On the normalisation of the cosmic star formation history

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