The formation and fragmentation of the ring appearing in the collapse of a rotating cloud

Numerical simulations of the collapse of a slowly rotating cloud have been performed, assuming either isothermality, or a barotropic equation of state that reproduces the expected thermal behaviour of protostellar gas. A ring appears in the late stages of the collapse of a rotating cloud, and we have investigated the effect of differential rotation on the formation and fragmentation of this ring. In the simulations presented here, we have used Godunov‐type particle hydrodynamics to avoid the side effects of artificial viscosity in a differentially rotating cloud. The initial state of a cloud is characterized by and , where , Ω and are the thermal, gravitational and rotational energies, respectively. If the initial angular velocity, ω, of a cloud is proportional to r − P , then in the isothermal simulations, a ring forms if P is larger than 0.5, provided β o ≲ 0.035 . In the simulations using a barotropic equation of state, with α o = 0.6 and β o ≲ 0.035 , a ring is always formed, irrespective of whether P ≤ 0.5 or P > 0.5 . However, the mechanism and time of ring formation are different in the two extremes, as are the final configurations. Strong differential rotation ( P > 0.5) is more effective in inducing fragmentation than solid‐body rotation ( P = 0) , in the sense that fragmentation tends to occur earlier and to produce more fragments when P is larger.