Wide Binaries Research Articles

The rotation rate of single- and double-lined southern O stars. Determining what increases the rotation rate in binaries

We determined the projected rotational velocity ($v i$) of 238 southern O stars selected from the Galactic O-star Survey. The sample contains 130 spectroscopic single stars (C) single-lined binaries (SB1), and SB2 systems (including eight triples). We applied the Fourier method to high-resolution spectra taken at Cerro Murphy, Chile, and supplemented by archival spectra. The overall $v i$ statistics peaks at slow rotators (40-100\,km/s) with a tail towards medium (100-200\,km/s) and fast rotators (200-400\,km/s). Binaries, on average, show increased rotation, which differs for close orb < 10$\,d) and wide binaries (10\,d $< orb <$ 3700\,d), and for primaries and secondaries. The spin-up of close binaries is well explained by the superposition of spin-orbit synchronisation and mass transfer via Roche-lobe overflow. The increased rotation of wide binaries, however, needs another explanation. Therefore, we discuss various spin-up mechanisms. Timescale arguments lead us to favour a scenario where wide O binaries are spun-up by a combination of cloud or disk fragmentation, which lays the basis of triple and multiple stars, and the subsequent merging or swallowing of low-mass by higher-mass stars or proto-stars.

A generative model for Gaia astrometric orbit catalogs: selection functions for binary stars, giant planets, and compact object companions

Astrometry from {} DR3 has produced a sample of $$170,000 Keplerian orbital solutions, with many more anticipated in the next few years. These data have enormous potential to constrain the population of binary stars, giant planets, and compact objects in the Solar neighborhood. But in order to use the published orbit catalogs for statistical inference, it is necessary to understand their selection function: what is the probability that a binary with a given set of properties ends up in a catalog? We show that such a selection function for the {} DR3 astrometric binary catalog can be forward-modeled from the {} scanning law, including individual 1D astrometric measurements, the fitting of a cascade of astrometric models, and quality cuts applied in post-processing. We populate a synthetic Milky Way model with binary stars and generate a mock catalog of astrometric orbits. The mock catalog is quite similar to the DR3 astrometric binary sample, suggesting that our selection function is a sensible approximation of reality. Our fitting also produces a sample of spurious astrometric orbits similar to those found in DR3; these are mainly the result of scan angle-dependent astrometric biases in marginally resolved wide binaries. We show that {} sensitivity to astrometric binaries falls off rapidly at high eccentricities, but only weakly at high inclinations. We predict that DR4 will yield ∼1 million astrometric orbits, mostly for bright ( G≲15) systems with long periods ( d). We provide code to simulate and fit realistic {} epoch astrometry for any data release and determine whether any hypothetical binary would receive a cataloged orbital solution.

Spin–Orbit Alignment of Early-type Astrometric Binaries and the Origin of Slow Rotators

The spin–orbit alignment of binary stars traces their formation and accretion history. Previous studies of spin–orbit alignment have been limited to small samples, slowly rotating solar-type stars, and/or wide visual binaries that not surprisingly manifest random spin–orbit orientations. We analyze 917 Gaia astrometric binaries across periods P = 100–3000 days (a = 0.5–5 au) that have B8-F1 IV/V primaries (M 1 = 1.5–3 M ⊙) and measured projected rotational velocities v sin i. The primary stars in face-on orbits exhibit substantially smaller v sin i compared to those in edge-on orbits at the 6σ level, demonstrating significant spin–orbit alignment. The primaries in our astrometric binaries are rotating more slowly than their single-star or wide-binary counterparts and therefore comprise the slow-rotator population in the observed bimodal rotational velocity distribution of early-type stars. We discuss formation models of close binaries where some of the disk angular momentum is transferred to the orbit and/or secondary spin, quenching angular momentum flow to the primary spin. The primaries in astrometric binaries with small mass ratios q = M 2/M 1 < 0.3 possess even smaller v sin i, consistent with model predictions. Meanwhile, astrometric binaries with large eccentricities e > 0.4 do not display spin–orbit alignment or spin reduction. Using a Monte Carlo technique, we measure a spin–orbit alignment fraction of F align = 75% ± 5% and an average spin reduction factor of 〈S align〉 = 0.43 ± 0.04. We conclude that 75% of close A-type binaries likely experienced circumbinary disk accretion and probably formed via disk fragmentation and inward disk migration. The remaining 25%, mostly those with e > 0.4, likely formed via core fragmentation and orbital decay via dynamical friction.

Double white dwarf binary population in MOCCA star clusters

There could be a significant population of double white dwarf binaries (DWDs) inside globular clusters (GCs); however, these binaries are often too faint to be individually observed. We have utilized a large number GC models evolved with the Monte Carlo Cluster Simulator (MOCCA) code to create a large statistical dataset of DWDs. These models include multiple-stellar populations, resulting in two distinct initial populations: one dense and the other less dense. Due to the lower density of one population, a large number of objects escape during the early GC evolution, leading to a high mass-loss rate. In this dataset we have analyzed three main groups of DWDs, namely in-cluster binaries, escaped binaries, and binaries formed from the isolated evolution of primordial binaries. We compared the properties of these groups to observations of close and wide binaries. We find that the number of escaping DWDs is significantly larger than the number of in-cluster binaries and those that form via the isolated evolution of all primordial binaries in our GC models. This suggests that dynamics play an important role in the formation of DWDs. For close binaries, we found a good agreement in the separations of escaped binaries and isolated binaries, but in-cluster binaries showed slight differences. We could not reproduce the observed extremely low mass WDs due to the limitations of our stellar and binary evolution prescriptions. For wide binaries, we also found a good agreement in the separations and masses, after accounting for observational selection effects. Even though the current observational samples of DWDs are extremely biased and incomplete, we conclude that our results compare reasonably well with observations.

Massive star cluster formation

Two main mechanisms have classically been proposed for the formation of runaway stars. In the binary supernova scenario (BSS), a massive star in a binary explodes as a supernova, ejecting its companion. In the dynamical ejection scenario, a star is ejected during a strong dynamical encounter between multiple stars. We propose a third mechanism for the formation of runaway stars: the subcluster ejection scenario (SCES), where a subset of stars from an infalling subcluster is ejected out of the cluster via a tidal interaction with the contracting gravitational potential of the assembling cluster. We demonstrate the SCES in a star-by-star simulation of the formation of a young massive cluster from a 106 M⊙ gas cloud using the TORCH framework. This star cluster forms hierarchically through a sequence of subcluster mergers determined by the initial turbulent, spherical conditions of the gas. We find that these mergers drive the formation of runaway stars in our model. Late-forming subclusters fall into the central potential, where they are tidally disrupted, forming tidal tails of runaway stars that are distributed highly anisotropically. Runaways formed in the same SCES have similar ages, velocities, and ejection directions. Surveying observations, we identify several SCES candidate groups with anisotropic ejection directions. The SCES is capable of producing runaway binaries: two wide dynamical binaries in infalling subclusters were tightened through ejection. This allows for another velocity kick via subsequent via a subsequent BSS ejection. An SCES-BSS ejection is a possible avenue for the creation of hypervelocity stars unbound to the Galaxy. The SCES occurs when subcluster formation is resolved. We expect nonspherical initial gas distributions to increase the number of calculated runaway stars, bringing it closer to observed values. The observation of groups of runaway stars formed via the SCES can thus reveal the assembly history of their natal clusters.

Early Planet Formation in Embedded Disks. XI. A High-resolution View Toward the BHR 71 Class 0 Protostellar Wide Binary

We present Atacama Large Millimeter/submillimeter Array (ALMA) observations of the binary Class 0 protostellar system BHR 71 IRS1 and IRS2 as part of the Early Planet Formation in Embedded Disks (eDisk) ALMA Large Program. We describe the 12CO (J = 2–1), 13CO (J = 2–1), C18O (J = 2–1), H2CO (J = 32,1–22,0), and SiO (J = 5–4) molecular lines along with the 1.3 mm continuum at high spatial resolution (∼0.″08 or ∼5 au). Dust continuum emission is detected toward BHR 71 IRS1 and IRS2, with a central compact component and extended continuum emission. The compact components are smooth and show no sign of substructures such as spirals, rings, or gaps. However, there is a brightness asymmetry along the minor axis of the presumed disk in IRS1, possibly indicative of an inclined geometrically and optically thick disk-like component. Using a position–velocity diagram analysis of the C18O line, clear Keplerian motions were not detected toward either source. If Keplerian rotationally supported disks are present, they are likely deeply embedded in their envelope. However, we can set upper limits of the central protostellar mass of 0.46 M ⊙ and 0.26 M ⊙ for BHR 71 IRS1 and BHR 71 IRS2, respectively. Outflows traced by 12CO and SiO are detected in both sources. The outflows can be divided into two components, a wide-angle outflow and a jet. In IRS1, the jet exhibits a double helical structure, reflecting the removal of angular momentum from the system. In IRS2, the jet is very collimated and shows a chain of knots, suggesting episodic accretion events.

The JWST/NIRISS Deep Spectroscopic Survey for Young Brown Dwarfs and Free-floating Planets

The discovery and characterization of free-floating planetary-mass objects (FFPMOs) is fundamental to our understanding of star and planet formation. Here we report results from an extremely deep spectroscopic survey of the young star cluster NGC1333 using Near-InfraRed Imager and Slitless Spectrograph (NIRISS) wide field slitless spectroscopy on the James Webb Space Telescope. The survey is photometrically complete to K ∼ 21, and includes useful spectra for objects as faint as K ∼ 20.5. The observations cover 19 known brown dwarfs, for most of which we confirm spectral types using NIRISS spectra. We discover six new candidates with L-dwarf spectral types that are plausible planetary-mass members of NGC1333, with estimated masses between 5 and 15 M Jup. One, at ∼5 M Jup, shows clear infrared excess emission and is a good candidate to be the lowest-mass object known to have a disk. We do not find any objects later than mid-L spectral type (M ≲ 4 M Jup). The paucity of Jupiter-mass objects, despite the survey’s unprecedented sensitivity, suggests that our observations reach the lowest-mass objects that formed like stars in NGC1333. Our findings put the fraction of FFPMOs in NGC1333 at ∼10% of the number of cluster members, significantly more than expected from the typical log-normal stellar mass function. We also search for wide binaries in our images and report a young brown dwarf with a planetary-mass companion.

Gaia BH1 and BH2 — Evolutionary Models with Overshooting of the Black Hole Progenitors within the Present-Day Binary Separation

Abstract Three black holes (BHs) in wide binaries — Gaia BH1, BH2 and BH3 — were recently discovered. The likely progenitors of the BHs were massive stars that experienced a supergiant phase, reaching radii of ∼1000R⊙, before collapsing to form the BH. Such radii are difficult to accommodate with the present-day orbits of BH1 and BH2 — with semi-major axes of 1.4 and 3.7 au, respectively. In this letter, we show that the maximal radii of the supergiants are not necessarily so large, and realistic stellar evolution models, with some assumed overshooting above the convective core into the radiative stellar envelope, produce substantially smaller maximal radii. The limited expansion of supergiants is consistent with the empirical Humphreys-Davidson limit — the absence of red supergiants above an upper luminosity limit, notably lower than the highest luminosity of main-sequence stars. We propose that the evolution that led to the formation of Gaia BH1 and BH2 simply did not involve an expansion to the cool supergiant phase.

Fundamental Tests of White Dwarf Cooling Physics with Wide Binaries

We present follow-up spectroscopy and a detailed model atmosphere analysis of 29 wide double white dwarfs, including eight systems with a crystallized C/O core member. We use the state-of-the-art evolutionary models to constrain the physical parameters of each star, including the total age. Assuming that the members of wide binaries are coeval, any age difference between the binary members can be used to test the cooling physics for white dwarf stars, including potential delays due to crystallization and 22Ne distillation. We use our control sample of 14 wide binaries with noncrystallized members to show that this method works well; the control sample shows an age difference of only ΔAge = −0.03 ± 0.15 Gyr between its members. For the eight crystallized C/O core systems we find a cooling anomaly of ΔAge = 1.13−1.07+1.20 Gyr. Even though our results are consistent with a small additional cooling delay (∼1 Gyr) from 22Ne distillation and other neutron-rich impurities, the large uncertainties make this result not statistically significant. Nevertheless, we rule out cooling delays longer than 3.6 Gyr at the 99.7% (3σ) confidence level for 0.6–0.9 M ⊙ white dwarfs. Further progress requires larger samples of wide binaries with crystallized massive white dwarf members. We provide a list of subgiant + white dwarf binaries that could be used for this purpose in the future.

Close Encounters of Wide Binaries Induced by the Galactic Tide: Implications for Stellar Mergers and Gravitational-wave Sources

A substantial fraction of stars can be found in wide binaries with projected separations between ∼102 and 105 au. In the standard lore of binary physics, these would evolve as effectively single stars that remotely orbit one another on stationary Keplerian ellipses. However, embedded in their Galactic environment, the low binding energy of wide binaries makes them exceptionally prone to perturbations from the gravitational potential of the Milky Way and encounters with passing stars. Employing a fully relativistic N-body integration scheme, we study the impact of these perturbations on the orbital evolution of wide binaries along their trajectory through the Milky Way. Our analysis reveals that the torques exerted by the Galaxy can cause large-amplitude oscillations of the binary eccentricity to 1 − e ≲ 10−8. As a consequence, the wide binary members pass close to each other at periapsis, which, depending on the type of binary, potentially leads to a mass transfer or collision of stars or to an inspiral and subsequent merger of compact remnants due to gravitational-wave radiation. Based on a simulation of 105 wide binaries across the Galactic field, we find that this mechanism could significantly contribute to the rate of stellar collisions and binary black hole mergers as inferred from observations of luminous red novae and gravitational-wave events by LIGO/Virgo/Kagra. We conclude that the dynamics of wide binaries, despite their large mean separation, can give rise to extreme interactions between stars and compact remnants.

Neutron Star Kicks plus Rockets as a Mechanism for Forming Wide Low-eccentricity Neutron Star Binaries

Recent neutron star surface observations corroborate a long-standing theory that neutron stars may be accelerated over extended periods after their birth. We analyze how these prolonged rocket-like accelerations, combined with rapid birth kicks, impact binary orbits. We find that even a small contribution of rocket kicks combined with instantaneous natal kicks can allow binaries to reach period–eccentricity combinations unattainable in standard binary evolution models. We propose these kick + rocket combinations as a new channel to form wide low-eccentricity neutron star binaries such as Gaia NS1, as well as inducing stellar mergers months to years after a supernova to cause peculiar high-energy transients.

Revising Properties of Planet–Host Binary Systems. IV. The Radius Distribution of Small Planets in Binary Star Systems Is Dependent on Stellar Separation* *Based on observations obtained with the Hobby–Eberly Telescope, which is a joint project of the University of Texas at Austin, the Pennsylvania State University, Ludwig-Maximilians-Universität München, and Georg-August-Universität Göttingen.

Small planets (R p ≤ 4 R ⊕) are divided into rocky super-Earths and gaseous sub-Neptunes separated by a radius gap, but the mechanisms that produce these distinct planet populations remain unclear. Binary stars are the only main-sequence systems with an observable record of the protoplanetary disk lifetime and mass reservoir, and the demographics of planets in binaries may provide insights into planet formation and evolution. To investigate the radius distribution of planets in binary star systems, we observed 207 binary systems hosting 283 confirmed and candidate transiting planets detected by the Kepler mission, then recharacterized the planets while accounting for the observational biases introduced by the secondary star. We found that the population of planets in close binaries (ρ ≤ 100 au) is significantly different from the planet population in wider binaries (ρ > 300 au) or single stars. In contrast to planets around single stars, planets in close binaries appear to have a unimodal radius distribution with a peak near the expected super-Earth peak of R p ∼ 1.3 R ⊕ and a suppressed population of sub-Neptunes. We conclude that we are observing the direct impact of a reduced disk lifetime, smaller mass reservoir, and possible altered distribution of solids reducing the sub-Neptune formation efficiency. Our results demonstrate the power of binary stars as a laboratory for exploring planet formation and as a controlled experiment of the impact of varied initial conditions on mature planet populations.

A High-resolution Imaging Survey of Massive Young Stellar Objects in the Magellanic Clouds

Constraints on the binary fraction of massive young stellar objects (mYSOs) are important for binary and massive star formation theory. Here, we present speckle imaging of 34 mYSOs located in the Large Magellanic Cloud (1/2 Z ⊙) and Small Magellanic Cloud (∼1/5 Z ⊙), probing projected separations in the 2000 to 20,000 au (at angular scales of 0.″02–0.″2) range, for stars above 8 M ⊙. We find two wide binaries in the Large Magellanic Cloud (from a sample of 23 targets), but none in a sample of 11 in the Small Magellanic Cloud, leading us to adopt a wide binary fraction of 9% ± 5% and <5%, respectively. We rule out a wide binary fraction greater than 35% in the Large Magellanic Cloud and 38% in the Small Magellanic Cloud at the 99% confidence level. This is in contrast to the wide binary fraction of mYSOs in the Milky Way (presumed to be 1 Z ⊙), which within the physical parameter space probed by this study is ∼15%–60% from the literature. We argue that while selection effects could be responsible for the lower binary fraction observed, it is more likely that there are underlying physical mechanisms responsible for the observed properties. This indicates that metallicity and environmental effects may influence the formation of wide binaries among massive stars. Future larger, more statistically significant samples of high-mass systems in low-metallicity environments for comparison to the Milky Way, are essential to confirm or repudiate our claim.

Primeval very low-mass stars and brown dwarfs – VIII. The first age benchmark L subdwarf, a wide companion to a halo white dwarf

Abstract We report the discovery of five white dwarf + ultracool dwarf systems identified as common proper motion wide binaries in the Gaia Catalogue of Nearby Stars. The discoveries include a white dwarf + L subdwarf binary, VVV 1256−62AB, a gravitationally-bound system located 75.6$^{+1.9}_{-1.8}$ pc away with a projected separation of 1375$^{+35}_{-33}$ au. The primary is a cool DC white dwarf with a hydrogen dominated atmosphere, and has a total age of $10.5^{+3.3}_{-2.1}$ Gyr, based on white dwarf model fitting. The secondary is an L subdwarf with a metallicity of [M/H] = $-0.72^{+0.08}_{-0.10}$ (i.e. [Fe/H] = −0.81 ± 0.10) and Teff = 2298$^{+45}_{-43}$ K based on atmospheric model fitting of its optical to near infrared spectrum, and likely has a mass just above the stellar/substellar boundary. The subsolar metallicity of the L subdwarf and the system’s total space velocity of 406 km/s indicates membership in the Galactic halo, and it has a flat eccentric Galactic orbit passing within 1 kpc of the centre of the Milky Way every ∼0.4 Gyr and extending to 15-31 kpc at apogal. VVV 1256−62B is the first L subdwarf to have a well-constrained age, making it an ideal benchmark of metal-poor ultracool dwarf atmospheres and evolution.

Wide Post-common Envelope Binaries from Gaia: Orbit Validation and Formation Models

Astrometry from Gaia DR3 has enabled the discovery of a sample of 3000+ binaries containing white dwarfs (WD) and main-sequence (MS) stars in relatively wide orbits, with orbital periods P orb = (100–1000) days. This population was not predicted by binary population synthesis models before Gaia and—if the Gaia orbits are robust—likely requires very efficient envelope ejection during common envelope evolution (CEE). To assess the reliability of the Gaia solutions, we measured multi-epoch radial velocities (RVs) of 31 WD+MS binary candidates with P orb = (40–300) days and AstroSpectroSB1 orbital solutions. We jointly fit the RVs and astrometry, allowing us to validate the Gaia solutions and tighten constraints on component masses. We find a high success rate for the Gaia solutions, with only 2 out of the 31 systems showing significant discrepancies between their Gaia orbital solutions and our RVs. Joint fitting of RVs and astrometry allows us to directly constrain the secondary-to-primary flux ratio S , and we find S≲0.02 for most objects, confirming the companions are indeed WDs. We tighten constraints on the binaries’ eccentricities, finding a median e ≈ 0.1. These eccentricities are much lower than those of normal MS+MS binaries at similar periods, but much higher than predicted for binaries formed via stable mass transfer. We present MESA single and binary evolution models to explore how the binaries may have formed. The orbits of most binaries in the sample can be produced through CEE that begins when the WD progenitor is an AGB star, corresponding to initial separations of 2–5 au. Roughly 50% of all post-common envelope binaries are predicted to have first interacted on the AGB, ending up in wide orbits like these systems.

Revisiting the Tertiary-induced Binary Black Hole Mergers: The Role of Superthermal Wide Tertiary Eccentricity Distributions

Recent studies show that the eccentricity distribution of wide binaries (semimajor axis ≳103 au) observed by Gaia tends to favor large eccentricities more strongly than the canonical thermal distribution (P(e) ∝ e)—such distributions are termed “superthermal.” Motivated by this observation, we revisit the formation channel of black hole (BH) binary mergers in triple stellar systems and study the impact of superthermal eccentricity distributions in the outer binaries. We explore the persistence of the highly eccentric outer orbits after each component in a stellar triple has undergone mass loss due to supernova explosions. We find that the outer eccentricity distribution can remain significantly superthermal for modestly hierarchical BH triples satisfying a in/a out ≳ 0.005 (where a in and a out are the semimajor axes of the inner and outer orbits), and are otherwise shaped by mass-loss induced kicks and dynamical instability. We then study the impact of these different outer eccentricity distributions of the remaining BH triples on mergers via the tertiary-induced channel. Of interest, we find that mergers can sometimes be produced even when the initial stellar orbits are near alignment (not subject to the von-Zeipel–Lidov–Kozai effect; ZLK effect) as long as the system is sufficiently hierarchical. On the other hand, although the impact of the octupole-order ZLK effect is much greater when the outer binary is more eccentric, we find that the merger fraction only changes modestly for extreme outer eccentricity distributions because the largest eccentricities tend to lead to dynamical instability.

WIYN Open Cluster Study. XC. Barium Surface Abundances of Blue Straggler Stars in the Open Clusters NGC 7789 and M67

We investigate barium (Ba) abundances in blue straggler stars (BSSs) in two open clusters, NGC 7789 (1.6 Gyr) and M67 (4 Gyr), as signatures of asymptotic-giant-branch (AGB) mass transfer. We combine our findings with previous Ba abundance analyses of NGC 6819 (2.5 Gyr) and NGC 188 (7 Gyr). Out of 35 BSSs studied in NGC 7789, NGC 6819, and M67, 15 (43% ± 11%) are Ba enriched; no BSSs in NGC 188 are Ba enriched. The Ba abundances of enriched BSSs show an anticorrelation with cluster age, ranging from an enrichment of [Ba/Fe] ∼ +1.5 dex in NGC 7789 to [Ba/Fe] ∼ +1.0 dex in M67. The Ba-enriched BSSs all lie in the same region of the H-R diagram, irrespective of cluster age or distance from the main-sequence turnoff. Our data suggest a link between AGB donor mass and mass-transfer efficiency in BSSs, in that less massive AGB donors tend to undergo more conservative mass transfer. We find that 40% ± 16% of the Ba-enriched BSSs are in longer-period spectroscopic binaries with orbital periods less than 5000 days. Those Ba-enriched BSSs that do not exhibit radial-velocity variability suggest AGB mass transfer in wide binaries by either wind mass transfer or wind Roche-lobe overflow. Given the preponderance of long orbital periods in the BSSs of M67 and NGC 188 and the frequency of Ba enrichment in NGC 7789, NGC 6819, and M67, it may be that AGB mass transfer is the dominant mechanism of BSS formation in open clusters older than 1 Gyr.

A critical review of recent Gaia wide binary gravity tests

ABSTRACT Over the last couple of years, the appearance of the third data release from the Gaia satellite has triggered various wide binary low acceleration gravity tests. Wide binaries with typical total masses $\approx 1.0 - 1.6\,\mathrm{ M}_{\odot }$ and separations above a few thousand au probe the low acceleration $a \lesssim a_{0}$ regime, where at galactic and larger scales gravitational anomalies typically attributed to the presence of an as yet undetected dark matter component appear, where $a_{0} \approx 1.2\times 10^{-10}$ m s$^{-2}$ is the acceleration scale of Modified Newtonian Dynamics (MOND). Thus, studies of the relative velocities and separations on the plane of the sky, $v_{2\mathrm{ D}}$ and $s_{2\mathrm{ D}}$, respectively, of wide binary stars extending to separations above a few kau, provide an independent approach on the empirical study of gravity in the interesting $a \lesssim a_{0}$ acceleration range. Two independent groups, through complementary approaches, have obtained evidence for a departure from Newtonian predictions in the low acceleration regime, in consistency with MOND expectations for wide binary orbits in the Solar Neighbourhood. Two other groups however, have instead reported results showing a clear preference for Newtonian gravity over various MOND alternatives tested, over the same low acceleration regime. We here take a critical look at the various studies in question, from sample selection to statistical treatment of the wide binary relative velocities obtained. We discover a couple of critical problems in the formal design and statistical implementation shared by the two latter groups, and show explicitly how these yield biased conclusions.

On Binary Formation from Three Initially Unbound Bodies

We explore three-body binary formation (3BBF), the formation of a bound system via gravitational scattering of three initially unbound bodies (3UB), using direct numerical integrations. For the first time, we consider systems with unequal masses, as well as finite-size and post-Newtonian effects. Our analytically derived encounter rates and numerical scattering results reproduce the 3BBF rate predicted by Goodman & Hut for hard binaries in dense star clusters. We find that 3BBF occurs overwhelmingly through nonresonant encounters and that the two most-massive bodies are never the most likely to bind. Instead, 3BBF favors pairing the two least-massive bodies (for wide binaries) or the most- plus least-massive bodies (for hard binaries). 3BBF overwhelmingly favors wide-binary formation with superthermal eccentricities, perhaps helping to explain the eccentric wide binaries observed by Gaia. Hard-binary formation is far rarer, but with a thermal eccentricity distribution. The semimajor axis distribution scales cumulatively as a 3 for hard and slightly wider binaries. Although mergers are rare between black holes when including relativistic effects, direct collisions occur frequently between main-sequence stars—more often than hard 3BBF. Yet, these collisions do not significantly suppress hard 3BBF at the low-velocity dispersions typical of open or globular clusters. Energy dissipation through gravitational radiation leads to a small probability of a bound, hierarchical triple system forming directly from 3UB.

Eccentricity dynamics of wide binaries – II. The effect of stellar encounters and constraints on formation channels

ABSTRACT Gaia wide stellar binaries (separations $\sim 10^3{\!-\!}10^{4.5}$ au) are observed to have a superthermal eccentricity distribution function (DF), well-fit by $P(e) \propto e^\alpha$ with $\alpha \sim 1.2$. In a previous paper, we proved that this DF cannot have been produced by Galactic tidal torques starting from any realistic DF that was not already superthermal. Here, we consider the other major dynamical effect on wide binaries: encounters with passing stars. We derive and solve the Fokker–Planck equation governing the evolution of binaries in semimajor axis and eccentricity under many weak, impulsive, penetrative stellar encounters. We show analytically that these encounters drive the eccentricity DF towards thermal on the same time-scale as they drive the semimajor axes a towards disruption, $t_\mathrm{dis}\sim 4\, \mathrm{Gyr}\, (a/10^4\, \mathrm{AU})^{-1}$. We conclude that the observed superthermal DF must derive from an even more superthermal (i.e. higher $\alpha$) birth distribution. This requirement places strong constraints on the dominant binary formation channels. A testable prediction of our theory is that $\alpha$ should be a monotonically decreasing function of binary age.