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 \sim 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 _ { \odot } > M _ { * } > 0.1 M _ { \odot } ) .
The luminosity function of the Galactic disk is statistically consistent with that measured from volume complete samples in the solar neighborhood .
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 _ { \odot } and 0.12 M _ { \odot } , where the best fit MF turns over at 0.17 M _ { \odot } .
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 ) ; a broken power law returns \alpha =2.04 at masses greater than log M = -0.5 ( M=0.32 M _ { \odot } ) , and \alpha =0.2 at lower masses .
These results agree well with most previous investigations , though differences in the analytic formalisms adopted to describe those mass functions , as well as the range over which the data are fit , 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 .
Having validated this method to generate a low-mass luminosity function from matched SDSS/2MASS datasets , future studies will extend this technique to the entirety of the SDSS footprint .