2013ApJ...773..131H

Prestellar cores are approximated by singular polytropic spheres. Their early evolution is studied analytically with a Bondi-like scheme. The considered approximation is meaningful for polytropic exponents γ between 0 and 6/5, implying radial power-law density profiles between r.^–1 and r ^–2.5. Gravitationally unstable Jeans and Bonnor-Ebert masses differ at most by a factor of 3.25. Tidally stable prestellar cores must have a mean density contrast ≳ 8 with respect to the external parent cloud medium. The mass-accretion rate relates to the cube of equivalent sound speed, as in Shu's seminal paper. The prestellar masses accreted over 10⁵ years cover the whole stellar mass spectrum; they are derived in simple closed form, depending only on the polytropic equation of state. The stellar masses that can be formed via strict conservation of angular momentum are at most of the order of a brown dwarf.