Binary Mass Ratio Distribution Research Articles

Goodbye to Chi by Eye: A Bayesian Analysis of Photometric Binaries in Six Open Clusters

We present a robust methodology for identifying photometric binaries in star clusters. Using Gaia DR3, Pan-STARRS, and Two Micron All Sky Survey data, we self-consistently define the cluster parameters and binary demographics for the open clusters (OCs) NGC 2168 (M35), NGC 7789, NGC 6819, NGC 2682 (M67), NGC 188, and NGC 6791. These clusters span in age from ∼200 Myr (NGC 2168) to more than ∼8 Gyr (NGC 6791) and have all been extensively studied in the literature. We use the Bayesian Analysis of Stellar Evolution software suite to derive the age, distance, reddening, metallicity, binary fraction, and binary mass-ratio posterior distributions for each cluster. We perform a careful analysis of our completeness and also compare our results to previous spectroscopic surveys. For our sample of main-sequence stars with masses between 0.6 and 1 M ⊙, we find that these OCs have similar binary fractions that are also broadly consistent with the field multiplicity fraction. Within the clusters, the binary fraction increases dramatically toward the cluster centers, likely a result of mass segregation. Furthermore nearly all clusters show evidence of mass segregation within the single and binary populations. The OC binary fraction increases significantly with cluster age in our sample, possibly due to a combination of mass-segregation and cluster-dissolution processes. We also find a hint of an anticorrelation between binary fraction and cluster central density as well as total cluster mass, possibly due to an increasing frequency of higher-energy close stellar encounters that inhibit long-period binary survival and/or formation.

MASS RATIO AND ECCENTRICITY DISTRIBUTIONS OF YOUNG SPECTROSCOPIC BINARY STARS

We collected the information about 83 pre-main sequence double-lined spectroscopic binaries. Among them there are Ae/Be Herbig stars, T Tauri stars and red dwarfs. The eccentricity – period relation, the mass ratio and eccentricity distributions of young spectroscopic binaries are constructed and analyzed. The overwhelming majority of close binaries with \(P {{10}^{d}}\) have eccentricity near to zero, the stars less than 1 million years old are rare among them. The mass ratio distribution of systems with \(P {{10}^{d}}\) has a prominent maximum in a range of \(q = 0.9{\kern 1pt} - {\kern 1pt} 1.0\). The number of young spectroscopic binaries with \(P {{10}^{d}}\) does not decrease with decreasing mass ratio as sharply as in the case of close binary stars, about 12% of these stars have \(q 0.5\). The paper is based on a talk presented at the astrophysical memorial seminar “Novelties in Understanding the Evolution of Binary Stars”, dedicated to the 90th anniversary of Professor M.A. Svechnikov.

The role of the turbulence driving mode for the initial mass function

ABSTRACT Turbulence is a critical ingredient for star formation, yet its role for the initial mass function (IMF) is not fully understood. Here we perform magnetohydrodynamical (MHD) simulations of star cluster formation including gravity, turbulence, magnetic fields, stellar heating, and outflow feedback to study the influence of the mode of turbulence driving on IMF. We find that simulations that employ purely compressive turbulence driving (COMP) produce a higher fraction of low-mass stars as compared to simulations that use purely solenoidal driving (SOL). The characteristic (median) mass of the sink particle (protostellar) distribution for COMP is shifted to lower masses by a factor of ∼1.5 compared to SOL. Our simulation IMFs capture the important features of the observed IMF form. We find that turbulence-regulated theories of the IMF match our simulation IMFs reasonably well in the high-mass and low-mass range, but underestimate the number of very low-mass stars, which form towards the later stages of our simulations and stop accreting due to dynamical interactions. Our simulations show that for both COMP and SOL, the multiplicity fraction is an increasing function of the primary mass, although the multiplicity fraction in COMP is higher than that of SOL for any primary mass range. We find that binary mass ratio distribution is independent of the turbulence driving mode. The average specific angular momentum of the sink particles in SOL is a factor of 2 higher than that for COMP. Overall, we conclude that the turbulence driving mode plays a significant role in shaping the IMF.

Preferential accretion and circumbinary disc precession in eccentric binary systems

ABSTRACT We present a suite of high-resolution hydrodynamic simulations of binaries immersed in circumbinary accretion discs (CBDs). For the first time, we investigate the preferential accretion rate as a function of both eccentricity eb and mass ratio qb in a densely sampled parameter space, finding that when compared with circular binaries, (i) mass ratios grow more efficiently in binaries on moderately eccentric orbits (0.0 ≲ eb ≲ 0.4), and (ii) high eccentricities (eb ≳ 0.6) suppress mass ratio growth. We suggest that this non-monotonic preferential accretion behaviour may produce an observable shift in the mass ratio distributions of stellar binaries and massive black hole binaries. We further find that the response of a CBD can be divided into three regimes, depending on eccentricity and mass ratio: (i) CBDs around circular binaries always precess freely, whereas CBDs around eccentric binaries either (ii) undergo forced precession or (iii) remain locked at an angle with respect to the binary periapsis. Forced precession in eccentric binaries is associated with strong modulation of individual accretion rates on the precession time-scale, a potentially observable signature in accreting binaries with short orbital periods. We provide CBD locking angles and precession rates as a function of eb and qb for our simulation suite.

Orbital Parameters and Binary Properties of 37 FGK Stars in the Cores of Open Clusters NGC 2516 and NGC 2422

Abstract We present orbits for 24 binaries in the field of open cluster NGC 2516 (∼150 Myr) and 13 binaries in the field of open cluster NGC 2422 (∼130 Myr) using results from a multiyear radial-velocity (RV) survey of the cluster cores. Six of these systems are double-lined spectroscopic binaries. We fit these RV variable systems with orvara, a MCMC-based fitting program that models Keplerian orbits. We use precise stellar parallaxes and proper motions from Gaia EDR3 to determine cluster membership. We impose a barycentric RV prior on all cluster members; this significantly improves our orbital constraints. Two of our systems have periods between five and 15 days, the critical window in which tides efficiently damp orbital eccentricity. These binaries should be included in future analyses of circularization across similarly-aged clusters. We also find a relatively flat distribution of binary mass ratios, consistent with previous work. With the inclusion of TESS light curves for all available targets, we identity target 378–036252 as a new eclipsing binary. We also identify a field star whose secondary has a mass in the brown dwarf range, as well as two cluster members whose RVs suggest the presence of an additional companion. Our orbital fits will help constrain the binary fraction and binary properties across stellar age and across stellar environment.

Detailed evolutionary models of massive contact binaries – I. Model grids and synthetic populations for the Magellanic Clouds

ABSTRACT The majority of close massive binary stars with initial periods of a few days experience a contact phase, in which both stars overflow their Roche lobes simultaneously. We perform the first dedicated study of the evolution of massive contact binaries and provide a comprehensive prediction of their observed properties. We compute 2790 detailed binary models for the Large and Small Magellanic Clouds each, assuming mass transfer to be conservative. The initial parameter space for both grids span total masses from 20 to 80$\, \mathrm{M}_\odot$ , orbital periods of 0.6–2 d and mass ratios of 0.6–1.0. We find that models that remain in contact over nuclear time-scales evolve towards equal masses, echoing the mass ratios of their observed counterparts. Ultimately, the fate of our nuclear-time-scale models is to merge on the main sequence. Our predicted period–mass ratio distributions of O-type contact binaries are similar for both galaxies, and we expect 10 such systems together in both Magellanic Clouds. While we can largely reproduce the observed distribution, we overestimate the population of equal-mass contact binaries. This situation is somewhat remedied if we also account for binaries that are nearly in contact. Our theoretical distributions work particularly well for contact binaries with periods <2 d and total masses $\lessapprox 45\, \mathrm{M}_\odot \,$. We expect stellar winds, non-conservative mass transfer, and envelope inflation to have played a role in the formation of the more massive and longer-period contact binaries.

The mass-ratio distribution of tertiary-induced binary black hole mergers

ABSTRACT Many proposed scenarios for black hole (BH) mergers involve a tertiary companion that induces von Zeipel–Lidov–Kozai (ZLK) eccentricity cycles in the inner binary. An attractive feature of such mechanisms is the enhanced merger probability when the octupole-order effects, also known as the eccentric Kozai mechanism, are important. This can be the case when the tertiary is of comparable mass to the binary components. Since the octupole strength [∝(1 − q)/(1 + q)] increases with decreasing binary mass ratio q, such ZLK-induced mergers favour binaries with smaller mass ratios. We use a combination of numerical and analytical approaches to fully characterize the octupole-enhanced binary BH mergers and provide semi-analytical criteria for efficiently calculating the strength of this enhancement. We show that for hierarchical triples with semimajor axial ratio a/aout ≳ 0.01–0.02, the binary merger fraction can increase by a large factor (up to ∼20) as q decreases from unity to 0.2. The resulting mass-ratio distribution for merging binary BHs produced in this scenario is in tension with the observed distribution obtained by the LIGO/VIRGO collaboration, although significant uncertainties remain about the initial distribution of binary BH masses and mass ratios.

Modeling Unresolved Binaries of Open Clusters in the Color–Magnitude Diagram. I. Method and Application of NGC 3532

Abstract The binary properties of open clusters place crucial constraints on star formation theory and clusters’ dynamical evolution. We develop a comprehensive approach that models the color–magnitude diagram (CMD) of the cluster members as a mixture of single stars and photometric unresolved binaries. This method enables us to infer the binary properties, including the binary fraction f b and binary mass ratio distribution index γ q when a power law is assumed, with high accuracy and precision, which was unfeasible in conventional methods. We employ a modified Gaussian process to determine the main-sequence ridgeline and its scatter from the observed CMD as model input. As a first example, we apply the method to the open cluster NGC 3532 with the Gaia DR2 photometry. For the cluster members within a magnitude range corresponding to FGK dwarfs, we obtain f b = 0.267 ± 0.019 and γ q = −0.10 ± 0.22 for binaries with mass ratio q > 0.2. The f b value is consistent with the previous work on NGC 3532 and smaller than that of field stars. The close-to-zero γ q indicates that the mass ratios of binaries follow a nearly uniform distribution. For the first time, we unveil that the stars with smaller mass or in the inner region tend to have lower f b and a more positive value of γ q due to the lack of low mass ratio binaries. The clear dependences of binary properties on mass and radius are most likely caused by the internal dynamics. In this scheme, binaries with smaller primary mass or lower mass ratio have smaller binding energy; hence, they are more vulnerable to dynamical disruption, especially in the inner region where stars interact more frequently.

The effect of differential accretion on the gravitational wave background and the present-day MBH binary population

ABSTRACT Massive black hole binaries (MBHBs) form as a consequence of galaxy mergers. However, it is still unclear whether they typically merge within a Hubble time, and how accretion may affect their evolution. These questions will be addressed by pulsar timing arrays (PTAs), which aim to detect the gravitational wave (GW) background (GWB) emitted by MBHBs during the last Myr of inspiral. Here, we investigate the influence of differential accretion on MBHB merger rates, chirp masses, and the resulting GWB spectrum. We evolve an MBHB sample from the Illustris hydrodynamic cosmological simulation using semi-analytical models and for the first time self-consistently evolve their masses with binary accretion models. In all models, MBHBs coalesce with median total masses up to 1.5 × 108 M⊙, up to 3−4 times larger than in models neglecting accretion. In our model with the largest plausible impact, the median mass ratio of coalescing MBHBs increases by a factor 3.6, the coalescence rate by $52.3{{\ \rm per\ cent}}$, and the GWB amplitude by a factor 4.0, yielding a dimensionless GWB strain $A_{yr^{-1}} = 1 \times 10^{-15}$. Our model that favours accretion on to the primary MBH reduces the median mass ratio of coalescing MBHBs by a factor of 2.9, and yields a GWB amplitude $A_{yr^{-1}} = 3.1 \times 10^{-16}$. This is nearly indistinguishable from our model neglecting accretion, despite higher MBHB masses at coalescence. We further predict binary separation and mass ratio distributions of stalled MBHBs in the low-redshift Universe, and find that these depend sensitively on binary accretion models. This presents the potential for combined electromagnetic and GW observational constraints on merger rates and accretion models of MBHB populations.

Unresolved Binaries and Galactic Clusters’ Mass Estimates

Abstract Binary stars are present in all stellar systems, yet their role is far from being fully understood. We investigate the effect of unresolved binaries in the derivation of open clusters’ mass by star counts. We start from the luminosity functions of five open clusters: IC 2714, NGC 1912, NGC 2099, NGC 6834, and NGC 7142. Luminosity functions are obtained via star counts extracted from the 2MASS database. The fraction of binaries is considered to be independent of stellar magnitude. We take into account different assumptions for the binary mass ratio distribution and assign binary masses using the so-called luminosity-limited pairing method and Monte-Carlo simulations. We show that cluster masses increase when binary stars are appropriately taken into account.

Star formation history: Modeling of visual binaries

Most stars form in binary or multiple systems. Their evolution is defined by masses of components, orbital separation and eccentricity. In order to understand star formation and evolutionary processes, it is vital to find distributions of physical parameters of binaries.We have carried out Monte Carlo simulations in which we simulate different pairing scenarios: random pairing, primary-constrained pairing, split-core pairing, and total and primary pairing in order to get distributions of binaries over physical parameters at birth. Next, for comparison with observations, we account for stellar evolution and selection effects. Brightness, radius, temperature, and other parameters of components are assigned or calculated according to approximate relations for stars in different evolutionary stages (main-sequence stars, red giants, white dwarfs, relativistic objects). Evolutionary stage is defined as a function of system age and component masses. We compare our results with the observed IMF, binarity rate, and binary mass-ratio distributions for field visual binaries to find initial distributions and pairing scenarios that produce observed distributions.

Black hole binaries dynamically formed in globular clusters

We investigate properties of black hole (BH) binaries formed in globular clusters via dynamical processes, using direct N-body simulations. We pay attention to effects of BH mass function on the total mass and mass ratio distributions of BH binaries ejected from clusters. Firstly, we consider BH populations with two different masses in order to learn basic differences from models with single-mass BHs only. Secondly, we consider continuous BH mass functions adapted from recent studies on massive star evolution in a low metallicity environment, where globular clusters are formed. In this work, we consider only binaries that are formed by three-body processes and ignore stellar evolution and primordial binaries for simplicity. Our results imply that most BH binary mergers take place after they get ejected from the cluster. Also, mass ratios of dynamically formed binaries should be close to one or likely to be less than 2:1. Since the binary formation efficiency is larger for higher-mass BHs, it is likely that a BH mass function sampled by gravitational-wave observations would be weighed toward higher masses than the mass function of single BHs for a dynamically formed population. Applying conservative assumptions regarding globular cluster populations such as small BH mass fraction and no primordial binaries, the merger rate of BH binaries originated from globular clusters is estimated to be at least 6.5 per yr per Gpc^3. Actual rate can be up to more than several times of our conservative estimate.

Two twin binaries with nearly identical components: KIC 4826439 and KIC 6045264

Abstract Two twin binaries, KIC 4826439 and KIC 6045264, with very similar component stars were found photometrically based on Kepler eclipsing binary light curves. The absolute parameters of the massive components are 1.156(0.03) M⊙, 1.881(0.02) R⊙, 6065 K for KIC 4826439, and 0.874(0.3) M⊙, 1.206(0.02) R⊙, 6169(30) K for KIC 6045264. The differences between the components are less than two percent for all the parameters. A very low proportion of twin binaries (2/1592 ≈ 0.13%) was found, which does not support the previous findings of excesses of twins on binary mass ratio distribution, but supports a deficiently low proportion of twins. A new method is used to work out the absolute parameters of the two twins without the radial velocities. This method requires the solution of the light curves, the spectra, and the evolutionary isochrones covering the complete stellar parameter space, simultaneously. We also studied their evolution tracks: KIC 4826439 will experience an unstable mass transfer stage followed by an unclear ending, and KIC 6045264 will become a single star via an over-contact phase. It seems highly unlikely that the two twin binaries will produce twin degenerate binaries, although they have quite similar components.

The mass ratio distribution of MBH binaries in the hierarchical model**Supported by the National Natural Science Foundation of China.

We present different mass ratio distributions of massive black hole (MBH) binaries due to different mechanisms involved in binary evolution. A binary system of MBHs forms after the merger of two galaxies, which has three stages: the dynamical friction stage, the stellar scattering or circumbinary disk stage, and the gravitational radiation stage. The second stage was once believed to be the “final parsec problem” (FPP) as the binary stalled at this stage because of the depletion of stars. Now, the FPP has been shown to no longer be a problem. Here we get two different mass ratio distributions of MBH binaries under two mechanisms, stellar scattering and the circumbinary disk interaction. For the circumbinary disk mechanism, we assume that the binary shrinks by interaction with a circumbinary disk and the two black holes (BHs) have different accretion rates in the simulation. We apply this simple assumption to the hierarchical coevolution model of MBHs and dark matter halos, and we find that there will be more equal-mass MBH binaries in the final coalescence for the case where the circumbinary mechanism operates. This is mainly because the secondary BH in the circumbinary disk system accretes at a higher rate than the primary one.

STELLAR LOCI II. A MODEL-FREE ESTIMATE OF THE BINARY FRACTION FOR FIELD FGK STARS

We propose a Stellar Locus OuTlier (SLOT) method to determine the binary fraction of main-sequence stars statistically. The method is sensitive to neither the period nor mass-ratio distributions of binaries, and able to provide model-free estimates of binary fraction for large numbers of stars of different populations in large survey volumes. We have applied the SLOT method to two samples of stars from the SDSS Stripe 82, constructed by combining the re-calibrated SDSS photometric data with respectively the spectroscopic information from the SDSS and LAMOST surveys. For the SDSS spectroscopic sample, we find an average binary fraction for field FGK stars of $41%\pm2%$. The fractions decrease toward late spectral types, and are respectively $44%\pm5%$, $43%\pm3%$, $35%\pm5%$, and $28%\pm6%$ for stars of $g-i$ colors between 0.3 -- 0.6, 0.6 -- 0.9, 0.9 -- 1.2, and 1.2 - 1.6\,mag. A modest metallicity dependence is also found. The fraction decreases with increasing metallicity. For stars of [Fe/H] between $-0.5$ - 0.0, $-1.0$ - $-0.5$, $-1.5$ - $-1.0$, and $-2.0$ - $-1.5$\,dex, the inferred binary fractions are $37%\pm3%$, $39%\pm3%$, $50%\pm9%$, and $53%\pm20%$, respectively. We have further divided the sample into stars from the thin disk, the thick disk, the transition zone between them, and the halo. The results suggest that the Galactic thin and thick disks have comparable binary fractions, whereas the Galactic halo contains a significantly larger fraction of binaries. Applying the method to the LAMOST spectroscopic sample yields consistent results. Finally, other potential applications and future work with the method are discussed.

A method to deconvolve mass ratio distribution of binary stars

To better understand the evolution of stars in binary systems as well as to constrain the formation of binary stars, it is important to know the binary mass-ratio distribution. However, in most cases, i.e. for single-lined spectroscopic binaries, the mass ratio cannot be measured directly but only derived as the convolution of a function that depends on the mass ratio and the unknown inclination angle of the orbit on the plane of the sky. We extend our previous method to deconvolve this inverse problem (Cure et al. 2014), i.e., we obtain as an integral the cumulative distribution function (CDF) for the mass ratio distribution. After a suitable transformation of variables it turns out that this problem is the same as the one for rotational velocities $v \sin i$, allowing a close analytic formulation for the CDF. We then apply our method to two real datasets: a sample of Am stars binary systems, and a sample of massive spectroscopic binaries in the Cyg OB2 Association.} {We are able to reproduce the previous results of Boffin (2010) for the sample of Am stars, while we show that the mass ratio distribution of massive stars shows an excess of small mass ratio systems, contrarily to what was claimed by Kobulnicky et al. (2014). Our method proves very robust and deconvolves the distribution from a sample in just a single step.

BINARY CEPHEIDS: SEPARATIONS AND MASS RATIOS IN 5M☉BINARIES

Deriving the distribution of binary parameters for a particular class of stars over the full range of orbital separations usually requires the combination of results from many different observing techniques (radial velocities, interferometry, astrometry, photometry, direct imaging), each with selection biases. However, Cepheids---cool, evolved stars of $\sim$$5\, M_\odot$---are a special case because ultraviolet spectra will immediately reveal any companion star hotter than early type A, {\it regardless of the orbital separation}. We have used {\it International Ultraviolet Explorer} (\IUE) UV spectra of a complete sample of all 76 Cepheids brighter than V=8 to create a list of {\it all 18} Cepheids with companions more massive than $2.0\, M_\odot$. Orbital periods of many of these binaries are available from radial-velocity studies, or can be estimated for longer-period systems from detected velocity variability. In an imaging survey with the {\it Hubble Space Telescope} Wide Field Camera 3, we resolved three of the companions (those of $\eta$ Aql, S Nor, and V659 Cen), allowing us to make estimates of the periods out to the long-period end of the distribution. Combining these separations with orbital data in the literature, we derive an unbiased distribution of binary separations, orbital periods, and mass ratios. The distribution of orbital periods shows that the $5\, M_\odot$ binaries have systematically shorter periods than do $1\, M_\odot$ stars. Our data also suggest that the distribution of mass ratios depends both on binary separation and system multiplicity. The distribution of mass ratios as a function of orbital separation, however, does not depend on whether a system is a binary or a triple.

The binary companion mass ratio distribution: an imprint of the star formation process?

We explore the effects of dynamical evolution in dense clusters on the companion mass ratio distribution (CMRD) of binary stars. Binary systems are destroyed by interactions with other stars in the cluster, lowering the total binary fraction and significantly altering the initial semi-major axis distribution. However, the shape of the CMRD is unaffected by dynamics; an equal number of systems with high mass ratios are destroyed compared to systems with low mass ratios. We might expect a weak dependence of the survivability of a binary on its mass ratio because its binding energy is proportional to both the primary and secondary mass components of the system. However, binaries are broken up by interactions in which the perturbing star has a significantly higher energy (by a factor of >10, depending on the particular binary properties) than the binding energy of the binary, or through multiple interactions in the cluster. We therefore suggest that the shape of the observed binary CMRD is an outcome of the star formation process, and should be measured in preference to the distributions of orbital parameters, such as the semi-major axis distribution.

BINARY FREQUENCIES IN A SAMPLE OF GLOBULAR CLUSTERS. I. METHODOLOGY AND INITIAL RESULTS

Binary stars are thought to be a controlling factor in globular cluster evolution, since they can heat the environmental stars by converting their binding energy to kinetic energy during dynamical interactions. Through such interaction, the binaries determine the time until core collapse. To test predictions of this model, we have determined binary fractions for 35 clusters. Here we present our methodology with a representative globular cluster NGC 4590. We use HST archival ACS data in the F606W and F814W bands and apply PSF-fitting photometry to obtain high quality color-magnitude diagrams. We formulate the star superposition effect as a Poisson probability distribution function, with parameters optimized through Monte-Carlo simulations. A model-independent binary fraction of (6.2 +- 0.3)% is obtained by counting stars that extend to the red side of the residual color distribution after accounting for the photometric errors and the star superposition effect. A model-dependent binary fraction is obtained by constructing models with a known binary fraction and an assumed binary mass-ratio distribution function. This leads to a binary fraction range of 6.8% to 10.8%, depending on the assumed shape to the binary mass ratio distribution, with the best fit occurring for a binary distribution that favors low mass ratios (and higher binary fractions). We also represent the method for radial analysis of the binary fraction in the representative case of NGC 6981, which shows a decreasing trend for the binary fraction towards the outside, consistent with theoretical predictions for the dynamical effect on the binary fraction.

Characterizing a cluster’s dynamic state using a single epoch of radial velocities

Radial velocity measurements can be used to constrain the dynamical state of a stellar cluster. However, for clusters with velocity dispersions smaller than a few km/s the observed radial velocity distribution tends to be dominated by the orbital motions of binaries rather than the stellar motions through the potential well of the cluster. Our goal is to characterize the intrinsic velocity distribution of a cluster from a single epoch of radial velocity data, even for a cluster with a velocity dispersion of a fraction of a km/s, using a maximum likelihood procedure. Assuming a period, mass ratio, and eccentricity distribution for the binaries in the observed cluster this procedure fits a dynamical model describing the velocity distribution for the single stars and center of masses of the binaries, simultaneously with the radial velocities caused by binary orbital motions, using all the information available in the observed velocity distribution. We find that the fits to the intrinsic velocity distribution depend only weakly on the binary properties assumed, so the uncertainty in the fitted parameters tends to be dominated by statistical uncertainties. Based on Monte Carlo simulations we provide an estimate of how these statistical uncertainties vary with the velocity dispersion, binary fraction, and the number of observed stars, which can be used to estimate the sample size needed to reach a specific accuracy. Finally we test the method on the well-studied open cluster NGC 188, showing that it can reproduce a velocity dispersion of only 0.5 km/s using a single epoch of the multi-epoch radial velocity data. If the binary period, mass ratio, and eccentricity distribution of the observed stars are roughly known, this procedure can be used to correct for the effect of binary orbital motions on an observed velocity distribution. [Abridged]