Radius relations for low-metallicity M-dwarf stars

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.