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 and stellar mass functions in the local universe. We estimate corrections for passband shifting and galaxy evolution, as well as present-day stellar mass-to-light (M/L) ratios, by fitting the optical - near- infrared galaxy data with simple models. Accounting for the 8% galaxy overdensity in the SDSS early data release region, the optical and near- infrared luminosity functions we construct for this sample agree with most recent literature optical and near- infrared determinations within the uncertainties. We argue that 2MASS is biased against low surface brightness galaxies and use SDSS plus our knowledge of stellar populations to estimate the "true'' K-band luminosity function. This has a steeper faint end slope and a slightly higher overall luminosity density than the direct estimate. Furthermore, assuming a universally applicable stellar initial mass function (IMF), we find good agreement between the stellar mass function we derive from the 2MASS/ SDSS data and that derived by Cole et al. The faint end slope for the stellar mass function is steeper than - 1.1, reflecting the low stellar M/L ratios characteristic of low-mass galaxies. We estimate an upper limit to the stellar mass density in the local universe Omega(*)h = 2.0 +/- 0.6 x 10(-3) by assuming an IMF as rich in low-mass stars as allowed by observations of galaxy dynamics in the local universe. The stellar mass density may be lower than this value if a different IMF with fewer low-mass stars is assumed. Finally, we examine type-dependence in the optical and near- infrared luminosity functions and the stellar mass function. In agreement with previous work, we find that the characteristic luminosity or mass of early-type galaxies is larger than for later types, and the faint end slope is steeper for later types than for earlier types. Accounting for typing uncertainties, we estimate that at least half, and perhaps as much as 3/4, of the stellar mass in the universe is in early-type galaxies. As an aid to workers in the field, we present in an Appendix the relationship between model stellar M/L ratios and colors in SDSS/2MASS passbands, an updated discussion of near- infrared stellar M/L ratio estimates, and the volume-corrected distribution of g- and K-band stellar M/L ratios as a function of stellar mass.