# Exploring the M-dwarf Luminosity--Temperature--Radius Relationships using Gaia DR2

## TL;DR

This study uses Gaia DR2 data to empirically analyze the relationships between luminosity, temperature, and radius in M-dwarfs, revealing a modest radius inflation not explained by magnetism and highlighting the importance of metallicity precision.

## Contribution

It provides the first large-scale empirical relationships for M-dwarfs using Gaia data, quantifies radius inflation, and assesses the limitations of current measurement techniques.

## Key findings

- M-dwarf radii are inflated by 3-7% compared to models.
- Current measurement accuracy is 2.4%, limited mainly by metallicity data.
- Stellar magnetism does not account for the observed radius inflation.

## Abstract

There is growing evidence that M-dwarf stars suffer radius inflation when compared to theoretical models, suggesting that models are missing some key physics required to completely describe stars at effective temperatures $(T_{\rm SED})$ less than about 4000K. The advent of Gaia DR2 distances finally makes available large datasets to determine the nature and extent of this effect. We employ an all-sky sample, comprising of $>$15\,000 stars, to determine empirical relationships between luminosity, temperature and radius. This is accomplished using only geometric distances and multiwave-band photometry, by utilising a modified spectral energy distribution fitting method. The radii we measure show an inflation of $3 - 7\%$ compared to models, but no more than a $1 - 2\%$ intrinsic spread in the inflated sequence. We show that we are currently able to determine M-dwarf radii to an accuracy of $2.4\%$ using our method. However, we determine that this is limited by the precision of metallicity measurements, which contribute $1.7\%$ to the measured radius scatter. We also present evidence that stellar magnetism is currently unable to explain radius inflation in M-dwarfs.