Emissivity Statistics in Turbulent, Compressible MHD Flows and the Density-Velocity Correlation

In this paper we test the results of a recent analytical study by Lazarian and Pogosyan, on the statistics of emissivity in velocity channel maps, in the case of realistic density and velocity fields obtained from numerical simulations of MHD turbulence in the interstellar medium (ISM). To compensate for the lack of well-developed inertial ranges in the simulations due to the limited resolution, we apply a procedure for modifying the spectral slopes of the fields while preserving the spatial structures. We find that the density and velocity are moderately correlated in space and prove that the analytical results by Lazarian and Pogosyan hold in the case when these fields obey the fluid conservation equations. Our results imply that the spectra of velocity and density can be safely recovered from the position-position-velocity (PPV) data cubes available through observations, and confirm that the relative contributions of the velocity and density fluctuations to those of the emissivity depend on the velocity resolution used and on the steepness of the density spectral index. Furthermore, this paper supports previous reports that an interpretation of the features in the PPV data cubes as simple density enhancements (i.e., ``clouds'') can be often erroneous, as we observe that changes in the velocity statistics substantially modify the statistics of emissivity within the velocity data cubes.