Radii of 88 M Subdwarfs and Updated Radius Relations for Low-metallicity M-dwarf Stars

M subdwarfs are low-metallicity M dwarfs that typically inhabit the halo population of the Galaxy. Metallicity controls the opacity of stellar atmospheres; in metal-poor stars, hydrostatic equilibrium is reached at a smaller radius, leading to smaller radii for a given effective temperature. We compile a sample of 88 stars that span spectral classes K7 to M6 and include stars with metallicity classes from solar-metallicity dwarf stars to the lowest metallicity ultra subdwarfs to test how metallicity changes the stellar radius. We fit models to Palomar Double Spectrograph (DBSP) optical spectra to derive effective temperatures (T _eff) and we measure bolometric luminosities (L _bol) by combining broad wavelength-coverage photometry with Gaia parallaxes. Radii are then computed by combining the T _eff and L _bol using the Stefan-Boltzman law. We find that for a given temperature, ultra subdwarfs can be as much as five times smaller than their solar-metallicity counterparts. We present color-radius and color-surface brightness relations that extend down to [Fe/H] of -2.0 dex, in order to aid the radius determination of M subdwarfs, which will be especially important for the WFIRST exoplanetary microlensing survey.