On the galaxy stellar mass function, the mass-metallicity relation and the implied baryonic mass function

A comparison between published field galaxy stellar mass functions (GSMFs) shows that the cosmic stellar mass density is in the range 4-8 per cent of the baryon density (assuming Omega(b) = 0.045). There remain significant Sources Of uncertainty for the dust correction and underlying stellar mass-to-fight ratio even assuming I reasonable Universal stellar initial mass function. We determine the z < 0.05 GSMF using the New York University Value-Added Galax Catalog sample of 49968 galaxies derived from the Sloan Digital Sky Survey and various estimates of stellar mass. The GSMF shows clear evidence for a low-mass upturn and is fitted with a double Schechter function that has alpha(2) similar or equal to -1.6. At masses below similar to 10(8.5) M-circle dot, the GSMF may be significantly incomplete because of missing low-surface-brightness galaxies. One interpretation of the stellar mass-metallicity relation is that it is primarily caused by a lower fraction of available baryons converted to stars in low-mass galaxies. Using this principle, we determine a simple relationship between baryonic mass and stellar mass and present an 'implied baryonic mass function'. This function has a faint-end slope, alpha(2) similar or equal to -1.9. Thus, we find evidence that the slope of the low-mass end of the galaxy mass function Could plausibly be as steep as the halo mass function. We illustrate the relationship between halo baryonic mass function -> galaxy baryonic mass function -> GSMF. This demonstrates the requirement for peak galaxy formation efficiency at baryonic masses similar to 10(11) M-circle dot corresponding to a minimum in feedback effects. The baryonic-infall efficiency may have levelled off at lower masses.