We use cosmological simulations to study a characteristic evolution pattern of high redshift galaxies. Early, stream-fed, highly perturbed, gas-rich discs undergo phases of dissipative contraction into compact, star-forming systems ("blue" nuggets) at z ∼ 4 − 2. The peak of gas compaction marks the onset of central gas depletion and inside-out quenching into compact ellipticals (red nuggets) by z ∼ 2. These are sometimes surrounded by gas rings or grow extended dry stellar envelopes. The compaction occurs at a roughly constant specific starformation rate (SFR), and the quenching occurs at a constant stellar surface density within the inner kpc (Σ 1 ). Massive galaxies quench earlier, faster, and at a higher Σ 1 than lower-mass galaxies, which compactify and attempt to quench more than once. This evolution pattern is consistent with the way galaxies populate the SFR-size-mass space, and with gradients and scatter across the main sequence. The compaction is triggered by an intense inflow episode, involving (mostly minor) mergers, counter-rotating streams or recycled gas, and is commonly associated with violent disc instability. The contraction is dissipative, with the inflow rate >SFR, and the maximum Σ 1 anti-correlated with the initial spin parameter . The central quenching is triggered by the high SFR and stellar/supernova feedback (maybe also AGN feedback) due to the high central gas density, while the central inflow weakens as the disc vanishes. Suppression of fresh gas supply by a hot halo allows the longterm maintenance of quenching once above a threshold halo mass, inducing the quenching downsizing.

We present a detailed comparison of fundamental dark matter halo properties retrieved by a substantial number of different halo finders. These codes span a wide range of techniques including friends‐of‐friends, spherical‐overdensity and phase‐space‐based algorithms. We further introduce a robust (and publicly available) suite of test scenarios that allow halo finder developers to compare the performance of their codes against those presented here. This set includes mock haloes containing various levels and distributions of substructure at a range of resolutions as well as a cosmological simulation of the large‐scale structure of the universe. All the halo‐finding codes tested could successfully recover the spatial location of our mock haloes. They further returned lists of particles (potentially) belonging to the object that led to coinciding values for the maximum of the circular velocity profile and the radius where it is reached. All the finders based in configuration space struggled to recover substructure that was located close to the centre of the host halo, and the radial dependence of the mass recovered varies from finder to finder. Those finders based in phase space could resolve central substructure although they found difficulties in accurately recovering its properties. Through a resolution study we found that most of the finders could not reliably recover substructure containing fewer than 30–40 particles. However, also here the phase‐space finders excelled by resolving substructure down to 10–20 particles. By comparing the halo finders using a high‐resolution cosmological volume, we found that they agree remarkably well on fundamental properties of astrophysical significance (e.g. mass, position, velocity and peak of the rotation curve). We further suggest to utilize the peak of the rotation curve, vmax, as a proxy for mass, given the arbitrariness in defining a proper halo edge.

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.