Multiple power-law tails in the density and column-density distribution in contracting star-forming clumps

We present a numerical study of the evolution of power-law tails (PLTs) in the (column-)density distributions (N-PDF, ρ-PDF) in contracting star-forming clumps in primordial gas, without and with some initial rotational and/or turbulent support. In all considered runs multiple PLTs emerge shortly after the formation of the first protostar. The first PLT (PLT 1) in the ρ-PDF is a stable feature with slope q1 ≃ −1.3 which corresponds – under the condition of preserved spherical symmetry – to the outer envelope of the protostellar object with density profile ρ∝l−2 in the classical Larson-Penston collapse model, where l is the radius. The second PLT (PLT 2) in the ρ-PDF is stable in the pure-infall runs but fluctuates significantly in the runs with initial support against gravity as dozens of protostars form and their mutual tidal forces change the density structure. Its mean slope, 〈q2〉 ≃ −2, corresponds to a density profile of ρ∝l−3/2 which describes a core in free fall in the classical Larson-Penston collapse model or an attractor solution at scales with dominating protostellar gravity. PLT 1 and PLT 2 in the N-PDFs are generally consistent with the observational data of Galactic low-mass star-forming regions from Herschel data. In the runs with initial support against gravity a third PLT (PLT 3) in the ρ-PDFs appears simultaneously with or after the emergence of PLT 2. It is very shallow, with mean slope of 〈q3〉 ≃ −1, and is associated with the formation of thin protostellar accretion disks.