---
title: "Molecular cloud collapse and magnetic support"
description: "Follow gas from pressure and Jeans growth to directional magnetic support, numerical resolution and a pinned IMF paper."
canonical_url: "https://sandboxphysics.com/stories/molecular-clouds/"
language: "en"
page_type: "story"
alternate_languages:
  zh-CN: "https://sandboxphysics.com/zh/stories/molecular-clouds/"
last_modified: "2026-11-04"
---

Molecular clouds

# Molecular cloud collapse and magnetic support

Sandbox Physics · 2026-11-04

A compressed patch of gas can rebound or gather more gas. Begin with that picture, derive the wave, then ask which numerical and astrophysical conclusions the calculation can support.

1. L1

   ## [Why cold gas can gather into dense structures](https://sandboxphysics.com/stories/molecular-clouds/why-cold-clouds-gather/)

   Cold gas still has pressure. Follow a density ripple as it rebounds or grows, and see why the Jeans scale depends on both sound speed and gravity.

2. L1

   ## [How the Jeans scale separates oscillation and growth](https://sandboxphysics.com/stories/molecular-clouds/jeans-length-and-a-clouds-mass/)

   Derive the Jeans dispersion relation from mass, pressure and gravity, then calculate growth, initial velocities and the separately defined spherical Jeans mass.

3. L2

   ## [Magnetic support depends on direction](https://sandboxphysics.com/stories/molecular-clouds/magnetic-support-has-a-direction/)

   Derive the linear gravity–MHD modes and compare compression along, across and oblique to a magnetic field. Direction changes the Jeans response.

4. L3

   ## [When a grid can no longer resolve contraction](https://sandboxphysics.com/stories/molecular-clouds/when-a-cloud-grid-stops-being-evidence/)

   Follow cell averages, mass flux and periodic gravity, then separate grid, time and reference errors using actual convergence failures and a Jeans-cell stop.

5. L3

   ## [Replaying an official Jeans initial condition](https://sandboxphysics.com/stories/molecular-clouds/replay-the-official-jeans-input/)

   Read a pinned native Athena input, recover its three-dimensional wavevector and recompute stable and growing modes before checking a separate gas solver.

6. L4

   ## [One converged mass scale does not establish an IMF](https://sandboxphysics.com/stories/molecular-clouds/why-a-converged-mass-is-not-the-imf/)

   Read the resolution figures in Guszejnov 2020 v1, separating mass-weighted medians, number distributions and claims about a stellar initial mass function.

## Sources and calculation scope

1. [Chandrasekhar & Fermi 1953, Problems of Gravitational Stability in the Presence of a Magnetic Field](https://adsabs.harvard.edu/pdf/1953ApJ...118..116C)

   Section V, pages 138–141, equations 158–173. The original uses an adiabatic sound derivative and Gaussian magnetic units; the chapters state their isothermal derivative and SI normalization. Original paper linked, not redistributed.

2. [Athena++ native Jeans input and regression at commit 053bc738d5c85dac717326b4338b34c7db4e715d](https://github.com/PrincetonUniversity/athena/tree/053bc738d5c85dac717326b4338b34c7db4e715d)

   Complete BSD-3-Clause members: inputs/hydro/athinput.jeans\_3d, src/pgen/jeans.cpp, and the stable/unstable gravity regression scripts. The tutorial computes the equivalent first-order Fourier mode; it does not compile or execute Athena.

3. [Federrath & Klessen 2012, arXiv:1209.2856v1](https://arxiv.org/abs/1209.2856v1)

   Pinned v1, sections 2.2/2.4, 3.1–3.3 and 7: isothermal driven three-dimensional MHD, sink criteria, the statistical magnetic-pressure approximation and its limitations. Their driving, sinks and numerical dynamo requirement are not part of the gas-patch calculation.

4. [Guszejnov et al. 2020, Can magnetized turbulence set the mass scale of stars? arXiv:2002.01421v1](https://arxiv.org/abs/2002.01421v1)

   Pinned v1, sections 2–4, Figures 8–10 and equations 8–11/17/22–23. Read the mass-weighted percentiles and the number distribution separately. The Figure 8 model-name pairing and approximate dimensional example are preserved in context; no author correction is assumed.

5. [Molecular-cloud Jeans standalone scientific reproduction](https://sandboxphysics.com/stories/molecular-clouds/materials/molecular-cloud-jeans-science.zip)

   Independent finite-volume and oversampled pseudospectral producers; analytic Jeans and full linear MHD references; all ten support cases, a fixed longer case, original official inputs and retained failures. Default replay actually recomputes its scientific steps offline after ordinary Python dependencies are installed.