On the evolution of the density probability density function in strongly self-gravitating systems

摘要: The time evolution of the probability density function (PDF) mass is formulated and solved for systems in free-fall using a simple approximate collapse sphere. We demonstrate that pressure-free results power-law tail on high-density side PDF. slope quickly asymptotes to functional form PV (ρ)∝ρ–1.54 (volume-weighted) PDF PM (ρ)∝ρ–0.54 corresponding mass-weighted distribution. From approximation we derive analytic descriptions accretion, finding dynamically quiet with narrow PDFs lead retarded star formation low rates (SFRs). Conversely, strong turbulent motions broaden accelerate causing bursting mode formation. Finally, compare our theoretical work observations. measured SFRs are consistent model during early phases collapse. Comparison observed column those derived from suggests star-forming cores roughly free-fall.