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
$(T_{\rm SED})$ 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.
