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

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 (approximate to 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 (a). 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 a. The latter is often assumed to be reduced by the presence of magnetic fields, although the reduction in alpha 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 delta approximate to B-2/4p gamma p(gas) (where B is the strength of the local vertical magnetic field). In the context of delta models in which B is not allowed to exceed a 'ceiling' of 10(6) G, we find that the revised R and L can also be fitted, within the error bars, in a finite region of the f-delta plane. The permitted values of delta 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.