Exposing the plural nature of molecular clouds

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.

Statistical model for filamentary structures of molecular clouds

“…It has been observed in the early 1990s that a probabilistic reformulation of turbulence intermittency analysis in terms of wavelet transforms of the velocity field was a powerful alternative to velocity increments (Muzy et al 1993;Arnéodo et al 1995;Frisch 1995). More recently, Robitaille et al (2014Robitaille et al ( , 2019 discovered a similar anomalous scaling signature, generally attributed to turbulence intermittency, in Herschel column density maps using PDFs of wavelet coefficients at different spatial scales.…”

“…To calculate the modified random cascade model, we used the Fan wavelet transform (Kirby 2005;Robitaille et al 2019). The Fan wavelet is a rotated version of the classical Morlet wavelet and is designed to optimally sample all azimuthal directions in Fourier space.…”

“…8, the multiplicative operation in our models produces a progressive non-Gaussian contribution towards the small scales at which the Fourier analysis is not sensitive. Compared to the fBm power law, which was chosen to be similar to the power laws measured on Gaussian components of the multiscale segmentation performed by Robitaille et al (2014Robitaille et al ( , 2019, the random cascade model power Equation 11 can be considered as the equivalent of the structure function defined in Eq. 10, used here in models of column density maps, where laws have a shallower power law than those measured for the non-Gaussian components.…”

“…More recently, some studies on thermal dust emission observed by Herschel raised the question why contrasted filamentary structures, which appear to have a characteristic width (Arzoumanian et al 2011(Arzoumanian et al , 2019, do not produce any break or kink in the Fourier power spectrum (Panopoulou et al 2017). Robitaille et al (2014Robitaille et al ( , 2019 showed using the multiscale non-Gaussian segmentation (MnGSeg) technique 1 that filamentary structures are in fact dominating the scale-free Fourier power spectrum. This result demonstrated that dense coherent structures of the ISM also have a hierarchical geometry (most likely multifractal and intimately linked to the formation of stars) and that this geometry is intertwined with the monofractal and diffuse component of molecular clouds.…”

A centroid-based modelling approach to lens inversion for gravitationally lensed systems

“…This work also made use of the following software: SciPy [11], PyCharm [12], NumPy [13], Astropy [14], and AstroImageJ [15].…”