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We utilize high-resolution cosmological simulations to reveal that high-redshift galaxies tend to undergo a robust ‘wet compaction’ event when near a ‘golden’ stellar mass of $\sim \!\!10^{10}\, \rm M_\odot$ . This is a gaseous shrinkage to a compact star-forming phase, a ‘blue nugget’ (BN), followed by central quenching of star formation to a compact passive stellar bulge, a ‘red nugget’ (RN), and a buildup of an extended gaseous disc and ring. Such nuggets are observed at cosmic noon and seed today’s early-type galaxies. The compaction is triggered by a drastic loss of angular momentum due to, e.g. wet mergers, counter-rotating cold streams, or violent disc instability. The BN phase marks drastic transitions in the galaxy structural, compositional, and kinematic properties. The transitions are from star forming to quenched inside-out, from diffuse to compact with an extended disc or ring and a stellar envelope, from dark matter to baryon central dominance, from prolate to oblate stellar shape, from pressure to rotation support, from low to high metallicity, and from supernova to AGN feedback. The central black hole growth, first suppressed by supernova feedback when below the golden mass, is boosted by the compaction, and the black hole keeps growing once the halo is massive enough to lock in the supernova ejecta.

We present a simple model for the response of a dissipationless spherical system to an instantaneous mass change at its centre, describing the formation of flat cores in dark matter haloes and ultra-diffuse galaxies (UDGs) from feedback-driven outflow episodes in a specific mass range. This model generalizes an earlier simplified analysis of an isolated shell into a system with continuous density, velocity, and potential profiles. The response is divided into an instantaneous change of potential at constant velocities due to a given mass-loss or mass-gain, followed by energy-conserving relaxation to a new Jeans equilibrium. The halo profile is modelled by a two-parameter function with a variable inner slope and an analytic potential profile, which enables determining the associated kinetic energy at equilibrium. The model is tested against NIHAO cosmological zoom-in simulations, where it successfully predicts the evolution of the inner dark matter profile between successive snapshots in about 75 per cent of the cases, failing mainly in merger situations. This model provides a simple understanding of the formation of dark matter halo cores and UDGs by supernova-driven outflows, and a useful analytic tool for studying such processes.