# An analysis of the turbulence in the central region of M 42 through structure functions

## TL;DR

This study analyzes the turbulence in the Huygens Region of M 42 using structure functions, revealing two flow regimes that align with a generalized Larson's Law, and provides a mathematically sound methodology for such analysis.

## Contribution

It introduces a rigorous method for calculating the second order structure function of astronomical velocity fields and identifies two distinct turbulence regimes in M 42.

## Key findings

- Turbulence in M 42 lies between Kolmogorov and Burgers regimes.
- Identified two separate flow regimes in the region.
- Turbulence follows a generalized Larson's Law with S2~δr^{0.74-0.76}.

## Abstract

Here, we analyse the character of the turbulence of the Huygens Region in the Orion Nebula (M 42) using structure functions. We compute the second order structure function of a high resolution velocity map in H$\alpha$ obtained through the {\emph MUSE} instrument. Ours is one of the few works that follows a mathematically sound methodology for calculating the second order structure function of astronomical velocity fields. Because of that our results will be useful for future comparisons with other studies of M 42 or other regions. We first analyse the Probability Distribution Function (PDF) and found it consistent with those resulting from numerical simulations of solenoidal turbulence. After a further analysis of the data, we found two possible separate motions or at least regimes in the region. This is confirmed later through the calculation of several filtered structure functions. We found that the turbulence in the Huygens Region is between the Kolmogorov regime ($S_2\propto\delta r^{2/3}$) and the Burgers regime ($S_2\propto\delta r$). We found that the turbulence in the region consists on two flow regimes that reproduce a generalised Larson's Law, $S_2\sim\delta r^{0.74-0.76}$.