Kainulainen, Federrath & Henning (2014)

What we use it for (cross-referenced via PP20 / BM19)¶

Kainulainen et al. (2014) analyse the volume-density PDF of a sample of nearby molecular clouds, building a 3-D dense-gas estimate from column-density maps via hierarchical prolate spheroids. Two numbers flow into the gravoturbulence chain:

• Radial-profile slope $p \approx 1.67$. Parmentier & Pasquali (2020, §3) quote the Kainulainen sample mean as $p\approx1.67$ (range $1<p<2.2$); BM19 (§3.2) likewise use $p=1.67$ (with $p\equiv\kappa=3/\alpha$). This is the canonical observational anchor for the PP20 magnification factor: $\zeta(1.67)\approx1.79$.

• Dense-gas threshold $s_\mathrm{th}\approx4.2$. PP20 report the Kainulainen averaged threshold number density $n_\mathrm{th}=n_0 e^{s_\mathrm{th}}\approx6700\,\mathrm{cm^{-3}}$ ($n_0\approx100$), i.e. $s_\mathrm{th}\approx4.2$; BM19 (§3.2) use the Kainulainen YSO-count critical density $s_\mathrm{crit}\approx4$ as an observational anchor for the PDF transition density $s_t$.

Use in progenax¶

• The magnification factor ζ — three ways to compute it — anchors $\zeta(p = 1.67) \approx 1.79$ (AC3 spot value).

• Gravoturbulent + PP20 validation — the $\zeta(1.67)$ regression anchor.

• Burkhart & Mocz (2019) — Kainulainen $s_\mathrm{crit}\approx4$ as the observational check on $s_t$.

Notes¶

• Unverified primary source. To fully verify, read the published Kainulainen+2014 (Science 344, 183) directly and confirm $p\approx1.67$ and $s_\mathrm{th}\approx4.2$. Until then these are second-hand (PP20/BM19) values.