Accretion with cooling, turbulence (Ma ~ 0.35), and e_rot = 0.3 (green): evolution of the physical and normalized accretion rate (cf. Fig. 5; the average of Ṁ_• in the top panel has 0.1 Myr step). The dashed line is the average cooling rate (1 Myr step). The solid black line is the adiabatic rotating model (Sect. 3). Chaotic cold accretion drives the dynamics as long as Ta < 1. Recurrent collisions in the cold phase cancel angular momentum and boost the accretion rate up to two orders of magnitude with respect to the Bondi rate. The accretion rate is linearly tied to Ṁ_cool again.