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We construct a steady analytic accretion flow model for a finite rotating gas cloud that accretes material to a central gravitational object. The pressure gradients of the flow are considered to be negligible, and so the flow is ballistic. We also assume a steady flow and consider the particles at the boundary of the spherical cloud to be rotating as a rigid body, with a fixed amount of inwards radial velocity. This represents a generalization to the traditional infinite gas cloud model described by Ulrich. We show that the streamlines and density profiles obtained deviate largely from the ones calculated by Ulrich. The extra freedom in the choice of the parameters on the model can naturally account for the study of protostars formed in dense clusters by triggered mechanisms, where a wide variety of external physical mechanisms determine the boundary conditions. Also, as expected, the model predicts the formation of an equatorial accretion disc about the central object with a radius different from the one calculated by Ulrich.

Analytic solutions to the accretion of a rotating finite cloud towards a central object – I. Newtonian approach