Emissivity statistics in turbulent compressible magnetohydrodynamic 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 t he case of realistic density and velocity fields obtained from numerical si mulations of magnetohydrodynamic turbulence in the interstellar medium. To compensate for the lack of well-developed inertial ranges in the simulation s owing to the limited resolution, we apply a procedure for modifying the s pectral slopes of the fields while still preserving the spatial structures. We find that the density and velocity are moderately correlated in space, and we prove that the analytical results by Lazarian and Pogosyan hold in t he case when these fields obey the fluid conservation equations. Our result s imply that the spectra of velocity and density can be safely recovered fr om the position-position-velocity (PPV) data cubes available through observ ations and confirm that the relative contributions of the velocity and dens ity fluctuations to those of the emissivity depend on the velocity resoluti on used and on the steepness of the density spectral index. Furthermore, th is paper supports previous reports that an interpretation of the features i n the PPV data cubes as simple density enhancements (i.e., "clouds") can of ten be erroneous, as we observe that changes in the velocity statistics sub stantially modify the emissivity statistics within the velocity data cubes.