Marks & Kroupa (2012)

Abstract (paraphrased)¶

Applies inverse dynamical population synthesis — evolving a universal initial binary population in clusters of varying density and matching the result to observed multiplicity fractions — to eight young regions (Taurus, ρ Oph, Chamaeleon, Orion/ONC, IC 348, Upper Sco A, Praesepe, Pleiades). Constrains each region’s birth stellar mass $M_{\rm ecl}$ and half-mass radius $r_h$. Identifies a stellar-mass–half-mass-radius relation for cluster-forming cloud clumps and shows that environment-dependent dynamical evolution shapes present-day binary populations.

Key relations used by progenax (verified against the paper)¶

Half-mass radius–mass relation (Abstract; Sect. 4).

The slope $0.13\pm0.04$ and the proportionality are stated in the abstract; the prefactor 0.1 is the calibrated value (also quoted verbatim by Jeřábková et al. (2018), Eq. 8).

Half-mass density (§2.1, p. 2). The dynamical evolution of a cluster’s binary population is driven by the 8π half-mass density

i.e. clusters of the same $\rho_{\rm ecl}$ are dynamically equivalent. This is the authoritative definition behind the density used in the Marks (2012) / Jeřábková (2018) $\alpha_3$–$\rho$ relations.

Use in progenax¶

• progenax.imf.environment.compute_r_half — implements (1).

• progenax.imf.environment.compute_rho_ecl — implements (2) (8π half-mass density).

• Underpins the mass-based IGIMF path (Jeřábková et al. (2018), Marks et al. (2012)).

Notes¶

The 8π definition (2) is the reason progenax does not use Jeřábková (2018) Eq. 8’s “4π” form: Eq. 8 is internally inconsistent with Jeřábková’s own $\log_{10}\rho_{\rm ecl}=0.61\log_{10}M_{\rm ecl}+2.08$ relation (which is 8π). progenax’s compute_rho_ecl reproduces Marks (2012) Table 1 densities exactly. The companion paper Marks & Kroupa (2011), MNRAS 417, 1702 provides the binary-population dynamical operator (period / mass-ratio distributions) used elsewhere in progenax’s binary modelling.