Duquennoy & Mayor (1991) - progenax — differentiable initial conditions for N-body simulations

Abstract (paraphrased)¶

A CORAVEL radial-velocity survey of a complete, volume-limited sample of 164 G-dwarf (F7–G9 IV/V/VI) primaries from the Gliese catalogue, combined with visual and common-proper-motion data, yields the present-day distributions of orbital period, eccentricity and mass ratio in an unbiased sample. The orbital-period distribution is unimodal and remarkably well approximated by a Gaussian in $\log P$ with a median period of 180 yr. Tight binaries ( $P < 11$ d) are all tidally circularized; intermediate periods follow a bell-shaped eccentricity distribution; wide binaries ( $P > 1000$ d) tend toward the thermal $f(e) = 2e$ . This is the foundational dataset for solar-type binary statistics.

Verified facts¶

Period distribution (§7.3, p. 514, Fig. 7). The orbital periods follow

f(\log P) = C \exp\!\left[-\frac{(\log P - \overline{\log P})^2}{2\,\sigma_{\log P}^2}\right], \qquad \overline{\log P} = 4.8,\quad \sigma_{\log P} = 2.3,\quad P\ \text{in days}

(1)

(median period $\simeq 180$ yr $= 10^{4.8}$ d).

Eccentricity distribution (§6.1, §7.2). Three period regimes:

$P < 10$ d: tidally circularized, $e \approx 0$ . The circularization period is $P_{\rm circ} \approx 11.6$ d (last circularized binary HD 13974 at 10.0 d; first eccentric HD 17433 at 13.2 d).
$10 < P < 1000$ d: bell-shaped, mean $\bar e = 0.31 \pm 0.04$ .
$P > 1000$ d: tends toward the thermal $f(e) = 2e$ — the distribution expected if it is a function of energy only (Ambartsumian 1937).

Use in progenax¶

progenax.binaries.LogNormalPeriod — its defaults $\mu_{\log P} = 4.8$ , $\sigma_{\log P} = 2.3$ (days) are DM91 §7.3 verbatim ((1)). See Raghavan et al. (2010) for the modern revision (median ~300 yr, $\sigma \approx 2.28$ ).
progenax.binaries.LogisticThermalEccentricity — the smooth circular→thermal heuristic is motivated by DM91’s three-period model; defaults $P_{\rm circ}=10$ d ( $\approx$ DM91 11.6 d) and $P_{\rm thermal}=1000$ d (DM91 wide-thermal onset).
progenax.binaries.MassDependentBinaryConfig — DM91 is the low-mass (solar-type) prescription.

Notes¶

DM91 is the canonical solar-type multiplicity reference. Its wide-binary $f(e)=2e$ traces to Ambartsumian (1937) (energy-only distribution) — the same thermal law in progenax.binaries.ThermalEccentricity (see Heggie (1975)). The faithful Moe & Di Stefano ( $e^\eta$ ) eccentricity model is in Moe & Di Stefano (2017).