[Paper Review] COMPRESSIBILITY AND DENSITY FLUCTUATIONS IN MOLECULAR-CLOUD TURBULENCE

Liubin Pan, Paolo Padoan+2 more|arXiv (Cornell University)|Oct 15, 2015

Astrophysics and Star Formation Studies2 references3 citations

TL;DR

This study investigates turbulence in molecular clouds driven by supernova explosions, finding it to be only mildly compressive (compressive-to-solenoidal ratio ≈ 0.3), lower than the equilibrium value of 0.5 in idealized simulations. The results show that gravity does not significantly alter compressibility or mean velocity, and density fluctuations follow a lognormal distribution with a high-density power-law tail when self-gravity is included, supporting realistic star formation models.

ABSTRACT

The compressibility of molecular cloud (MC) turbulence plays a crucial role in star formation models, because it controls the amplitude and distribution of density fluctuations. The relation between the compressive ratio (the ratio of powers in compressive and solenoidal motions) and the statistics of turbulence has been studied systematically only in idealized simulations with random external forces. In this work, we analyze a simulation of large-scale turbulence (250 pc) driven by supernova (SN) explosions that has been shown to yield realistic MC properties. We demonstrate that SN driving results in MC turbulence that is only mildly compressive, with the turbulent ratio of compressive to solenoidal modes ≈ 0.3 on average, lower than the equilibrium value of 0.5 found in the inertial range of isothermal simulations with random solenoidal driving. We also find that the compressibility of the turbulence is not noticeably affected by gravity, nor is the mean cloud expansion or contraction velocity (MCs do not collapse as a whole even if their own prestellar cores collapse to form stars). Furthermore, the clouds follow the same relation between the rms density and the rms velocity as in isothermal turbulence and their average gas density PDF is described well by a lognormal distribution, with the addition of a high-density power-law tail when self-gravity is included. Subject headings: ISM: kinematics and dynamics – MHD – stars: formation – turbulence

Motivation & Objective

• To understand how supernova-driven turbulence affects the compressibility of molecular clouds.
• To determine whether gravity alters the compressive nature of turbulence or cloud-scale velocity dispersion.
• To assess whether the density probability distribution function (PDF) of molecular clouds matches theoretical expectations under realistic driving mechanisms.
• To compare SN-driven turbulence with idealized simulations to evaluate the validity of standard turbulence models in star formation contexts.

Proposed method

• Simulating large-scale (250 pc) molecular cloud turbulence driven by supernova explosions, using a magnetohydrodynamic (MHD) framework.
• Measuring the ratio of compressive to solenoidal velocity power to quantify compressibility, comparing it to theoretical equilibrium values.
• Analyzing the root-mean-square (rms) density and velocity fluctuations to test the scaling relation observed in isothermal turbulence.
• Computing the probability distribution function (PDF) of gas density, particularly assessing deviations from lognormality and the emergence of high-density power-law tails.
• Comparing results with and without self-gravity to isolate its influence on turbulence compressibility and density structure.

Experimental results

Research questions

• RQ1 What is the compressive ratio of turbulence in molecular clouds when driven by supernova explosions?
• RQ2 How does self-gravity affect the compressibility of molecular cloud turbulence?
• RQ3 Does the relation between rms density and rms velocity in molecular clouds remain consistent with isothermal turbulence under SN driving?
• RQ4 Is the density PDF of molecular clouds well described by a lognormal distribution, and does self-gravity induce a high-density power-law tail?
• RQ5 How does the turbulent compressibility in SN-driven simulations compare to that in idealized simulations with random solenoidal forcing?

Key findings

• Supernova-driven turbulence in molecular clouds exhibits a compressive-to-solenoidal velocity power ratio of approximately 0.3, significantly lower than the equilibrium value of 0.5 found in idealized isothermal simulations.
• The compressibility of turbulence is not noticeably affected by self-gravity, indicating that large-scale cloud dynamics remain stable despite local core collapse.
• The mean expansion or contraction velocity of molecular clouds is unaffected by gravity, confirming that clouds do not collapse as a whole even when prestellar cores form.
• The relation between rms density and rms velocity in the clouds follows the same scaling as in isothermal turbulence, supporting the universality of this scaling under realistic driving.
• The average gas density PDF is well described by a lognormal distribution, with a high-density power-law tail emerging when self-gravity is included.
• The presence of a power-law tail in the density PDF under self-gravity suggests enhanced formation of dense structures, consistent with star formation processes.