Li, GuangXing
(2018):
Scalefree gravitational collapse as the origin of rho similar to r(2) density profile  a possible role of turbulence in regulating gravitational collapse.
In: Monthly Notices of the Royal Astronomical Society, Vol. 477, No. 4: pp. 49514956

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Abstract
Astrophysical systems, such as clumps that form star clusters share a density profile that is close to rho similar to r(2). We prove analytically this density profile is the result of the scalefree nature of the gravitational collapse. Therefore, it should emerge in many different situations as long as gravity is dominating the evolution for a period that is comparable or longer than the freefall time, and this does not necessarily imply an isothermal model, as many have previously believed. To describe the collapse process, we construct a model called the turbulenceregulated gravitational collapse model, where turbulence is sustained by accretion and dissipates in roughly a crossing time. We demonstrate that a rho similar to r(2) profile emerges due to the scalefree nature the system. In this particular case, the rate of gravitational collapse is regulated by the rate at which turbulence dissipates the kinetic energy such that the infall speed can be 2050 per cent of the freefall speed (which also depends on the interpretation of the crossing time based on simulations of driven turbulence). These predictions are consistent with existing observations, which suggests that these clumps are in the stage of turbulenceregulated gravitational collapse. Our analysis provides a unified description of gravitational collapse in different environments.