Abstract
We present evidence that there is an M dwarf problem similar to the previously identified G dwarf and K dwarf problems: the number of low-metallicity M dwarfs is not sufficient to match simple closed-box models of local Galactic chemical evolution. We estimated the metallicity of 4141 M dwarf stars with spectra from the Sloan Digital Sky Survey (SDSS) using a molecular band strength versus metallicity calibration developed using high resolution spectra of nearby M dwarfs. Using a sample of M dwarfs with measured magnitudes, parallaxes, and metallicities, we derived a relation that describes the absolute magnitude variation as a function of metallicity. When we examined the metallicity distribution of SDSS stars, after correcting for the different volumes sampled by the magnitude-limited survey, we found that there is an M dwarf problem, with the number of M dwarfs at [Fe/H] ~ -0.5 less than 1% the number at [Fe/H] = 0, where a simple model of Galactic chemical evolution predicts a more gradual drop in star numbers with decreasing metallicity.
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