An analytical model for the history of cosmic star formation

By L. Hernquist, Volker Springel. 2002

189 citations recorded by the source corpus.

We use simple analytic reasoning to identify physical processes that drive the evolution of the cosmic star formation rate, ρ * , in cold dark matter universes. Based on our analysis, we formulate a model to characterize the redshift dependence of ρ * and compare it with results obtained from a set of hydrodynamic simulations that include star formation and feedback. We find that the cosmic star formation rate is described by two regimes. At early times, densities are sufficiently high and cooling times sufficiently short that abundant quantities of star-forming gas are present in all dark matter haloes that can cool by atomic processes. Consequently, ρ * generically rises exponentially as z decreases, independent of the details of the physical model for star formation, but dependent on the normalization and shape of the cosmological power spectrum. This part of the evolution is dominated by gravitationally driven growth of the halo mass function. At low redshifts, densities decline as the universe expands to the point that cooling is inhibited, limiting the amount of star-forming gas available. We find that in this regime the star formation rate scales approximately as ρ * H(z) 4 / 3 , in proportion to the cooling rate within haloes. We demonstrate that the existence of these two regimes leads to a peak in the star formation rate at an intermediate redshift z = z p e a k . We discuss how the location of this peak depends on our model parameters, and show that the peak cannot occur above a limiting redshift of z 8.7. For the star formation efficiency adopted in our numerical simulations, z p e a k 5-6, with half of all stars forming at redshifts larger than z ≃ 2.2. We derive analytic expressions for the full star formation history and show that they match our simulation results to better than ≃10 per cent. Using various approximations, we reduce the expressions to a simple analytic fitting function for ρ * that can be used to compute global cosmological quantities that are directly related to the star formation history. As examples, we consider the integrated stellar density, the supernova and gamma-ray burst rates observable on Earth, the metal enrichment history of the Universe, and the density of compact objects. We also briefly discuss the expected dependence of the star formation history on cosmological parameters and the physics of the gas.

Subfields: Astronomy and Astrophysics, Instrumentation

View Paper: https://www.semanticscholar.org/paper/506d738efaaa57abaf9705d3ff0837cb7ede6a74

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Citations in the corpus

Modelling feedback from stars and black holes in galaxy mergers (2004, background): “In particular, Springel & Hernquist (2003b) have shown that our coarse-graining procedure leads to a numerically converged estimate for the cosmic star formation history of the Universe (Hernquist & Springel 2003) that agrees well with low redshift observations.”
Subaru Deep Survey. VI. A Census of Lyman Break Galaxies at z ≃ 4 and 5 in the Subaru Deep Fields: Clustering Properties (2003, result): “This suggestion may not be consistent with the theoretical prediction that the star-formation efficiency increases with redshift (e.g., Hernquist & Springel 2003).”
ON THE LACK OF EVOLUTION IN GALAXY STAR FORMATION EFFICIENCY (2012, background): “This may explain past successes in reproducing the cosmic SFR with a variety of incompatible physical models (e.g., Hernquist & Springel 2003; Bouché et al. 2010; Krumholz & Dekel 2012; Davé et al. 2012) — the cosmic SFR for z < 2 alone is a poor discriminant between models.”
The anti‐hierarchical growth of supermassive black holes (2004, background): “…of the formation of groups and clusters (see e.g. Cavaliere & Vittorini 2000), the expansion of the Universe affecting the gas cooling efficiency (Hernquist & Springel 2003; Di Matteo et al. 2003), the progressive depletion of the cold gas reservoirs within galaxies needed to power accretion and…”
The evolution of the galaxy UV luminosity function at redshifts z ≃ 8 – 15 from deep JWST and ground-based near-infrared imaging (2022, methodology): “3 support the conclusion of McLeod et al. (2015, 2016) (in line with the long-standing analytical prediction of Hernquist & Springel (2003)), that 𝜌UV continues to display a steady, exponential decline with increasing redshift out to at least 𝑧 ' 12.”
The Relation between Quasar and Merging Galaxy Luminosity Functions and the Merger-driven Star Formation History of the Universe (2006, unknown): “…the total (integrated over all morphological types), extinction-corrected SFR density estimated in Hopkins & Beacom (2006) (similar to, e.g., Cole et al. 2001; Hopkins 2004; or predictions of cosmological simulations, e.g., Springel & Hernquist 2003b; Hernquist & Springel 2003) as the dotted line.”
Evolution of the Intergalactic Opacity: Implications for the Ionizing Background, Cosmic Star Formation, and Quasar Activity (2008, methodology): “…plot the predicted rate per unit redshift per unit steradian in arbitrary units11 under this assumption, dNGRB dtdzdΩ ∝ ρ̇⋆(z) cd2(z) (1 + z)H(z) , (47) where d(z) is the comoving distance to redshift z, for both the Hernquist & Springel (2003) and Hopkins & Beacom (2006) SFRs shown in Figure 12.”
Simulations of Early Structure Formation: Primordial Gas Clouds (2003, methodology): “In Figure 18, we compare the star-formation at very high redshifts (20 z 30) computed from our model and that of Hernquist & Springel (2003) for z 20.”
THE IMPACT OF COLD GAS ACCRETION ABOVE A MASS FLOOR ON GALAXY SCALING RELATIONS (2009, methodology): “Similarly to our model, Hernquist & Springel (2003) used an analytical approach and reach similar conclusions.”
Fueling Low-Level AGN Activity through Stochastic Accretion of Cold Gas (2006, background): “…from observations (e.g., Kennicutt 1998; Rownd & Young 1999; Martin & Kennicutt 2001), cosmological simulations (e.g., Springel & Hernquist 2003; Hernquist & Springel 2003; Nagamine et al. 2004, 2005a,b), simulations of star formation rate evolution in isolated disk galaxies (Li et al.…”
A census of metals and baryons in stars in the local universe (2007, methodology): “…Nagamine et al. (2006), who explore four different approaches: a two-component Fossil model, an Eulerian hydrodynamic simulation, the analytic SFH of Hernquist & Springel (2003) based on their cosmological smoothed particle hydrodynamics simulations, and the semi-analytic model of Cole et al.…”
Moving mesh cosmology: the hydrodynamics of galaxy formation (2011, result): “…results are in line with the expectation that gas cooling and condensation in this simulated system are determined entirely by the gas properties at the cooling radius (Bertschinger 1989; White & Frenk 1991; Hernquist & Springel 2003) which corresponds very closely between the simulation codes.”
The physics driving the cosmic star formation history (2009, background): “…reaches a broad maximum at intermediate redshift and then decreases as it is quenched by lower cooling rates in hotter and lower density gas, gas exhaustion and self-regulated feedback from stars and BHs, in broad agreement with previous work (e.g. White & Frenk 1991; Hernquist & Springel 2003).”
Galaxies–intergalactic medium interaction calculation – I. Galaxy formation as a function of large-scale environment (2009, methodology): “We believe that this is only partly due to our inclusion of metal line cooling that affects the SFR particularly at lower redshift, as discussed and illustrated in the analytical model of Hernquist & Springel (2003).”
Galaxy ecology: groups and low-density environments in the SDSS and 2dFGRS (2003, background): “…heating and stripping of the hot halo gas is likely to influence star formation (e.g. Diaferio et al. 2001; Cole et al. 2000; Blanton et al. 1999; Hernquist & Springel 2003), yet blue galaxies within such groups appear to have a normal W0(Hα) distribution, suggesting normal, recent star…”
Formation of z~6 Quasars from Hierarchical Galaxy Mergers (2006, background): “Detecting these galaxies and determining their contribution to reionization will be crucial to understanding the EOR (Hernquist & Springel 2003; Barton et al. 2004; Davé et al. 2006).”