A&A 469, 595-605 (2007)

DOI: 10.1051/0004-6361:20066962

## Statistical properties of dust far-infrared emission

**M.-A. Miville-Deschênes**

^{1, 2}, G. Lagache^{1}, F. Boulanger^{1}, and J.-L. Puget^{1}^{1}Institut d'Astrophysique Spatiale, Université Paris-Sud, Bât. 121, 91405 Orsay, France

e-mail: mamd@ias.u-psud.fr

^{2}Canadian Institute for Theoretical Astrophysics, University of Toronto, 60 St. George Street, Toronto, ON, M5S 3H8, Canada

(Received 18 December 2006 / Accepted 4 April 2007)

** Abstract ***Context.*
Far-infrared dust emission has a self-similar structure which reveals the complex dynamical processes
that shape the interstellar medium. The description of the statistical properties of this emission
gives important constraints on the physics of the interstellar medium but it is also a useful way
to estimate the contamination of diffuse interstellar emission in the cases where it is considered a nuisance.
*Aims.*
The main goals of this analysis of the power spectrum and non-Gaussian properties of far-infrared
dust emission are 1) to estimate the power spectrum of interstellar matter density in three dimensions;
2) to review and extend previous estimates of the cirrus noise due to dust emission; and 3)
to produce simulated dust emission maps that reproduce the observed statistical properties.
*Methods.*
To estimate the statistical properties of dust emission we analyzed the
power spectrum and wavelet decomposition of 100 m IRIS data (an improved version of the IRAS data)
over 55% of the sky. The simulation of realistic infrared emission maps is based on
modified Gaussian random fields.
*Results.*
The main results are the following. 1) The cirrus noise level as a function of brightness
has been previously overestimated. It is found to be proportional to
instead of
,
where
is the local average brightness at 100 m.
This scaling is in accordance with the fact that the brightness fluctuation level
observed at a given angular scale on the sky is the sum of fluctuations of increasing
amplitude with distance on the line of sight.
2) The spectral index of dust emission at scales between 5 arcmin and 12.5° is
on average but shows significant variations over the sky. Bright regions have systematically
steeper power spectra than diffuse regions.
3) The skewness and kurtosis of brightness fluctuations are high, indicative of strong
non-Gaussianity. Unlike the standard deviation of the fluctuations, the skewness
and kurtosis do not depend significantly on brightness, except in
bright regions (>10 MJy sr^{-1}) where they are systematically higher, probably due to contrasted
structures related to star formation activity.
4) Based on our characterization of the 100 m power spectrum we provide a prescription of
the cirrus confusion noise as a function of wavelength and scale.
5) Finally we present a method based on a modification of Gaussian random fields
to produce simulations of dust maps which reproduce the power spectrum and non-Gaussian properties of
interstellar dust emission.

**Key words:**methods: statistical

**--**ISM: structure

**--**infrared: ISM

**--**ISM: dust, extinction

**©**

*ESO 2007*