Onset of convection near a point source of heat and gravity

A paradoxical symmetry breaking—development of a unidirectional flow via thermal instability—is predicted by an analytical solution for compressible convection near a point source of both heat and gravity. Such a flow can propel a cosmic hot body (e.g., a protostar) in a molecular cloud. This convection emerges at the critical Rayleigh number Ra=1(1+1)[2¹(1+1)+1+3μV/2]γ/(γ-1), where 1 is the number of flow cells, μV is the second-to-first viscosity ratio, and γ is the specific heat ratio.