The massive end of the luminosity and stellar mass functions: dependence on the fit to the light profile

In addition to the large systematic differences arising from assumptions about the stellar mass-to-light ratio, the massive end of the stellar mass function is rather sensitive to how one fits the light profiles of the most luminous galaxies. We quantify this by comparing the luminosity and stellar mass functions based on the Sloan Digital Sky Survey (SDSS) cmodel magnitudes, and PyMorph single-Sersic and Sersic-exponentialfits to the surface brightness profiles of galaxies in the SDSS. The PyMorph fits return more light, so that the predicted masses are larger than when cmodel magnitudes are used. As a result, the total stellar mass density at z similar to 0.1 is about 1.2 times larger than in our previous analysis of the SDSS. The differences are most pronounced at the massive end, where the measured number density of objects having M* >= 6 x 10(11) M-circle dot is approximately five times larger. Alternatively, at number densities of 10(-6) Mpc(-3), the limiting stellar mass is two times larger. The differences with respect to fits by other authors, typically based on Petrosian-like magnitudes, are even more dramatic, although some of these differences are due to sky-subtraction problems, and are sometimes masked by large differences in the assumed M*/L (even after scaling to the same initial mass function). Our results impact studies of the growth and assembly of stellar mass in galaxies, and of the relation between stellar and halo mass, so we provide simple analytic fits to these new luminosity and stellar mass functions and quantify how they depend on morphology, as well as the binned counts in electronic format. While these allow one to quantify the differences which arise because of the assumed light profile, and we believe our Sersic-exponential based results to be the most realistic of the models we have tested, we caution that which profile is the most appropriate at the high-mass end is still debated.