Star Formation Rate Distributions: Inadequacy of the Schechter Function

TL;DR

Galaxy luminosity functions differ fundamentally based on whether they trace stellar mass or current star formation rate, with SFR functions requiring a different mathematical form than the Schechter function used for mass functions.

Contribution

This paper demonstrates that star formation rate distributions cannot be accurately modeled by the Schechter function and proposes the Saunders function as a better fit, highlighting a key difference in galaxy luminosity functions.

Findings

SFR distributions have a shallower bright-end decline than Schechter functions.

The Saunders function provides a superior fit to SFR distributions.

UV and H alpha LFs appear Schechter-like due to dust correction effects.

Abstract

In this paper we posit that galaxy luminosity functions (LFs) come in two fundamentally different types depending on whether the luminosity traces galaxy stellar mass or its current star formation rate (SFR). Mass function types reflect the older stars and therefore the stellar mass distribution, while SFR function types arise from the young stars and hence the distribution of SFRs. Optical and near-infrared LFs are of the mass function type, and are well fit by a Schechter function (power law with an exponential cutoff at the bright end). In contrast, LFs of the SFR function type are of a different form, one that cannot be adequately described by a Schechter function. We demonstrate this difference by generating SFR distributions for mock samples of galaxies drawn from a Schechter stellar mass distribution along with established empirical relations between the SFR and stellar mass. Compared with the Schechter function, SFR distributions have a shallower decline at the bright end, which can be traced to the large intrinsic scatter of SFRs at any given stellar mass. A superior description of SFR distributions is given by the "Saunders" function, which combines a power law with a Gaussian at the high end. We show that the Schechter-like appearance of UV and H alpha LFs, although they are LFs of SFR function type, results when luminosities are not corrected for dust, or when average statistical corrections are used because individual attenuation measurements are not available. We thus infer that the non-Schechter form of the far-IR LFs is a true reflection of the underlying SFR distribution, rather than the purported artifact of AGN contamination.