Quantification of molecular cloud structure using the Delta -variance
F. Bensch, J. Stutzki, V. Ossenkopf;
AaA, 2001, 366, 636
ABSTRACT:We present a detailed study of the Delta -variance as a method to quantify molecular cloud structure.
The Delta -variance was introduced by
Stutzki et al.
(1998) to analyze the drift behaviour of scalar functions and is
used to characterize the spatial structure of observed molecular cloud
images.
For fractional Brownian motion structures (fBm-fractals),
characterized by a power law power spectrum and random phases, the Delta -variance
allows to determine the power spectral index beta .
We present algorithms to
determine the Delta -variance for discretely sampled maps and study the
influence of white noise, beam smoothing and the finite spatial extent of the
maps.
We find that for images with beta >3, edge effects can bias the
structure parameters when determined by means of a Fourier transform
analysis.
In contrast, the Delta -variance provides a reliable estimate for the
spectral index beta , if determined in the spatial domain.
The effects of noise
and beam smoothing are analytically represented in a leading order
approximation.
This allows to use the Delta -variance of observed maps even at scales where
the influence of both effects becomes significant, allowing to derive the
spectral index beta over a wider range and thus more reliably than possible
otherwise.
The Delta -variance is applied to velocity integrated spectral line maps
of several clouds observed in rotational transitions of
12CO and 13CO.
We find that the spatial structure of the
emission is well characterized by a power law power spectrum in all cases.
For
linear scales larger than ~ 0.5 pc the spectral index is remarkably uniform for
the different clouds and transitions observed (2.5<=beta
<=2.8).
Significantly larger values (beta ga3 ) are found for observations made with higher
linear resolution toward the molecular cloud MCLD
123.5+24.9 in the Polaris Flare, indicating a smoother
spatial structure of the emission at small scales (<0.5 pc).
KEYWORDS: interstellar medium (ism): clouds, ism: structure, ism: individual objects: polaris flare, turbulence, methods: data analysis
PERSOKEY:turbulence, ,
CODE: bensch2001