How to interpret near-infrared polarisation spectra of active M dwarfs?

Abstract

Analyses of global magnetic fields in M dwarfs rely on many approximations regarding the derivation of average line profiles from spectropolarimetric data, interpreting them with analytical functions and modelling them using Zeeman Doppler imaging (ZDI). These assumptions have not been systematically tested. We assessed the accuracy of standard treatments of average polarisation profiles in M dwarfs and their interpretation with ZDI. We focused on the filling-factor approach, which attempts to represent coexisting global and small-scale fields. We performed polarised radiative transfer calculations across the near-infrared spectrum of a typical M dwarf. From these theoretical spectra, we derived mean Stokes profiles and approximated them with different line-synthesis methods. To test the recovery of global fields, we performed ZDI inversions using simulated Stokes V observations for low- and high-activity cases. The analytical approximation of mean polarisation profiles reproduces Stokes I and V only for fields up to ~1 kG and fails for linear polarisation. ZDI with single-line analytical Stokes V profiles is adequate for weakly magnetic M dwarfs with fields below a few hundred gauss. However, combined with the filling-factor formalism, this traditional modelling approach produces unphysical local fields and distorted global geometries for active M dwarfs with multi-kilogauss fields. These issues are mitigated using a new mapping technique based on theoretical Stokes profiles that account for both global and randomly distributed small-scale fields. Our study reveals fundamental limitations of current ZDI analyses of active M dwarfs and questions the reliability of some published maps. (abridged)

Figures (7)

• Figure 1: Composite magnetic field configurations and corresponding integral magnetic observables for superpositions of global and small-scale magnetic fields. Columns in panel (a): Maps of the combined magnetic field for the same global dipolar geometry ($B_{\rm d}=1$ kG, $\beta=60\degr$) with an added isotropic small-scale field of varying strength (0--2 kG, indicated above each column). These plots display flattened polar projections of the radial, meridional, and azimuthal magnetic field components. In each polar plot, the thick circle marks the stellar equator, and dotted lines indicate latitude intervals of 30. Panel (b): Mean longitudinal magnetic field, $\langle B_{\rm z} \rangle$ (top) and the mean field modulus, (bottom) for the three superpositions of small-scale and global fields (solid lines) as well as for the small-scale field alone (dashed lines).
• Figure 2: Theoretical near-infrared M-dwarf synthetic spectra and corresponding LSD profiles. Left panels: Disk-centre Stokes $I$ spectra computed for a model atmosphere with $T_{\rm eff}=3500$ K and $\log g = 5.0$, both with (red) and without (black) molecular line opacity. A 100 G line-of-sight magnetic field was adopted for these calculations. Blue bars above the spectra mark the positions of atomic lines included in the LSD mask, with bar lengths proportional to their central depths. Grey rectangles highlight wavelength regions excluded from the analysis because they are heavily contaminated by telluric absorption in typical ground-based observations. Right panels: Corresponding LSD profiles: Stokes $I$ (upper) and Stokes $V$ (lower).
• Figure 3: Comparison of disk-centre Stokes parameter LSD profiles computed using detailed radiative transfer calculations (symbols connected by solid black lines) and the single-line UR approximation (red lines). The dotted blue lines show LSD Stokes $I$ profiles before continuum re-normalisation. Each row displays a different Stokes parameter: $I$ (top), $V$ (middle), and $Q$ (bottom). The columns correspond to increasing magnetic field strengths, ranging from 100 G to 10 kG. In all panels, the magnetic field vector is inclined at an angle of 45 to the line of sight.
• Figure 4: Centre-to-limb variation of LSD line profiles (a) and continuum intensity (b). Panel (a) compares Stokes $IVQ$ LSD profiles computed with full radiative transfer calculations (black symbols connected with solid lines) to those obtained using the single-line UR approximation for $b = 5$ (thick red lines) and $b = 0.27$ (thin blue lines). The latter value is consistent with the continuum limb-darkening coefficient $\eta = 0.21$. In all cases the magnetic field strength is 1 kG and the field vector is inclined by 45 relative to the line of sight. Panel (b) compares the continuum limb-darkening predicted by detailed radiative-transfer calculations (black symbols connected with solid lines) with a linear limb-darkening law using $\eta = 0.21$ (red line).
• Figure 5: Effect of isotropic small-scale magnetic fields with different strengths on the disk-centre Stokes $IVQ$ LSD profiles. Each column presents the Stokes parameter profiles for a given local field strength, $B$, and a 45 inclination relative to the line of sight. Different colours correspond to increasing strength of the small-scale field, $B_{\rm s}$. Panel (a): LSD Stokes profiles for inactive stars ($B=60$--200 G, $B_{\rm s}=100$--400 G). Panel (b): LSD Stokes profiles for active stars ($B=0.5$--2.0 kG, $B_{\rm s}=0.5$--4.0 kG).