Molecular clouds
Molecular cloud collapse and magnetic support
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.
L1
Why cold gas can gather into dense structures
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.
L1
How the Jeans scale separates oscillation and growth
Derive the Jeans dispersion relation from mass, pressure and gravity, then calculate growth, initial velocities and the separately defined spherical Jeans mass.
L2
Magnetic support depends on direction
Derive the linear gravity–MHD modes and compare compression along, across and oblique to a magnetic field. Direction changes the Jeans response.
L3
When a grid can no longer resolve contraction
Follow cell averages, mass flux and periodic gravity, then separate grid, time and reference errors using actual convergence failures and a Jeans-cell stop.
L3
Replaying an official Jeans initial condition
Read a pinned native Athena input, recover its three-dimensional wavevector and recompute stable and growing modes before checking a separate gas solver.
L4
One converged mass scale does not establish an 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
- Chandrasekhar & Fermi 1953, Problems of Gravitational Stability in the Presence of a Magnetic Field
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.
- Athena++ native Jeans input and regression at commit 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.
- Federrath & Klessen 2012, arXiv: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.
- Guszejnov et al. 2020, Can magnetized turbulence set the mass scale of stars? arXiv: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.
- Molecular-cloud Jeans standalone scientific reproduction
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.