Gravoturbulence

This section covers the framework that links cloud-scale density structure to the integrated star formation rate. The chain is:

1. Density PDF — the volume-density distribution $p_V(\rho)$ in a turbulent self-gravitating cloud, parameterised by Mach number and forcing geometry Federrath & Klessen, 2012.

2. Freefall-density factor (FDF) — the kernel $\rho/t_{\mathrm{ff}}(\rho) \propto \rho^{3/2}$ that weights local density by its star-forming efficiency.

3. ζ magnification factor — the geometric SFR boost over a uniform-density “top-hat” cloud, parameterised by the radial density-profile slope $p$ Parmentier & Pasquali, 2020, computed three ways (analytic / cored / direct-3D).

4. BM19 framework — the dense-gas SFR formalism that combines all the above into a predictive forward model for cloud-integrated SFR Burkhart, 2018Burkhart & Mocz, 2019.

5. Inference — running the chain backwards to recover natal cloud parameters from observed substructure.

Map of the section¶

Reading order¶

For a student first encountering the framework: read in TOC order (Density PDFs and the freefall-density factor → The magnification factor ζ — three ways to compute it → BM19 dense-gas SFR framework), then Differentiable inference — natal cloud parameters from cluster substructure as the capstone that inverts the forward chain. Each chapter assumes only the conventions established in the previous one.

For a researcher already familiar with the literature: jump directly to The magnification factor ζ — three ways to compute it for the ζ derivation, the three computation modes, and the Historical Note on the 2026-04-28 transcription bug fix, or to BM19 dense-gas SFR framework for the full forward chain that consumes ζ.

For implementation work: each chapter ends with a code snippet showing the corresponding gravoturb API. The module reference is the package source under src/experimental/gravoturb/ (see its README.md and VALIDATION_SUMMARY.md); this experimental subsystem has no generated website API page.

Why ζ is computed three ways¶

The three ζ-computation modes (all in The magnification factor ζ — three ways to compute it) are not redundant — each captures a different physical situation:

• PP20 analytic ζ(p) is exact for pure power-law profiles, which is a useful idealisation but rarely realistic for individual clouds.

• Cored profile ζ numerically integrates a $\rho \propto [1+(r/r_c)^2]^{-p/2}$ profile that is flat in the inner core and power-law outside — a much better description of real molecular clouds with thermal-pressure-supported centres.

• Direct 3D ζ measures ζ from an arbitrary 3D density field with no parametric assumption — the right choice when you have a simulation snapshot or detailed observation.

For HMC-based inference of cloud parameters from observed SFR, all three are differentiable and gravoturb exposes them through a unified API. The choice of which to use depends on the level of cloud parameterisation in the inference target.

Implementation, validation & references¶

• In code: the experimental, repo-only gravoturb package under src/experimental/gravoturb/ (theory/, field/, inference/); it is not in the released wheel and has no generated website API page — the module reference is the package source, its README.md, and its VALIDATION_SUMMARY.md (both repo-only, under src/experimental/gravoturb/). Each chapter below carries its exact module path.

• Validated in: gravoturbulent PP20 and the AC1–AC17 acceptance suite (src/experimental/gravoturb/validation/acceptance.py, summarised in VALIDATION_SUMMARY.md).

• Primary sources: the density-PDF framework is Federrath & Klessen (2012); the PP20 magnification factor is Parmentier & Pasquali (2020), with the Kainulainen et al. (2014) observational anchor for $p \approx 5/3$; the BM19 framework is Burkhart (2018)Burkhart & Mocz (2019); Tan et al. (2006) provides some structural underpinning. Full notes in the bibliography; each chapter below points at the specific result(s) used.