Extraction of a second power-law tail of the density distribution in simulated clouds

The emergence and development of a power-law tail (PLT) at the high-density end of the observed column-density distribution is thought to be indicative for advanced evolution of star-forming molecular clouds. As shown from many numerical simulations, it corresponds to a morphologically analogous evolution of the mass-density distribution (\rhopdf). The latter may display also a second, shallower PLT at the stage of collapse of the first formed protostellar cores. It is difficult to estimate the parameters of a possible second PLT due to resolution constraints. To address the issue, we extend the method for the extraction of single PLTs from arbitrary density distributions suggested by Veltchev et al.(2019) to detect a second PLT. The technique is elaborated through tests on an analytic \rhopdf{} and applied to a set of hydrodynamical high-resolution simulations of isothermal self-gravitating clouds. In all but one case two PLTs were detected -- the first slope is always steeper and the second one is typically $\partial \ln V /\ln \rho \sim -1$. These results are in a good agreement with numerical and theoretical works and do suggest that the technique extracts correctly double PLTs from smooth PDFs.