Statistical properties and correlation length in star-forming molecular clouds: II. Gravitational potential and virial parameter

TL;DR

This paper assesses how well global observable estimates like mass and size can determine key physical quantities such as gravitational energy and virial parameter in star-forming molecular clouds, using ergodic theory to evaluate statistical validity.

Contribution

It applies ergodic theory to compare observational and numerical estimates of physical properties of molecular clouds, highlighting when global measurements are sufficient.

Findings

Global measurements can accurately estimate physical quantities in certain observed clouds.

Numerical simulations in periodic boxes require additional information for accurate estimates.

A derived relationship compares virial parameters between observational and simulation contexts.

Abstract

In the first article of this series, we have used the ergodic theory to assess the validity of a statistical approach to characterize various properties of star-forming molecular clouds (MCs) from a limited number of observations or simulations. This allows the proper determination of confidence intervals for various volumetric averages of statistical quantities obtained form observations or numerical simulations. In this joint paper, we apply the same formalism to a different kind of (observational or numerical) study of MCs. Indeed, as observations cannot fully unravel the complexity of the inner density structure of star forming clouds, it is important to know whether global observable estimates, such as the total mass and size of the cloud, can give an accurate estimation of various key physical quantities that characterize the dynamics of the cloud. Of prime importance is the correct determination of the total gravitational (binding) energy and virial parameter of a cloud. We show that, whereas for clouds that are not in a too advanced stage of star formation, such as Polaris or Orion B, the knowledge of only their mass and size is sufficient to yield an accurate determination of the aforementioned quantities from observations (i.e. in real space). In contrast, we show that this is no longer true for numerical simulations in a periodic box. We derive a relationship for the ratio of the virial parameter in these two respective cases.