The Optical and Near‐Infrared Properties of Galaxies. I. Luminosity and Stellar Mass Functions

We use a large sample of galaxies from the Two Micron All Sky Survey (2MASS)and the Sloan Digital Sky Survey (SDSS) to calculate galaxy luminosity andstellar mass functions in the local Universe. We estimate k-corrections,evolution corrections, and stellar mass-to-light ratios (M/Ls) by fitting thegalaxy colors with simple models. Our optical and near-infrared luminosityfunctions agree with most recent literature optical and near-infrareddeterminations within the uncertainties. We argue that 2MASS is biased againstlow surface brightness galaxies, and use SDSS plus our knowledge of stellarpopulations to estimate that the true K-band luminosity function has a steeperfaint end slope than the direct estimate. Assuming a universally-applicablestellar initial mass function (IMF), we derive the stellar mass function ofgalaxies. The faint end slope slope for the stellar mass function is steeperthan -1.1, reflecting the low stellar M/Ls characteristic of low-mass galaxies.We estimate an upper limit to the stellar mass density in the local UniverseOmega* h = 0.0020+/-0.0006 by assuming an IMF as rich in low-mass stars asallowed by observations of galaxy dynamics. Finally, we find that thecharacteristic luminosity or mass of early-type galaxies is larger than forlater types, and the faint end slope is steeper for later types than forearlier types. Accounting for typing uncertainties, we estimate that at leasthalf, and perhaps as much as 3/4, of the stellar mass in the Universe is inearly-type galaxies. We present also SDSS/2MASS color-M/L correlations, anupdated discussion of near-infrared stellar M/L estimates, and thevolume-corrected distribution of g and K-band stellar M/Ls as a function ofstellar mass. [Abridged]