2022A&A...663A.113J


Query : 2022A&A...663A.113J

2022A&A...663A.113J - Astronomy and Astrophysics, volume 663A, 113-113 (2022/7-1)

Statistical properties and correlation length in star-forming molecular clouds. I. Formalism and application to observations.

JAUPART E. and CHABRIER G.

Abstract (from CDS):

Observations of molecular clouds (MCs) show that their properties exhibit large fluctuations. The proper characterization of the general statistical behavior of these fluctuations, from a limited sample of observations or simulations, is of prime importance to understand the process of star formation. In this article, we use the ergodic theory for any random field of fluctuations, as commonly used in statistical physics, to derive rigorous statistical results. We outline how to evaluate the autocovariance function (ACF) and the characteristic correlation length of these fluctuations. We then apply this statistical approach to astrophysical systems characterized by a field of density fluctuations, notably star-forming clouds. When it is difficult to determine the correlation length from the empirical ACF, we show alternative ways to estimate the correlation length. Notably, we give a way to determine the correlation length of density fluctuations from the estimation of the variance of the volume and column-density fields. We show that the statistics of the column-density field is hampered by biases introduced by integration effects along the line of sight and we explain how to reduce these biases. The statistics of the probability density function (PDF) ergodic estimator also yields the derivation of the proper statistical error bars. We provide a method that can be used by observers and numerical simulation specialists to determine the latter. We show that they (i) cannot be derived from simple Poisson statistics and (ii) become increasingly large for increasing density contrasts, severely hampering the accuracy of the high end part of the PDF because of a sample size that is too small. As templates of various stages of star formation in MCs, we then examine the case of the Polaris and Orion B clouds in detail. We calculate, from the observations, the ACF and the correlation length in these clouds and show that the latter is on the order of ∼1% of the size of the cloud. This justifies the assumption of statistical homogeneity when studying the PDF of star-forming clouds. These calculations provide a rigorous framework for the analysis of the global properties of star-forming clouds from limited statistical observations of their density and surface properties.

Abstract Copyright: © E. Jaupart and G. Chabrier 2022

Journal keyword(s): methods: statistical - ISM: clouds - Oort Cloud - ISM: structure - ISM: kinematics and dynamics

Simbad objects: 4

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Number of rows : 4
N Identifier Otype ICRS (J2000)
RA
ICRS (J2000)
DEC
Mag U Mag B Mag V Mag R Mag I Sp type #ref
1850 - 2024
#notes
1 NAME Taurus Complex SFR 04 41.0 +25 52           ~ 4412 0
2 NAME Ori B MoC 05 41 43.0 -01 54 44           ~ 1373 0
3 NAME Polaris Flare MoC 11 00 14.8 +86 10 52           ~ 192 1
4 NAME Ophiuchus Molecular Cloud SFR 16 28 06 -24 32.5           ~ 3625 1

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