The Spectral Correlation Function (SCF) is a statistical tool for analyzing
and inter-comparing spectral-line maps. The SCF was initially developed by
our group to test the validity of theoretical models of molecular clouds
(Rosolowsky et al. 1999). The main goal was to develop an algorithm that
measured not just the distribution of line properties (e.g. centroid
velocity analysis, autocorrelation functions, etc.), but the spatial
distribution of line shapes as well.
There are two versions of the SCF in use today. Version 1.0 computes a
number from 1 (perfect correlation) to 0 (no correlation) that measures, at
every position in a map, how similar each spectrum is to all its nearest
neighbors. SCF v1.0 was used by Rosolowsky, Goodman, Wilner & Williams
(1999) to demonstrate the its ability to discriminate amongst various
observed and simulated spectral-line maps (Data Page for this Paper). Ballesteros-Paredes,
Vazquez-Semadeni & Goodman (2002) used the SCF to compare observed and
simulated maps of the atomic ISM.
The IDL code for SCF v1.0 is available here.
Another version of the SCF, v2.0, analyzes the correlation amongst spectra
in a map as a function of spatial scale. The SCF v2.0 value for a spatial
lag of 1 pixel is the same as for SCF v1.0, but the statistic is also
computed for all possible spatial lags up to 1/3 the map size. The effects
of noise and sampling on SCF v2.0 are discussed in detail by Padoan,
Rosolowsky & Goodman (2001). Padoan, Kim, Goodman & Stavely-Smith (2001)
used SCF v2.0 to map out the scale height of the the Large Magellanic Cloud,
a nearly face-on galaxy.
Padoan, Goodman & Juvela (2003) present an extensive SCF v2.0 analysis of
observed and simulated 13CO maps of molecular clouds. The conclusion of
their analysis is that existing MHD simulations are coming close to
synthesizing "real" conditions for clouds with low Mach number, but that the
simulations do not have enough dynamic range to accurately model high Mach
number flows like those found in dense star-forming regions.
The IDL code for SCF v2.0 is available here.
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