Extended Hernquist-Springel formalism for cosmic star formation

We present a revised and extended version of the analytic model for cosmic star formation originally given by Hernquist & Springel in 2003. The key assumption of this formalism is that star formation proceeds from cold gas, at a rate that is limited by an internal consumption timescale at early times, or by the rate of generation of gas via cooling at late times. These processes are analysed as a function of the mass of dark matter haloes and integrated over the halo population. We modify this approach in two main ways to make it more general: (1) halo collapse times are included explicitly, so that the behaviour is physically reasonable at late times; (2) allowance is made for a mass-dependent baryon fraction in haloes, which incorporates feedback effects. This model reproduces the main features of the observed baryonic Tully-Fisher relationship, and is consistent with observational estimates of the baryon mass fraction in the intergalactic medium. With minimal adjustment of parameters, our approach reproduces the observed history of cosmic star formation within a factor of two over the redshift range $0 < z < 10$. This level of agreement is comparable to that achieved by state-of-the-art cosmological simulations. Our simplified apparatus has pedagogical value in illuminating the results of such detailed calculations, and also serves as a means for rapid approximate exploration of non-standard cosmological models.