  We study the observable signatures of self-gravitating MHD turbulence by
applying the probability density functions (PDFs) and the spatial density power
spectrum to synthetic column density maps. We find that there exists three
characterizable stages of the evolution of the collapsing cloud which we term
"early," "intermediate," and "advanced." At early times, i.e. $t<0.15t_{ff}$,
the column density has a power spectral slope similar to nongravitating
supersonic turbulence and a lognormal distribution. At an intermediate stage,
i.e. $0.15t_{ff}< t \leq 0.35t_{ff}$, there exists signatures of the prestellar
cores in the shallower PDF and power spectrum power law slopes. The column
density PDF power law tails at these times have line of sight averaged slopes
ranging from -2.5 to -1.5 with shallower values belonging to simulations with
lower magnetic field strength. The density power spectrum slope becomes shallow
and can be characterized by $P(k)=A_1k^{\beta_2}e^{-k/k_c}$, where $A_1$
describes the amplitude, $k^{\beta_2}$ describes the classical power law
behavior and the scale $k_c$ characterizes the turn over from turbulence
dominated to self-gravity dominated. At advanced stages of collapse, i.e.
$\approx t>0.35t_{ff}$, the power spectral slope is positive valued, and a
dramatic increase is observed in the PDF moments and the Tsallis incremental
PDF parameters, which gives rise to deviations between PDF-sonic Mach number
relations. Finally, we show that the imprint of gravity on the density power
spectrum can be replicated in non-gravitating turbulence by introducing a
delta-function with amplitude equivalent to the maximum valued point in a given
self-gravitating map. We find that the turbulence power spectrum restored
through spatial filtering of the high density material.
