Modelling the structure of star clusters with fractional Brownian motion

Abstract

The degree of fractal substructure in molecular clouds can be quantified by comparing them with Fractional Brownian Motion (FBM) surfaces or volumes. These fields are self-similar over all length scales and characterised by a drift exponent $H$, which describes the structural roughness. Given that the structure of molecular clouds and the initial structure of star clusters are almost certainly linked, it would be advantageous to also apply this analysis to clusters. Currently, the structure of star clusters is often quantified by applying $\mathcal{Q}$ analysis. $\mathcal{Q}$ values from observed targets are interpreted by comparing them with those from artificial clusters. These are typically generated using a Box-Fractal (BF) or Radial Density Profile (RDP) model. We present a single cluster model, based on FBM, as an alternative to these models. Here, the structure is parameterised by $H$, and the standard deviation of the log-surface/volume density $\sigma$. The FBM model is able to reproduce both centrally concentrated and substructured clusters, and is able to provide a much better match to observations than the BF model. We show that $\mathcal{Q}$ analysis is unable to estimate FBM parameters. Therefore, we develop and train a machine learning algorithm which can estimate values of $H$ and $\sigma$, with uncertainties. This provides us with a powerful method for quantifying the structure of star clusters in terms which relate to the structure of molecular clouds. We use the algorithm to estimate the $H$ and $\sigma$ for several young star clusters, some of which have no measurable BF or RDP analogue.

arXiv comment11 Pages, accepted by MNRAS

References in corpus (27)

• Scikit-learn: Machine Learning in Python
• Gaia Data Release 2. Summary of the contents and survey properties
• The Gaia mission
• The Photodetector Array Camera and Spectrometer (PACS) on the Herschel Space Observatory
• The Herschel-SPIRE instrument and its in-flight performance
• From filamentary clouds to prestellar cores to the stellar IMF: Initial highlights from the Herschel Gould Belt survey
• Clouds, filaments and protostars: the Herschel Hi-GAL Milky Way
• The Star Formation Rate of Turbulent Magnetized Clouds: Comparing Theory, Simulations, and Observations
• Observations of IC348: The Disk Population at 2-3 Million Years
• The Disk Population of the Taurus Star-Forming Region
• The statistical Analysis of Star Clusters
• The Stellar Population of the Chamaeleon I Star-Forming Region
• ISOCAM observations of the rho Ophiuchi cloud: Luminosity and mass functions of the pre-main sequence embedded cluster
• What determines the density structure of molecular clouds ? A case study of Orion B with Herschel
• The dynamical evolution of fractal star clusters: the survival of substructure
• Dynamical evolution of star forming regions
• A Spitzer census of the IC 348 nebula
• On the nature of star-forming filaments: II. Sub-filaments and velocities
• Evolving structures of star-forming clusters
• Testing the universality of star formation - I. Multiplicity in nearby star-forming regions
• The Complex Distribution of Recently Formed Stars. Bimodal Stellar Clustering in the Star-Forming Region NGC 346
• Very Low Mass Stars and Brown Dwarfs of the Young Open Cluster IC2391
• On the spatial distributions of dense cores in Orion B
• Statistical comparison of clouds and star clusters
• Characterizing the structure of diffuse emission in Hi-GAL maps
• ${\mathcal{Q}}^{+}$: Characterising the structure of young star clusters
• Predicting the Neutral Hydrogen Content of Galaxies From Optical Data Using Machine Learning

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• S2D2: Small-scale Significant substructure DBSCAN Detection I. NESTs detection in 2D star-forming regions
• Characterising lognormal fractional-Brownian-motion density fields with a Convolutional Neural Network