Gaia Gaps and the Physics of Low-Mass Stars. I. The Fully Convective
  Boundary
  The Gaia M-dwarf gap is a significant under-density of stars observed near
$M_G = 10.2$ in a color-magnitude diagram for stars within 200 pc of the Sun.
It has been proposed that the gap is the manifestation of structural
instabilities within stellar interiors due to non-equilibrium $^{3}$He fusion
prior to some stars becoming fully convective. To test this hypothesis, we use
Dartmouth stellar evolution models, MARCS model atmospheres, and simple stellar
population synthesis to create synthetic $M_G$-($G_{\rm BP} - G_{\rm RP})$
color-magnitude diagrams. We confirm that the proposed $^{3}$He instability is
responsible for the appearance of the M-dwarf gap. Our synthetic gap shows
qualitatively similar features to the observed gap including: its vertical
extent in $M_G$, its slope in the color-magnitude diagram, and its relative
prominence at bluer colors as compared to redder colors. Furthermore,
corresponding over-densities of stars above the gap are reproduced by the
models. While qualitatively similar, the synthetic gap is approximately 0.2
magnitudes bluer and, accounting for this color offset, 0.16 magnitudes
brighter than the observed gap. Our results reveal that the Gaia M dwarf gap is
sensitive to conditions within cores of M dwarf stars, making the gap a
powerful tool for testing the physics of M dwarf stars and potentially using M
dwarfs to understand the local star formation history.
