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 μm 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 < I> instead of < I>1.5, where < I> is the local average brightness at 100 μm. 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 =-2.9 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 μm 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.
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