3D morphology of a random field from its 2D cross-section

Abstract

We show that both aspect ratios of randomly oriented triaxial ellipsoids (representing isosurfaces of an isotropic 3D random field) can be determined from a single 2D cross-section of their sample using the probability distribution of the filamentarity F of the structures seen in the cross-section (F=0 for a circle and F=1 for a line). The probability distribution of F has a robust form with a sharp maximum and truncation that are sensitive to the ellipsoids' aspect ratios. We show that the aspect ratios of triaxial ellipsoids with randomly distributed dimensions can still be recovered from the probability distribution of F. This method is applicable to many shape recognition and classification problems, here illustrated with neutral hydrogen density in the turbulent interstellar medium of the Milky Way. The gas distribution is shown to be filamentary with the mean axis ratio 1:2:20.

arXiv comment5 pages, 7 figures, discussion of Galactic turbulence and neutral hydrogen filaments extended; to be published in MNRAS Letters, http://mnrasl.oxfordjournals.org/

References in corpus (7)

• Interstellar Turbulence I: Observations and Processes
• Interstellar Turbulence II: Implications and Effects
• Clouds as Turbulent Density Fluctuations. Implications for pressure confinement and spectral line data interpretation
• GASS: The Parkes Galactic All-Sky Survey. II. Stray-Radiation Correction and Second Data Release
• Shapefinders: A new shape diagnostic for large scale structure
• Disentangling the Cosmic Web I: Morphology of Isodensity Contours
• Direct Minkowski Functional analysis of large redshift surveys: a new high--speed code tested on the luminous red galaxy Sloan Digital Sky Survey-DR7 catalogue

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