Abstract
We present the Multiscale non-Gaussian Segmentation (MnGSeg) analysis technique. This wavelet-based method combines the analysis of the probability distribution function (PDF) of map fluctuations as a function of spatial scales and the power spectrum analysis of a map. This technique allows us to extract the non-Gaussianities identified in the multiscaled PDFs usually associated with turbulence intermittency and to spatially reconstruct the Gaussian and the non-Gaussian components of the map. This new technique can be applied on any data set. In the present paper, it is applied on a Herschel column density map of the Polaris flare cloud. The first component has by construction a self-similar fractal geometry similar to that produced by fractional Brownian motion (fBm) simulations. The second component is called the coherent component, as opposed to fractal, and includes a network of filamentary structures that demonstrates a spatial hierarchical scaling (i.e. filaments inside filaments). The power spectrum analysis of the two components proves that the Fourier power spectrum of the initial map is dominated by the power of the coherent filamentary structures across almost all spatial scales. The coherent structures contribute increasingly from larger to smaller scales, without producing any break in the inertial range. We suggest that this behaviour is induced, at least partly, by inertial-range intermittency, a well-known phenomenon for turbulent flows. We also demonstrate that the MnGSeg technique is itself a very sensitive signal analysis technique that allows the extraction of the cosmic infrared background (CIB) signal present in the Polaris flare submillimetre observations and the detection of a characteristic scale for 0.1 ≲ l ≲ 0.3 pc. The origin of this characteristic scale could partly be the transition of regimes dominated by incompressible turbulence versus compressible modes and other physical processes, such as gravity.
Highlights
A good statistical characterisation and morphological analysis of the interstellar medium (ISM) is important for many astrophysical studies
We demonstrate that the Multiscale non-Gaussian Segmentation (MnGSeg) technique is itself a very sensitive signal analysis technique that allows the extraction of the cosmic infrared background (CIB) signal present in the Polaris flare submillimetre observations and the detection of a characteristic scale for 0.1 l 0.3 pc
By coupling the multiscaled probability distribution function (PDF) with the power spectrum analysis, this novel technique is sensitive to the progressive contribution of non-Gaussianities towards the small spatial scales
Summary
A good statistical characterisation and morphological analysis of the interstellar medium (ISM) is important for many astrophysical studies. Schneider et al (2011) and Elia et al (2014) concluded, by applying the ∆-variance on nearby molecular clouds and regions across the Galactic plane, that despite the presence of characteristic scales, the underlying cloud structure is self-similar This discrepancy between the common scale-free medium measured in the ISM and the presence of highly contrasted filamentary structures remains a fundamental issue in our understanding of the density distribution of the ISM. In this paper intermittency is considered in a broad sense as irregularities and alternation in the spatial statistical distribution of ISM properties and for density fluctuations in the case of the present study This definition corresponds closely to “the dual nature of molecular clouds” described in the review of Falgarone et al (2004), where the diffuse component, traced by the 12CO (J =1–0) line emission, is fractal and highly dynamical and the coherent (as opposed to fractal) component, traced by mid-infrared absorption and submillimetric dust thermal emission, is accurately described by a network of filaments and dense cores.
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