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.
We examine the evolution of the inner dark matter (DM) and baryonic density profile of a new sample of simulated field galaxies using fully cosmological, Lambda CDM, high resolution SPH + N-Body simulations. These simulations include explicit H2 and
metal cooling, star formation (SF) and supernovae (SNe) driven gas outflows. Starting at high redshift, rapid, repeated gas outflows following bursty SF transfer energy to the DM component and significantly flatten the originally `cuspy central DM mass profile of galaxies with present day stellar masses in the 10^4.5 -- 10^9.8 Msolar range. At z=0, the central slope of the DM density profile of our galaxies (measured between 0.3 and 0.7 kpc from their centre) is well fitted by rhoDM propto r^alpha with alpha simeq -0.5 + 0.35 log_10(Mstar/10^8Msolar) where Mstar is the stellar mass of the galaxy and 4 < log_10 Mstar < 9.4. These values imply DM profiles flatter than those obtained in DM--only simulations and in close agreement with those inferred in galaxies from the THINGS and LITTLE THINGS survey. Only in very small halos, where by z=0 star formation has converted less than ~ 0.03% of the original baryon abundance into stars, outflows do not flatten the original cuspy DM profile out to radii resolved by our simulations. The mass (DM and baryonic) measured within the inner 500 pc of each simulated galaxy remains nearly constant over four orders of magnitudes in stellar mass for Mstar 10^9 Msolar. This finding is consistent with estimates for faint Local Group dwarfs and field galaxies. These results address one of the outstanding problems faced by the CDM model, namely the strong discrepancy between the original predictions of cuspy DM profiles and the shallower central DM distribution observed in galaxies.
