2015AJ....149..140H

Based on a carefully constructed sample of dwarf stars, a new optical-near-infrared 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 18 M dwarfs with metallicities determined by high-resolution spectroscopy and the second part contains 49 dwarfs with metallicities obtained through moderate-resolution spectra. By applying this calibration to a large sample of around 1.3 million M dwarfs from the Sloan Digital Sky Survey and 2MASS, the metallicity distribution of this sample is determined and compared with those of previous studies. Using photometric parallaxes, the Galactic heights of M dwarfs in the large sample are also estimated. Our results show that stars farther from the Galactic plane, on average, have lower metallicity, which can be attributed to the age-metallicity relation. 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. Several more complicated Galactic chemical evolution models which have been proposed to resolve the G and K dwarf problems are tested and it is shown that these models could, to some extent, mitigate the M dwarf problem as well.