The Luminosity and Mass Functions of Low-Mass Stars in the Galactic Disk: I. The Calibration Region

We present measurements of the luminosity and mass functions of low-mass stars constructed from a catalog of matched Sloan Digital Sky Survey (SDSS) and 2 Micron All Sky Survey (2MASS) detections. This photometric catalog contains more than 25,000 matched SDSS and 2MASS point sources spanning ~30 square degrees on the sky. We have obtained follow-up spectroscopy, complete to J=16, of more than 500 low mass dwarf candidates within a 1 square degree sub-sample, and thousands of additional dwarf candidates in the remaining 29 square degrees. This spectroscopic sample verifies that the photometric sample is complete, uncontaminated, and unbiased at the 99% level globally, and at the 95% level in each color range. We use this sample to derive the luminosity and mass functions of low-mass stars over nearly a decade in mass (0.7 M_sun > M_* > 0.1 M_sun). We find that the logarithmically binned mass function is best fit with an M_c=0.29 log-normal distribution, with a 90% confidence interval of M_c=0.20--0.50. These 90% confidence intervals correspond to linearly binned mass functions peaking between 0.27 M_sun and 0.12 M_sun, where the best fit MF turns over at 0.17 M_sun. A power law fit to the entire mass range sampled here, however, returns a best fit of alpha=1.1 (where the Salpeter slope is alpha = 2.35). These results agree well with most previous investigations, though differences in the analytic formalisms adopted to describe those mass functions can give the false impression of disagreement. Given the richness of modern-day astronomical datasets, we are entering the regime whereby stronger conclusions can be drawn by comparing the actual datapoints measured in different mass functions, rather than the results of analytic analyses that impose structure on the data a priori. (abridged)