Observational Diagnostics of Self-Gravitating MHD Turbulence in Giant Molecular Clouds

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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<0.15tff, the column density has a power spectral slope similar to nongravitating supersonic turbulence and a lognormal distribution. At an intermediate stage, i.e. 0.15tff< t ≤ 0.35tff, 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)=A₁kβ²e⁻ᵏ/ᵏᶜ, where A₁ describes the amplitude, kβ² describes the classical power law behavior and the scale kc characterizes the turn over from turbulence dominated to self-gravity dominated. At advanced stages of collapse, i.e. ≈ t>0.35tff, 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.