On the fractal structure of molecular clouds
J. Stutzki, F. Bensch, A. Heithausen, V. Ossenkopf, M. Zielinsky;
AaA, 1998, 336, 697
ABSTRACT:We present a new method to analyze the structure of observed molecular cloud images which is the generalization of the Allan-variance method
traditionally used in the stability and drift analysis of instrumentation and
electronic devices.
Applied to integrated intensity maps of two molecular cloud
data sets, the method shows, together with an analysis of the phases of the
cloud images, the observed structures to be well characterized by what is
called a fractional Brownian motion (fBm)-structure in the context of
fractal images.
An fBm-structure results from a power law power spectrum of
the image and a completely random distribution of the image phases.
The
power law index beta of the power spectrum derived for two sample clouds turns
out to be close to 2.8.
For an fBm-structure, the power spectral index beta
determines other fractal measures such as the traditionally used box-counting
dimension and the fractal dimension describing iso-intensity contours via
their area-perimeter relation.
We use a large data set covering
observations at both large and small angular scales available for the Polaris Flare
(Heithausen et al.
\cite{heithausen1998}) as the sample cloud to test these
concepts.
The area-perimeter dimension independently measured for this cloud %,
d=1.6, is consistent with beta =2.8.
The fBm-concept allows easy generation
of realistic density representations for model clouds, to be used in
radiative transfer and other cloud simulations.
In a second step, we show that an
ensemble of randomly positioned clumps with a power law mass spectrum dN/dM ~
M(-alpha ) gives an fBm-image.
The power spectral index beta , the mass spectral
index alpha , and the power law index of the mass-size relation M ~ L(gamma )
turn out to be related: beta =gamma (3-alpha ).
The value of gamma derived
via this relation and the independently determined values for alpha and
beta is consistent with the value directly determined for the sample
cloud.
Our analysis confirms the recent suggestion by Elmegreen & Falgarone
(\cite{elmegreen1996}) that the mass distribution in molecular clouds is closely connected
with their fractal structure, although the detailed form of the relation
depends on the fractal structure model used.
We discuss the implications of
these results, obtained for the 2-dimensional observed images, for the
underlying 3-dimensional cloud density structure.
With some extrapolating
assumptions on the 3-dim structure, they imply that the 3-dimensional structure is
very much broken up, with the surface growing proportional to the
volume.
Clearly, additional information on the velocity structure, and in particular
its physical link to the assumed fBm-density structure, is needed to
describe the relevant properties of molecular cloud line shapes and line
radiative transfer.
The fBm-structure model allows an estimate on the
observability of molecular cloud structure down to much smaller angular scales than
presently reachable, e.g.
with interferometric observations.
It turns out
that, due to the steepness of the image power spectrum, these will be
extremely difficult.
Only the next generation large mm-wave array will bring
such observations into the regime of the feasible.
KEYWORDS: ism: structure, ism: clouds, ism: general
PERSOKEY:turbulence, ,
CODE: stutzki98