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.
