Precision modelling of M dwarf stars: the magnetic components of CM Draconis

Abstract

The eclipsing binary CM Draconis (CM Dra) contains two nearly identical red dwarfs of spectral class dM4.5. The masses and radii of the two components have been reported with unprecedentedly small statistical errors: for M, these errors are 1 part in 260, while for R, the errors reported by Morales et al. are 1 part in 130. When compared with standard stellar models with appropriate mass and age (≈4 Gyr), the empirical results indicate that both components are discrepant from the models in the following sense: the observed stars are larger in R (‘bloated’), by several standard deviations, than the models predict. The observed luminosities are also lower than the models predict. Here, we attempt at first to model the two components of CM Dra in the context of standard (non‐magnetic) stellar models using a systematic array of different assumptions about helium abundances (Y), heavy element abundances (Z), opacities and mixing length parameter (α). We find no 4‐Gyr‐old models with plausible values of these four parameters that fit the observed L and R within the reported statistical error bars. However, CM Dra is known to contain magnetic fields, as evidenced by the occurrence of star‐spots and flares. Here we ask: can inclusion of magnetic effects into stellar evolution models lead to fits of L and R within the error bars? Morales et al. have reported that the presence of polar spots results in a systematic overestimate of R by a few per cent when eclipses are interpreted with a standard code. In a star where spots cover a fraction f of the surface area, we find that the revised R and L for CM Dra A can be fitted within the error bars by varying the parameter α. The latter is often assumed to be reduced by the presence of magnetic fields, although the reduction in α as a function of B is difficult to quantify. An alternative magnetic effect, namely inhibition of the onset of convection, can be readily quantified in terms of a magnetic parameter δ≈B2/4πγpgas (where B is the strength of the local vertical magnetic field). In the context of δ models in which B is not allowed to exceed a ‘ceiling’ of 106 G, we find that the revised R and L can also be fitted, within the error bars, in a finite region of the f–δ plane. The permitted values of δ near the surface leads us to estimate that the vertical field strength on the surface of CM Dra A is about 500 G, in good agreement with independent observational evidence for similar low‐mass stars. Recent results for another binary with parameters close to those of CM Dra suggest that metallicity differences cannot be the dominant explanation for the bloating of the two components of CM Dra.

Magnetism, dynamo action and the solar-stellar connection

“…For example, Mullan and MacDonald (2001) explored the possibility that some of the observed properties of these stars might arise if the interior was not fully convective but instead possessed a small stable core, arising from the stabilizing influence of a sufficiently strong magnetic field. The fields required to completely stabilize the interior are up to 100 MG; somewhat less extreme fields have been examined in several later papers (e.g., Chabrier et al 2007;MacDonald and Mullan 2012Feiden and Chaboyer 2012, modeled using various forms of mixinglength theory (accounting for the influence of magnetism either by simply reducing the mixing-length parameter α or through more complex prescriptions). Within the mixing-length prescriptions adopted by MacDonald and Mullan (2014) or Feiden and Chaboyer (2014), the fields required to yield significant radius inflation would be quite strong, typically 1 MG or more at some regions within the interior; Feiden and Chaboyer (2014) ultimately find such fields to be unlikely, whereas MacDonald and Mullan (2014) are more sanguine about their prospects.…”

Apparent Non-Coevality Among the Stars in Upper Scorpio: Resolving the Problem Using a Model of Magnetic Inhibition of Convection

“…The original GT criterion depended on a single magnetic inhibition parameter, δ. However, in view of dynamo considerations which cannot be expected to generate a magnetic field that is stronger than a certain limit, when the GT criterion is applied to stars, the introduction of a second parameter is also advisable: an upper limit, or "ceiling", should be imposed on the magnetic field strength, Bceil (MacDonald & Mullan 2012). An important aspect of our "two-parameter' solutions is noteworthy: our magnetoconvective bestfit solutions for any given star are much more sensitive to the value of the parameter δ than to the value of the second parameter, Bceil.…”

Fundamental properties of lower main‐sequence stars

“…CM Dra is the poster child for these anomalies (see also discussions by Feiden et al 2011, Spada & Demarque 2012, and MacDonald & Mullan 2012. It is presumed to be a Population II binary based on its extreme kinematics, although its precise age is not known.…”

“…Activity is known to inhibit convective transport of energy in the stellar interiors, and this in turn leads to larger radii and cooler temperatures. There is at least a first-order theoret-ical understanding of these processes (e.g., Gough & Taylor 1966;Mullan & MacDonald 2001;Chabrier, Gallardo & Baraffe 2007;MacDonald & Mullan 2012), as well as empirical evidence that the use of a smaller mixing length parameter α ML in the models (to emulate reduced convective efficiency) does indeed improve the fit to the observations. Spot coverage associated with stellar activity reduces the radiating surface area, and this can also contribute to the discrepancies.…”