On the effects of projection on morphology

We study the effects of projection of three-dimensional data onto the plane of the sky by means of numerical simulations of turbulence in the interste llar medium including the magnetic held, parameterized cooling and diffuse and stellar heating, self-gravity, and rotation. We compare the physical-sp ace density and velocity distributions with their representation in positio n-position-velocity (PPV) space ("channel maps"), noting that the latter ca n be interpreted in two ways: either as maps of the column density's spatia l distribution (at a given line-of-sight [LOS] velocity) or as maps of the spatial distribution of a given value of the LOS velocity (weighted by dens ity). This ambivalence appears related to the fact that the spatial and PPV representations of the data give significantly different views. First, the morphology in the channel maps more closely resembles that of the spatial distribution of the LOS velocity component than that of the density field, as measured by pixel-to-pixel correlations between images. Second, the chan nel maps contain more small-scale structure than three-dimensional slices o f the density and velocity fields, a fact evident both in subjective appear ance and in the power spectra of the images. This effect may be due to a ps eudorandom sampling (along the LOS) of the gas contributing to the structur e in a channel map: the positions sampled along the LOS (chosen by their LO S velocity) may vary significantly from one position in the channel map to the next.