Sana et al. (2012)

Abstract (paraphrased)¶

A homogeneous spectroscopic analysis of the O-star population of six nearby Galactic open clusters (71 single + multiple O-type objects), sensitive to orbital periods up to ~10 yr. Simultaneously measures the intrinsic binary fraction and the period, mass-ratio, and eccentricity power-law distributions, correcting for observational biases via Monte-Carlo simulation. Concludes that over 70% of all massive stars exchange mass with a companion (one third merging), so binary interaction dominates massive-star evolution.

Intrinsic distributions (verified against the paper, p. 444–445)¶

The observed binary fraction is $f_{\rm obs}=40/71=0.56$. After bias correction, the intrinsic distributions (power laws in $\log_{10}P$, $q$, $e$ with exponents $\pi,\kappa,\eta$) and binary fraction are

The period power law $f(\log P)\propto(\log P)^{\pi}$ spans $\log_{10}(P/\mathrm{d}) \in [0.15,\,3.5]$ (Fig. 2): from $P \approx 1.4$ d to $\approx 3162$ d $\approx 9$ yr. The negative $\pi$ is a strong preference for close pairs (Öpik-like but steeper); $\kappa \approx -0.1$ is a nearly uniform mass-ratio distribution (no preference for equal masses, contra a “thermal” or twin-peaked $q$). Sana also fit the eccentricity power law $p(e)\propto e^{\eta}$; the slope is reported in their supplementary Table S3 (not in the main report held here — short-period O-stars are weighted to small $e$; see Moe & Di Stefano (2017)). Integrating these implies 71% of O-type stars interact with a companion.

Use in progenax¶

• Binary period distributions — the OB-type $\log P$ distribution.

• progenax.binaries.SanaOBPeriod — period distribution with slope $\pi=-0.55$, default range $\log_{10}(P/\mathrm{d}) \in [0.15, 3.5]$ (Fig. 2).

• progenax.imf.BinaryIMF.massive_stars() — uses $f_{\rm bin}=0.69$ ((1)) and a PowerLawMassRatio(γ=-0.1) (Sana’s $\kappa=-0.1$, uniform $q$) for OB populations.

Notes¶

The intrinsic O-star binary fraction $f_{\rm bin}=0.69$ is the value progenax’s massive_stars() factory adopts (not 0.70). Combined with Moe & Di Stefano (2017), which extends the statistics to lower masses and resolves the period–mass-ratio interrelation, this is the empirical foundation for massive-binary population synthesis.