We present models of the components of the systems KOI-126 and CM Draconis , the two eclipsing binary systems known to date to contain stars with masses low enough to have fully convective interiors .
We are able to model satisfactorily the system KOI-126 , finding consistent solutions for the radii and surface temperatures of all three components , using a solar-like value of the mixing-length parameter \alpha in the convection zone , and PHOENIX NextGen 1D model atmospheres for the surface boundary conditions .
Depending on the chemical composition , we estimate the age of the system to be in the range 3 – 5 Gyr .
For CM Draconis , on the other hand , we can not reconcile our models with the observed radii and T _ { eff } using the current metal-poor composition estimate based on kinematics .
Higher metallicities lessen but do not remove the discrepancy .
We then explore the effect of varying the mixing length parameter \alpha .
As previously noted in the literature , a reduced \alpha can be used as a simple measure of the lower convective efficiency due to rotation and induced magnetic fields .
Our models show a sensitivity to \alpha ( for \alpha < 1.0 ) sufficient to partially account for the radius discrepancies .
It is , however , impossible to reconcile the models with the observations on the basis of the effect of the reduced \alpha alone .
We therefore suggest that the combined effects of high metallicity and \alpha reduction could explain the observations of CM Draconis .
For example , increasing the metallicity of the system towards super-solar values ( i.e . Z = 2 Z _ { \odot } ) yields an agreement within 2 \sigma with \alpha = 1.0 .