Mind your Ps and Qs: the Interrelation between Period (P) and Mass-ratio (Q) Distributions of Binary Stars

We compile observations of early-type binaries identified via spectroscopy, eclipses, long-baseline interferometry, adaptive optics, common proper motion, etc. Each observational technique is sensitive to companions across a narrow parameter space of orbital periods P and mass ratios q = M_comp/M_1. After combining the samples from the various surveys and correcting for their respective selection effects, we find the properties of companions to O-type and B-type main-sequence (MS) stars differ among three regimes. First, at short orbital periods P < 20 days (separations a < 0.4 AU), the binaries have small eccentricities e = 0.5, and exhibit a small excess of twins q > 0.95. Second, the companion frequency peaks at intermediate periods log P (days) = 3.5 (a = 10 AU), where the binaries have mass ratios weighted toward small values q = 0.2-0.3 and follow a Maxwellian "thermal" eccentricity distribution. Finally, companions with long orbital periods log P (days) = 5.5-7.5 (a = 200-5,000 AU) are outer tertiary components in hierarchical triples, and have a mass ratio distribution across q = 0.1-1.0 that is nearly consistent with random pairings drawn from the initial mass function. We discuss these companion distributions and properties in the context of binary star formation and evolution. We also reanalyze the binary statistics of solar-type MS primaries, taking into account that (30+/-10)% of single-lined spectroscopic binaries likely contain white dwarf companions instead of low-mass stellar secondaries. The mean frequency of stellar companions with q > 0.1 and log P (days) < 8.0 per primary increases from 0.50+/-0.04 for solar-type MS primaries to 2.1+/-0.3 for O-type MS primaries. We fit joint probability density functions f(M_1,q,P,e) to the corrected distributions, which can be incorporated into binary population synthesis studies.Comment: Accepted in ApJS; this version includes the updated figures, text, and equations as it appears in the accepted version; a Monte Carlo code that generates a population of zero-age MS single stars and binaries according to the corrected joint distribution f(M_1,q,P,e) is available upon request via emai

Dynamical Formation of Close Binaries During the Pre-main-sequence Phase

Solar-type binaries with short orbital periods ($P_{\rm close}$ $\equiv$ 1 - 10 days; $a$ $\lesssim$ 0.1 AU) cannot form directly via fragmentation of molecular clouds or protostellar disks, yet their component masses are highly correlated, suggesting interaction during the pre-main-sequence (pre-MS) phase. Moreover, the close binary fraction of pre-MS stars is consistent with that of their MS counterparts in the field ($F_{\rm close}$ = 2.1%). Thus we can infer that some migration mechanism operates during the early pre-MS phase ($\tau$ $\lesssim$ 5 Myr) that reshapes the primordial separation distribution. We test the feasibility of this hypothesis by carrying out a population synthesis calculation which accounts for two formation channels: Kozai-Lidov (KL) oscillations and dynamical instability in triple systems. Our models incorporate (1) more realistic initial conditions compared to previous studies, (2) octupole-level effects in the secular evolution, (3) tidal energy dissipation via weak-friction equilibrium tides at small eccentricities and via non-radial dynamical oscillations at large eccentricities, and (4) the larger tidal radius of a pre-MS primary. Given a 15% triple star fraction, we simulate a close binary fraction from KL oscillations alone of $F_{\rm close}$ $\approx$ 0.4% after $\tau$ = 5 Myr, which increases to $F_{\rm close}$ $\approx$ 0.8% by $\tau$ = 5 Gyr. Dynamical ejections and disruptions of unstable coplanar triples in the disk produce solitary binaries with slightly longer periods $P$ $\approx$ 10 - 100 days. The remaining $\approx$60% of close binaries with outer tertiaries, particularly those in compact coplanar configurations with log $P_{\rm out}$ (days) $\approx$ 2 - 5 ($a_{\rm out}$ $<$ 50 AU), can be explained only with substantial extra energy dissipation due to interactions with primordial gas.Comment: Accepted by ApJ; 23 pages; 8 figures; this version incorporates changes made to address comments by refere

Do most planetary nebulae derive from binaries? I Population synthesis model of the galactic planetary nebula population produced by singlestars and binaries

We present a population synthesis calculation to derive the total number of planetary nebulae (PN) in the Galaxy that descend from single stars and stars in binary systems. Using the most recent literature results on galactic and stellar formation as well as stellar evolution, we predict the total number of galactic PNe with radii <0.9 pc to be (46,000 +/- 13,000). We do not claim this to be the complete population, since there can be visible PNe with radii larger than this limit. However, by taking this limit, we make our predicted population inherently comparable to the observationally-based value of Peimbert, who determined (7200 +/- 1800) PNe should reside in the Galaxy today. Our prediction is discrepant with the observations at the 2.9-sigma level, a disagreement which we argue is meaningful in view of our specific treatment of the uncertainty. We conclude that it is likely that only a subset of the stars thought to be capable of making a visible PN, actually do. In the second paper in this series, an argument will be presented that the bulk of the galactic PN population might be better explained if only binaries produce PNe. The predicted PN formation rate density from single stars and binaries is (1.1 +/- 0.5) x 10^{-12} PN/yr per cubic pc in the local neighborhood. This number is lower than the most recent PN birthrate density estimates of 2.1 x 10^{-12} PN/yr per cubic pc, which are based on local PN counts and the PN distance scale, but more in line with the white dwarf birthrate densities determined by Liebert et al. ((1.0 +/- 0.25) x 10^{-12} WD/yr per cubic pc). The predicted PN birthrate density will be revised down, if we assume that only binaries make PNe. This revision will imply that the PN distance scale has to be revised to larger values.Comment: 52 pages (referee format), 14 figures. Accepted by Ap

Formation of close binaries by disc fragmentation and migration, and its statistical modeling

Joint statistics of periods and mass ratios of close binaries and its dependence on primary mass can be explained by assuming that seed binary companions are formed by disc fragmentation at random intervals during assemblage of stellar mass and migrate inwards as they accrete from the circumbinary disk. A toy model based on simple prescriptions for the companion growth and migration reproduces such aspects of close solar-mass binaries as the distribution of binary periods P, the brown dwarf desert at short P, the nearly uniform distribution of mass ratios, and a population of equal-mass binaries (twins) that decreases linearly in frequency with logP. For massive stars, the model predicts a large fraction of early mergers, a distribution of logP with a negative slope, and a mass-ratio distribution that is also uniform but with a substantially reduced twin fraction. By treating disc fragmentation as a stochastic process, we also reproduce the observed properties of compact triples. Success of our toy model suggests that most close binaries and compact triples indeed formed by disc fragmentation followed by accretion-driven inward migration.Comment: Accepted by MNRAS; 15 pages, 11 figure

Common envelope evolution through planetary nebula eyes

The common envelope interaction is responsible for evolved close binaries. Among them are a minority of central stars of planetary nebula (PN). Recent observational results, however, point to most PN actually being in binary systems. We therefore ask the question if it is feasible that most, or even all Galactic PN derive from a common envelope interaction. Our recent calculation finds that if all single and binary primary stars with mass between ~1-8 Mo eject a PN, there would be many more PN in the galaxy than observed. On the other hand, the predicted number of post-common envelope PN is more in agreement with the total number of PN in the Galaxy. This is a new indication that binary interactions play a functional role in the creation of PN and an encouragement to intensify efforts to detect binary companions.Comment: 4 pages, one figure, proceedings of the 2005 Gdansk meeting PN as astronomical tools, in pres

How I Learned to Stop Worrying and Love Eclipsing Binaries

Relatively massive B-type stars with closely orbiting stellar companions can evolve to produce Type Ia supernovae, X-ray binaries, millisecond pulsars, mergers of neutron stars, gamma ray bursts, and sources of gravitational waves. However, the formation mechanism, intrinsic frequency, and evolutionary processes of B-type binaries are poorly understood. As of 2012, the binary statistics of massive stars had not been measured at low metallicities, extreme mass ratios, or intermediate orbital periods. This thesis utilizes large data sets of eclipsing binaries to measure the physical properties of B-type binaries in these previously unexplored portions of the parameter space. The updated binary statistics provide invaluable insight into the formation of massive stars and binaries as well as reliable initial conditions for population synthesis studies of binary star evolution. We first compare the properties of B-type eclipsing binaries in our Milky Way Galaxy and the nearby Magellanic Cloud Galaxies. We model the eclipsing binary light curves and perform detailed Monte Carlo simulations to recover the intrinsic properties and distributions of the close binary population. We find the frequency, period distribution, and mass-ratio distribution of close B-type binaries do not significantly depend on metallicity or environment. These results indicate the formation of massive binaries are relatively insensitive to their chemical abundances or immediate surroundings. Second, we search for low-mass eclipsing companions to massive B-type stars in the Large Magellanic Cloud Galaxy. In addition to finding such extreme mass-ratio binaries, we serendipitously discover a new class of eclipsing binaries. Each system comprises a massive B-type star that is fully formed and a nascent low-mass companion that is still contracting toward its normal phase of evolution. The large low-mass secondaries discernibly reflect much of the light they intercept from the hot B-type stars, thereby producing sinusoidal variations in perceived brightness as they orbit. These nascent eclipsing binaries are embedded in the hearts of star-forming emission nebulae, and therefore provide a unique snapshot into the formation and evolution of massive binaries and stellar nurseries. We next examine a large sample of B-type eclipsing binaries with intermediate orbital periods. To achieve such a task, we develop an automated pipeline to classify the eclipsing binaries, measure their physical properties from the observed light curves, and recover the intrinsic binary statistics by correcting for selection effects. We find the population of massive binaries at intermediate separations differ from those orbiting in close proximity. Close massive binaries favor small eccentricities and have correlated component masses, demonstrating they coevolved via competitive accretion during their formation in the circumbinary disk. Meanwhile, B-type binaries at slightly wider separations are born with large eccentricities and are weighted toward extreme mass ratios, indicating the components formed relatively independently and subsequently evolved to their current configurations via dynamical interactions. By using eclipsing binaries as accurate age indicators, we also reveal that the binary orbital eccentricities and the line-of-sight dust extinctions are anticorrelated with respect to time. These empirical relations provide robust constraints for tidal evolution in massive binaries and the evolution of the dust content in their surrounding environments. Finally, we compile observations of early-type binaries identified via spectroscopy, eclipses, long-baseline interferometry, adaptive optics, lucky imaging, high-contrast photometry, and common proper motion. We combine the samples from the various surveys and correct for their respective selection effects to determine a comprehensive nature of the intrinsic binary statistics of massive stars. We find the probability distributions of primary mass, secondary mass, orbital period, and orbital eccentricity are all interrelated. These updated multiplicity statistics imply a greater frequency of low-mass X-ray binaries, millisecond pulsars, and Type Ia supernovae than previously predicted.Astronom

The Close Binary Fraction of Solar-type Stars is Strongly Anti-correlated with Metallicity

There is now strong evidence that the close binary fraction (P < 10$^4$ days; a < 10 AU) of solar-type stars ($M_1$ = 0.6-1.5M$_{\odot}$) decreases significantly with metallicity. Although early surveys showed that the observed spectroscopic binary (SB) fractions in the galactic disk and halo are similar (e.g., Carney-Latham sample), these studies did not correct for incompleteness. In this study, we examine five different surveys and thoroughly account for their underlying selection biases to measure the intrinsic occurrence rate of close solar-type binaries. We re-analyze: (1) a volume-limited sample of solar-type stars, (2) an SB survey of high-proper-motion stars, (3) various SB samples of metal-poor giants, (4) the APOGEE survey of radial velocity (RV) variables, and (5) Kepler eclipsing binaries (EBs). The observed APOGEE RV variability fraction and Kepler EB fraction both decrease by a factor of $\approx$4 across $-$1.0 < [Fe/H] < 0.5 at the 22$\sigma$ and 9$\sigma$ confidence levels, respectively. After correcting for incompleteness, all five samples exhibit a quantitatively consistent anti-correlation between the intrinsic close binary fraction (a < 10 AU) and metallicity: $F_{\rm close}$ = 53%$\pm$12%, 40%$\pm$6%, 24%$\pm$4%, and 10%$\pm$3% at [Fe/H] = $-$3.0, $-$1.0, $-$0.2 (mean field metallicity), and +0.5, respectively. We present fragmentation models that explain why the close binary fraction of solar-type stars strongly decreases with metallicity while the wide binary fraction, close binary fraction of OB stars, and initial mass function are all constant across $-$1.5 < [Fe/H] < 0.5. The majority of solar-type stars with [Fe/H] < $-$1.0 will interact with a stellar companion, which has profound implications for binary evolution in old and metal-poor environments such as the galactic halo, bulge, thick disk, globular clusters, dwarf galaxies, and high-redshift universe.Comment: Submitted to ApJ, 31 pages, 20 figure