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.
