Effective temperature – radius relationship of M dwarfs

Abstract

M-dwarf stars provide very favourable conditions for finding habitable worlds beyond our solar system. The estimation of the fundamental parameters of the transiting exoplanets relies on the accuracy of the theoretical predictions for radius and effective temperature of the host M dwarf, therefore it is important to conduct multiple empirical tests of very low-mass star (VLM) models. These stars are the theoretical counterpart of M dwarfs. Recent determinations of mass, radius, and effective temperature of a sample of M dwarfs of known metallicity have disclosed an apparent discontinuity in the effective temperature-radius diagram that corresponds to a stellar mass of about 0.2 M⊙. This discontinuity has been ascribed to the transition from partially convective to fully convective stars. In this paper we compare existing VLM models to these observations, and find that theory does not predict any discontinuity at around 0.2 M⊙, but a smooth change in slope of the effective temperature-radius relationship around this mass value. The appearance of a discontinuity is due to naively fitting the empirical data with linear segments. Moreover, its origin is not related to the transition to fully convective structures. We find that this feature is instead an empirical signature for the transition to a regime where electron degeneracy provides an important contribution to the stellar equation of state, and it constitutes an additional test of the consistency of the theoretical framework for VLM models.