Multifractal analysis of the interstellar medium: first application to Hi-GAL observations

Elia, D.; Strafella, F.; Dib, Sami; Schneider, N.; Hennebelle, P.; Pezzuto, S.; Molinari, S.; Schisano, E.; Jaffa, Sarah E.

doi:10.1093/mnras/sty2170

Cited by 25 publications

(37 citation statements)

References 68 publications

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“…However, the extraction of a monofractal component covering all spatial scales and filling the whole field is a first step towards a better comprehension of how turbulence is related to the ISM gas structures. An important comparaison of multifractal analysis based on a box-counting approach has been recently done by Elia et al (2018) using Hi-GAL observations (a key programme of Herschel), fBm images, and numerical simulations. They found that all the investigated fields, which are located in the Galactic plane, exhibit a multifractal structure rather than a simple monofractal structure.…”

Section: Discussionmentioning

confidence: 99%

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Exposing the plural nature of molecular clouds

Robitaille

Motte

Schneider

et al. 2019

A&A

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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.

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Section: Discussionmentioning

confidence: 99%

“…Fractal models fail to reproduce the common sharp transition in intensity seen in the ISM. Recently, Elia et al (2018) has shown that fBm models are not a good approximation of the ISM, but that multifractal analysis offers a more complete characterisation of molecular cloud structures.…”

Section: Introductionmentioning

confidence: 99%

Exposing the plural nature of molecular clouds

Robitaille

Motte

Schneider

et al. 2019

A&A

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“…Moreover, Elia et al (2018) recently emphasised that the monofractal approach to characterising ISM structures underlies a certain degree of degeneracy as the statistical description of the regions is based on a single parameter, the fractal dimension. They proposed to analyse the multifractal properties of ISM structures in Galactic dust-continuum maps using the boxcounting approach.…”

Section: Introductionmentioning

confidence: 99%

Statistical model for filamentary structures of molecular clouds

Robitaille

Abdeldayem

Joncour

et al. 2020

A&A

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We propose a new statistical model that can reproduce the hierarchical nature of the ubiquitous filamentary structures of molecular clouds. This model is based on the multiplicative random cascade, which is designed to replicate the multifractal nature of intermittency in developed turbulence. We present a modified version of the multiplicative process where the spatial fluctuations as a function of scales are produced with the wavelet transforms of a fractional Brownian motion realisation. This simple approach produces naturally a log-normal distribution function and hierarchical coherent structures. Despite the highly contrasted aspect of these coherent structures against a smoother background, their Fourier power spectrum can be fitted by a single power law. As reported in previous works using the multiscale non-Gaussian segmentation (MnGSeg) technique, it is proven that the fit of a single power law reflects the inability of the Fourier power spectrum to detect the progressive non-Gaussian contributions that are at the origin of these structures across the inertial range of the power spectrum. The mutifractal nature of these coherent structures is discussed, and an extension of the MnGSeg technique is proposed to calculate the multifractal spectrum that is associated with them. Using directional wavelets, we show that filamentary structures can easily be produced without changing the general shape of the power spectrum. The cumulative effect of random multiplicative sequences succeeds in producing the general aspect of filamentary structures similar to those associated with star-forming regions. The filamentary structures are formed through the product of a large number of random-phase linear waves at different spatial wavelengths. Dynamically, this effect might be associated with the collection of compressive processes that occur in the interstellar medium.

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“…Since in the interstellar medium there exist structures spanning a large dynamic range of spatial scales, and since there is evidence for self-similarity across parts of this dynamic range, there have been several attempts to characterise the interstellar medium, and in particular star forming clouds, with fractal or multi-fractal parameters (e.g. Beech 1987;Bazell & Desert 1988;Falgarone et al 1991;Hetem & Lepine 1993;Stutzki et al 1998;Bensch et al 2001;Chappell & Scalo 2001;Sánchez et al 2005;Ossenkopf et al 2008a;Kauffmann et al 2010;Schneider et al 2013;Elia et al 2014; E-mail: matthew.bates@astro.cf.ac.uk Rathborne et al 2015;Elia et al 2018). Such characterisations can, in principle, allow one (a) to constrain the three dimensional structures and dynamics that underlie the observed two-dimensional projections; (b) to evaluate whether two observed regions might be statistically similar, even if their detailed structures are quite different; and (c) to compare the results of numerical simulations with observations, and with one another.…”

Section: Introductionmentioning

confidence: 99%

“…Beech 1987; Bazell & Desert 1988;Falgarone et al 1991;Hetem & Lepine 1993;Sánchez et al 2005;Federrath et al 2009;Rathborne et al 2015), and the box-counting dimension, D BC (e.g. Sánchez et al 2005;Federrath et al 2009;Elia et al 2018); D PA is usually preferred to D BC , because it tends to give less noisy results. A second group of metrics derive from structure, or structure-like, functions (e.g.…”

Section: Introductionmentioning

confidence: 99%

Characterizing lognormal fractional-Brownian-motion density fields with a convolutional neural network

Bates

Whitworth

Lomax

2020

Monthly Notices of the Royal Astronomical Society

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In attempting to quantify statistically the density structure of the interstellar medium, astronomers have considered a variety of fractal models. Here we argue that, to properly characterise a fractal model, one needs to define precisely the algorithm used to generate the density field, and to specify -at least -three parameters: one parameter constrains the spatial structure of the field; one parameter constrains the density contrast between structures on different scales; and one parameter constrains the dynamic range of spatial scales over which self-similarity is expected (either due to physical considerations, or due to the limitations of the observational or numerical technique generating the input data). A realistic fractal field must also be noisy and non-periodic. We illustrate this with the exponentiated fractional Brownian motion (xfBm) algorithm, which is popular because it delivers an approximately lognormal density field, and for which the three parameters are, respectively, the power spectrum exponent, β, the exponentiating factor, S, and the dynamic range, R. We then explore and compare two approaches that might be used to estimate these parameters: Machine Learning and the established ∆-Variance procedure. We show that for 2 ≤ β ≤ 4 and 0 ≤ S ≤ 3, a suitably trained Convolutional Neural Network is able to estimate objectively both β (with root-mean-square error β ∼ 0.12) and S (with S ∼ 0.29). ∆-variance is also able to estimate β, albeit with a somewhat larger error ( β ∼ 0.17) and with some human intervention, but is not able to estimate S.

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Multifractal analysis of the interstellar medium: first application to Hi-GAL observations

Cited by 25 publications

References 68 publications

Exposing the plural nature of molecular clouds

Exposing the plural nature of molecular clouds

Statistical model for filamentary structures of molecular clouds

Characterizing lognormal fractional-Brownian-motion density fields with a convolutional neural network

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