Kritsuk, Norman & Wagner (2011)

Abstract (paraphrased)¶

Studies the volume-weighted density probability distribution function (PDF) of supersonic, self-gravitating turbulent clouds using high-resolution simulations. Beyond the well-known lognormal core (from non-self-gravitating supersonic turbulence), the onset of self-gravity produces a power-law tail at high density, corresponding to gas in approximately isothermal gravitational collapse. The paper connects this power-law density PDF tail to the radial density structure of collapsing regions.

Role in progenax (attribution — UNVERIFIED)¶

progenax’s gravoturbulence chapter attributes to this work the α↔p mapping between the high-density power-law tail slope of the density PDF, $\alpha$, and the radial-profile slope $p$ of a collapsing region $\rho \propto r^{-p}$:

which follows (under spherical symmetry and a power-law volume↔density correspondence) from relating the amount of gas above a density threshold to the radial profile that produces it. The Burkhart-Mocz canonical window $\alpha \in [1.5, 3.0]$ maps to $p \in [1.0, 2.0]$ (marginally collapsing → singular isothermal). This mapping is the hand-off between the BM19 forward chain and the magnification-factor calculation.

Use in progenax¶

• Density PDFs and the freefall-density factor — the power-law tail and the α↔p mapping (1).

• BM19 dense-gas SFR framework — step 5 of the forward chain applies the mapping.

• The magnification factor ζ — three ways to compute it — consumes the resulting $p$ to compute the geometric SFR boost $\zeta(p)$.

• gravoturb (experimental) — pdf_slope_to_radial implements $p = 3/\alpha$; tests/experimental/unit/test_bm19.py verifies it.

Notes¶

The gravoturbulence subsystem is the experimental, repo-only gravoturb package (not in the released wheel). The α↔p mapping is also discussed alongside Federrath & Klessen (2012). Until the PDF is held and verified, treat the specific $p = 3/\alpha$ form as progenax’s working attribution rather than a confirmed transcription.