Statistical model for filamentary structures of molecular clouds -- The modified multiplicative random cascade model and its multifractal nature

Abstract

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.

arXiv comment11 pages, 8 figures, accepted on 30/06/2020

References in corpus (19)

• Astropy: A Community Python Package for Astronomy
• The multifractal nature of turbulent energy dissipation
• Comparing the statistics of interstellar turbulence in simulations and observations: Solenoidal versus compressive turbulence forcing
• Characterizing interstellar filaments with Herschel in IC5146
• Global Hierarchical Collapse In Molecular Clouds. Towards a Comprehensive Scenario
• The Formation and Destruction of Molecular Clouds and Galactic Star Formation
• Supersonic turbulence in the ISM: stellar extinction determinations as probes of the structure and dynamics of dark clouds
• Characterizing the properties of nearby molecular filaments observed with Herschel
• A Fractal Analysis of the HI Emission from the Large Magellanic Cloud
• Statistical properties of dust far-infrared emission
• A closer look at the "characteristic" width of molecular cloud filaments
• Multifractal Scaling, Geometrical Diversity, and Hierarchical Structure in the Cool Interstellar Medium
• Dissipative structures of diffuse molecular gas III -- Small-scale intermittency of intense velocity-shears
• Characterising Complexity in Solar Magnetogram Data using a Wavelet-based Segmentation Method
• Multifractal Analysis of the Interstellar Medium. First application to Hi-GAL Observations
• Centroid Velocity Statistics of Molecular Clouds
• How the power spectrum of dust continuum images may hide the presence of a characteristic filament width
• Continuous cascades in the wavelet space as models for synthetic turbulence
• Exposing the plural nature of molecular clouds : Extracting filaments and the CIB against the true scale-free interstellar medium

Cited by in corpus (9)

• The width of Herschel filaments varies with distance
• Mass segregation and sequential star formation in NGC 2264 revealed by Herschel
• A train of shocks at 3000 au scale? Exploring the clash of an expanding bubble into the NGC 1333 IRAS 4 region. SOLIS XIV
• S2D2: Small-scale Significant substructure DBSCAN Detection I. NESTs detection in 2D star-forming regions
• Description of turbulent dynamics in the interstellar medium: multifractal/microcanonical analysis I. Application to Herschel observations of the Musca filament
• Towards Synthetic Magnetic Turbulence with Coherent Structures
• Emergence of high-mass stars in complex fiber networks (EMERGE) V. From filaments to spheroids: the origin of the hub-filament systems
• The environmental imprint on molecular layering in the dusty streamer of M512
• Sutra : An integrated framework for identification and characterization of filaments in the interstellar medium