Photometric Calibrations of Metallicity and Temperature For M Dwarfs
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Based on a carefully collected sample of dwarf stars, a new empirical photometric calibration to estimate the metallicity of late-type K and early-to-mid-type M dwarfs is presented. The calibration sample has two parts; the first part includes 21 M dwarfs in common proper motion pairs with an FGK star or early-type M dwarf of known metallicity and the second part contains 50 dwarfs with metallicities obtained through moderate-resolution spectra. Using the most recent BT-Settl model atmospheres and the estimated effective temperatures of stars in the calibration sample, the synthetic colour-colour diagram most sensitive to M-dwarf temperatures is identified. By applying these methods to a large sample of around 1,300,000 M dwarfs from the Sloan Digital Sky Survey (SDSS) and the Two-Micron All Sky Survey (2MASS), the metallicity and temperature distributions of these small stars are determined. Using a photometric parallax, the Galactic heights of stars in the large sample are calculated. Our results show a shift in metallicity distribution toward lower metallicities as a function of Galactic height. The relation between metallicity and absolute magnitude is also investigated. A scarcity of metal-poor dwarf stars in the metallicity distribution relative to the Simple Closed Box Model indicates the existence of the “M dwarf problem,” similar to the previously known G and K dwarf problems. It is shown that the Galactic chemical evolution models proposed to solve the G and K dwarf problems could also be a solution of the M dwarf problem as well.