A&A 626, A86 (2019) https://doi.org/10.1051/0004-6361/201935315 Astronomy & © D. Shulyak et al. 2019 Astrophysics Magnetic fields in M dwarfs from the CARMENES survey D. Shulyak1,2 , A. Reiners1 , E. Nagel3 , L. Tal-Or1,4 , J. A. Caballero9 , M. Zechmeister2 , V. J. S. Béjar11,15 , M. Cortés-Contreras9 , E. L. Martin9 , A. Kaminski7 , I. Ribas5,6 , A. Quirrenbach7 , P. J. Amado8 , G. Anglada-Escudé8,10 , F. F. Bauer8 , S. Dreizler2 , E. W. Guenther12 , T. Henning13 , S. V. Jeffers2 , M. Kürster13 , M. Lafarga5,6 , D. Montes16 , J. C. Morales5,6 , and S. Pedraz14 1 Max-Planck-Institute für Sonnensystemforschung, Justus-von-Liebig-Weg 3, 37075 Göttingen, Germany e-mail: shulyak@mps.mpg.de 2 Institut für Astrophysik, Göttingen Universität, Friedrich-Hund-Platz 1, 37075 Göttingen, Germany 3 Hamburger Sternwarte, Gojenbergsweg 112, 21029 Hamburg, Germany 4 Department of Geophysics, Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, Tel Aviv 6997801, Israel 5 Institut de Ciéncies de l’Espai (ICE, CSIC), Campus UAB, c/ de Can Magrans s/n, 08193 Bellaterra, Barcelona, Spain 6 Institut d’Estudis Espacials de Catalunya (IEEC), 08034 Barcelona, Spain 7 Landessternwarte, Zentrum für Astronomie der Universität Heidelberg, Königstuhl 12, 69117 Heidelberg, Germany 8 Instituto de Astrofisica de Andalucia (IAA-CSIC), Glorieta de la Astronomia s/n, 18008 Granada, Spain 9 Centro de Astrobiologia (CSIC-INTA), ESAC, Camino Bajo del Castillo s/n, 28692 Villanueva de la Cañada, Madrid, Spain 10 Queen Mary University of London, Mile End Road, London E1 4NS, UK 11 Departamento de Astrofisica, Universidad de La Laguna, C/ Via Láctea s/n, La Laguna, Tenerife 38206, Spain 12 Thüringer Landessternwarte Tautenburg, Sternwarte 5, 07778 Tautenburg, Germany 13 Max-Planck-Institut für Astronomie, Königstuhl 17, 69117 Heidelberg, Germany 14 Centro Astronómico Hispano-Alemán (CSIC-MPG), Observatorio Astronómico de Calar Alto, Sierra de los Filabres, 04550 Gérgal, Almeria, Spain 15 Instituto de Astrofísica de Canarias, Vía Láctea, s/n E38205, La Laguna, Tenerife, Spain 16 Departamento de Física de la Tierra y Astrofísica and IPARCOS-UCM (Instituto de Física de Partículas y del Cosmos de la UCM), Facultad de Ciencias Físicas, Universidad Complutense de Madrid, 28040 Madrid, Spain Received 20 February 2019 / Accepted 14 April 2019 ABSTRACT Context. M dwarfs are known to generate the strongest magnetic fields among main-sequence stars with convective envelopes, but we are still lacking a consistent picture of the link between the magnetic fields and underlying dynamo mechanisms, rotation, and activity. Aims. In this work we aim to measure magnetic fields from the high-resolution near-infrared spectra taken with the CARMENES radial-velocity planet survey in a sample of 29 active M dwarfs and compare our results against stellar parameters. Methods. We used the state-of-the-art radiative transfer code to measure total magnetic flux densities from the Zeeman broadening of spectral lines and filling factors. Results. We detect strong kG magnetic fields in all our targets. In 16 stars the magnetic fields were measured for the first time. Our measurements are consistent with the magnetic field saturation in stars with rotation periods P < 4 d. The analysis of the magnetic filling factors reveal two different patterns of either very smooth distribution or a more patchy one, which can be connected to the dynamo state of the stars and/or stellar mass. Conclusions. Our measurements extend the list of M dwarfs with strong surface magnetic fields. They also allow us to better constrain the interplay between the magnetic energy, stellar rotation, and underlying dynamo action. The high spectral resolution and observa- tions at near-infrared wavelengths are the beneficial capabilities of the CARMENES instrument that allow us to address important questions about the stellar magnetism. Key words. stars: low-mass – stars: magnetic field – stars: rotation – stars: atmospheres 1. Introduction phenomena that we call stellar activity: amongst others, stel- lar spots, plages, hot chromospheres, and coronae, which are Magnetic fields are found in all types of stars throughout the observed indirectly via the analysis of, for example, emission Herzsprung–Russel diagram (Mathys et al. 2001). Among main- lines, X-rays, photometric variability (e.g., Irwin et al. 2011; sequence stars with outer convective envelopes, M dwarfs are Newton et al. 2017) and radio emission (e.g., McLean et al. know to generate strong kG magnetic fields (Saar & Linsky 2012). 1985; Johns-Krull & Valenti 1996; Reiners & Basri 2007, 2010; Perhaps one of the most remarkable findings was establish- Reiners et al. 2009). These fields are generated by convective ing the so-called rotation-activity relation (Noyes et al. 1984; dynamos that operate in stellar interiors and are powered by Kiraga & Stepien 2007; Reiners et al. 2014; Newton et al. 2017). stellar rotation (Pallavicini et al. 1981; Pizzolato et al. 2003; A key feature of this relation is the existence of two distinct Wright et al. 2011; Reiners et al. 2014). Dynamo-generated mag- branches (or groups) of stars that show very different behavior of netic fields reach the surface of a star and initiate a number of X-ray fluxes with stellar rotation. On the first branch the amount A86, page 1 of 24 Open Access article, published by EDP Sciences, under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Open Access funding provided by Max Planck Society. A&A 626, A86 (2019) of X-ray flux decreases as rotation periods of stars increase as Motivated by our recent findings and availability of the new they spin down due to the magnetic braking. This is direct evi- CARMENES instrument, in this work we have carried out the dence that stellar rotation powers dynamo action in these stars. first magnetic field measurements from the high-resolution near- On the contrary, when the rotation period reaches a certain value infrared spectroscopy in a subsample of stars with short rotation of about four days (the exact value is actually a function of periods. Because CARMENES does not have the capacity to the stellar mass), the X-ray fluxes show no (or very marginal) take polarimetry measurements, we performed measurements of dependence on rotation (Reiners et al. 2014). In this case, the the total magnetic flux density but we are not able to constrain stellar dynamo saturates and the amount of non-thermal energy dynamo states in our targets for which measurements of their released by a star reaches a certain limit. There might be sev- fields are done for the first time. Therefore, our main goal is to eral explanations for the observed phenomena, but it is generally constrain the relation between the magnetic field and stellar rota- believed that they are connected to the underlying dynamo (see tion and to mark targets with strong magnetic fields for future discussion in Reiners et al. 2014). spectropolarimetric follow up campaigns. Similar to the X-ray emission, Reiners et al. (2009) find the same two-branch behavior of magnetic flux densities with stellar 2. Observations rotation. In that paper, the value of the saturated magnetic field is not well constrained because of limitation of available analysis The detailed description of the CARMENES instrument and methods, but believed to be somewhere equal or slightly above the overview of the survey can be found in Quirrenbach et al. 4 kG. (2014); Alonso-Floriano et al. (2015); Reiners et al. (2018). As analysis methods improved, it has become possible to CARMENES is the first high-resolution spectrograph that simul- measure magnetic fields in M dwarfs from a direct spectrum taneously covers the optical and near-infrared (NIR) wavelength synthesis in atomic and molecular lines (Berdyugina & Solanki range between 520 and 1710 nm. In two channels (VIS and 2002; Afram et al. 2008; Shulyak et al. 2010, 2014). In their NIR), the instrument provides data at a resolution higher than investigation Shulyak et al. (2017, Sh2017 hereafter) reported R = 80 000. In particular, the NIR channel covers the wavelength the detection of the magnetic fields well above the presumed range 960–1000 nm that is essential for our analysis. saturated value in few M dwarf stars. The authors used rich spec- In this work we have concentrated on the subsample of tropolarimetric observations of a sample of stars obtained with 31 stars presented in Tal-Or et al. (2018) which we called the ESPaDOnS (Canada-France-Hawaii Telescope) and NARVAL RV-loud sample. All these stars had at least 11 measurements (Telescope Bernard Lyot) instruments and carried out magnetic over the last two years (2016–2017), projected rotational veloc- field measurements from atomic titanium (Ti) and molecular iron ity of greater than two, and radial velocity scatter amplitude hydride (FeH) lines. In particular, to date the strongest aver- greater than ten (as measured from the visual arm of the instru- age magnetic field of about hBi ≈ 7 kG was reported for the ment). Further details about RV-loud sample are summarized fully convective star WX UMa, which questioned the concept in Table 1 in Tal-Or et al. (2018). In this work we make use of the magnetic field saturation. Furthermore, Sh2017 were able of the near-infrared arm of CARMENES because this is where to measure magnetic fields in stars with large projected rotational our magnetically sensitive spectral features are located. The velocities (υ sin i, where υ is the equatorial rotation velocity and data reduction and wavelength calibration for the CARMENES i is the angle between the stellar rotation axis and the line of spectra is done with the dedicated tool CARACAL (Caballero sight) from the effect of magnetic intensification of the well sep- et al. 2016b), and the high-precision radial velocities are then arated Ti lines located in the Z-band. Because many M dwarfs computed using SERVAL package (Zechmeister et al. 2018). with short periods also have large υ sin i values, these stars were Additionally to radial velocities, SERVAL also produces a final previously excluded from the measurements of total magnetic co-added template spectrum of each star which is built from fields thus biasing results toward stars with relatively small υ sin i all available individual exposures. These templates represent values. a smoothed and oversampled version of the stellar spectrum Combining their results of magnetic field strength measure- with rejected obvious outliers (cosmic rays, night sky emis- ments with the results from the polarimetric studies of global sion lines, and others) and boosted signal-to-noise ratio (S/N). magnetic field geometries presented in Morin et al. (2010), We also used these templates for some of our magnetic field Sh2017 find that the stars that generate strongest fields are measurements. also those with very simple, dipole-dominant magnetic field The NIR spectra from CARMENES are often affected by geometries, while stars with multipole-dominant global fields strong telluric absorption from atmospheric water. This is a chal- do not generate fields stronger than ≈4 kG. They also point out lenge for our analysis because several of the Ti lines are at wave- that from their limited sample (25 stars) it could be seen that lengths close to telluric water lines. We rejected observations the magnetic field in stars with dipole-dominated geometry does of Ti lines when contamination by telluric lines systematically not show an obvious saturation effect. These findings provide affected our profile analysis. the first observational evidence for the existence of two distinct In Table 1 we provide information on the number of indi- dynamo states in M dwarfs that differ not only in the geometry vidual exposures taken per star, number of used spectra after of the large-scale magnetic field, which has been known since rejecting those with very low S/N and/or telluric removal arti- the extensive polarimetric campaign reported in Morin et al. facts, and the S/N of the finally co-added spectra that were used (2010), but also in total magnetic energy generated. To explain in the analysis of the magnetic fields. the observed dichotomy of dipole- vs. multipole-dominant magnetic fields, an idea of bi-stable dynamo models is proposed 3. Methods and confirmed with dedicated simulations (Gastine et al. 2013). The finding of Sh2017 that the magnetic fields may not saturate Our magnetic field measurements are based on the direct spectral in particular stars or that they saturate to a much larger values synthesis of spectroscopic features subject to the photospheric that previously thought needs to be confirmed through additional magnetic fields. In order to predict observed line profiles we uti- observations and theoretical models. lized the M AGNESYN spectrum synthesis code, which is the part A86, page 2 of 24 D. Shulyak et al.: Magnetic fields in M dwarfs from the CARMENES survey Table 1. Summary of observations. the whole Wing–Ford band is virtually free from telluric con- tamination. However, the fundamental problem with FeH lines is the absence of an accurate theory for the calculation of Landé Karmn No. of taken No. of used S /N of coadded g-factors (Asensio Ramos & Trujillo Bueno 2006; Berdyugina & spectra spectra spectra Solanki 2002). Apart from a few examples (Harrison et al. Ti/FeH Ti/FeH 2008; Crozet et al. 2012, 2014), the laboratory measurements J01033+623 19 7/7 190/257 are not available for the lines that are most important for mag- J01352-072 11 5/9 145/248 netic field analysis. On the other hand, the g-factors for Ti lines J02088+494 16 2/13 80/370 are accurately known and can be computed assuming stan- J03473-019 11 7/9 195/274 dard Russell–Saunders coupling scheme. Unfortunately, these J04472+206 12 2/6 82/182 Ti lines do suffer from strong telluric contamination. In par- J05365+113 55 13/17 280/448 ticular, the Ti I λ974.3 nm line is essential for disentangling J06000+027 14 5/10 156/285 magnetic broadening from the effects of metallicity and rota- J07446+035 34 26/26 428/585 tion because this line has zero magnetic sensitivity (i.e., effective J08298+267 11 5/5 165/218 g-factor geff = 0), but very often the profile of this line is severely J09449-123 11 2/9 93/260 distorted by a nearby telluric feature. A few more Ti lines J12156+526 13 4/10 146/300 are also affected by direct telluric hits. Therefore, it is essen- J12189+111 12 10/10 210/287 tial to extract maximum information by using both FeH and J14173+454 11 6/9 113/186 Ti lines and cross checking consistency between the results. For J15218+209 38 30/30 420/607 that, we used semi-empirical Landé g-factors for FeH lines as J15499+796 16 3/6 65/181 described in Shulyak et al. (2010), and removed telluric contribu- J16313+408 11 7/8 118/167 tion from Ti lines by direct modeling of telluric absorption with J16555-083 105 43/79 164/348 the M OLEC F IT1 tool (Smette et al. 2015; Kausch et al. 2015). J16570-043 13 4/6 176/378 Removing telluric features with M OLEC F IT was done by J17338+169 14 5/9 133/223 fitting the atmospheric transmission model to the observed spec- J18022+642 16 7/13 157/280 trum and adjusting mixing ratios of corresponding atmospheric J18189+661 13 6/12 164/288 gases, such as H2 O and CO2 . The atmospheric temperature and J18356+329 (a) 11 1/5 30/87 pressure as a function of altitude for a given observing time were J18498-238 41 2/31 149/755 extracted from the Global Data Assimilation System (GDAS) J19169+051S 33 17/24 121/187 database2 . The other essential parameters such as, surface tem- J19255+096 (a) 26 2/12 24/74 perature and pressure, local humidity, and airmass, are taken J19511+464 13 6/9 164/286 from the fits files generated by the instrument software. Cur- J20093-012 14 10/10 133/189 rent version of M OLEC F IT utilizes molecular line lists from J22012+283 12 10/10 219/296 the HITRAN database3 . After the state of the Earth’s atmo- J22468+443 93 26/79 404/1071 sphere has been defined, the code runs Levenberg-Marquardt J22518+317 11 4/9 146/282 χ2 -minimization algorithm to find best fit molecular number J23548+385 11 5/9 143/247 densities. The code can also fit polynomials of different orders for the normalization of the transmission spectrum. Once the Notes. (a) The two stars marked were excluded from the analysis of stellar best fit parameters have been found, the observed spectrum is magnetic fields due to very low S/N of the finally co-added spectra. divided by the predicted transmission model. This procedure was applied to each individual CARMENES exposure. The accu- racy of the telluric removal depends strongly on the S/N of the of the LL MODELS stellar atmosphere package (Shulyak et al. data and atmospheric humidity. For instance, if telluric lines are 2004). The radiative transfer equation is solved in all four Stokes deep then even small mismatch between model and observa- parameters for a given configuration of the magnetic field. Our tions in line cores may give rise to strong artifacts after spectra approach to measure magnetic fields is mostly the same as in our division. Therefore, the application of the same procedure to early study of active M dwarfs presented in Sh2017. spectra obtained at different seasons and/or different observato- There are two main problems that limit our analysis of cool ries can lead to deviations the spectra corrected for atmospheric star spectra. First, despite obvious improvements in molecu- transmission. lar opacity, most of the spectra of M dwarfs are still far from In stars with large projected rotational velocities, the rota- being a satisfactory fit to the accuracy required by modern high- tional broadening dominates the shape of line profiles, which resolution spectrographs. Much of the background opacity is still means that narrow and dense FeH lines become strongly blended missing, or not accurate enough. This becomes gradually worse and it is difficult or even impossible to accurately constrain the in late-type M dwarfs where molecules dominate opacity in all strength of surface magnetic fields from FeH lines alone. To the spectral domains. Second, the line formation itself is not well contrary, Ti lines are well separated from each other and remain understood because of uncertainties in model atmospheres and unblended even with largest υ sin i’s found in M dwarf stars. line broadening mechanisms. Therefore, it is very difficult to Strong telluric contamination is the only reason these lines were choose a proper set of spectral lines that would accurately sep- never used in magnetic field studies. However, if telluric contam- arate effects of the magnetic field and atmospheric parameters ination can be accurately removed, these lines become perfect (e.g., effective temperature, metallicity, rotation, etc.). Similar to Sh2017, we used lines of the FeH molecule at λλ990–995 nm 1 https://www.eso.org/sci/software/pipelines/skytools/ of the Wing–Ford F 4 ∆ − X 4 ∆ transitions, as well as Ti lines molecfit located at λλ960–980 nm. We chose FeH lines because they con- 2 https://ready.arl.noaa.gov/gdas1.php tain magnetically very sensitive and weakly sensitive lines, and 3 https://www.cfa.harvard.edu/hitran A86, page 3 of 24 A&A 626, A86 (2019) probes of magnetic fields in fast rotating stars because one can 1.0 J12156+526 1.0 J12156+526 use the effect of magnetic intensification to measure magnetic 0.8 = 5.5 kG 0.8 = 4.5 kG flux density. For instance, in the case of a saturated spectral Teff = 3400 K log(g) = 4.9 Teff = 3400 K log(g) = 4.9 0.6 0.6 line, its equivalent width will be proportional to the intensity υ ⋅ sin = 37.6 km⋅s−1 i υ ⋅ sin = 37.6 km⋅s−1 i f f of the magnetic field and the number of individual Zeeman 0.4 0.4 components, so-called Zeeman pattern (Landi Degl’Innocenti & 0.2 0.2 Landolfi 2004). Therefore, at large υ sin i the depths of individ- 0.00 2 4 6 8 10 12 14 16 18 20 0.00 2 4 6 8 10 12 14 16 18 20 ual spectral lines subject to strong magnetic field will depend on B, kG B, kG their Zeeman patterns. The lines of Ti in λλ960–980 nm region all have very different Zeeman patterns and thus one can fit their Fig. 1. Example of magnetic filling factors of J12156+526 as derived from Ti I lines. Original distribution contains high field components depths to measure intensity of the magnetic field (provided that (left panel), and ignoring them with subsequent re-scaling of the rest other stellar parameters are known). The obvious caveats in this of filling factors drops the average magnetic field by 1 kG (right panel). analysis is that the magnetic intensification (to a certain degree) can be mimicked by other effects, such as, for example, metal- licity or temperature effects: changing either of them will make their spectral types employing dedicated calibrations (Kenyon & lines look deeper or shallower, so that one can always satisfacto- Hartmann 1995; Golimowski et al. 2004). We took spectral types rily fit a magnetically sensitive line with a non-magnetic model from the CARMENCITA database (Alonso-Floriano et al. 2015; by adjusting atmospheric parameters. Therefore, using the mag- Caballero et al. 2016a). The other parameter – surface gravity netic insensitive Ti I λ974.3 nm line is the only way to break this log(g) – was calculated from the stellar radii and mass assum- degeneracy because it helps to constrain stellar parameters sepa- ing R ∝ M 0.9 relation which provides surface gravities close to rately from the magnetic field. From the magnetic intensification those predicted by stellar evolution models (Dotter et al. 2008; we can only measure magnetic fields that are strong enough to Bressan et al. 2012). We did not use effective temperatures and noticeably affect the equivalent widths of spectroscopic lines. surface gravities from Passegger et al. (2018) because they were Nevertheless, this effect opened a way to measure magnetic not able to derive such parameters for the most active and fastest fields in stars with extreme υ sin i values that was for many years rotating CARMENES stars, which just comprise our sample. believed impossible (Kochukhov & Lavail 2017; Sh2017). The transition parameters of Ti lines were extracted from the Our approach is to measure magnetic flux density from unpo- Vienna Atomic Line Database (VALD; Ryabchikova et al. 2015), larized light (i.e., Stokes – I). This way we can capture the and for FeH lines we used molecular constants taken from Dulick magnetic fields that are organized at both large and small scales. et al. (2003)4 . Transition probabilities for some of these lines However, the geometry of the magnetic field remains uncon- were corrected according to Wende et al. (2010). strained, meaning that we are blind to the sign of the field that Also, similar to Sh2017, we treated pressure broadening by we are looking at. To address this question one would need including contributions from hydrogen and helium only and additional polarimetric observations with another instrument(s). ignore contribution from molecular hydrogen H2 because it Still, strong surface magnetic fields in stars with convective grossly overestimates the observed widths of atomic lines espe- envelopes originate from spots and other active regions that dif- cially at late spectral types (see, e.g., Pavlenko et al. 2007). fer in, for example, size or number, distorting profiles of spectral Another source of line broadening is the velocity field caused lines differently from a case where the magnetic field was homo- by convective motions. However, as shown by 3D hydrody- geneously distributed over the stellar surface. This gives us a namic simulations (Wende et al. 2009), the velocity fields in possibility to measure what we call the complexity of surface atmospheres of M dwarfs with temperatures T eff < 3500 K are field by assuming a distribution of magnetic field components well below 1 km s−1 . This has a weak impact on line profiles, |B|i each covering a particular portion of the star represented leaving the Zeeman effect and rotation to be the dominating by filling factor P fi . The total magnetic field is then a simple broadening mechanisms. Therefore, we assumed zero micro- and sum hBi = |B|i fi . We used the Levenberg–Marquardt mini- macroturbulent velocities in all calculations. mization algorithm to find best fit values of filling factors for The filling factors that we derive with our method sometimes a given combination of atmospheric parameters. We simultane- show high-field magnetic components. A characteristic exam- ously processed rotational velocity, atmospheric abundance of a ple is illustrated in Fig. 1, where we show the filling factors of given element, continuum scaling factor for each spectral region J12156+526 as derived from the Ti lines. Here we derive a very that we fit, and 11 filling factors distributed between 0 and 20 kG smooth distribution of filling factors between 0 and 10 kG, but as free parameters. The continuum scaling factors are needed to then we also find two stand-alone magnetic field components at account for possible mismatch between observed and predicted the tailed 18 and 20 kG, respectively. As mentioned in Sh2017, spectra that may originate from, for example, artifacts left after these components result from the code trying to fit details in flat fielding and/or order merging, missing molecular opacity, observed line profiles originated from the poor data quality uncertainties in model atmospheres, amongst others. We note and/or bad understanding of background molecular absorption. that because the stellar continuum cannot be accurately defined, The filling factors of these components are small, but they con- especially in late type M dwarfs with strong absorption caused by tribute a significant fraction to the final result: ignoring them numerous photospheric water lines in the vicinity of our Ti lines, drop the average magnetic field from 5.5 to 4.5 kG, respec- we fit a low order polynomial to each CARMENES echelle order tively. We note that the magnetic components with strongest field prior to merging them into single 1D spectrum. This spectrum appear always irregardless of the choice of the limiting magnetic is thus normalized to stellar pseudo-continuum, but small off- field. In other words, it does not matter if one truncates the final sets could still be present and we account for them in our fitting magnetic component to, for instance, 15 kG instead of 20 kG approach with additional scaling factors. because the 15 kG magnetic component will then simply appear Similar to Sh2017, we computed theoretical line profiles to have a large filling factor etc. We also were not able to use too using MARCS model atmospheres (Gustafsson et al. 2008). The effective temperatures of our sample stars were computed from 4 http://bernath.uwaterloo.ca/FeH A86, page 4 of 24 D. Shulyak et al.: Magnetic fields in M dwarfs from the CARMENES survey Table 2. Magnetic field measurements. Karmn Name Gl/GJ SpT T eff log(g) Ti I lines FeH lines P hBi number K dex α(Ti) υ sin i hBi α(Fe) υ sin i hBi d adopted dex km s−1 kG dex km s−1 kG kG J01033+623 V388 Cas 51 M5.0 3200 5.1 −6.98 ± 0.02 11.7 ± 0.2 5.0 −4.42 ± 0.01 11.3 ± 0.1 4.7 1.06 4.8 ± 0.3 J01352-072 Barta 161 12 M4.0 3400 4.9 −6.99 ± 0.03 47.8 ± 0.7 5.8 −4.73 ± 0.02 41.8 ± 0.5 4.6 0.7031 5.8 ± 1.0 J02088+494 G 173-039 3136 M3.5 3400 4.9 −6.91 ± 0.02 22.9 ± 0.4 4.9 −4.55 ± 0.01 21.3 ± 0.2 4.5 0.748 4.9 ± 1.0 J03473-019 G 080-021 M3.0 3500 4.9 −6.93 ± 0.01 5.7 ± 0.1 3.2 −4.46 ± 0.01 6.4 ± 0.1 3.1 3.88 3.2 ± 0.1 J04472+206 RX J0447.2+2038 M5.0 3200 5.1 −7.01 ± 0.03 46.5 ± 0.6 5.7 −4.93 ± 0.03 37.5 ± 0.7 5.2 0.342 5.7 ± 1.0 J05365+113 V2689 Ori 208 M0.0 3800 4.7 −6.99 ± 0.01 0.4 ± 1.1 1.0 −4.73 ± 0.01 2.9 ± 0.1 1.3 12.04 1.2 ± 0.3 J06000+027 G 099-049 3379 M4.0 3400 4.9 −6.82 ± 0.02 6.5 ± 0.2 2.0 −4.28 ± 0.01 5.6 ± 0.1 3.0 1.81 2.5 ± 1.0 J07446+035 YZ CMi 285 M4.5 3300 5.0 −6.93 ± 0.02 4.5 ± 0.1 4.7 −4.41 ± 0.01 5.4 ± 0.1 4.4 2.78 4.6 ± 0.3 J08298+267 DX Cnc 1111 M6.5 2700 5.3 −7.19 ± 0.03 12.4 ± 0.4 3.0 −5.02 ± 0.01 10.4 ± 0.1 3.6 0.459 3.3 ± 0.6 J09449-123 G 161-071 M5.0 3200 5.1 −7.08 ± 0.03 30.1 ± 0.6 5.3 −4.70 ± 0.01 27.3 ± 0.3 4.5 0.306 5.3 ± 1.0 J12156+526 StKM 2-809 M4.0 3400 4.9 −6.90 ± 0.02 37.6 ± 0.4 4.5 −4.83 ± 0.01 28.0 ± 0.3 4.2 <0.4 4.5 ± 1.0 J12189+111 GL Vir 1156 M5.0 3200 5.1 −6.89 ± 0.02 15.4 ± 0.3 3.3 −4.22 ± 0.01 15.3 ± 0.1 4.0 0.491 3.6 ± 0.7 J14173+454 RX J1417.3+4525 M5.0 3200 5.1 −7.05 ± 0.03 13.8 ± 0.4 5.1 −4.56 ± 0.01 15.3 ± 0.1 5.3 <0.7 5.2 ± 0.2 J15218+209 OT Ser 9520 M1.5 3600 4.8 −6.95 ± 0.02 3.9 ± 0.2 3.3 −4.49 ± 0.01 5.0 ± 0.1 3.1 3.372 3.2 ± 0.2 J15499+796 LP 022-420 M5.0 3200 5.1 −6.86 ± 0.02 27.7 ± 0.5 3.4 −4.73 ± 0.02 22.9 ± 0.5 4.2 <0.3 3.4 ± 1.0 J16313+408 G 180-060 3959 M5.0 3200 5.1 −6.92 ± 0.02 7.5 ± 0.2 4.1 −4.31 ± 0.01 8.1 ± 0.1 4.0 0.51 4.1 ± 0.1 J16555-083 vB 8 644 C M7.0 2600 5.3 −7.21 ± 0.04 5.8 ± 0.5 2.6 −5.07 ± 0.01 7.0 ± 0.1 3.0 <1.0 2.8 ± 0.4 J16570-043 LP 686-027 1207 M3.5 3400 4.9 −6.93 ± 0.02 10.5 ± 0.2 3.1 −4.31 ± 0.01 10.7 ± 0.1 3.5 1.21 3.3 ± 0.4 J17338+169 1RXS J173353.5+165515 M5.5 3000 5.2 −7.15 ± 0.04 36.6 ± 1.0 6.9 −5.18 ± 0.03 29.1 ± 0.6 4.5 0.27 6.9 ± 1.0 J18022+642 LP 071-082 M5.0 3200 5.1 −6.90 ± 0.02 10.6 ± 0.2 3.8 −4.37 ± 0.01 10.9 ± 0.1 4.7 0.28 4.3 ± 0.9 J18189+661 LP 071-165 4053 M4.5 3300 5.0 −6.59 ± 0.04 15.6 ± 0.3 1.8 −4.30 ± 0.02 14.4 ± 0.2 3.4 <0.7 2.6 ± 1.6 J18498-238 V1216 Sgr 729 M3.5 3400 4.9 −6.73 ± 0.03 5.4 ± 0.2 1.8 −4.27 ± 0.01 4.1 ± 0.1 2.6 2.87 2.2 ± 0.8 J19169+051S V1298 Aql (vB 10) 752 B M8.0 2500 5.3 −7.55 ± 0.10 5.1 ± 0.5 2.2 −5.11 ± 0.01 5.4 ± 0.1 2.4 0.8 2.3 ± 0.2 J19511+464 G 208-042 1243 M4.0 3400 4.9 −6.87 ± 0.02 23.3 ± 0.3 3.2 −4.53 ± 0.01 21.1 ± 0.2 3.3 0.594 3.2 ± 1.0 J20093-012 SCR J2009-0113 M5.0 3200 5.1 −6.95 ± 0.03 5.1 ± 0.2 3.1 −4.31 ± 0.01 5.9 ± 0.1 3.4 <1.8 3.2 ± 0.3 J22012+283 V374 Peg 4247 M4.0 3400 4.9 −6.84 ± 0.01 36.3 ± 0.3 4.4 −4.53 ± 0.01 31.5 ± 0.3 4.4 0.45 4.4 ± 1.0 J22468+443 EV Lac 873 M3.5 3400 4.9 −6.90 ± 0.02 4.5 ± 0.2 4.2 −4.44 ± 0.01 5.1 ± 0.1 4.0 4.379 4.1 ± 0.2 J22518+317 GT Peg 875.1 M3.0 3500 4.9 −6.90 ± 0.02 14.3 ± 0.2 3.1 −4.49 ± 0.01 13.2 ± 0.1 3.7 1.64 3.4 ± 0.6 J23548+385 RX J2354.8+3831 M4.0 3400 5.0 −6.92 ± 0.02 4.3 ± 0.2 4.8 −4.34 ± 0.01 4.7 ± 0.1 4.4 4.76 4.6 ± 0.4 Notes. For stars without measured rotational periods we esimate them from υ sin i values and stellar radii estimated from spectral types. The last column lists adopted values of the surface magnetic fields. For stars with υ sin i < 20 km s−1 they were taken as a mean between meaurements from Ti and FeH lines, respectively, and the error bars were assumed to be the corresponding difference between these measurements. For stars with υ sin i > 20 km s−1 we adopt measurements from the Ti lines and similar to Shulyak et al. (2017) assume conservative uncertainties of 1 kG. The rotational velocities derived from Ti lines should be preferred over those derived from FeH lines. few magnetic field components because we would under-fit pro- poor data quality (see Table 1). We summarize our magnetic field files of spectral lines. Because we have no physically motivated measurements in Table 2 and describe them in detail below. In reason to believe that these high field components truly exist, we addition, we provide our model fits to individual spectral lines in ignored them in our estimates of stellar magnetic fields. Appendix A (Figs. A.1–A.29). We note that because filling fac- While the initial guess for abundances and υ sin i does not tors are correlated parameters, it was not possible to estimate have a strong impact on the final results, this is not always the robust error bars on the values of the magnetic field strength case for filling factors. Again, we find that this is more often an and filling factors from our approach. Besides, the formal errors issue for stars with poor data quality. Interestingly, even if fill- from the chi-square fit on the parameters are likely underesti- ing factor distributions look different, the total magnetic field mating the true uncertainties because of additional sources of strength is usually not affected much (with a scatter on the order uncertainties such as, choice of the spectral lines, accuracy of of a few hundred Gauss in our sample). The stars for which the telluric correction. It appears very difficult to quantify all the initial guess of filling factors also affects the resulting field possible sources because we would need to run a lot more indi- strength are those with υ sin i > 20 km s−1 and only when we vidual measurements for each star which is very computationally derive fields from FeH lines. This is expected because strong demanding. Therefore, similar to our previous works we put a blending of FeH lines and uncertainties in their transition and conservative 1 kG error bars on measured magnetic fields in magnetic parameters act together contributing to the uncertainty stars with υ sin i > 20 km s−1 . For the rest of the sample we pro- of the results. vide uncertainties on the derived magnetic fields as a difference between measurements from FeH and Ti lines, similar to Sh2017. 4. Results 4.1. Magnetic fields of sample stars Our present sample comprises of 29 active stars with short rota- tion periods ranging between 10 and 0.1 d. Among them, there In Fig. 2 we compare magnetic fields measured from Ti and are 16 objects without previous magnetic field measurements, FeH lines, respectively. In general, we obtain very consistent and 5 objects with υ sin i > 30 km s−1 . Two stars, J18356+329 estimates of the magnetic fields from Ti and FeH lines in and J19255+096, were excluded from the analysis because of stars with good data quality and relatively small υ sin i values, A86, page 5 of 24 A&A 626, A86 (2019) 8000 4.2. Comparison with previous measurements 7000 40 Our sample contains 12 objects with previously measured mag- netic fields, in nine of which we find a good agreement between 6000 literature values and our measurements. Stars for which our new 5000 30 measurements disagree with previous results are J01033+623, BS, G (FeH) J01352-072 J15218+209, and J19169+051. υ sin i, km s−1 4000 J17338+169 In J01033+623, Sh2017 measured a field of hBi = 6.1 kG J18189+661 20 from the ESPaDOnS data, while from CARMENES data we 3000 derive much weaker hBi = 4.8 kG. This is because now we 2000 derive more smooth distribution of filling factors with a reduced 10 12 kG component. If we exclude this component from our fit 1000 to ESPaDOnS data we get very close hBi = 5 kG average field, but then the fit to the data looks worse. The same discrepancy 0 0 1000 2000 3000 4000 5000 6000 7000 8000 is found for FeH lines, and at this point it is difficult to decide BS, G (Ti) which of the fit should be preferred. Fig. 2. Comparison between the magnetic field measurements from Ti In J15218+209 we find a 0.5 kG stronger field from and FeH lines with υ sin i color coded. Dashed and dash-dotted lines CARMENES data both from Ti and FeH lines, but our FeH represent 1 and 2 kG deviations from the central line, respectively. spectrum is very noisy. The difference in measured magnetic field from Ti lines could be explained by quite different, that is, we measure υ sin i = 3.9 km s−1 and υ sin i = 4.9 km s−1 from such as, for example, J03473-019, J05365+113, J07446+035, CARMENES and ESPaDOnS spectra, respectively. We find that J15218+209, and J22468+443 (see Table 2). Thus, despite the higher υ sin i measured from the ESPaDOnS data is likely of telluric removal problem and uncertainties in magnetic due to the telluric removal artifact that affected the profile of the g-factors, both Ti and FeH lines can be successfully used for the magnetic insensitive Ti I λ974.3 nm line which made it broader magnetic field measurements. in ESPaDOnS data. At the same time, for stars J06000+027 and J18498-238 we In J19169+051S we measure a stronger field of hBi = 2.2 kG obtain very different estimates even though the data for these compared to previous estimate of hBi = 1.3 kG from Reiners & stars look relatively good and their υ sin i values are relatively Basri (2007). Our fit to Ti lines in this star was not very accu- small, too (see Table 2). We note that in these stars we measure rate because we could use only four lines and the observed line systematically higher υ sin i from Ti lines compared to FeH lines profiles were affected by surrounding strong molecular features and hence lower values of magnetic fields, which can partly be prominent at these cool temperatures. On the other hand, FeH due to the distortion of the magnetic insensitive Ti I λ974.3 nm spectrum looks better and from them we derive still field of line by telluric removal procedure. If we fixed υ sin i in these hBi = 2.4 kG. We note that Reiners & Basri (2007) measured stars to the lower values (i.e., to the values derived from the fit to field in J19169+051S indirectly, that is, without employing radia- FeH lines) we always obtain estimates close to that derived from tive transfer models, which could explain the difference in the FeH lines. It is thus possible that inaccuracies in υ sin i values magnetic fields between their and our measurements. On the can explain the observed discrepancy in derived magnetic fields other hand, our understanding of line formation in cool tem- in these objects. peratures of late type M dwarfs is far from been satisfactorily In three stars we find a deviation of more than 1 kG between understood. Uncertainties in, for example, molecular broadening measurements from Ti and FeH lines, and we marked them with can bias our results. This question needs to be addressed on a their names in Fig. 2. The largest deviations of 2.4 kG is found in larger sample of stars. J17338+169. In this star the red wing of the Ti λ974.3 nm line is affected by telluric removal artifact (see Fig. A.19). Alternatively, 4.3. Complexity of surface magnetic fields we used different individual spectra to fit this line and obtained a weaker field of hBi = 6 kG with higher υ sin i = 39 km s−1 instead We used magnetic filling factors in our attempts to measure mag- of hBi = 6.9 kG, but the large deviation between measurements netic fields because complex shapes of magnetically sensitive from Ti and FeH still remained. In J01352-072 the fit to FeH spectral lines in M dwarfs can not be represented by a single spectrum is very inaccurate. In addition, we were only able to use magnetic field component. In order to recover accurate distri- half of the region covered by FeH lines. At the same time, our fit butions of filling factors data with very high S/N are required. to Ti lines is much more accurate. In J18189+661 we could not Moreover, filling factors are sensitive to the available magnetic accurately remove telluric feature from the Ti I 974.3 nm line information (i.e., set of spectral lines) and atmospheric param- that made this line look deeper. As a result, we measured an eters (especially elemental abundance and rotation broadening). overestimated Ti abundance and hence a weaker magnetic field Therefore, the filling factors presented in this paper should be from Ti lines compared to that from FeH lines. taken with caution, at least for fast rotating stars. The results are In stars with rotation velocities υ sin i > 20 km s−1 we often shown on Figs. 3 and 4 as derived from Ti lines. (but not always) measure weaker fields from FeH lines com- Our filling factors seem to show two distinct patterns. pared to Ti lines. The same effect was observed and explained We detect either very smooth distributions (e.g., J01033+623, in Sh2017 as being likely caused by strong line blending which J07446+035, J08298+267 – Fig. 4, J12156+526 – Fig. 3), or leads to the degeneracy in fitting parameters (i.e., temperature, more patchy patterns with distinct dominant magnetic field com- abundance, rotation). The results of these measurements depend ponents (e.g., J02088+494 – Fig. 3, J16555-083, J22012+283 – strongly on data quality and set of FeH lines used for the Fig. 4, J18022+642, J18189+661 – Fig. 3). In our sample analysis. Especially in fast rotating stars the result of our mea- there are four M dwarfs that, according to their spectral types surements from Ti lines must be preferred over values derived (SpT < M3.5), should have partly convective envelopes (J03473- from FeH lines. 019, J05365+113, J15218+209, J22518+317), while the rest A86, page 6 of 24 D. Shulyak et al.: Magnetic fields in M dwarfs from the CARMENES survey 1.0 J05365+113 1.0 J03473-019 1.0 J16570-043 0.8 = 1.0 kG 0.8 = 3.2 kG 0.8 = 3.1 kG Teff = 3800 K Teff = 3500 K Teff = 3400 K 0.6 log(g) = 4.7 0.6 log(g) = 4.9 0.6 log(g) = 4.9 υ ⋅ sin = 0.4 km⋅s−1 i υ ⋅ sin = 5.7 km⋅s−1 i υ ⋅ sin = 10.5 km⋅s−1 i f f f 0.4 0.4 0.4 0.2 0.2 0.2 0.00 2 4 6 8 10 12 14 16 18 20 0.00 2 4 6 8 10 12 14 16 18 20 0.00 2 4 6 8 10 12 14 16 18 20 B, kG B, kG B, kG 1.0 J19511+464 1.0 J18189+661 1.0 J18022+642 0.8 = 3.2 kG 0.8 = 1.8 kG 0.8 = 3.8 kG Teff = 3400 K Teff = 3300 K Teff = 3200 K 0.6 log(g) = 4.9 0.6 log(g) = 5.0 0.6 log(g) = 5.1 υ ⋅ sin = 23.3 km⋅s−1 i υ ⋅ sin = 15.6 km⋅s−1 i υ ⋅ sin = 10.6 km⋅s−1 i f f f 0.4 0.4 0.4 0.2 0.2 0.2 0.00 2 4 6 8 10 12 14 16 18 20 0.00 2 4 6 8 10 12 14 16 18 20 0.00 2 4 6 8 10 12 14 16 18 20 B, kG B, kG B, kG 1.0 J06000+027 1.0 J18498-238 1.0 J22518+317 0.8 = 2.0 kG 0.8 = 1.8 kG 0.8 = 3.1 kG Teff = 3400 K Teff = 3400 K Teff = 3500 K 0.6 log(g) = 4.9 0.6 log(g) = 4.9 0.6 log(g) = 4.9 υ ⋅ sin = 6.4 km⋅s−1 i υ ⋅ sin = 5.4 km⋅s−1 i υ ⋅ sin = 14.3 km⋅s−1 i f f f 0.4 0.4 0.4 0.2 0.2 0.2 0.00 2 4 6 8 10 12 14 16 18 20 0.00 2 4 6 8 10 12 14 16 18 20 0.00 2 4 6 8 10 12 14 16 18 20 B, kG B, kG B, kG 1.0 J12156+526 1.0 J01352-072 1.0 J23548+385 0.8 = 4.5 kG 0.8 = 5.8 kG 0.8 = 4.8 kG Teff = 3400 K Teff = 3400 K Teff = 3400 K 0.6 log(g) = 4.9 0.6 log(g) = 4.9 0.6 log(g) = 5.0 υ ⋅ sin = 37.6 km⋅s−1 i υ ⋅ sin = 47.8 km⋅s−1 i υ ⋅ sin = 4.3 km⋅s−1 i f f f 0.4 0.4 0.4 0.2 0.2 0.2 0.00 2 4 6 8 10 12 14 16 18 20 0.00 2 4 6 8 10 12 14 16 18 20 0.00 2 4 6 8 10 12 14 16 18 20 B, kG B, kG B, kG 1.0 J17338+169 1.0 J20093-012 1.0 J16313+408 0.8 = 6.9 kG 0.8 = 3.1 kG 0.8 = 4.1 kG Teff = 3000 K Teff = 3200 K Teff = 3200 K 0.6 log(g) = 5.2 0.6 log(g) = 5.1 0.6 log(g) = 5.1 υ ⋅ sin = 36.6 km⋅s−1 i υ ⋅ sin = 5.1 km⋅s−1 i υ ⋅ sin = 7.5 km⋅s−1 i f f f 0.4 0.4 0.4 0.2 0.2 0.2 0.00 2 4 6 8 10 12 14 16 18 20 0.00 2 4 6 8 10 12 14 16 18 20 0.00 2 4 6 8 10 12 14 16 18 20 B, kG B, kG B, kG Fig. 3. Distribution of filling factors as derived from Ti lines. The stars are sorted according to the S/N of their spectra (S/N decreases from left to the right and top to bottom). should be fully convective objects. However, we do not observe (Fig. 3) we derive a very weak magnetic field with only two an obvious change in the complexity of the fields between these magnetic components (0 and 2 kG, respectively). two groups. For instance, the distribution of filling factors in In our sample, we find several objects with remarkably very partly convective J03473-019 and J22518+317 (Fig. 3) can be similar properties of their magnetic fields. For the two stars compared to, for example, those of fully convective J19169+051S with largest υ sin i values, J01352-072 (Fig. 3) and J04472+206 (Fig. 4) and J19511+464 (Fig. 3). The only noticable feature is (Fig. 3), we recover the same average magnetic fields with identi- that fully convective stars tend to have stronger average magnetic cal filling factors. The only difference between these stars is that fields represented by magnetic components of stronger strength. J04472+206 is one spectral type cooler. Next, we find a twin of For instance, in the hottest partly convective star J05365+113 J07446+035 (very well studied M dwarf YZ CMi, Fig. 4), which A86, page 7 of 24 A&A 626, A86 (2019) 1.0 J14173+454 1.0 J09449-123 1.0 J04472+206 0.8 = 5.1 kG 0.8 = 5.3 kG 0.8 = 5.7 kG Teff = 3200 K Teff = 3200 K Teff = 3200 K 0.6 log(g) = 5.1 0.6 log(g) = 5.1 0.6 log(g) = 5.1 υ ⋅ sin = 13.8 km⋅s−1 i υ ⋅ sin = 30.1 km⋅s−1 i υ ⋅ sin = 46.5 km⋅s−1 i f f f 0.4 0.4 0.4 0.2 0.2 0.2 0.00 2 4 6 8 10 12 14 16 18 20 0.00 2 4 6 8 10 12 14 16 18 20 0.00 2 4 6 8 10 12 14 16 18 20 B, kG B, kG B, kG 1.0 J02088+494 1.0 J15499+796 0.8 = 4.9 kG 0.8 = 3.4 kG Teff = 3400 K Teff = 3200 K 0.6 log(g) = 4.9 0.6 log(g) = 5.1 υ ⋅ sin = 22.9 km⋅s−1 i υ ⋅ sin = 27.7 km⋅s−1 i f f 0.4 0.4 0.2 0.2 0.00 2 4 6 8 10 12 14 16 18 20 0.00 2 4 6 8 10 12 14 16 18 20 B, kG B, kG Fig. 3. continued. is J23548+385 (not studied at all, Fig. 3). Both stars have very rotation periods are from Díez Alonso et al. (2019) and Morin similar filling factors, average magnetic field, projected rota- et al. (2010 and references therein). tional velocities, but slightly different spectral types. In addition, The general pattern of increasing magnetic field strength as another famous M dwarf J22468+443 (EV Lac) has filling fac- period decreases down to about P ≈ 4 d is evident from Fig. 5. tors similar to J07446+035 and J23548+385, although its average When M dwarfs rotate faster, the regime becomes activity satu- magnetic field is noticeably weaker. ration in terms of X-ray fluxes (Noyes et al. 1984; Reiners et al. We next looked for a connection between our filling fac- 2014). The magnetic field strength in this regime show large tors and the geometry of large scale magnetic fields. In our scatter with values between 2 and 7 kG. The magnetic field in sample, we have nine stars for which the geometry of their GJ 3622 was measured in Sh2017 and its magnitude seems to be surface magnetic fields was previously derived from polarimet- too weak as for the rotation period of P = 1.5 d. It is thus impor- ric measurements. In particular, Morin et al. (2010) showed tant to obtain new magnetic field measurements for this star in that partly convective M dwarfs tend to have complex multi- future studies. pole fields with strong toroidal contribution, while stars that From Fig. 5 it is difficult to see a well defined trend of the are fully convective generate dipole-dominant predominantly magnetic flux density increasing with rotation for periods below poloidal magnetic fields. Following this classification, in Fig. 4 four days. We are currently lacking accurate magnetic field mea- we grouped M dwarfs in columns depending on whether the star surements in stars with ultra-short periods and our current results has dipole-dominant magnetic field (left column) or more com- are consistent with the generally accepted conclusion that the plex multipole-dominant field (right column). One can see that magnetic flux density saturates in stars with saturated activity. there is no obvious difference in filling factors between these More work needs to be done to fully address this effect. two groups. A smooth distribution is found for dipole-dominant J01033+623 on one side, and multipole-dominant J08298+267 5. Discussion and J19169+051S on the other side. Likewise, J07446+035 and J22468+443 have almost identical filling factors but their 5.1. Magnetic filling factors magnetic field geometries were found to be very different. Nev- ertheless, there seems to be one common feature that is intrinsic From our analysis of filling factors we find two distinct patterns to complex multipole fields as observed from filling factors, in their distribution. The first pattern is a very smooth distri- which is the appearance of strong zero-field components. This bution of filling factors and the second looks more patchy and zero-field component is strongest in four out of five stars with can not be approximated by a smooth function. It is difficult to multipole-donimant fields with an exception of J22468+443. find strict connections between patterns in our filling factors and other essential stellar parameters such as rotation or temperature. 4.4. Magnetic field and rotation However, it is possible to draw some preliminary conclusions. First, we find no clear difference in patterns of filling fac- The detection of very strong magnetic fields in M dwarfs needs tors between fully and partially convective stars. However, we to be understood in terms of underlying dynamo processes. observe that fully convective stars tend to have stronger aver- Because dynamos in these stars are powered by convective age magnetic fields represented by stronger magnetic compo- motions subject to stellar rotation, it is essential to compare our nents. This reflects the conclusion already drawn in previous magnetic field measurements with rotation periods which we investigations that fully convective stars generate on average plot in Fig. 5. We also plot measurements from Sh2017 and other stronger surface magnetic fields (Reiners & Basri 2007). literature sources for stars that are not in our sample. We also Second, there seems to be no pronounced difference in fill- include recent measurements of the magnetic field in the eclips- ing factors for stars that are known to have different geometries ing binary system YY Gem (Kochukhov & Shulyak 2019). The of their large scale fields. Our Fig. 4 suggests that stars with A86, page 8 of 24 D. Shulyak et al.: Magnetic fields in M dwarfs from the CARMENES survey Dipole-dominant Multipole-dominant same average magnetic fields with identical filling factors. The 1.0 J01033+623 1.0 J08298+267 other twins are J07446+035 and J23548+385. These stars have 0.8 = 5.0 kG 0.8 = 3.0 kG very close υ sin i’s, spectral types, average magnetic fields, and Teff = 3200 K log(g) = 5.1 Teff = 2700 K log(g) = 5.3 pattern of filling factors. Because J07446+035 has stable dipole- 0.6 0.6 υ ⋅ sin = 11.7 km⋅s−1 i υ ⋅ sin = 12.4 km⋅s−1 i dominant magnetic field geometry (Morin et al. 2008) we predict f f 0.4 0.4 that this should be the same for J23548+385. However, for 0.2 0.2 J22468+443 with a multipole-dominant field, we also derive 0.00 2 4 6 8 10 12 14 16 18 20 0.00 2 4 6 8 10 12 14 16 18 20 filling factors that look surprisingly similar to those of dipole- B, kG B, kG dominant J07446+035. A possible explanation would be just a 1.0 J07446+035 1.0 J12189+111 coincidence because J22468+443 has complex variable mag- netic field and it might just have happened that the star was 0.8 = 4.7 kG 0.8 = 3.3 kG Teff = 3300 K Teff = 3200 K observed when its surface field was simple. Because the spectra 0.6 log(g) = 5.0 υ ⋅ sin = 4.5 km⋅s−1 i 0.6 log(g) = 5.1 υ ⋅ sin = 15.4 km⋅s−1 i of J22468+443 has very high S/N, we looked for a possible sea- sonal magnetic field variation between spectra obtained in 2016 f f 0.4 0.4 0.2 0.2 (June–December) and 2017 (January–October). For each year, we co-added individual spectra to build a high S/N template as 0.00 2 4 6 8 10 12 14 16 18 20 0.00 2 4 6 8 10 12 14 16 18 20 B, kG B, kG described in Sect. 3. We find that line profiles of Ti did not show J15218+209 J16555-083 any significant changes, as can be seen from the top panel of 1.0 1.0 Fig. 6 where we plot spectra obtained in 2016 and 2017 around 0.8 = 3.3 kG 0.8 = 2.6 kG three magnetic sensitive Ti lines. We also derive filling factors Teff = 3600 K Teff = 2600 K 0.6 log(g) = 4.8 0.6 log(g) = 5.3 for these two data sets and found them to be very similar with ⋅ sin = 3.9 km⋅s−1 ⋅ sin = 5.8 km⋅s−1 υ i υ i only marginal change in the total magnetic field strength, as illus- f f 0.4 0.4 trated in the bottom panel of Fig. 6. We note that J22468+443 0.2 0.2 was observed to have very strong variability of the large scale 0.00 2 4 6 8 10 12 14 16 18 20 0.00 2 4 6 8 10 12 14 16 18 20 component of its magnetic field with large areas of positive and B, kG B, kG negative fields located in the same hemisphere (see Fig. 4 in 1.0 J22012+283 1.0 J19169+051S Morin et al. 2008). Such features have never been detected in 0.8 = 4.4 kG 0.8 = 2.2 kG stars with dipole-dominant fields (e.g., WX UMa, AD Leo, and Teff = 3400 K log(g) = 4.9 Teff = 2500 K log(g) = 5.3 Gl 51) and thus we still place J22468+443 in the group of stars 0.6 0.6 υ ⋅ sin = 36.3 km⋅s−1 i υ ⋅ sin = 5.1 km⋅s−1 i with complex multipole fields. Additional spectropolarimetric f f 0.4 0.4 measurements will surely help to address this question in more 0.2 0.2 detail. 0.00 2 4 6 8 10 12 14 16 18 20 0.00 2 4 6 8 10 12 14 16 18 20 Next, with certain exceptions we can conclude that M dwarfs B, kG B, kG of spectral types around M7.0 and later tend to have smooth 1.0 J22468+443 distributions of their filling factors with obviously dominant = 4.2 kG zero-field magnetic component like, for example, J08298+267 0.8 Teff = 3400 K and J19169+051S, with an exception of J16555-083 which shows 0.6 log(g) = 4.9 υ ⋅ sin = 4.8 km⋅s−1 i more patchy filling factors pattern (Fig. 4). If confirmed with f 0.4 future studies, this would imply that magnetic dynamo in stars 0.2 at the very cool end of the M-type sequence fails to generate 0.00 2 4 6 8 10 12 14 16 18 20 large spots and perhaps decays out because temperatures of this B, kG objects are too cool to support efficient dynamo action. In stars with large υ sin i > 20 km s−1 we usually find smooth Fig. 4. Distribution of filling factors as derived from Ti lines for stars distribution of filling factors that peak at non-zero magnetic with known geometry of their large-scale magnetic fields. Left column: field component. This could mean that the stars have simple dipole-dominant, right column: multipole-dominant. dipole-dominant magnetic fields, that is, consistent with what one would expect in fully convective objects with short rotation multipole-dominant fields seem to have stronger zero field mag- periods. netic component compared to stars with dipole-dominant fields. In this work we have not studied the rotational variability in This is an interesting observation because it may tell us that these individual line profiles which could be caused by variable mag- stars have different spot distributions and, perhaps, spot sizes on netic field strength over the stellar surface. This variability could their surfaces compared to stars with dipole-dominant fields. For be seen in stars with largest υ sin i values due to a better spatial instance, spots that are present in a few small localized areas resolution provided by the Doppler broadened line profiles. The on a visible disk of the star while the rest of the photosphere first evidence of such variability was reported in Kochukhov & is non-magnetic would result in strong zero field component. Lavail (2017) for the B component of the binary system Gl 65. On the contrary, a large spot or groups of spots around mag- At the same time, no line profile variability was recently detected netic poles that occupy considerable fraction of the stellar disk by Kochukhov & Shulyak (2019) in another fast rotating binary would have a reduced zero field component or even none if YY Gem, possibly implying that the variability is very weak due observed at small inclination. Recent analysis of stellar spots in a to a different distribution of small scale magnetic fields over the binary system Gl 65-AB seem to support this idea (Barnes et al. surface of these stars compared to the case of Gl 65 B. Unfortu- 2017). It would be thus interesting to combine polarimetric and nately, the S/N of individual spectra for our stars is much lower photometric techniques to address this question in future. than those used in both mentioned above studies and we could Another remarkable finding is the detection of twins in not detect any significant variability above the photon noise limit. our sample. In stars J01352-072 and J04472+206 we recover This also implies that the total magnetic field strength remains A86, page 9 of 24 A&A 626, A86 (2019) 104 CARMENES (dipole) CARMENES (multipole) CARMENES (unknown) 1 GJ 3622 31 DX Cnc 2 Gl 49 32 G 161-071 15 Literature (dipole) 3 Gl 182 33 StKM 2-809 41 Literature (multipole) 4 CE Boo 34 GL Vir Literature (unknown) 5 DT Vir 35 RX J1417.3+4525 20 24 6 AD Leo 36 OT Ser 27 7 AU Mic 37 LP 022-420 32 35 8 GJ 1224 38 GJ 3959 25 23 9 GJ 1245 B 39 vB 8 1942 3348 30 51 10 CN Leo 40 GJ 1207 18 38 49 11 LP 412-31 41 1RXS J173353.5+165515 12 GJ 3379 42 LP 071-082 34 11 17 13 Gl 493.1 43 GJ 4053 37 31 46 9 21 22 40 5047 3626 14 GJ 1154 A 15 WX UMa 44 Gl 729 45 vB 10 6 16 DS Leo 46 GJ 1243 39 83 17 EQ Peg A 47 2MASS J20091824-0113377 Bs , G 43 2910 5 18 EQ Peg B 48 V374 Peg 19 BL Cet 49 EV Lac 45 12 44 7 20 UV Cet 50 GT Peg 13 14 21 YY Gem A 51 RX J2354.8+3831 22 YY Gem B 4 23 Wolf 47 24 Barta 161 12 25 GJ 3136 26 G 080-021 1 27 RX J0447.2+2038 28 Gl 208 28 29 GJ 3379 30 YZ CMi 103 0.1MO• 16 0.3MO• 2 0.5MO• 0.1 1.0 10.0 P, d Fig. 5. Average magnetic fields in stars from our sample as a function of rotation period. Measurements in stars with known dipole and multipole states are shown as solid upward- and downward-pointing triangles, respectively. Stars with unknown dynamo states are shown as solid blue circles. Our measurements from this work are shown with blue color and the literature values are shown with the red one. The symbol size scales with stellar mass (see legend on the plot). The horizontal dashed line marks the 4 kG threshold of saturated magnetic field assigned to stars with multipole dynamo regime. Similar to our previous works we include conservative 1 kG error bars on measured magnetic fields in stars with υ sin i > 20 km s−1 . very much stable over the time spawn of our observations and linked to the properties of the initial magnetic field that existed does not bias our analysis. However, it is no doubt important to during the star formation (Gastine et al. 2013). Furthermore, study line profile variability in future studies. when the rotation decreases (e.g., due to the magnetic braking), a fully convective star may change its dynamo state from a stable 5.2. Magnetic field and rotation dipole-dominant to a variable complex magnetic field thereby developing magnetic cycles, that is, the magnetic field geometry Our new measurements add nine new objects to the set of will vary with time (Yadav et al. 2016). stars having very strong fields above 4 kG and one object From our CARMENES data we do not have information (J05365+113) to the subsample of stars with long rotation period about the geometry of the magnetic fields in our stars, but from and weak fields. From Fig. 5 one can still see a large scatter our measurements we find objects with very strong fields and in magnetic fields for stars with periods shorter than 4 d and it fast rotation so we predict that they should have dipole-dominant remains inconclusive whether magnetic fields keep growing as fields. It is therefore essential to follow up these stars with spec- periods decrease or do they saturate to some maximum magnetic tropolarimetric observations. This would help to better constrain field which could be defined by the stellar dynamo state, as sug- the connection between field intensity, geometry, and the rotation gested in Sh2017. Additional measurements are clearly needed. of the star. In particular, it is needed to analyze stars with ultra-short rotation There are many more potential applications of our findings, periods P < 0.3 d. as magnetic fields play critical role in all stages of stellar and Another important property of stellar magnetic fields is even planetary evolution. For instance, knowing magnetic prop- the geometry of their large scale components. The current erties of stars is one of the pieces in the puzzle called stellar understanding of stellar magnetism predicts complex multipole- activity and includes understanding connections between the dominant magnetic fields in partly convective M dwarfs and magnetic fields, rotation braking, stellar spots, X-ray fluxes, and more simple, dipole-dominant fields in stars that are fully con- finally understanding the hazardous environment around plan- vective (Morin et al. 2010; Gastine et al. 2013). However, there ets orbiting these active stars (Vidotto et al. 2015; Garraffo et al. are cases of a fast rotating fully convective object that gener- 2017). Very strong magnetic fields may even have a direct impact ate complex mostly multipole fields (e.g., DX Cnc, GJ 1245 B, on the planetary structure by providing additional source of and Gl Vir). Rotation alone can not explain this observation energy via the induction heating (Kislyakova et al. 2017, 2018). because both types of geometries are found in stars that have Especially M dwarfs with dipole dynamo states are interesting similar spectral types and rotation periods. It is believed that objects in this regard because they maintain stable large scale dynamo in M dwarfs (at least when they are fully convective) magnetic fields whose energy decay with a separation to the become bi-stable and the choice of the dynamo state is somehow star much slower compared to stars with multipole-dominant A86, page 10 of 24 D. Shulyak et al.: Magnetic fields in M dwarfs from the CARMENES survey magnetic field saturation, however the magnetic field may as 1.0 well still grow at least in stars with dipole dynamo states. 0.9 – Our analysis of filling factors points toward the existence of particular features in their patterns that may help to distin- 0.8 guish between the stars that have different dynamo states Normalized flux and/or spot patterns. 0.7 – We find two stars, J07446+035 and J23548+385, that are twins in terms of their average magnetic fields and distri- 0.6 bution of filling factors. It would be interesting to compare the geometry of their global magnetic fields and test whether 0.5 they are the same as well. This would be an important 0.4 additional test for our analysis methods. 2016 2017 – Our study adds 16 new objects to the list of stars with strong magnetic fields and short rotation periods. However, 976.5 977.0 977.5 978.0 978.5 979.0 979.5 Wavelength, nm in order to fully characterize magnetic properties of stars and to put our findings in the context of bi-stable dynamos 2016 2017 we lack information about the geometry of large scale mag- 1.0 J22468+443 1.0 J22468+443 netic fields and instruments with polarimetric capabilities = 4.1 kG = 4.2 kG 0.8 Teff = 3400 K 0.8 Teff = 3400 K are needed. Thus, the next logical step would be to follow 0.6 log(g) = 4.9 0.6 log(g) = 4.9 up our targets with polarimetry and derive maps of their ⋅ sin = 4.8 km⋅s−1 ⋅ sin = 4.5 km⋅s−1 photospheric magnetic fields. υ i υ i f f 0.4 0.4 0.2 0.2 Acknowledgement. CARMENES is an instrument for the Centro Astronómico 0.00 2 4 6 8 10 12 14 16 18 20 0.00 2 4 6 8 10 12 14 16 18 20 Hispano-Alemán de Calar Alto (CAHA, Almeria, Spain). CARMENES is B, kG B, kG funded by the German Max-Planck-Gesellschaft (MPG), the Spanish Consejo Superior de Investigaciones Cientificas (CSIC), the European Union through Fig. 6. Mean CARMENES spectra (top panel) around three magnetic FEDER/ERF FICTS-2011-02 funds, and the members of the CARMENES Consortium (Max-Planck-Institut für Astronomie, Instituto de Astrofisica de sensitive Ti lines obtained in 2016 (full black line) and 2017 (dashed Andalucia, Landessternwarte Königstuhl, Institut de Ciéncies de l’Espai, Insi- red line) and corresponding filling factors derived from these data sets tut für Astrophysik Göttingen, Universidad Complutense de Madrid, Thüringer (bottom panel). Landessternwarte Tautenburg, Instituto de Astrofisica de Canarias, Hamburger Sternwarte, Centro de Astrobiologia and Centro Astronómico Hispano-Alemán), with additional contributions by the Spanish Ministry of Economy, the German fields. Ultra-fast rotating M dwarfs are very interesting and exotic Science Foundation through the Major Research Instrumentation Programme objects in many ways. and DFG Research Unit FOR2544 “Blue Planets around Red Stars”, the Klaus Tschira Stiftung, the states of Baden-Württemberg and Niedersachsen, and by From our analysis we find that in six stars with periods the Junta de Andalucia. L.T.-O. acknowledges support from the Israel Science P < 0.3 d we find three of them missing a significant zero field Foundation (grant No. 848/16). This work has made use of the VALD database, component in their filling factor distributions. If confirmed with operated at Uppsala University, the Institute of Astronomy RAS in Moscow, and future studies and it will appear that all stars with ultra-short the University of Vienna. We also acknowledge the use of electronic databases SIMBAD and NASA’s ADS. periods show little of the non-magnetic areas, this would imply that most of the stellar surface is covered with active regions – an effect which was proposed as one of the possible reason for References activity saturation (Jeffries et al. 2011; Reiners et al. 2014). More Afram, N., Berdyugina, S. V., Fluri, D. M., Solanki, S. K., & Lagg, A. 2008, accurate magnetic field measurements in late type M dwarfs, A&A, 482, 387 especially those with periods P < 0.3 d, are therefore essential Alonso-Floriano, F. J., Morales, J. C., Caballero, J. A., et al. 2015, A&A, 577, to explore properties of stellar dynamos in this parameter range. A128 Asensio Ramos, A., & Trujillo Bueno, J. 2006, ApJ, 636, 548 Barnes, J. R., Jeffers, S. V., Haswell, C. A., et al. 2017, MNRAS, 471, 811 Berdyugina, S. V., & Solanki, S. K. 2002, A&A, 385, 701 6. Summary Bressan, A., Marigo, P., Girardi, L., et al. 2012, MNRAS, 427, 127 Caballero, J. A., Cortés-Contreras, M., Alonso-Floriano, F. J., et al. 2016a, In this work we present the first magnetic field measurements in 19th Cambridge Workshop on Cool Stars, Stellar Systems, and the Sun from the high-resolution NIR spectroscopic observations taken (CS19), 148 with the CARMENES instrument. We specifically concentrated Caballero, J. A., Guàrdia, J., López del Fresno, M., et al. 2016b, Proc. SPIE, 9910, on the so-called RV-loud sample of 31 M dwarfs presented in 99100E Tal-Or et al. (2018) because these stars are expected to have Crozet, P., Tourasse, G., Ross, A., Paletou, F., & López Ariste, A. 2012, EAS Pub. Ser., 58, 63 strong magnetic fields as indicated by analysis of their activity Crozet, P., Ross, A. J., Alleq, N., et al. 2014, in Magnetic Fields throughout Stellar indicators. We employed the most advanced current radiative Evolution, eds. P. Petit, M. Jardine, & H. C. Spruit, IAU Symp., 302, 164 transfer model to measure average magnetic fields from the Díez Alonso, E., Caballero, J. A., Montes, D., et al. 2019, A&A, 621, A126 Zeeman broadening of atomic and molecular lines. Our main Dotter, A., Chaboyer, B., Jevremović, D., et al. 2008, ApJS, 178, 89 Dulick, M., Bauschlicher, Jr. C. W., Burrows, A., et al. 2003, ApJ, 594, 651 conclusions are summarized as follows: Garraffo, C., Drake, J. J., Cohen, O., Alvarado-Gómez, J. D., & Moschou, S. P. – We detect strong magnetic fields hBi > 1 kG in all our tar- 2017, ApJ, 843, L33 gets. In 16 of them the measurements were done for the first Gastine, T., Morin, J., Duarte, L., et al. 2013, A&A, 549, L5 time. In 12 of them our data indicate a presence of very Golimowski, D. A., Leggett, S. K., Marley, M. S., et al. 2004, AJ, 127, 3516 strong fields above 4 kG. Gustafsson, B., Edvardsson, B., Eriksson, K., et al. 2008, A&A, 486, 951 – We observe 17 stars with short rotation periods P < 1 d Harrison, J. 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A., et al. 2018, A&A, 612, A49 Kislyakova, K. G., Noack, L., Johnstone, C. P., et al. 2017, Nat. Astron., 1, 878 Ryabchikova, T., Piskunov, N., Kurucz, R. L., et al. 2015, Phys. Scr., 90, 054005 Kislyakova, K. G., Fossati, L., Johnstone, C. P., et al. 2018, ApJ, 858, 105 Saar, S. H., & Linsky, J. L. 1985, ApJ, 299, L47 Kochukhov, O., & Lavail, A. 2017, ApJ, 835, L4 Shulyak, D., Tsymbal, V., Ryabchikova, T., Stütz, C., & Weiss, W. W. 2004, Kochukhov, O., & Shulyak, D. 2019, ApJ, 873, 69 A&A, 428, 993 Landi Degl’Innocenti, E., & Landolfi, M. 2004, Polarization in Spectral Lines, Shulyak, D., Reiners, A., Wende, S., et al. 2010, A&A, 523, A37 Astrophys. Space Sci. Lib. (Dordrecht: Kluwer Academic Publishers), 307 Shulyak, D., Reiners, A., Seemann, U., Kochukhov, O., & Piskunov, N. 2014, Mathys, G., Solanki, S. K., & Wickramasinghe, D. T. 2001, in Magnetic Fields A&A, 563, A35 Across the Hertzsprung-Russell Diagram, ASP Conf. 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Shulyak et al.: Magnetic fields in M dwarfs from the CARMENES survey Appendix A: Model fit to the observed spectra in FeH and Ti lines λ978.33 nm, geff = 1.49 λ967.55 nm, geff = 1.34 λ968.89 nm, geff = 1.50 λ974.36 nm, geff = 0.00 λ977.03 nm, geff = 1.55 λ978.77 nm, geff = 1.50 λ978.36 nm, geff = 1.49 1.0 Normalized flux 0.8 0.6 0.1 nm observations magnetic model non-magnetic model 0.4 λ (nm) 1.05 λλ990.0 - 990.4 λλ991.6 - 992.0 λλ992.8 - 993.2 λλ993.8 - 994.1 λλ994.1 - 994.4 λλ994.3 - 994.6 λλ994.7 - 995.2 λλ995.3 - 995.6 λλ995.5 - 996.0 0.90 Normalized flux 0.75 0.60 0.1 nm observations magnetic model non-magnetic model λ (nm) Fig. A.1. Model fit to Ti and FeH lines in J01033+623. We show the comparison between observed and predicted spectra for a set of Ti (top panel) and FeH lines (bottom panel). Black circles – observations; red full line – best fit model spectrum; blue dashed line – spectrum computed assuming zero magnetic field. λ978.33 nm, geff = 1.49 λ967.55 nm, geff = 1.34 λ968.89 nm, geff = 1.50 λ974.36 nm, geff = 0.00 λ977.03 nm, geff = 1.55 λ978.36 nm, geff = 1.49 λ978.77 nm, geff = 1.50 1.05 Normalized flux 0.90 0.75 0.1 nm observations magnetic model non-magnetic model λ (nm) 0.96 Normalized flux 0.90 0.84 0.78 observations magnetic model non-magnetic model 0.72 989.8 990.4 991.0 991.6 λ (nm) Fig. A.2. Same as in Fig. A.1 but for J01352-072. A86, page 13 of 24 A&A 626, A86 (2019) λ978.33 nm, geff = 1.49 λ967.55 nm, geff = 1.34 λ968.89 nm, geff = 1.50 λ974.36 nm, geff = 0.00 λ977.03 nm, geff = 1.55 λ978.77 nm, geff = 1.50 1.05 λ978.36 nm, geff = 1.49 Normalized flux 0.90 0.75 0.60 0.1 nm observations magnetic model non-magnetic model 0.45 λ (nm) λλ994.4 - 994.6 λλ994.7 - 995.2 λλ995.3 - 995.5 λλ995.6 - 995.9 1.04 Normalized flux 0.96 0.88 0.80 0.1 nm observations magnetic model non-magnetic model λ (nm) Fig. A.3. Same as in Fig. A.1 but for J02088+494. λ978.33 nm, geff = 1.49 λ964.74 nm, geff = 1.53 λ967.55 nm, geff = 1.34 λ968.89 nm, geff = 1.50 λ974.36 nm, geff = 0.00 λ977.03 nm, geff = 1.55 λ978.77 nm, geff = 1.50 λ978.36 nm, geff = 1.49 1.0 Normalized flux 0.8 0.6 0.4 0.1 nm observations magnetic model non-magnetic model λ (nm) 1.1 λλ989.7 - 989.9 λλ990.0 - 990.4 λλ991.6 - 992.0 λλ992.8 - 993.1 λλ993.9 - 994.0 λλ994.1 - 994.3 λλ994.4 - 994.6 λλ994.7 - 995.2 λλ995.3 - 995.5 λλ995.6 - 995.9 λλ997.1 - 997.1 1.0 Normalized flux 0.9 0.8 0.7 0.1 nm observations magnetic model non-magnetic model λ (nm) Fig. A.4. Same as in Fig. A.1 but for J03473-019. A86, page 14 of 24 D. Shulyak et al.: Magnetic fields in M dwarfs from the CARMENES survey λ978.33 nm, geff = 1.49 λ967.55 nm, geff = 1.34 λ968.89 nm, geff = 1.50 λ974.36 nm, geff = 0.00 λ977.03 nm, geff = 1.55 λ978.36 nm, geff = 1.49 λ978.77 nm, geff = 1.50 1.05 Normalized flux 0.90 0.75 0.1 nm observations magnetic model non-magnetic model λ (nm) 0.96 Normalized flux 0.88 0.80 0.72 observations magnetic model non-magnetic model 0.64 989.8 990.4 991.0 991.6 λ (nm) Fig. A.5. Same as in Fig. A.1 but for J04472+206. λ978.33 nm, geff = 1.49 λ963.83 nm, geff = 1.42 λ964.74 nm, geff = 1.53 λ967.55 nm, geff = 1.34 λ968.89 nm, geff = 1.50 λ974.36 nm, geff = 0.00 λ977.03 nm, geff = 1.55 λ978.77 nm, geff = 1.50 λ978.36 nm, geff = 1.49 1.0 Normalized flux 0.8 0.6 0.4 0.1 nm observations magnetic model non-magnetic model 0.2 λ (nm) 1.1 λλ989.7 - 989.9 λλ990.0 - 990.4 λλ991.6 - 992.0 λλ992.8 - 993.1 λλ993.9 - 994.0 λλ994.1 - 994.3 λλ994.4 - 994.6 λλ994.7 - 995.2 λλ995.3 - 995.5 λλ995.6 - 995.9 λλ997.1 - 997.1 1.0 Normalized flux 0.9 0.8 0.7 0.1 nm observations magnetic model non-magnetic model λ (nm) Fig. A.6. Same as in Fig. A.1 but for J05365+113. λ978.33 nm, geff = 1.49 λ964.74 nm, geff = 1.53 λ967.55 nm, geff = 1.34 λ968.89 nm, geff = 1.50 λ974.36 nm, geff = 0.00λ977.03 nm, geff = 1.55 λ978.77 nm, geff = 1.50 λ978.36 nm, geff = 1.49 1.0 Normalized flux 0.8 0.6 0.4 0.1 nm observations magnetic model non-magnetic model λ (nm) 1.05 λλ989.7 - 989.9 λλ990.0 - 990.4 λλ991.6 - 992.0 λλ992.8 - 993.1 λλ993.9 - 994.0 λλ994.1 - 994.3 λλ994.4 - 994.6 λλ994.7 - 995.2 λλ995.3 - 995.5 λλ995.6 - 995.9 Normalized flux 0.90 0.75 0.60 0.1 nm observations magnetic model non-magnetic model λ (nm) Fig. A.7. Same as in Fig. A.1 but for J06000+027. A86, page 15 of 24 A&A 626, A86 (2019) λ978.33 nm, geff = 1.49 λ964.74 nm, geff = 1.53 λ967.55 nm, geff = 1.34 λ968.89 nm, geff = 1.50 λ974.36 nm, geff = 0.00 λ977.03 nm, geff = 1.55 λ978.77 nm, geff = 1.50 λ978.36 nm, geff = 1.49 1.0 Normalized flux 0.8 0.6 0.4 0.1 nm observations magnetic model non-magnetic model λ (nm) 1.05 λλ989.7 - 989.9 λλ990.0 - 990.4 λλ991.6 - 992.0 λλ992.8 - 993.1 λλ993.9 - 994.0 λλ994.1 - 994.3 λλ994.4 - 994.6 λλ994.7 - 995.2 λλ995.3 - 995.5 λλ995.6 - 995.9 λλ997.1 - 997.2 0.90 Normalized flux 0.75 0.60 0.1 nm observations magnetic model non-magnetic model λ (nm) Fig. A.8. Same as in Fig. A.1 but for J07446+035. λ978.33 nm, geff = 1.49 λ967.55 nm, geff = 1.34 λ968.89 nm, geff = 1.50 λ974.36 nm, geff = 0.00 λ977.03 nm, geff = 1.55 λ978.77 nm, geff = 1.50 λ978.36 nm, geff = 1.49 1.0 Normalized flux 0.8 0.6 0.4 0.1 nm observations magnetic model non-magnetic model λ (nm) λλ989.7 - 989.9 λλ990.0 - 990.4 λλ991.6 - 992.0 λλ992.8 - 993.1 λλ993.9 - 994.0 λλ994.1 - 994.3 λλ994.4 - 994.6 λλ994.7 - 995.2 λλ995.3 - 995.5 λλ995.6 - 995.9 1.0 Normalized flux 0.8 0.6 0.4 0.1 nm observations magnetic model non-magnetic model λ (nm) Fig. A.9. Same as in Fig. A.1 but for J08298+267. λ978.33 nm, geff = 1.49 λ967.55 nm, geff = 1.34 λ968.89 nm, geff = 1.50 λ974.36 nm, geff = 0.00 λ977.03 nm, geff = 1.55 λ978.77 nm, geff = 1.50 1.05 λ978.36 nm, geff = 1.49 Normalized flux 0.90 0.75 0.60 0.1 nm observations magnetic model non-magnetic model λ (nm) 1.05 λλ988.5 - 991.9 λλ994.3 - 997.5 Normalized flux 0.90 0.75 0.1 nm 0.60 observations magnetic model non-magnetic model λ (nm) Fig. A.10. Same as in Fig. A.1 but for J09449-123. A86, page 16 of 24 D. Shulyak et al.: Magnetic fields in M dwarfs from the CARMENES survey λ978.33 nm, geff = 1.49 λ963.83 nm, geff = 1.42 λ964.74 nm, geff = 1.53 λ967.55 nm, geff = 1.34 λ968.89 nm, geff = 1.50 λ974.36 nm, geff = 0.00 λ977.03 nm, geff = 1.55 λ978.77 nm, geff = 1.50 1.05 λ978.36 nm, geff = 1.49 Normalized flux 0.90 0.75 0.1 nm 0.60 observations magnetic model non-magnetic model λ (nm) 0.96 Normalized flux 0.88 0.80 0.72 observations magnetic model non-magnetic model 989.5 991.0 992.5 994.0 995.5 λ (nm) Fig. A.11. Same as in Fig. A.1 but for J12156+526. λ978.33 nm, geff = 1.49 λ964.74 nm, geff = 1.53 λ967.55 nm, geff = 1.34 λ968.89 nm, geff = 1.50 λ974.36 nm, geff = 0.00 λ977.03 nm, geff = 1.55 λ978.77 nm, geff = 1.50 λ978.36 nm, geff = 1.49 1.0 Normalized flux 0.8 0.6 0.1 nm observations magnetic model non-magnetic model 0.4 λ (nm) 1.05 λλ991.6 - 992.0 λλ994.1 - 994.4 λλ994.3 - 994.6 λλ995.3 - 995.6 λλ995.5 - 996.0 0.90 Normalized flux 0.75 0.60 0.1 nm observations magnetic model non-magnetic model λ (nm) Fig. A.12. Same as in Fig. A.1 but for J12189+111. A86, page 17 of 24 A&A 626, A86 (2019) λ978.33 nm, geff = 1.49 λ964.74 nm, geff = 1.53 λ967.55 nm, geff = 1.34 λ968.89 nm, geff = 1.50 λ974.36 nm, geff = 0.00 λ977.03 nm, geff = 1.55 λ978.77 nm, geff = 1.50 λ978.36 nm, geff = 1.49 1.0 Normalized flux 0.8 0.6 0.1 nm observations magnetic model non-magnetic model λ (nm) 1.05 λλ989.7 - 990.0 λλ990.0 - 990.5 λλ991.6 - 992.0 λλ992.8 - 993.2 λλ994.1 - 994.4 λλ994.3 - 994.6 λλ994.7 - 995.2 λλ995.3 - 995.6 λλ995.5 - 996.0 Normalized flux 0.90 0.75 0.1 nm 0.60 observations magnetic model non-magnetic model λ (nm) Fig. A.13. Same as in Fig. A.1 but for J14173+454. λ978.33 nm, geff = 1.49 λ964.74 nm, geff = 1.53 λ967.55 nm, geff = 1.34 λ968.89 nm, geff = 1.50 λ977.03 nm, geff = 1.55 λ974.36 nm, geff = 0.00 λ978.77 nm, geff = 1.50 λ978.36 nm, geff = 1.49 1.0 Normalized flux 0.8 0.6 0.4 0.1 nm observations magnetic model non-magnetic model λ (nm) 1.1 λλ989.7 - 989.9 λλ990.0 - 990.5 λλ991.6 - 992.0 λλ992.8 - 993.2 λλ994.1 - 994.4 λλ994.3 - 994.6 λλ994.7 - 995.2 λλ995.3 - 995.6 λλ995.6 - 996.0 λλ997.0 - 997.2 1.0 Normalized flux 0.9 0.8 0.7 0.1 nm observations magnetic model non-magnetic model λ (nm) Fig. A.14. Same as in Fig. A.1 but for J15218+209. λ978.33 nm, geff = 1.49 λ967.55 nm, geff = 1.34 λ968.89 nm, geff = 1.50 λ974.36 nm, geff = 0.00 λ977.03 nm, geff = 1.55 λ978.36 nm, geff = 1.49 λ978.77 nm, geff = 1.50 1.05 Normalized flux 0.90 0.75 0.60 0.1 nm observations magnetic model non-magnetic model λ (nm) 1.0 0.9 Normalized flux 0.8 0.7 0.6 observations magnetic model non-magnetic model 989.5 990.0 990.5 991.0 991.5 λ (nm) Fig. A.15. Same as in Fig. A.1 but for J15499+796. A86, page 18 of 24 D. Shulyak et al.: Magnetic fields in M dwarfs from the CARMENES survey λ978.33 nm, geff = 1.49 λ967.55 nm, geff = 1.34 λ968.89 nm, geff = 1.50 λ974.36 nm, geff = 0.00 λ977.03 nm, geff = 1.55 λ978.77 nm, geff = 1.50 λ978.36 nm, geff = 1.49 1.0 Normalized flux 0.8 0.6 0.4 0.1 nm observations magnetic model non-magnetic model λ (nm) 1.05 λλ989.7 - 989.9 λλ990.0 - 990.4 λλ991.6 - 992.0 λλ994.1 - 994.3 λλ994.4 - 994.6 λλ994.7 - 995.2 λλ995.3 - 995.5 λλ995.6 - 995.9 0.90 Normalized flux 0.75 0.60 0.1 nm 0.45 observations magnetic model non-magnetic model λ (nm) Fig. A.16. Same as in Fig. A.1 but for J16313+408. λ967.55 nm, geff = 1.34 λ968.89 nm, geff = 1.50 λ974.36 nm, geff = 0.00 λ977.03 nm, geff = 1.55 λ978.33 nm, geff = 1.49 λ978.77 nm, geff = 1.50 1.00 λ978.36 nm, geff = 1.49 Normalized flux 0.75 0.50 0.25 0.1 nm observations magnetic model non-magnetic model 0.00 λ (nm) λλ989.7 - 989.9 λλ990.0 - 990.4 λλ991.6 - 992.0 λλ992.8 - 993.1 λλ993.9 - 994.0 λλ994.1 - 994.3 λλ994.4 - 994.6 λλ994.7 - 995.2 λλ995.3 - 995.5 λλ995.6 - 995.9 1.0 0.8 Normalized flux 0.6 0.4 0.1 nm observations magnetic model non-magnetic model 0.2 λ (nm) Fig. A.17. Same as in Fig. A.1 but for J16555-083. λ978.33 nm, geff = 1.49 λ967.55 nm, geff = 1.34 λ968.89 nm, geff = 1.50 λ974.36 nm, geff = 0.00 λ977.03 nm, geff = 1.55 λ978.77 nm, geff = 1.50 λ978.36 nm, geff = 1.49 1.0 Normalized flux 0.8 0.6 0.4 0.1 nm observations magnetic model non-magnetic model λ (nm) 1.05 λλ989.7 - 989.9 λλ990.0 - 990.4 λλ991.6 - 992.0 λλ992.8 - 993.1 λλ994.1 - 994.3 λλ994.4 - 994.6 λλ994.7 - 995.2 λλ995.3 - 995.5 λλ995.6 - 995.9 Normalized flux 0.90 0.75 0.1 nm 0.60 observations magnetic model non-magnetic model λ (nm) Fig. A.18. Same as in Fig. A.1 but for J16570-043. A86, page 19 of 24 A&A 626, A86 (2019) λ978.33 nm, geff = 1.49 λ964.74 nm, geff = 1.53 λ967.55 nm, geff = 1.34 λ968.89 nm, geff = 1.50 λ974.36 nm, geff = 0.00 λ977.03 nm, geff = 1.55 λ978.77 nm, geff = 1.50 1.05 λ978.36 nm, geff = 1.49 Normalized flux 0.90 0.75 0.60 0.1 nm observations magnetic model non-magnetic model λ (nm) 1.05 λλ989.0 - 990.8 λλ995.2 - 996.5 Normalized flux 0.90 0.75 0.1 nm 0.60 observations magnetic model non-magnetic model λ (nm) Fig. A.19. Same as in Fig. A.1 but for J17338+169. λ978.33 nm, geff = 1.49 λ964.74 nm, geff = 1.53 λ967.55 nm, geff = 1.34 λ968.89 nm, geff = 1.50 λ974.36 nm, geff = 0.00 λ977.03 nm, geff = 1.55 λ978.77 nm, geff = 1.50 λ978.36 nm, geff = 1.49 1.0 Normalized flux 0.8 0.6 0.4 0.1 nm observations magnetic model non-magnetic model λ (nm) 1.05 λλ990.0 - 990.4 λλ991.6 - 992.0 λλ992.8 - 993.1 λλ994.1 - 994.3 λλ995.3 - 995.5 0.90 Normalized flux 0.75 0.60 0.1 nm observations magnetic model non-magnetic model λ (nm) Fig. A.20. Same as in Fig. A.1 but for J18022+642. A86, page 20 of 24 D. Shulyak et al.: Magnetic fields in M dwarfs from the CARMENES survey λ978.33 nm, geff = 1.49 λ964.74 nm, geff = 1.53 λ967.55 nm, geff = 1.34 λ968.89 nm, geff = 1.50 λ974.36 nm, geff = 0.00 λ977.03 nm, geff = 1.55 λ978.77 nm, geff = 1.50 λ978.36 nm, geff = 1.49 1.0 Normalized flux 0.8 0.6 0.1 nm observations magnetic model non-magnetic model 0.4 λ (nm) 1.05 λλ990.0 - 990.4 λλ991.6 - 992.0 λλ994.4 - 994.6 λλ995.3 - 995.5 λλ995.6 - 995.9 Normalized flux 0.90 0.75 0.60 0.1 nm observations magnetic model non-magnetic model λ (nm) Fig. A.21. Same as in Fig. A.1 but for J18189+661. λ978.33 nm, geff = 1.49 λ964.74 nm, geff = 1.53 λ967.55 nm, geff = 1.34 λ968.89 nm, geff = 1.50 λ977.03 nm, geff = 1.55 λ974.36 nm, geff = 0.00 λ978.77 nm, geff = 1.50 λ978.36 nm, geff = 1.49 1.0 Normalized flux 0.8 0.6 0.4 0.1 nm observations magnetic model non-magnetic model λ (nm) 1.05 λλ990.0 - 990.4 λλ993.9 - 994.0 λλ994.1 - 994.3 λλ994.4 - 994.6 λλ994.7 - 995.2 λλ995.3 - 995.5 λλ995.6 - 995.9 Normalized flux 0.90 0.75 0.60 0.1 nm observations magnetic model non-magnetic model λ (nm) Fig. A.22. Same as in Fig. A.1 but for J18498-238. A86, page 21 of 24 A&A 626, A86 (2019) λ978.33 nm, geff = 1.49 λ964.74 nm, geff = 1.53 λ967.55 nm, geff = 1.34 λ974.36 nm, geff = 0.00 λ978.77 nm, geff = 1.50 1.00 λ978.36 nm, geff = 1.49 Normalized flux 0.75 0.50 0.25 0.1 nm observations magnetic model non-magnetic model λ (nm) λλ989.7 - 989.9 λλ990.0 - 990.4 λλ991.6 - 992.0 λλ993.9 - 994.0 λλ994.1 - 994.3 λλ994.4 - 994.6 λλ994.7 - 995.2 λλ995.3 - 995.5 λλ995.6 - 995.9 1.00 0.75 Normalized flux 0.50 0.25 0.1 nm observations magnetic model non-magnetic model λ (nm) Fig. A.23. Same as in Fig. A.1 but for J19169+051S. λ978.33 nm, geff = 1.49 λ967.55 nm, geff = 1.34 λ968.89 nm, geff = 1.50 λ974.36 nm, geff = 0.00 λ977.03 nm, geff = 1.55 λ978.77 nm, geff = 1.50 1.05 λ978.36 nm, geff = 1.49 Normalized flux 0.90 0.75 0.60 0.1 nm observations magnetic model non-magnetic model λ (nm) 0.96 Normalized flux 0.88 0.80 0.72 observations magnetic model non-magnetic model 0.64 989.5 991.0 992.5 994.0 995.5 λ (nm) Fig. A.24. Same as in Fig. A.1 but for J19511+464. A86, page 22 of 24 D. Shulyak et al.: Magnetic fields in M dwarfs from the CARMENES survey λ978.33 nm, geff = 1.49 λ967.55 nm, geff = 1.34 λ968.89 nm, geff = 1.50 λ974.36 nm, geff = 0.00 λ977.03 nm, geff = 1.55 λ978.77 nm, geff = 1.50 1.00 λ978.36 nm, geff = 1.49 Normalized flux 0.75 0.50 0.25 0.1 nm observations magnetic model non-magnetic model λ (nm) 1.05 λλ989.7 - 989.9 λλ990.0 - 990.4 λλ991.6 - 992.0 λλ992.8 - 993.1 λλ994.1 - 994.3 λλ994.4 - 994.6 λλ994.7 - 995.2 λλ995.3 - 995.5 λλ995.6 - 995.9 0.90 Normalized flux 0.75 0.60 0.1 nm 0.45 observations magnetic model non-magnetic model λ (nm) Fig. A.25. Same as in Fig. A.1 but for J20093-012. λ978.33 nm, geff = 1.49 λ963.83 nm, geff = 1.42 λ964.74 nm, geff = 1.53 λ967.55 nm, geff = 1.34 λ968.89 nm, geff = 1.50 λ974.36 nm, geff = 0.00 λ977.03 nm, geff = 1.55 λ978.77 nm, geff = 1.50 1.05 λ978.36 nm, geff = 1.49 Normalized flux 0.90 0.75 0.60 0.1 nm observations magnetic model non-magnetic model λ (nm) 0.96 Normalized flux 0.88 0.80 0.72 observations magnetic model non-magnetic model 0.64 989.5 991.0 992.5 994.0 995.5 λ (nm) Fig. A.26. Same as in Fig. A.1 but for J22012+283. λ978.33 nm, geff = 1.49 λ964.74 nm, geff = 1.53 λ967.55 nm, geff = 1.34 λ968.89 nm, geff = 1.50 λ974.36 nm, geff = 0.00 λ977.03 nm, geff = 1.55 λ978.77 nm, geff = 1.50 λ978.36 nm, geff = 1.49 1.0 Normalized flux 0.8 0.6 0.4 0.1 nm observations magnetic model non-magnetic model λ (nm) 1.05 λλ989.7 - 989.9 λλ990.0 - 990.4 λλ991.6 - 992.0 λλ992.8 - 993.1 λλ993.9 - 994.0 λλ994.1 - 994.3 λλ994.4 - 994.6 λλ994.7 - 995.2 λλ995.3 - 995.5 Normalized flux 0.90 0.75 0.60 0.1 nm observations magnetic model non-magnetic model λ (nm) Fig. A.27. Same as in Fig. A.1 but for J22468+443. A86, page 23 of 24 A&A 626, A86 (2019) λ978.33 nm, geff = 1.49 λ963.83 nm, geff = 1.42 λ964.74 nm, geff = 1.53 λ967.55 nm, geff = 1.34 λ968.89 nm, geff = 1.50 λ974.36 nm, geff = 0.00 λ977.03 nm, geff = 1.55 λ978.77 nm, geff = 1.50 λ978.36 nm, geff = 1.49 1.0 Normalized flux 0.8 0.6 0.1 nm observations magnetic model non-magnetic model 0.4 λ (nm) 1.1 λλ989.7 - 989.9 λλ990.0 - 990.4 λλ991.6 - 992.0 λλ992.8 - 993.1 λλ994.1 - 994.3 λλ994.4 - 994.6 λλ994.7 - 995.2 λλ995.3 - 995.5 λλ995.6 - 995.9 1.0 Normalized flux 0.9 0.8 0.1 nm 0.7 observations magnetic model non-magnetic model λ (nm) Fig. A.28. Same as in Fig. A.1 but for J22518+317. λ978.33 nm, geff = 1.49 λ963.83 nm, geff = 1.42 λ964.74 nm, geff = 1.53 λ967.55 nm, geff = 1.34 λ968.89 nm, geff = 1.50 λ974.36 nm, geff = 0.00 λ977.03 nm, geff = 1.55 λ978.77 nm, geff = 1.50 λ978.36 nm, geff = 1.49 1.0 Normalized flux 0.8 0.6 0.4 0.1 nm observations magnetic model non-magnetic model λ (nm) 1.05 λλ989.7 - 989.9 λλ990.0 - 990.4 λλ991.6 - 992.0 λλ992.8 - 993.1 λλ993.9 - 994.0 λλ994.1 - 994.3 λλ994.4 - 994.6 λλ994.7 - 995.2 λλ995.3 - 995.5 Normalized flux 0.90 0.75 0.60 0.1 nm observations magnetic model non-magnetic model λ (nm) Fig. A.29. Same as in Fig. A.1 but for J23548+385. A86, page 24 of 24