Toy models for galaxy formation versus simulations

Abstract

We describe simple useful toy models for key processes of galaxy formation in its most active phase, at z > 1, and test the approximate expressions against the typical behaviour in a suite of high-resolution hydro-cosmological simulations of massive galaxies at z = 4 − 1. We address in particular the evolution of (a) the total mass inflow rate from the cosmic web into galactic haloes based on the EPS approximation, (b) the penetration of baryonic streams into the inner galaxy, (c) the disc size, (d) the implied steady-state gas content and star-formation rate (SFR) in the galaxy subject to mass conservation and a universal star-formation law, (e) the inflow rate within the disc to a central bulge and black hole as derived using energy conservation and self-regulated Q ∼ 1 violent disc instability (VDI), and (f) the implied steady state in the disc and bulge. The toy models provide useful approximations for the behaviour of the simulated galaxies. We find that (a) the inflow rate is proportional to mass and to (1 + z) 5/2 , (b) the penetration to the inner halo is ∼ 50% at z = 4 − 2, (c) the disc radius is ∼ 5% of the virial radius, (d) the galaxies reach a steady state with the SFR following the accretion rate into the galaxy, (e) there is an intense gas inflow through the disc, comparable to the SFR, following the predictions of VDI, and (f) the galaxies approach a steady state with the bulge mass comparable to the disc mass, where the draining of gas by SFR, outflows and disc inflows is replenished by fresh accretion. Given the agreement with simulations, these toy models are useful for understanding the complex phenomena in simple terms and for back-of-the-envelope predictions.

NIHAO IX: the role of gas inflows and outflows in driving the contraction and expansion of cold dark matter haloes

“…For ∼ 10 12 M⊙ haloes at z ∼ 2, Dekel et al (2013) finds p ∼ 0.5. For simplicity here we assume p = 1.…”

Star formation sustained by gas accretion

“…At early times, when galaxies were generally of low mass, and at recent times in the case of low-mass galaxies, a significant fraction of the gas from cosmological accretion remains cold and falls directly to the center (Birnboim and Dekel 2003;Semelin and Combes 2005;Stewart et al 2011a;van de Voort et al 2011). Figure 2 shows when the cold and hot accretion regimes operate as a function of halo mass and redshift (from Dekel et al 2013). Haloes below ∼10 12 M are dominated by cold accretion at all redshifts, whereas even high-mass galaxies at z > 1 could have some cold accretion in streams that penetrate the surrounding hot haloes (see also Ocvirk et al 2008;Dekel et al 2009;Kereš et al 2009;Stewart et al 2011a).…”

“…Numerical simulations produce galaxies that are originally very dynamic, but as time goes on they enter a quasi-stationary phase where inflows and outflows balance the SFR (Finlator and Davé 2008;Schaye et al 2010;Bouche et al 2010;Fraternali and Tomassetti 2012;Davé et al 2012;Dekel et al 2013;Bothwell et al 2013;Feldmann 2013;Altay et al 2013;Forbes et al 2014). Such equilibrium follows naturally from the gas-consumption timescale τ g being shorter than the other relevant timescales in the problem.…”

“…It is primarily dark-matter accretion carrying along baryons-intermittent but with a marked global trend. The average mass accretion rate into haloes of mass M halo at redshift z may be approximated by a formula in Dekel et al (2013;see also Lilly et al 2013 andDavé et al 2012),…”

“…Above this line the gas is all shock heated shutting off the gas supply for star formation. This schematic is based on analytic spherically symmetric calculations by Dekel and Birnboim (2006) and has been taken from Dekel et al (2013). The slanted dashed line is the critical mass in the Press-Schechter formalism, above which structures form are similar to the Keplerian velocities in the outer parts of disks.…”