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*Astron. Astrophys. 336, 697-720 (1998)*
## On the fractal structure of molecular clouds
**
J. Stutzki,
F. Bensch,
A. Heithausen,
V. Ossenkopf and
M. Zielinsky
**
Physikalisches Institut der Universität zu
Köln, Zülpicher Strasse 77, D-50937 Köln, Germany
(lastname@ph1.uni-koeln.de)
*Received 5 January 1998 / Accepted 5 May 1998*
**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 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
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.
1998) as the sample cloud to test these concepts. The area-perimeter
dimension independently measured for this cloud is consistent with
. 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 gives an
*fBm* -image. The power spectral index , the
mass spectral index , and the power law index of
the mass-size relation turn out to be related:
. The value of derived via
this relation and the independently determined values for
and is consistent with the
value directly determined for the sample cloud. Our analysis confirms
the recent suggestion by Elmegreen & Falgarone (1996) 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.
**Key words:** ISM:
structure
ISM: clouds
ISM: general
*Present address: Radioastronomisches Institut der Universität Bonn, Auf dem Hügel 71, D-53121 Bonn, Germany*
*Send offprint requests to:* J. Stutzki
This article contains no SIMBAD objects.
### Contents
© European Southern Observatory (ESO) 1998
Online publication: July 20, 1998
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