2018MNRAS.481.2062M

Low-mass dense cores evolve during a long period of slow quasi-static contraction. In this paper, the steady-state collapse of low-mass clouds that are accreting gas from the external medium after the point of protostar formation is studied. In this model, the protostar of mass m_* is accreting spherically symmetric gas from a cloud with a finite outer radius. The finite outer boundary is an open one, at which the subsonic gas creeps inwards towards the central protostar. The magnetic field and thermal effects are ignored for simplicity and the gas is taken to be isothermal or polytropic. It is found that about 30 per cent of the cloud radius is moving supersonically for the isothermal cloud. For the polytropic cloud with γ= 4/3 and γ= 5/3, about 10 per cent and 10^–3 per cent of the cloud radius are moving supersonically, respectively. The sonic point spreads outwards at a speed of about 0.1 c_ s_ for the isothermal cloud and at lowered speeds for the polytropic cases, where c_s is the ambient sound speed. The results show that the supersonic velocities are spatially confined and spread subsonically and the mass accretion rates are lower than c_ s_^3/G for both the isothermal and the polytropic clouds, in agreement with the observational studies. But, in this study, half of the cloud mass is accumulated in the inner region of the cloud for each state, in contradiction to the observational studies. Magnetic or thermal effects may retard the accumulation of such a high mass in the inner region of the cloud.