Toy models for galaxy formation versus simulations

Abstract

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