Precision modeling of M?dwarfs has become worthwhile in recent years due to the increasingly precise values of masses and radii which can be obtained from eclipsing binary studies. In a recent paper, Torres has identified four prime M?dwarf pairs with the most precise empirical determinations of masses and radii. The measured radii are consistently larger than standard stellar models predict by several percent. These four systems potentially provide the most challenging tests of precision evolutionary models of cool dwarfs at the present time. We have previously modeled M?dwarfs in the context of a criterion due to Gough & Tayler in which magnetic fields inhibit the onset of convection according to a physics-based prescription. In the present paper, we apply our magnetoconvective approach to the four prime systems in the Torres list. Going a step beyond what we have already modeled in CM Dra (one of the four Torres systems), we note that new constraints on magnetoconvective models of M?dwarfs are now available from empirical estimates of magnetic field strengths on the surfaces of these stars. In the present paper, we consider how well our magnetoconvective models succeed when confronted with this new test of surface magnetic field strengths. Among the systems listed by Torres, we find that plausible magnetic models work well for CM Dra, YY Gem, and CU Cnc. (The fourth system in Torres's list does not yet have enough information to warrant magnetic modeling.) Our magnetoconvection models of CM Dra, YY Gem, and CU Cnc yield predictions of the magnetic fluxes on the stellar surface which are consistent with the observed correlation between magnetic flux and X-ray luminosity.
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