The Inclination Correction to The Turbulence Structure Function of Thin Molecular Clouds and Its Application

TL;DR

This paper develops an inclination correction method for turbulence structure functions in thin molecular clouds, enabling more accurate energy cascade rate measurements from core velocity dispersion data regardless of cloud orientation.

Contribution

It introduces a correction formula accounting for the intersection angle, extending previous methods to non-perpendicular cloud orientations using elliptic integrals.

Findings

Derived a correction formula for inclination angle effects.

Expressed the correction factor using elliptic integrals.

Facilitates accurate turbulence measurements in various cloud orientations.

Abstract

The energy cascade rate of turbulence can be measured with the structure function. In practice, the 3D velocity of the gas in molecular cloud is hard to measure, which makes the measurement of structure function difficult. In the case of thin molecular clouds perpendicular to the line of sight, the structure function $S^2_{ tt}$ can be measured with core velocity dispersion (CVD), ${\rm CVD}^2=\frac{1}{2}S^2_{ tt}$. This method was extended to the case when the thin molecular cloud is not perpendicular to the line of sight, with intersection angle $\theta$, ${\rm CVD}^2=\frac{1}{2}S^2_{ tt}\left(1-\frac{1}{8}\cos^2\theta\right)R^{2/3}$, where $R$ can be expressed with elliptic integrals of the second kind $E(k,\varphi)$ as $R=\frac{2}{\pi}E(\cos\theta,\frac{\pi}{2})$.