The Effects of Noise and Sampling on the Spectral Correlation Function

The effects of noise and sampling on the ``Spectral Correlation Function''(SCF) introduced by Rosolowsky et al. 1999 are studied using observationaldata, numerical simulations of magneto-hydrodynamic turbulence, and simplemodels of Gaussian spectral line profiles. The most significant innovations ofthis paper are: i) the normalization of the SCF based on an analytic model forthe effect of noise; ii) the computation of the SCF as a function of thespatial lag between spectra within a map. By computing of the dependence of theSCF on the spatial lag, S_o(dr), we have been able to conclude that: 1) S_o(dr)is a power law, with slope in the range of scales l_i-l_o. 2) The correlationouter scale, l_o, is determined by the size of the map, and no evidence for atrue departure from self-similarity on large scales has been found. 3) Thecorrelation inner scale, l_i, is a true estimate of the smallest self-similarscale in a map. 4) The spectral slope in a given region, is independent ofvelocity resolution (above a minimum resolution threshold), spatial resolution,and average spectrum quality. 5) Molecular transitions which trace higher gasdensity yield larger values of the spectral slope than transitions tracinglower gas density. 6) Nyquist sampling, bad pixels in detector arrays, andreference sharing data acquisition need to be taken into account for a correctdetermination of the SCF at lag dr=1. The value of the spectral slope, however,can be computed correctly without a detailed knowledge of observationalprocedures.Comment: 28 pages, 12 figures included. To be published in The Astrophysical Journa