A Synergy of the Velocity Gradients Technique and the Probability
  Density Functions for Identifying Gravitational Collapse in Self-Absorbing
  Media
  The Velocity Gradients Technique (VGT) and the Probability Density Functions
(PDFs) of mass density are tools to study turbulence, magnetic fields, and
self-gravity in molecular clouds. However, self-absorption can significantly
make the observed intensity different from the column density structures. In
this work, we study the effects of self-absorption on the VGT and the intensity
PDFs utilizing three synthetic emission lines of CO isotopologs $^{12}$CO
(1-0), $^{13}$CO (1-0), and C$^{18}$O (1-0). We confirm that the performance of
VGT is insensitive to the radiative transfer effect. We numerically show the
possibility of constructing 3D magnetic fields tomography through VGT. We find
that the intensity PDFs change their shape from the pure log-normal to a
distribution that exhibits a power-law tail depending on the optical depth for
supersonic turbulence. We conclude the change of CO isotopologs' intensity PDFs
can be independent of self-gravity, which makes the intensity PDFs less
reliable in identifying gravitational collapsing regions. We compute the
intensity PDFs for a star-forming region NGC 1333 and find the change of
intensity PDFs in observation agrees with our numerical results. The synergy of
VGT and the column density PDFs confirms that the self-gravitating gas occupies
a large volume in NGC 1333.
