The Global and Small-scale Magnetic Fields of Fully Convective, Rapidly Spinning M Dwarf Pair GJ65 A and B

The quality of ESPaDOnS polarization observations of GJ65 is insufficient for an analysis of polarization signatures in individual spectral lines. Consequently, we applied the least-squares deconvolution procedure (LSD; Donati et al. 1997; Kochukhov et al. 2010) to derive high S/N mean Stokes V profiles based on a line mask containing 1690 atomic absorption lines deeper than 0.2 of the continuum. The LSD atomic line mask was derived from a line list retrieved from the VALD3 database (Ryabchikova et al. 2015) using T_eff = 2900 K, $\mathrm{log}g\,=\,5.0$ MARCS model atmosphere (Gustafsson et al. 2008). Application of LSD yielded an S/N gain of about 20, allowing us to detect circular polarization signals in all observations of both components.

Examination of the LSD Stokes V profiles of GJ65 A and B reveals a stark difference between the two stars. As demonstrated by Figure 1, the primary shows low-amplitude polarization signatures that change significantly from one observation to the next. On the other hand, the secondary consistently exhibits morphologically simpler and stronger antisymmetric signatures indicative of a positive large-scale magnetic field. The mean longitudinal magnetic field $\langle {B}_{{\rm{z}}}\rangle$, estimated from the first moment of the Stokes V LSD profiles (Wade et al. 2000) and reported in the last column of Table 1, ranges from +400 to +700 G for GJ65 B and from 0 to +150 G for GJ65 A.

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We further analyzed the Stokes V LSD profiles of GJ65 with the Zeeman Doppler imaging (ZDI; Kochukhov 2016) inversion technique to obtain detailed field topology models. ZDI was previously applied to a sample of active M dwarf stars of different masses by Donati et al. (2008), Morin et al. (2008, 2010), and Hébrard et al. (2016). These studies revealed global fields with strengths up to several kG and demonstrated that early-M, partially convective dwarfs typically have weak and complex magnetic field structures, while mid-M stars tend to show strong axisymmetric dipolar field topologies, and late-M, fully convective dwarfs exhibit a mixture of both types of field geometries (see the review by Morin 2012).

Our ZDI analysis of GJ65 was carried out with the code described by Kochukhov et al. (2014) and Rosén et al. (2016). Similar to the latter paper, the local Stokes parameter profiles were approximated with the Unno–Rachkovsky solution of the polarized radiative transfer equations (Landi Degl'Innocenti & Landolfi 2004). The central wavelength and effective Landé factor of the model profiles were adopted according to the average values of the LSD line mask; the line strength was adjusted to match the equivalent width of the observed LSD intensity profile.

The magnetic field was represented using a spherical harmonic expansion, with the maximum angular degree ℓ_max = 5. The magnetic inversions were regularized by penalizing a contribution of higher ℓ modes (see Kochukhov et al. 2014). This magnetic mapping methodology is very similar to previous applications of ZDI to active mid- and late-M dwarfs (Morin et al. 2008, 2010) with the exception that here we do not apply global field filing factors to improve the fit to the observed Stokes V profiles. Furthermore, since observations of GJ65 cover about 10%–14% of the rotation cycles of the components, we accounted for the phase smearing by integrating the model LSD profiles over appropriate phase intervals.

The eight spectropolarimetric observations of GJ65 B have an adequate phase coverage to obtain a detailed map of the surface magnetic field. On the other hand, the four spectra available for GJ65 A cover only about half of the rotational period. Nevertheless, this data set is sufficient to derive an approximate ZDI map that can be meaningfully compared with the inversion results for GJ65 B.

Taking into account results of the Stokes I DI modeling by Barnes et al. (2016), we adopted projected rotational velocities v sin i = 28.6 km s⁻¹ for GJ65 A and 32.0 km s⁻¹ for GJ65 B, respectively, and an inclination angle of i = 60° for both stars. This value agrees within error bars with the inclination angles that follow from the above $v\sin i$, the rotation periods determined by Barnes et al. (2016), and the radii measured by Kervella et al. (2016).

The global magnetic field maps of GJ65 AB are presented in Figure 1 along with a comparison of the observed and computed LSD Stokes V profiles. It is evident that the large-scale field of GJ65 B (peak local strength 2.34 kG, mean strength 1.34 kG) is considerably stronger than the field of GJ65 A (peak local strength 0.84 kG, mean strength 0.34 kG). The field of GJ65 B is also predominantly dipolar (92% of the field energy is contained in ℓ = 1 components) and axisymmetric (89% of the energy is in m < ℓ/2 components). In contrast, the field of GJ65 A has a larger contribution of higher-ℓ(70% of the energy is in ℓ = 1 components) and non-axisymmetric (56% of the energy is in m < ℓ/2 components) modes. The fields of both stars are largely poloidal (89%–93% of the energy is in poloidal components).

Details of the field topology of GJ65 A are less precisely determined than for the B component due to an incomplete phase coverage obtained for the primary. Nevertheless, the basic conclusion that the primary's field structure must be less axisymmetric and more complex is supported by the complex Stokes V LSD line shapes observed at phases 0.533 and 0.638. Such Stokes V profile morphologies are not observed in any of the eight observations available for GJ65 B.

An analysis of Zeeman broadening and intensification of spectral lines enables an estimate of the total magnetic flux, which contains contributions of both the large-scale field and the small-scale magnetic structures unresolved by polarimetry. Previous studies applied this diagnostic method to atomic and molecular lines in the Stokes I spectra of many low-mass stars and brown dwarfs, detecting fields with typical strengths of 2–4 kG (Johns-Krull & Valenti 1996; Reiners & Basri 2007; Reiners et al. 2009; Shulyak et al. 2014). In a recent study by D. Shulyak (2017, in preparation; see also summary in Kochukhov et al. 2017) magnetic fields of up to 6.4 kG were found in several active, rapidly rotating (P_rot = 0.4–0.8 days) M4–6 dwarfs. The GJ65 components are spinning about a factor of two faster than any of the M dwarf stars with direct magnetic field measurements in the literature.

Our field strength measurements take advantage of a group of Ti i lines at λ 9744–9788 Å. These lines correspond to the transitions between similar energy levels, hence the relative scale of their oscillator strengths, obtained from VALD, is well-known. One of these lines, Ti i 9743.61 Å has zero effective Landé factor, meaning that this spectral feature is entirely insensitive to magnetic field. Then, a magnetic field strength can be determined using a differential spectrum synthesis analysis of magnetically sensitive lines, e.g., Ti i 9770.30, 9783.31, 9787.69 Å, relative to Ti i 9743.61 Å. This magnetic intensification diagnostic does not rely on interpreting details of the line profile shapes and therefore can be applied to rapidly rotating stars, such as the GJ65 components.

Some of the Ti i lines mentioned above are significantly affected by the telluric absorption features. We used the Molecfit tool (Smette et al. 2015) to model the telluric spectrum and remove its contribution from stellar observations. Then, the four spectra of GJ65 A and eight spectra of GJ65 B were averaged, yielding high-quality intensity spectra for each star.

The magnetic field effects on the Ti i lines were studied with the help of the Synmast code (Kochukhov et al. 2010), which solves the polarized radiative transfer equation at several limb angles for a given line list, model atmosphere, and prescribed magnetic field strength and orientation. In this study, we adopted a homogeneous radial magnetic field. This assumption has no bearing on the final analysis results since the disk-integrated Stokes I spectra are not particularly sensitive to the field orientation and, in any case, sample a wide range of field orientations with respect to the observer for any field geometry.

Based on the radii and masses given by Kervella et al. (2016), we adopted log g = 5.1 for both components of GJ65 and used the solar-metallicity MARCS model atmospheres with T_eff = 3000 K for the primary and 2900 K for the secondary. The probable effective temperature uncertainty of ∼100 K does not introduce significant differential effects for the studied Ti i lines.

For both GJ65 A and B our spectrum synthesis reproduces the observed width and intensity of Ti i 9743.61 Å with the solar abundance of titanium and $v\sin i$ given by Barnes et al. (2016). At the same time, the three other Ti i lines are clearly too weak without a magnetic field (see Figure 2). Adjusting the field strength to match the observed intensity of each of these lines separately, we found $\langle B\rangle$ = 5.0 ± 0.5 kG for GJ65 A and $\langle B\rangle$ = 5.7 ± 0.6 kG for GJ65 B, with the error bars corresponding to the scatter of measurements derived from individual lines.

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As illustrated by Figure 2, theoretical spectrum for a 5 kG field covering the entire stellar surface provides a satisfactory fit to all Ti i lines in GJ65 A. However, magnetically sensitive lines in GJ65 B exhibit a more triangular shape than predicted by calculations. This anomaly is not observed for the Ti i 9743.61 Å line in GJ65 B and is not seen for any of the Ti i lines in GJ65 A. This suggests the presence of a strong-field component in the field distribution in GJ65 B, which is responsible for the extended wings of magnetically sensitive lines. To test this hypothesis, we applied to both stars a two-component model fit, combining a non-magnetic spectrum with calculations for a given field strength covering a fraction f of the stellar surface. This model succeeds in improving the fit to GJ65 B spectra (see Figure 2), yielding B = 10.5 ± 1.2 kG, f = 0.6 ± 0.1, and $\langle B\rangle$ = B f = 6.7 ± 0.6 kG. On the other hand, results of the two-component model fit for GJ65 A (B = 6.0 ± 1.5 kG, f = 0.9 ± 0.1, and $\langle B\rangle$ = Bf = 5.2 ± 0.5 kG) are compatible with the single-component fit.

These results were obtained using the mean spectra of GJ65 AB. We have also examined individual observations, finding no appreciable variability of the Ti i lines in GJ65 A. The secondary component, on the other hand, shows a weak rotational modulation of Ti i line shapes. This variability, illustrated in Figure 3, appears to be magnetic in nature because it is absent in the magnetic null line Ti i 9743.61 Å but present in other Ti i transitions. Fitting the phase resolved spectra of GJ65 B with the two-component model described above reveals a coherent, single-wave variation of B from 8 to 11 kG and $\langle B\rangle$ from 5.7 to 7.0 kG, with the maximum of both parameters occurring at phase 0.5. To our knowledge, this is the first report of a rotational modulation of the magnetic field intensity derived from Stokes I spectra of an M dwarf.

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