The Effects of Noise and Sampling on the Spectral Correlation Function

Abstract

The effects of noise and sampling on the ``Spectral Correlation Function'' (SCF) introduced by Rosolowsky et al. 1999 are studied using observational data, numerical simulations of magneto-hydrodynamic turbulence, and simple models of Gaussian spectral line profiles. The most significant innovations of this paper are: i) the normalization of the SCF based on an analytic model for the effect of noise; ii) the computation of the SCF as a function of the spatial lag between spectra within a map. By computing of the dependence of the SCF 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 correlation outer scale, l_o, is determined by the size of the map, and no evidence for a true departure from self-similarity on large scales has been found. 3) The correlation inner scale, l_i, is a true estimate of the smallest self-similar scale in a map. 4) The spectral slope in a given region, is independent of velocity resolution (above a minimum resolution threshold), spatial resolution, and average spectrum quality. 5) Molecular transitions which trace higher gas density yield larger values of the spectral slope than transitions tracing lower gas density. 6) Nyquist sampling, bad pixels in detector arrays, and reference sharing data acquisition need to be taken into account for a correct determination of the SCF at lag dr=1. The value of the spectral slope, however, can be computed correctly without a detailed knowledge of observational procedures.