On the Normalization of the Cosmic Star Formation History

Abstract

Strong constraints on the cosmic star formation history (SFH) have recently\nbeen established using ultraviolet and far-infrared measurements, refining the\nresults of numerous measurements over the past decade. Taken together, the most\nrecent and robust data indicate a compellingly consistent picture of the SFH\nout to redshift z~6, with especially tight constraints for z<~1. We fit these\ndata with simple analytical forms, and derive conservative bands to indicate\npossible variations from the best fits. Since the z<~1 SFH data are quite\nprecise, we investigate the sequence of assumptions and corrections that\ntogether affect the SFH normalisation, to test their accuracy, both in this\nredshift range and beyond. As lower limits on this normalisation, we consider\nthe evolution in stellar mass density, metal mass density, and supernova rate\ndensity, finding it unlikely that the SFH normalisation is much lower than\nindicated by our direct fit. Additionally, predictions from the SFH for\nsupernova type Ia rate densities tentatively suggests delay times of ~3 Gyr. As\na corresponding upper limit on the SFH normalisation, we consider the\nSuper-Kamiokande (SK) limit on the electron antineutrino flux from past\ncore-collapse supernovae, which applies primarily to z<~1. We find consistency\nwith the SFH only if the neutrino temperatures from SN events are relatively\nmodest. Constraints on the assumed initial mass function (IMF) also become\napparent. The traditional Salpeter IMF, assumed for convenience by many\nauthors, is known to be a poor representation at low stellar masses (<~ 1 solar\nmass), and we show that recently favoured IMFs are also constrained. In\nparticular, somewhat shallow, or top-heavy, IMFs may be preferred, although\nthey cannot be too top-heavy. (Abridged)\n