans T Tauristars, ZAMS stars, and older main sequence stars, shown inFig. 10 (with additional data from Folsom et al. in prep).Ros´en et al. (2016) found similar results using a smallersample of stars, but with multiple epochs of observationfor most targets. For the ZAMS and older main sequencestars, there is a clear power law trend towards decreas-ing magnetic field strength with increasing rotation period.The power law relation in rotation period becomes tighterwhen made in terms of Rossby number (here the ratio ofthe rotation period to convective turnover time), shown inFig. 11. However, for both period and Rossby number, thetwo fastest rotators in the sample do not follow the gen-eral trend. They have strengths comparable to more moder-ately rotating stars, suggesting a saturation of the large-scalemagnetic field strength roughly around a Rossby number of0.1. Vidotto et al. (2014) found some evidence for satura-tion of magnetic field at low Rossby number based on M-dwarfs, thus due to increasing convective turnover time. Onthe other hand, Folsom et al. (2016) present evidence of thissaturation due to decreasing rotation period.The classical T Tauri stars are distinct from the ZAMSstars in the geometry of their magnetic fields, as well astheir large magnetic field strengths. The cTTS magneticfields are generally mostly symmetric about their rotationaxis, dominantly poloidal (as opposed to toroidal), and usu-ally fairly simple. In contrast, older PMS stars and ZAMSstars have more non-axisymmetric fields, mixes of poloidaland toroidal geometries, and are generally more complex,even for the same Rossby number. A comparison of cTTSs < B > ( G ) Toupies (ZAMS)BCoolMaPP (T Tauri)MaTYSSE (wTTS)
Fig. 11
Average large-scale magnetic field strength fromZDI as a function of Rossby number, for the same sample asFig. 10. The solid line is a power law fit for larger Rossbynumbers, and the dashed line is a hypothetical saturationlevel for small Rossby number.from MaPP and older PMS and ZAMS stars from Toupiesis shown in Fig. 12.The di ff erence in magnetic properties between cTTSand older stars was suggested to be a consequence of theirlarge di ff erence in internal stellar structure by Gregory etal. (2012). Most of the magnetic cTTSs observed so far arefully convective, or have very small radiative cores. Thusthe convective properties of the stars are likely very di ff er-ent from more evolved solar-mass stars, and they likely donot possess a tachocline. This is similar to the di ff erencein magnetic properties between fully convective M-dwarfsand partly convective main sequence K stars (e.g. Morin etal 2010). Further observations of more evolved pre-main se-quence stars support this interpretation (Folsom et al. 2016).Classical T Tauri stars di ff er from ZAMS stars, not justin their structure, but also in that they are accreting andlikely strongly interacting with their disks. An investiga-tion of (non-accreting) wTTSs in the same parameter rangecan test whether this impacts surface magnetic fields. TheMaTYSSE project is studying wTTSs, but so far resultsfor only a few stars have been published (e.g. Donati et al.2014, 2015). These early results are somewhat inconclusive,in that the wTTS magnetic fields are, on average somewhatweaker and more complex than the cTTS fields. But they arestill stronger for a given Rossby number, and more poloidaland axisymmetric, than the fields of ZAMS stars. Thus morework needs to be done to extend this sample.There is now a well established trend of decreasinglarge-scale magnetic field strength with age, from the PMSthrough the main sequence. On the PMS, this trend seems tobe largely driven by structural changes in the stars. On themain sequence, this is largely driven by the rotational evolu-tion of the stars. There is a good correlation between large-scale magnetic field strength and Rossby number, down to aRossby number of ∼ Copyright line will be provided by the publisher T eff (K) L ( L ⊙ ) A x i s y mm e t r y ( s h a p e ) / P o l o i d a l ( c o l o u r ) (cid:0) B (cid:1) ( G ) Fig. 12
Classical T Tauri stars (thick blue outlines) fromthe MaPP project and older PMS / ZAMS stars (thin blackoutlines) from the Toupies project. Evolutionary tracks(dashed lines) and isochrones (dotted lines) are shown. Thethick dashed blue line indicates where the radiative corehas developed to 50% of the star, by mass. Symbol size in-dicates mean magnetic field strength. Symbol colour andshape indicate how poloidal the magnetic field is and howaxisymmetric the poloidal field is, respectively.is tentative evidence for saturation of the large-scale mag-netic field below a Rossby number ∼ ff erences in the stars. Low-mass stars – understood here as M dwarfs – have at-tracted a lot of interest during the past few years. In par-ticular, their magnetic fields and activity are at the core ofseveral important topics of research. A fundamental issueabout M dwarfs is to understand how the dynamo mecha-nisms change from the most massive M dwarfs – which arepartly convective like the Sun – to the least massive ones –which are fully convective – and how this change a ff ects thesurface magnetic field and activity (see e.g. Morin 2012).A better understanding of the magnetic fields of M dwarfsis also expected to induce progress on several puzzles suchas their rotational evolution (e.g. Newton et al. 2016) or therelation between chromospheric and coronal emissions tak-ing place at various wavelengths (e.g. Williams et al. 2014).Moreover, M dwarfs have recently become the main tar-gets of planet search programs, and the need to better un-derstand and model their magnetism is twofold. First, theirtime-dependent magnetic activity generates radial velocityfluctuations and brightness variations which can impede thedetection of orbiting planets or even mimic the presence ofsuch planets (e.g. Bonfils et al. 2007). Second, knowing thestellar magnetic field, particle wind and levels of high en-ergy emission (UV and X-rays), as well as their evolution with stellar age is key to assessing the potential habitabilityof detected planets (e.g. Ribas et al. 2016).The surface magnetic fields of M dwarfs can be studiedusing di ff erent, and often complementary, approaches (seee.g. Morin et al. 2013). More details on the techniques andon results for cool stars in general can be found in Rein-ers (2012) and Morin et al. (2016) for instance. Activitymeasurements correspond to features distributed across theelectromagnetic spectrum which generally result from theinteraction of the magnetic field with the stellar atmosphere.An important result of activity measurements of M dwarfs– either chromospheric H α emission, or coronal emissionat radio and X-ray wavelengths – is that fully convectivemid-M dwarfs follow a rotation-activity relation very simi-lar to that of more massive partly-convective stars : the ac-tivity level increases toward faster rotation until a saturationplateau is reached, for a Rossby number of about 0.1 (e.g.McLean et al. 2012; Wright & Drake 2016). In addition, Mdwarfs display long-term variability of their activity levels,with even hints of possible activity cycles (Gomes da Silvaet al. 2012).An alternative and complementary approach consists indirectly measuring the magnetic field at photospheric levelthrough the Zeeman e ff ect on spectral lines. Such mea-surements can be carried out either in unpolarised or inpolarised light, in both cases using high resolution spec-troscopy. From unpolarised spectroscopy it is possible toderive the average magnetic field of the star. This quantity issometimes referred to as a “magnetic flux” – although it hasthe dimension of a magnetic flux density – to stress that itdoes not correspond to the measurement of a local magneticfield strength on a point of the stellar surface. These mea-surements are e ffi cient to measure magnetic fields regard-less of their complexity and have been used to study ener-getic aspects of stellar dynamos (Christensen et al. 2009),but provide very little constraint on the field geometry. Us-ing high-resolution and high-signal to noise spectra thismethod can also provide constraints on the distribution oflocal field strength on the stellar surface (e.g. Shulyak etal. 2014). This method has been successfully applied to Mdwarfs, first using atomic lines for early- to mid M-dwarfs(e.g. Johns-Krull & Valenti 1996). With its extension to theFeH molecule, it has become possible to measure magneticfields of stars spanning the whole M spectral type, withlow to moderate projected rotational velocities (e.g. Rein-ers & Basri 2007). These measurements have shown thatboth partly- and fully-convective early- to mid-M dwarfsfollow a similar rotation-magnetic field relation, exactly aswas found for activity measurements. At high Rossby num-ber (slow rotation) the measured average magnetic field isanti-correlated with Ro , whereas below a saturation thresh-old of Ro (cid:39) . ff ect in po-larised light brings again di ff erent information on stellarmagnetic fields. Due to the mutual cancellation of polarised Copyright line will be provided by the publisher sna header will be provided by the publisher 11 signals arising from neighbouring areas of opposite polari-ties, spectropolarimetry is only sensitive to the large-scalecomponent of the field. Conversely to unpolarised spec-troscopy, this approach is also sensitive to the orientationof the magnetic field vector. The ZDI technique has beenintroduced to make full use of the information containedin spectropolarimetric data (in most cases restricted to cir-cular polarisation only, see Sect. 2.3): from a time-seriesof polarised spectra sampling at least a stellar rotation cy-cle, it reconstructs the magnetic field vector at the surfaceof the star (see Semel 1989; Donati et al. 2006). This ap-proach has been applied to a sample of active early- to mid-M dwarfs, showing for the first time a change in the mag-netic properties at the fully-convective boundary (see Do-nati et al. 2008; Morin et al. 2008). Fully-convective starsindeed appeared to generate magnetic fields with a stronglarge-scale component dominated by the axial dipole, whilefor partly-convective ones the large-scale component of thefield (i.e. the component probed by spectropolarimetry) isweaker and more complex. Interestingly, the latest develop-ment of dynamo numerical simulations now reconcile themeasurements in unpolarised and polarised light, with mag-netic fields exhibiting both an energetically dominant small-scale component and a large-scale component dominated bythe axial dipole mode (Yadav et al. 2015). On the observa-tional side, the latest studies are now overcoming the limita-tions of the first samples, with measurements in unpolarisedlight being extended to rapid rotators (see Sect. 6.1) andspectropolarimetric surveys exploring moderate rotators inthe unsaturated regime (H´ebrard et al. 2016).Going towards later spectral types, very-low mass starsand ultracool dwarfs exhibit intriguing behaviours whenobserved with these di ff erent approaches. Their chromo-spheric activity decreases towards late spectral types (e.g.Reiners & Basri 2010). X-ray and radio luminosities ex-hibit a large scatter for rapid rotators, resulting in a breakof the “G¨udel-Benz” correlation with rapidly-rotating ultra-cool dwarfs often appearing radio-bright and X-ray faint,but the opposite situation is also observed (e.g. Williams etal. 2014). Magnetic field measurements in unpolarised spec-troscopy also reveal the existence of rapidly rotating starswith average surface fields well below the saturation value,taken as a hint of the fading of the rotation-dominated dy-namo (Reiners & Basri 2010). On their side, spectropolari-metric observations show the co-existence of two groups ofstars with radically di ff erent types of large-scale magneticfields within a narrow range of stellar parameters (Morin etal. 2010), which have been tentatively attributed to a bista-bility of the stellar dynamo (e.g. Gastine et al. 2013). It ishowever still a matter of debate to which extent these dif-ferent observations are connected together, or for instanceif some of them can be related to the physical conditionsin the atmospheres of ultracool objects (e.g. Mohanty et al.2002) or to the emission mechanisms (e.g. Hallinan et al.2008). During the past decade, large strides have been madein characterising and understanding the magnetic fields andactivity of M dwarfs. However, our knowledge of these starsstill remains very partial and several important puzzles areto be addressed. During the next few years, spectrographsand spectropolarimeters operating in the near-infrared willstudy extensively large samples of M dwarfs with the aim todiscover rocky planets orbiting them (Delfosse et al. 2013;Oliva et al. 2014; Quirrenbach et al. 2014). The synergy be-tween these programs and studies of magnetic activity oflow-mass stars – with the need to model stellar activity bothfor planet detection and characterisation (e.g. H´ebrard et al.2016; Donati et al. 2015; Ribas et al. 2016) – are expectedto contribute decisively to the next important advances inthe field. Since the first detection of strong magnetic fields in Mdwarfs in mid-80s (Saar & Linsky 1985), several tens of in-dividual measurements were obtained with di ff erent instru-ments and wavelength regions (Johns-Krull & Valenti 1996,2000; Reiners & Basri 2007, 2010; Reiners et al. 2009;Kochukhov et al. 2009; Shulyak et al. 2014). These mea-surements showed that the strength of the maximum possi-ble surface magnetic field reaches values around 3–4 kG inthe coolest M dwarf stars. Fields stronger than this have notbeen detected in any low-mass star, which was viewed asan evidence for the magnetic field saturation (Reiners et al.2009), similar to the saturation of stellar activity in terms of,e.g., X-ray fluxes which occurs for stars with rotational pe-riods shorter than a few days (see, e.g., Shulyak et al. 2014).Note, however, that all available measurements show largescatter between 2 kG and 4 kG, the latter being an upperlimit of the field that could be measured at that time withavailable techniques (Reiners & Basri 2007).Thanks to development of new analysis methods andtechniques, it is now possible to look at magnetic proper-ties of stars in more detail. In order to better understandthe magnetism in M dwarfs we used data collected overseveral years with the twin spectropolarimeters ESPaDOnSand NARVAL mounted at the 3 . I spectra by utilising up-to-dateradiative transfer modelling and di ff erent spectroscopic di-agnostics.Our analysis resulted in the detection of the strongest (cid:104) B (cid:105) ≈ . Copyright line will be provided by the publisher rot =2.24dBs = 3.1 kGGJ 1245 BM5.5υ·sini=8 km/sP rot =0.71dBs = 3.1 kGWX UmaM6.0υ·sini=5 km/sP rot =0.78dBs = 6.4 kG
FeH
Rb I, geff = 1.33
Ti I, geff = 1.37
Fig. 13
Detection of very strong magnetic field in WX UMa. We show example fits to magnetic sensitive spectral linesin WX UMa and a few other magnetic M dwarfs. Black dots – observed spectra; blue line – predicted zero field spectra;red line – best fit spectrum with the magnetic field. The text on the left side of first column lists for each stars its name,spectral class, derived projected rotational velocity ( v sin i , where i is the inclination angle between stellar rotation axis andthe line-of-sight), rotational period, and the average surface magnetic field. Rotation periods are taken from ZDI studies(Morin et al. 2008, 2010). In the case of WX UMa one can see a clear Zeeman splitting in Rb I and Ti I lines, as well asa characteristic magnetic sensitive FeH feature at 994 . . Ti I, geff = 1.35
Ti I, geff = 0.00
Ti I, geff = 1.55
Fig. 14
Example fit to Ti i lines in the spectra of fast ro-tating M dwarf V374 Peg with v sin i ≈
35 km s − . Blackdiamonds – observations; full red line – best fit model with (cid:104) B (cid:105) = . g e ff ) is listed for each line in the titleof corresponding subplot.We have also measured magnetic fields above 5 kG inthree other stars GJ 51, EQ Peg B, and V374 Peg. However,these stars have rather large v sin i values which makes it im-possible to see Zeeman splitting in individual lines. Thus,to measure magnetic fields in these stars we relied on thee ff ect of magnetic intensification of spectral lines (LandiDegl’Innocenti & Landolfi 2004) which predicts that thedepth of a magnetic sensitive line broadened by rotationwill be increased depending on its Zeeman pattern. Thistechnique is sensitive only to fields that are strong enoughto produce observable changes in the equivalent widths ofspectral lines. We found that Ti i lines in λλ ff ort of removing tel-luric absorption from all stellar spectra of all stars by ap-plying the M olec F it software package (Smette et al. 2015;Kausch et al. 2015). As an example, our Figure 14 demon-strates the model fit to selected Ti i lines in M dwarfs starV374 Peg which has v sin i ≈
35 km s − .Thus, we reported for the first time a detection of themagnetic fields in M dwarfs beyond the “classical” satura-tion limit which was previously believed to be ≈ Results of the stellar magnetic field studies presented hereemphasize the value of obtaining complementary con-straints using di ff erent methods. Specifically, it is necessaryto combine the Zeeman broadening analysis of intensityspectra which measures the total magnetic flux with the po-larisation analysis of the large-scale field geometry. We haveseen that it is not always straightforward to reconcile thetwo diagnostic methods, especially for the low-mass, fullyconvective dwarfs. The implications of this disagreement,for example the likely co-existence of the small and large-scale magnetic field structures at stellar surfaces, need to be Copyright line will be provided by the publisher sna header will be provided by the publisher 13 taken into account by observational studies and addressedby theoretical models.At the same time, the comparison of the interferometricspot imaging with indirect Doppler spot mapping has pro-vided encouraging results for a few cool stars accessible tointerferometry. In particular, the question of the reality of acool polar spot, debated for many years, appears to be set-tled. A combination of interferometric information with thetraditional spectroscopic Doppler mapping of cool spots isa promising future direction for lifting the degeneracies ofthe latter technique and deriving some of the more uncertainstar spot parameters (e.g. temperature contrasts).We have witnessed a considerable progress in polari-metric field detections and analysis of main-sequence solar-like stars. Magnetic fields have been detected in hundredsof stars and mapped using ZDI in dozens of objects. A fewstars show evidence of cyclic evolution of the field strengthand topology, which is many cases not compatible with theactivity cycles established from indirect proxy observations.In this context, recently reported discoveries of stars demon-strating a coherent, solar-like evolution of di ff erent proxiesand direct magnetic fields indicators are particularly note-worthy.Magnetic studies of young stars, especially open clus-ter members, are providing novel constraints on magneticfields during the early stages of stellar evolution. These con-straints are critical for understanding the shedding of angu-lar momentum and activity decline as stars evolve towardsthe main sequence. The key science with the upcomingPEPSI polarimeter at the Large Binocular Telescope (LBT)will focus on solar-like cluster stars.The magnetism of low-mass stars is arguably the mostmysterious and di ffi cult topic. The fully convective starscan’t operate a tachocline dynamo and yet they exhibit aqualitatively similar rotation-activity relation as found inmore massive solar-like stars. Moreover, the dynamo pro-cess operating in M dwarfs produces moderately strong,globally organised magnetic fields which yield easily de-tectable polarisation signatures. On the other hand, muchstronger mean fields are evident from the Zeeman broad-ening analyses. The two types of magnetic measurementscannot be currently reconciled; considerable theoretical andmodelling e ff orts are needed to resolve this puzzle.The advancement of astronomical instrumentation hasbeen the driving force behind most of the recent progressin understanding cool star magnetism. Forthcoming com-missioning of the high-resolution spectropolarimeter at theequivalent 11.8m diameter LBT (PEPSI) and of the firsthigh-resolution night-time near-infrared spectropolarime-ters (Spirou, CRIRES + ) will likely answer some of the cur-rently open questions and also lead to new discoveries. Acknowledgements.
C.P. Folsom was supported by the grant ANR2011 Blanc SIMI5-6 020 01 “Toupies: Towards understandingthe spin evolution of stars” (http: // ipag.osug.fr / Anr Toupies / ). Healso thanks the IDEX initiative at Universit´e F´ed´erale Toulouse Midi-Pyr´en´ees (UFTMiP) for funding through the STEPS col-laboration program between IRAP / OMP and ESO. R. Fares ac-knowledges partial support from STFC consolidated grant num-ber ST / J001651 /
1. D. Shulyak acknowledges support from DFGproject CRC 963 “Astrophysical Flow Instabilities and Turbu-lence”. O. Kochukhov acknowledges support by the Swedish Re-search Council and the Swedish National Space Board. H. Korho-nen thanks the Fonden Dr. N.P. Wieth-Knudsens Observatoriumfor the travel grant that made it possible for her to attend CoolStars 19. J.D. Monnier and R.M. Roettenbacher acknowledge sup-port for the interferometric imaging work by the National ScienceFoundation (NSF) grant AST-1108963.
References
Baliunas, S.L., Donahue, R.A., Soon, W.H., et al. 1995, ApJ, 438,269Beuzit, J.-L., Feldt, M., Dohlen, K., et al. 2008, Proc. SPIE, 7014,701418Bonfils, X., Mayor, M., Delfosse, X., et al. 2007, A&A, 474, 293Boro Saikia, S., Je ff ers, S.V., Morin, J., et al. 2016, A&A, 594,A29Brown, S.F., Donati, J.-F., Rees, D.E., & Semel, M. 1991, A&A,250, 463Carroll, T.A., Strassmeier, K.G., Rice, J.B., & K¨unstler, A. 2012,A&A, 548, A95Christensen, U.R., Holzwarth, V., & Reiners, A. 2009, Nature,457, 167Delfosse, X., Donati, J.-F., Kouach, D., et al. 2013, in SF2A-2013,eds. L. Cambresy, F. Martins, E. Nuss, & A. Palacios, Pro-ceedings of the Annual meeting of the French Society of As-tronomy and Astrophysics, 497Donati, J.F. & Brown, S.F. 1997, A&A, 326, 1135Donati, J.-F., Gregory, S.G., Alencar, S.H.P., et al. 2011, MNRAS,417, 472Donati, J.-F., H´ebrard, E., Hussain, G.A.J., et al. 2014, MNRAS,444, 3220Donati, J.-F., H´ebrard, E., Hussain, G.A.J., et al. 2015, MNRAS,453, 3706Donati, J.-F., Howarth, D., Jardine, M.M., et al. 2006, MNRAS,370, 629Donati, J.-F., Jardine, M.M., Gregory, S.G., et al. 2008, MNRAS,386, 1234Donati, J.-F. & Landstreet, J. D. 2009, ARA&A, 47, 333Donati, J.-F., Morin, J., Petit, P., et al. 2008, MNRAS, 390, 545Donati, J.-F., Semel, M., Carter, B.D., Rees, D.E., & CollierCameron, A. 1997, MNRAS, 291, 658Duncan, D.K., Vaughan, A.H., Wilson, O.C., et al. 1991, ApJS, 76,383Fares, R. 2014, in IAU Symp. 302, Magnetic Fields throughoutStellar Evolution, eds. P. Petit, M. Jardine, H.C. Spruit, Cam-bridge University Press, 180Folsom, C.P., Petit, P., Bouvier, J., et al. 2016, MNRAS, 457, 580Gallet, F. & Bouvier, J. 2013, A&A, 556, A36Gallet, F. & Bouvier, J. 2015, A&A, 577, A98Gastine, T., Morin, J., Duarte, L., et al. 2013, A&A, 549, L5Gomes da Silva, J., Santos, N. C., Bonfils, X., et al. 2012, A&A,541, A9Gosain, S., Pevtsov, A.A., Rudenko, G.V., & Anfinogentov, S.A.2013, ApJ, 772, 52Gregory, S.G., Donati, J.-F., Morin, J., et al. 2012, ApJ, 755, 97Hallinan, G., Antonova, A., Doyle, J. G., et al. 2008, ApJ, 684, 644 Copyright line will be provided by the publisher ff ers, S.V., Petit, P., Marsden, S.C., et al. 2014, A&A, 569, A79Johns-Krull, C.M. & Valenti, J.A. 1996, ApJ, 459, L95Johns-Krull, C.M. & Valenti, J.A. 2000, in Stellar Clusters andAssociations: Convection, Rotation, and Dynamos, eds. R.Pallavicini, G. Micela, & S. Sciortino, ASP Conf. Ser., 198,371Kausch, W., Noll, S., Smette, A., et al. 2015, A&A, 576, A78Kloppenborg, B., Stencel, R., Monnier, J.D., et al. 2010, Nature,464, 870Kochukhov, O., Heiter, U., Piskunov, N., et al. 2009, in 15th Cam-bridge Workshop on Cool Stars, Stellar Systems, and the Sun,AIP Conf. Proc., 1094, 124Kochukhov, O., L¨uftinger, T., Neiner, C., Alecian, E., & MiMeSCollaboration. 2014, A&A, 565, A83Kochukhov, O., Makaganiuk, V., & Piskunov, N. 2010, A&A, 524,A5Kochukhov, O., Makaganiuk, V., Piskunov, N., et al. 2011, ApJ,732, L19Kochukhov, O., Mantere, M. J., Hackman, T., & Ilyin, I. 2013,A&A, 550, A84Kochukhov, O. & Piskunov, N. 2002, A&A, 388, 868Korhonen, H., Wittkowski, M., K˝ov´ari, Zs., et al. 2010, A&A, 515,A14Landi Degl’Innocenti, E., & Landolfi, M. 2004, Polarization inspectral lines, Astrophysics and Space Science Library, 307Lehmann, L.T., K¨unstler, A., Carroll, T.A., & Strassmeier, K.G.2015, AN, 336, 258Marsden, S.C., Jardine, M.M., Ram´ırez V´elez, J.C., et al. 2011,MNRAS, 413, 1922Marsden, S.C., Petit, P., Je ff ers, S.V., et al. 2014, MNRAS, 444,3517Metcalfe, T.S., Buccino, A.P., Brown, B.P., et al. 2013, ApJ, 763,L26McLean, M., Berger, E., & Reiners, A. 2012, ApJ, 746, 23Mohanty, S., Basri, G., Shu, F., Allard, F., & Chabrier, G. 2002,ApJ, 571, 469Monnier, J.D., Berger, J.-P., Milan-Gabet, R., & ten Brummelaar,T.A. 2004, Proc. SPIE, 5491 1370Monnier, J.D., Zhao, M., Pedretti, E., et al., 2007, Science, 317,342Morin, J. 2012, in EAS Publications Series, 57, eds. C. Reyl´e,C. Charbonnel, & M. Schultheis, 165Morin, J., Donati, J.-F., Petit, P., et al. 2008, MNRAS, 390, 567Morin, J., Donati, J.-F., Petit, P., et al. 2010, MNRAS, 407, 2269Morin, J., Hill, C.A., & Watson, C. A. 2016, in Tomographic Imag-ing of Stellar Surfaces and Interacting Binary Systems, eds.J.H.M. Bo ffi n, G. Hussain, J.-P. Berger, & L. Schmidtobreick,Springer International Publishing, 223Morin, J., Jardine, M., Reiners, A., et al. 2013, AN, 334, 48Newton, E.R., Irwin, J., Charbonneau, D., et al. 2016, ApJ, 821,93Oliva, E., Tozzi, A., Ferruzzi, D., et al. 2014, Proc. SPIE, 9147,91477R Petit, P., Louge, T., Th´eado, S., et al. 2014, PASP, 126, 469Pesnell, W.D., Thompson, B.J., & Chamberlin, P.C. 2012,Sol. Phys., 275, 3Piskunov, N. & Kochukhov, O. 2002, A&A, 381, 736Quirrenbach, A., Amado, P. J., Caballero, J. A., et al. 2014,Proc. SPIE, 9147, 91471FReiners, A. 2012, Living Reviews in Solar Physics, 9, 1Reiners, A. & Basri, G. 2007, ApJ, 656, 1121Reiners, A. & Basri, G. 2010, ApJ, 710, 924Reiners, A., Basri, G., & Browning, M. 2009, ApJ, 692, 538Ribas, I., Bolmont, E., Selsis, F., et al. 2016, arXiv:1608.06813Ribes, J.C. & Nesme-Ribes, E. 1993, A&A, 276, 549Ros´en, L. & Kochukhov, O. 2012, A&A, 548, A8Ros´en, L., Kochukhov, O., Hackman, T., & Lehtinen, J. 2016,A&A, 593, A35Ros´en, L., Kochukhov, O., & Wade, G.A. 2013, MNRAS, 436,L10Ros´en, L., Kochukhov, O., & Wade, G.A. 2015, ApJ, 805, 169Roettenbacher, R.M., Monnier, J.D., Fekel, F.C., et al. 2015, ApJ,809, 159Roettenbacher, R.M., Monnier, J.D., Korhonen, H., et al. 2016,Nature, 533, 217Saar, S.H. 1996, in IAU Symp. 176, Stellar Surface Structure, eds.K.G. Strassmeier, J.L. Linsky, Kluwer, Dordrecht, 237Saar, S.H. & Linsky, J.L. 1985, ApJ, 299, L47Schou, J., Scherrer, P.H., Bush, R.I., et al. 2012, Sol. Phys., 275,229Semel, M. 1989, A&A, 225, 456Shulyak, D., Reiners, A., Seemann, U., Kochukhov, O., &Piskunov, N. 2014, A&A, 563, A35Smette, A., Sana, H., Noll, S., et al. 2015, A&A, 576, A77Strassmeier, K.G. 2009, A&A Rev., 17, 251ten Brummelaar, T.A., McAlister, H.A., Ridgeway, S.T., et al.2005, ApJ, 628, 453Vidotto, A.A., Gregory, S.G., Jardine, M. et al. 2014, MNRAS,441, 2361Williams, P.K.G., Cook, B.A., & Berger, E. 2014, ApJ, 785, 9Wilson, O.C. 1978, ApJ, 226, 379Wittkowski, M., Sch¨oller, M., Hubrig, S., Posselt, B., & von derL¨uhe, O. 2002, AN, 323, 241Wright, N.J. & Drake, J.J. 2016, Nature, 535, 526Yadav, R.K., Christensen, U.R., Morin, J., et al. 2015, ApJ, 813,L31Zhao, M., Gies, D., Monnier, J.D., et al. 2008, ApJ, 684, L95n, G. Hussain, J.-P. Berger, & L. Schmidtobreick,Springer International Publishing, 223Morin, J., Jardine, M., Reiners, A., et al. 2013, AN, 334, 48Newton, E.R., Irwin, J., Charbonneau, D., et al. 2016, ApJ, 821,93Oliva, E., Tozzi, A., Ferruzzi, D., et al. 2014, Proc. SPIE, 9147,91477R Petit, P., Louge, T., Th´eado, S., et al. 2014, PASP, 126, 469Pesnell, W.D., Thompson, B.J., & Chamberlin, P.C. 2012,Sol. Phys., 275, 3Piskunov, N. & Kochukhov, O. 2002, A&A, 381, 736Quirrenbach, A., Amado, P. J., Caballero, J. A., et al. 2014,Proc. SPIE, 9147, 91471FReiners, A. 2012, Living Reviews in Solar Physics, 9, 1Reiners, A. & Basri, G. 2007, ApJ, 656, 1121Reiners, A. & Basri, G. 2010, ApJ, 710, 924Reiners, A., Basri, G., & Browning, M. 2009, ApJ, 692, 538Ribas, I., Bolmont, E., Selsis, F., et al. 2016, arXiv:1608.06813Ribes, J.C. & Nesme-Ribes, E. 1993, A&A, 276, 549Ros´en, L. & Kochukhov, O. 2012, A&A, 548, A8Ros´en, L., Kochukhov, O., Hackman, T., & Lehtinen, J. 2016,A&A, 593, A35Ros´en, L., Kochukhov, O., & Wade, G.A. 2013, MNRAS, 436,L10Ros´en, L., Kochukhov, O., & Wade, G.A. 2015, ApJ, 805, 169Roettenbacher, R.M., Monnier, J.D., Fekel, F.C., et al. 2015, ApJ,809, 159Roettenbacher, R.M., Monnier, J.D., Korhonen, H., et al. 2016,Nature, 533, 217Saar, S.H. 1996, in IAU Symp. 176, Stellar Surface Structure, eds.K.G. Strassmeier, J.L. Linsky, Kluwer, Dordrecht, 237Saar, S.H. & Linsky, J.L. 1985, ApJ, 299, L47Schou, J., Scherrer, P.H., Bush, R.I., et al. 2012, Sol. Phys., 275,229Semel, M. 1989, A&A, 225, 456Shulyak, D., Reiners, A., Seemann, U., Kochukhov, O., &Piskunov, N. 2014, A&A, 563, A35Smette, A., Sana, H., Noll, S., et al. 2015, A&A, 576, A77Strassmeier, K.G. 2009, A&A Rev., 17, 251ten Brummelaar, T.A., McAlister, H.A., Ridgeway, S.T., et al.2005, ApJ, 628, 453Vidotto, A.A., Gregory, S.G., Jardine, M. et al. 2014, MNRAS,441, 2361Williams, P.K.G., Cook, B.A., & Berger, E. 2014, ApJ, 785, 9Wilson, O.C. 1978, ApJ, 226, 379Wittkowski, M., Sch¨oller, M., Hubrig, S., Posselt, B., & von derL¨uhe, O. 2002, AN, 323, 241Wright, N.J. & Drake, J.J. 2016, Nature, 535, 526Yadav, R.K., Christensen, U.R., Morin, J., et al. 2015, ApJ, 813,L31Zhao, M., Gies, D., Monnier, J.D., et al. 2008, ApJ, 684, L95