Exploring the M-dwarf Luminosity–Temperature–Radius relationships using Gaia DR2

 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 less than about 4000 K. The advent of Gaia DR2 distances finally makes available large data sets 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 utilizing a modified spectral energy distribution fitting method. The radii we measure show an inflation of $3\!-\!7{{\ \rm per\ cent}}$ compared to models, but no more than a $1\!-\!2{{\ \rm per\ cent}}$ intrinsic spread in the inflated sequence. We show that we are currently able to determine M-dwarf radii to an accuracy of $2.4{{\ \rm per\ cent}}$ using our method. However, we determine that this is limited by the precision of metallicity measurements, which contribute $1.7{{\ \rm per\ cent}}$ to the measured radius scatter. We also present evidence that stellar magnetism is currently unable to explain radius inflation in M-dwarfs.