# The effective temperature -- radius relationship of M-dwarfs

## TL;DR

This paper compares theoretical models of M-dwarfs with observations, revealing a smooth temperature-radius relationship and identifying an empirical signature of electron degeneracy effects, rather than a discontinuity at 0.2 solar masses.

## Contribution

It demonstrates that the observed discontinuity is an artifact of data fitting and links the transition to electron degeneracy, refining understanding of low-mass star models.

## Key findings

- No predicted discontinuity at 0.2 solar masses in models.
- Empirical discontinuity is due to data fitting, not stellar structure transition.
- Transition to electron degeneracy influences the temperature-radius relationship.

## Abstract

M-dwarf stars provide very favourable conditions to find habitable worlds beyond our solar system. The estimation of the fundamental parameters of the transiting exoplanets rely on the accuracy of the theoretical predictions for radius and effective temperature of the host M-dwarf, hence the importance of multiple empirical tests of very low-mass star (VLM) models, 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 a supposed discontinuity in the effective temperature-radius diagram corresponding to a stellar mass of about 0.2Mo, that 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 0.2Mo, rather a smooth change of slope of the effective temperature-radius relationship around this mass value. The appearance of a discontinuity 5is due to naively fitting the empirical data with linear segments. Also, its origin is unrelated 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 EOS, and constitutes an additional test of the consistency of the theoretical framework for VLM models.