Hierarchical Triples Research Articles

Most extremely low mass white dwarfs with non-degenerate companions are inner binaries of hierarchical triples

Abstract Extremely-low-mass white dwarfs (ELM WDs) with non-degenerate companions are believed to originate from solar-type main-sequence binaries undergoing stable Roche lobe overflow mass transfer when the ELM WD progenitor is at (or just past) the termination of the main-sequence. This implies that the orbital period of the binary at the onset of the first mass transfer phase must have been ≲ 3 − 5 d. This prediction in turn suggests that most of these binaries should have tertiary companions since ≈90 per cent of solar-type main-sequence binaries in that period range are inner binaries of hierarchical triples. Until recently, only precursors of this type of binaries have been observed in the form of EL CVn binaries, which are also known for having tertiary companions. Here, we present high-angular-resolution images of TYC 6992-827-1, an ELM WD with a sub-giant (SG) companion, confirming the presence of a tertiary companion. Furthermore, we show that TYC 6992-827-1, along with its sibling TYC 8394-1331-1 (whose triple companion was detected via radial velocity variations), are in fact descendants of EL CVn binaries. Both TYC 6992-827-1 and TYC 8394-1331-1 will evolve through a common envelope phase, which depending on the ejection efficiency of the envelope, might lead to a single WD or a tight double WD binary, which would likely merge into a WD within a few Gyr due to gravitational wave emission. The former triple configuration will be reduced to a wide binary composed of a WD (the merger product) and the current tertiary companion.

Spectroscopy of eclipsing compact hierarchical triples

Context. Eclipsing compact hierarchical triples (CHTs) are systems in which a tertiary star orbits an eclipsing binary (EB) in an orbit of fewer than 1000 days. In a CHT, all three stars exist in a space that is less than 5 AU in radius. A low-mass CHT is an interesting case through which we can understand the formation of multiple stars and planets at such small scales. Aims. In this study, we combine spectroscopy and photometry to estimate the orbital, stellar, and atmospheric parameters of stars in a sample of CHTs. Using the complete set of parameters, we aim to constrain the metallicity and age of the systems. Methods. We used time-series spectroscopy to obtain radial velocities (RVs) and disentangled spectra. Using RV modelling, EB light curve modelling, and spectral analysis, we estimated the metallicities and temperatures. Using isochrone fitting, we constrained the ages of the system. We then combined observations of masses, outer eccentricities (e2), orbital periods, and age estimates of the systems from the literature. We compared the distributions of e2, and the tertiary mass ratio, q3 = M3/(M1 + M2), for three different metallicity ranges and two age ranges. Results. We have estimated the masses, radii, temperatures, metallicities, and ages of 12 stars in four CHTs. The CHT CD-32 6459 shows signs of von Zeipel-Lidov-Kozai oscillations, while CD-62 1257 can evolve to form a triple common envelope. The rest of the CHTs are old and have an M-dwarf tertiary. We find that the q3 distribution for CHTs with sub-solar metallicity has a uniform distribution but the systems with solar and above-solar metallicity peak between 0.5 and 1. When dividing them according to their ages, we find the q3 of old systems to be around 0.5. The eccentricity, e2, favours a value of around 0.3 irrespective of metallicity or age. The distributions of q3 and e2 resemble the distributions of the mass ratio and eccentricity of close field binaries.

Validation of Gaia DR3 Orbital and Acceleration Solutions with Hierarchical Triples

Using data from Gaia DR3, we construct a sample of 14,791 gravitationally bound wide pairs in which one of the components is an unresolved binary with an astrometric orbital or acceleration solution. These systems are hierarchical triples, with inner binary separations of order 1 au, and outer separations of 100–100,000 au. Leveraging the fact that the inner binary and outer tertiary should have nearly identical parallaxes, we use the sample to calibrate the parallax uncertainties for orbital and acceleration binary solutions. We find that the parallax uncertainties of orbital solutions are typically underestimated by a factor of 1.3 at G > 14, and by a factor of 1.7 at G = 8–14. The true parallax uncertainties are nevertheless a factor of ∼10 smaller than those of the single-star astrometric solutions for the same sources. The parallax uncertainties of acceleration solutions are underestimated by larger factors of 2–3 but still represent a significant improvement compared to the sources’ single-star solutions. We provide tabulated uncertainty inflation factors for astrometric binary solutions and make the catalog of hierarchical triples publicly available.

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.

Triage of the Gaia DR3 astrometric orbits. II. A census of white dwarfs

ABSTRACT The third data release of Gaia was the first to include orbital solutions assuming non-single stars. Here, we apply the astrometric triage technique of Shahaf et al. to identify binary star systems with companions that are not single main-sequence stars. Gaia’s synthetic photometry of these binaries is used to distinguish between systems likely to have white-dwarf companions and those that may be hierarchical triples. The study uncovered a population of nearly $3\, 200$ binaries, characterized by orbital separations on the order of an astronomical unit, in which the faint astrometric companion is probably a white dwarf. This sample increases the number of orbitally solved binary systems of this type by about two orders of magnitude. Remarkably, over 110 of these systems exhibit significant ultraviolet excess flux, confirming this classification and, in some cases, indicating their relatively young cooling ages. We show that the sample is not currently represented in synthetic binary populations, and is not easily reproduced by available binary population synthesis codes. Therefore, it challenges current binary evolution models, offering a unique opportunity to gain insights into the processes governing white-dwarf formation, binary evolution, and mass transfer.

Eccentric black hole mergers via three-body interactions in young, globular, and nuclear star clusters

Eccentric mergers are a signature of the dynamical formation channel of binary black holes (BBHs) in dense stellar environments and hierarchical triple systems. Here, we investigate the formation of eccentric mergers via binary-single interactions by means of 2.5 × 105 direct N-body simulations. Our simulations include post-Newtonian terms up to the 2.5th order and model the typical environment of young (YSCs), globular (GCs), and nuclear star clusters (NSCs). Around 0.6% (1%) of our mergers in NSCs (GCs) have an eccentricity > 0.1 when the emitted gravitational wave frequency is 10 Hz in the source frame, while in YSCs this fraction rises to 1.6%. Approximately ∼63% of these mergers are produced by chaotic, resonant interactions where temporary binaries are continuously formed and destroyed, while ∼31% arise from an almost direct collision of two black holes (BHs). Lastly, ∼6% of these eccentric mergers occur in temporary hierarchical triples. We find that binaries undergoing a flyby generally develop smaller tilt angles with respect to exchanges. This result challenges the idea that perfectly isotropic spin orientations are produced by dynamics. The environment dramatically affects BH retention: 0%, 3.1%, and 19.9% of all the remnant BHs remain in YSCs, GCs, and NSCs, respectively. The fraction of massive BHs also depends on the host cluster properties, with pair-instability (60 ≤ MBH/M⊙ ≤ 100) and intermediate-mass (MBH ≥ 100 M⊙) BHs accounting for approximately ∼44% and 1.6% of the mergers in YSCs, ∼33% and 0.7% in GCs, and ∼28% and 0.4% in NSCs, respectively.

Relativistic Phase Space Diffusion of Compact Object Binaries in Stellar Clusters and Hierarchical Triples

The LIGO/Virgo detections of compact object mergers have posed a challenge for theories of binary evolution and coalescence. One promising avenue for producing mergers dynamically is through secular eccentricity oscillations driven by an external perturber, be it a tertiary companion (as in the Lidov–Kozai, LK, mechanism) or the tidal field of the stellar cluster in which the binary orbits. The simplest theoretical models of these oscillations use a “doubly averaged” (DA) approximation, averaging both over the binary’s internal Keplerian orbit and its “outer” barycentric orbit relative to the perturber. However, DA theories do not account for fluctuations of the perturbing torque on the outer orbital timescale, which are known to increase a binary’s eccentricity beyond the maximum DA value, potentially accelerating mergers. Here we reconsider the impact of these short-timescale fluctuations in the test-particle quadrupolar limit for binaries perturbed by arbitrary spherical cluster potentials (including LK as a special case), in particular including 1pN general relativistic (GR) apsidal precession of the internal orbit. Focusing on the behavior of the binary orbital elements around peak eccentricity, we discover a new effect, relativistic phase space diffusion (RPSD), in which a binary can jump to a completely new dynamical trajectory on an outer orbital timescale, violating the approximate conservation of DA integrals of motion. RPSD arises from an interplay between secular behavior at extremely high eccentricity, short-timescale fluctuations, and rapid GR precession, and can change the subsequent secular evolution dramatically. This effect occurs even in hierarchical triples, but has not been uncovered until now.

ESPRESSO Observations of Gaia BH1: High-precision Orbital Constraints and no Evidence for an Inner Binary

We present high-precision radial velocity observations of Gaia BH1, the nearest known black hole (BH). The system contains a solar-type G star orbiting a massive dark companion, which could be either a single BH or an inner BH + BH binary. A BH + BH binary is expected in some models where Gaia BH1 formed as a hierarchical triple, which is attractive because they avoid many of the difficulties associated with forming the system through isolated binary evolution. Our observations test the inner binary scenario. We have measured 115 precise RVs of the G star, including 40 from ESPRESSO with a precision of 3–5 m s−1, and 75 from other instruments with a typical precision of 30–100 m s−1. Our observations span 2.33 orbits of the G star and are concentrated near a periastron passage, when perturbations due to an inner binary would be largest. The RVs are well-fit by a Keplerian two-body orbit and show no convincing evidence of an inner binary. Using REBOUND simulations of hierarchical triples with a range of inner periods, mass ratios, eccentricities, and orientations, we show that plausible inner binaries with periods P inner ≳ 1.5 days would have produced larger deviations from a Keplerian orbit than observed. Binaries with P inner ≲ 1.5 days are consistent with the data, but these would merge within a Hubble time and would thus imply fine-tuning. We present updated parameters of Gaia BH1's orbit. The RVs yield a spectroscopic mass function fMBH=3.9358±0.0002M⊙ —about 7000σ above the ∼2.5 M ⊙ maximum neutron star mass. Including the inclination constraint from Gaia astrometry, this implies a BH mass of M BH = 9.27 ± 0.10 M ⊙.

Stellar triples with chemically homogeneously evolving inner binaries

ABSTRACT Observations suggest that massive stellar triples are common. However, their evolution is not yet fully understood. We investigate the evolution of hierarchical triples in which the stars of the inner binary experience chemically homogeneous evolution (CHE), particularly to understand the role of the tertiary star in the formation of gravitational-wave (GW) sources. We use the triple-star rapid population synthesis code tres to determine the evolution of these systems at two representative metallicities: Z = 0.005 and Z = 0.0005. About half of all triples harbouring a CHE inner binary (CHE triples) experience tertiary mass transfer (TMT) episodes, an event which is rare for classically evolving stars. In the majority of TMT episodes, the inner binary consists of two main-sequence stars (58–60 per cent) or two black holes (BHs, 24–31 per cent). Additionally, we explore the role of von Zeipel-Lidov-Kozai (ZLK) oscillations for CHE triples. ZLK oscillations can result in eccentric stellar mergers or lead to the formation of eccentric compact binaries in systems with initial outer pericentre smaller than ∼ 1200 R⊙. Approximately 24–30 per cent of CHE triples form GW sources, and in 31 per cent of these, the tertiary star plays a significant role and leads to configurations that are not predicted for isolated binaries. We conclude that the evolution of CHE binaries can be affected by a close tertiary companion, resulting in astronomical transients such as BH–BH binaries that merge via GW emission orders of magnitude faster than their isolated binary counterparts and tertiary-driven massive stellar mergers.

The main evolutionary pathways of massive hierarchical triple stars

Context. So far, stellar population studies have mainly focused on the evolution of single and binary stars. Recent observations show that triple and higher order multiple star systems are ubiquitous in the local population, especially among massive stars. Introducing three-body dynamical effects can influence the evolution of an individual stellar system and can therefore affect the predicted rates of astrophysical sources that are a product of stellar evolution. Therefore, predictions of triple star evolution are necessary for a more complete understanding of the evolutionary behaviour of stellar populations and their end products. Aims. We aim to constrain the main evolutionary pathways of massive hierarchical triple star systems and to quantify the effect of the third star on the evolution of the system. Methods. We model the massive triple star population by performing simulations of triple star evolution with the TRES code, which combines stellar evolution with secular evolution of triple systems, and explore how robust the predictions of these simulations are under variations of uncertain initial conditions. We focus on coeval, hierarchical stellar triples in pre-mass-transfer phases. Results. Interactions are common among massive triple stars. The majority of systems (65%–77%) experience a phase of mass transfer in the inner binary, often with a main sequence donor star. This differs significantly from isolated binary evolution, where mass transfer is less frequent (52.3% instead of 67% for our fiducial model) and the donors are typically post-main sequence stars. Initial constraints for dynamical stability as well as eccentricity oscillations driven by the third body facilitate the occurrence of interactions, such as mass transfer. The requirement of dynamical stability at formation places quite stringent constraints on allowed orbital properties, reducing uncertainties in triple evolution that resort from these initial conditions. Ignoring three-body dynamics during evolution of non-interacting triples leads to triple compact-object systems with stronger eccentricity oscillations and thereby likely over-predicts the merger rate of compact objects in such systems.

Dynamics of supermassive black hole triples in the ROMULUS25 cosmological simulation

For a pair of supermassive black holes (SMBHs) in the remnant of a dual galaxy merger, well-known models exist to describe their dynamical evolution until the final coalescence accompanied by the emission of a low-frequency gravitational wave signal. In this article, we investigate the dynamical evolution of three SMBH triple systems recovered from the ROMULUS25 cosmological simulation to explore common dynamical evolution patterns and assess typical coalescence times. For this purpose, we construct initial conditions from the ROMULUS25 data and perform high-resolution gravitodynamical N-body simulations. We track the orbital evolution from the galactic inspiral to the formation of hard binaries at sub-parsec separation and use the observed hardening rates to project the time of coalescence. In all cases, the two heaviest black holes form an efficiently hardening binary that merges within fractions of the Hubble time. The lightest SMBH either gets ejected, forms a stable hierarchical triple system with the heavier binary, forms a hardening binary with the previously merged binary’s remnant, or remains on a wide galactic orbit. The coalescence times of the lighter black holes are thus significantly longer than for the heavier binary, as they experience lower dynamical friction and stellar hardening rates. We observe the formation of hierarchical triples when the density profile of the galactic nucleus is sufficiently steep.

Stability of hierarchical triples – II. The inclination ι = 140° resonance in the stability surface

ABSTRACT The stability of a hierarchical triple star may be decided by a simple criterion, which was derived in Paper I. However, there is a region in the phase space where the stability limit Qmax is raised by a factor of two in a small region of the phase space with respect to the surrounding phase space. The phase space is defined by the inner and outer eccentricities ein and eout, respectively, as well as by the inclination ιtot between the inner and outer orbits. Additional parameters of the phase space are the masses of the three bodies. We study by numerical integration the orbits of over 100 000 triple systems in the resonance region. We find that the instability that causes the high value of Qmax arises from the octupole Kozai–Lidov resonance. This resonance region has rather equal contributions from the quadrupole and octupole terms and leads to secular evolution with an amplitude larger than either of the two oscillations in isolation. The conditions for this situation are best satisfied near the relative inclination ι = 140°. Additionally, the relative orientation of the two orbits plays a decisive role: the resonance is found only at certain values of the orbit’s node line longitude Ω. An analytical approximation of the energy change in a single close encounter between the inner and outer systems suggests a cos 2Ω dependence of Qmax on Ω, which seems to be qualitatively valid. We model Qmax as a function of cos ι and ein by a Gaussian function.

Detached eclipsing binaries in compact hierarchical triples: triple-lined systems BD+442258 and KIC 06525196

ABSTRACT Compact hierarchical triples (CHTs) are systems with the tertiary star orbiting the inner binary in an orbit shorter than 1000 d. CHT with an eclipsing binary as its inner binary can help us extract a multitude of information about all three stars in the system. In this study, we use independent observational techniques to estimate the orbital, stellar, and atmospheric parameters of two triple-lined CHT: BD+44 2258 and KIC 06525196. We find that the masses of stars in BD+44 2258 are $1.011\pm 0.029$, $0.941\pm 0.033$, and $0.907\pm 0.065 \, {\rm M}_{\odot }$ while in KIC 06525196 the estimated masses are $1.0351\pm 0.0055$, $0.9712\pm 0.0039 $, and $0.777\pm 0.012 \, {\rm M}_{\odot }$. Using spectral disentangling, we obtained individual spectra of all the stars and combined it with light-curve modelling to obtain radii, metallicities, and temperatures. Using stellar evolution models from mesa, we constrain the log(age) of BD+44 2258 to be 9.89 and 9.49 for KIC 06525196. Two stars in BD+44 2258 are found to be sub-giants while all three stars in KIC 06525196 are main-sequence stars. We constrain the mutual inclinations to certain angles for BD+44 2258 and KIC 06525196 using numerical integration. Integrating with tidal interaction schemes and stellar evolution models, we find that KIC 06525196 is a stable system. But the inner binary of BD+44 2258 merges within 550 Myr. The time of this merger is affected by the orientation of the tertiary, even rushing the collapse by ∼100 Myr when the mutual inclination is close to 90○.

The McDonald Accelerating Stars Survey: Architecture of the Ancient Five-planet Host System Kepler-444

We present the latest and most precise characterization of the architecture for the ancient (≈11 Gyr) Kepler-444 system, which is composed of a K0 primary star (Kepler-444 A) hosting five transiting planets and a tight M-type spectroscopic binary (Kepler-444 BC) with an A–BC projected separation of 66 au. We have measured the system’s relative astrometry using the adaptive optics imaging from Keck/NIRC2 and Kepler-444 A’s radial velocities from the Hobby-Eberly Telescope and reanalyzed relative radial velocities between BC and A from Keck/HIRES. We also include the Hipparcos-Gaia astrometric acceleration and all published astrometry and radial velocities in an updated orbit analysis of BC’s barycenter. These data greatly extend the time baseline of the monitoring and lead to significant updates to BC’s barycentric orbit compared to previous work, including a larger semimajor axis ( au), a smaller eccentricity (e = 0.55 ± 0.05), and a more precise inclination (). We have also derived the first dynamical masses of B and C components. Our results suggest that Kepler-444 A’s protoplanetary disk was likely truncated by BC to a radius of ≈8 au, which resolves the previously noticed tension between Kepler-444 A’s disk mass and planet masses. Kepler-444 BC’s barycentric orbit is likely aligned with those of A’s five planets, which might be primordial or a consequence of dynamical evolution. The Kepler-444 system demonstrates that compact multiplanet systems residing in hierarchical stellar triples can form at early epochs of the universe and survive their secular evolution throughout cosmic time.

Wide Binaries as a Modified Gravity test: prospects for detecting triple-system contamination

Several recent studies have shown that velocity differences of very wide binary stars, measured to high precision with GAIA, can potentially provide an interesting test for modified-gravity theories which attempt to emulate dark matter; in essence, MOND-like theories (with external field effect included) predict that wide binaries (wider than $\sim 7$ kAU) should orbit $\sim 15\%$ faster than Newtonian for similar orbit parameters; such a shift is readily detectable in principle in the sample of 9,000 candidate systems selected from GAIA EDR3 by Pittordis and Sutherland (2022; PS22). However, the main obstacle at present is the observed "fat tail" of candidate wide-binary systems with velocity differences at $\sim 1.5 - 6 \times$ circular velocity; this tail population cannot be bound pure binary systems, but a possible explanation of the tail is triple or quadruple systems with unresolved or undetected additional star(s). While this tail can be modelled and subtracted, obtaining an accurate model for the triple population is crucial to obtain a robust test for modified gravity. Here we explore prospects for observationally constraining the triple population: we simulate a population of hierarchical triples "observed" as in PS22 at random epochs and viewing angles; then evaluate various possible methods for detecting the third star, including GAIA astrometry, RV drift, and several imaging methods from direct Rubin images, speckle imaging and coronagraphic imaging. Results are encouraging, typically 90 percent of the triple systems in the key regions of parameter space are detectable; there is a moderate "dead zone" of cool brown-dwarf companions at $\sim 25-100$ AU separation which are not detectable with any of our baseline methods. A large but feasible observing campaign can clarify the triple/quadruple population and make the gravity test decisive.

Anatomy of a Slow Merger: Dissecting Secularly Driven Inspirals of LIGO/Virgo Gravitational Wave Sources

The dozens of compact object mergers detected by LIGO/Virgo raise a key theoretical question: how do initially wide binaries shrink sufficiently quickly that they are able to merge via gravitational wave (GW) radiation within a Hubble time? One promising class of answers involves secular driving of binary eccentricity by some external tidal perturbation. This perturbation can arise due to the presence of a tertiary point mass, in which case the system exhibits Lidov-Kozai (LK) dynamics, or it can stem from the tidal field of the stellar cluster in which the binary orbits. While these secular tide-driven mechanisms have been studied exhaustively in the case of no GW emission, when GWs are included the dynamical behavior is still incompletely understood. In this paper we consider compact object binaries driven to merger via high-eccentricity excitation by (doubly averaged, test-particle quadrupole level) cluster tides—which includes LK-driven mergers as a special case—and include the effects of both general relativistic precession and GW emission. We provide for the first time an analytical understanding of the different evolutionary stages of the binary’s semimajor axis, secular oscillation timescale, and phase-space structure all the way to merger. Our results will inform future population synthesis calculations of compact object binary mergers from hierarchical triples and stellar clusters.

Forming hot subluminous stars from hierarchical triples – I. The role of an outer tertiary on formation channels

ABSTRACT We present evolutionary pathways for creating hot subdwarf OB (sdOB) stars from hierarchical triple configurations. We use the population synthesis code Multiple Stellar Evolution to follow the stellar, binary, and gravitational dynamical evolution of triple-star systems. To ascertain the effect of the outer tertiary, we also consider the evolution of the inner binary with the tertiary component removed. We find we are able to create sdOB stars in single, binary, and triple configurations. We also demonstrate that it is possible to form sdOBs in systems that undergo triple common envelope evolution, when the tertiary star undergoes unstable mass transfer on to the inner binary. We are unable to create single or wide sdOB systems without involving a merger earlier in the evolution. The triples can produce sdOBs in binaries with wide, non-interacting companions through binary interactions, which is impossible in isolated binaries. Owing to the closeness of the inner binary in hierarchical triples the formation channels associated with stable mass transfer are suppressed when compared to the isolated binary case.

Predicting the Stability of Hierarchical Triple Systems with Convolutional Neural Networks

The dynamical stability of hierarchical triple systems is a long-standing question in celestial mechanics and dynamical astronomy. Assessing the long-term stability of triples is challenging because it requires computationally expensive simulations. Here we propose a convolutional neural network model to predict the stability of equal-mass hierarchical triples by looking at their evolution during the first 5 × 105 inner binary orbits. We employ the regularized few-body code tsunami to simulate 5 × 106 hierarchical triples, from which we generate a large training and test data set. We develop 12 different network configurations that use different combinations of the triples’ orbital elements and compare their performances. Our best model uses six time series, namely, the semimajor axes ratio, the inner and outer eccentricities, the mutual inclination, and the arguments of pericenter. This model achieves excellent performance, with an area under the ROC curve score of over 95% and informs of the relevant parameters to study triple systems stability. All trained models are made publicly available, which allows predicting the stability of hierarchical triple systems 200 times faster than pure N-body methods.

The value-added catalogue of ASAS-SN eclipsing binaries: parameters of 30 000 detached systems

ABSTRACT Detached eclipsing binaries are a fundamental tool for measuring the physical parameters of stars that are effectively evolving in isolation. Starting from more than 40 000 eclipsing binary candidates identified by the All-Sky Automated Survey for Supernovae (ASAS-SN), we use PHOEBE to determine the sum of the fractional radii, the ratio of effective temperatures, the inclinations, and the eccentricities for 35 576 systems. We visually inspect all the light-curve models to verify the model fits and examine the TESS light curves, when available, to select systems with evidence for additional physics, such as spots, mass transfer, and hierarchical triples. We examine the distributions of the eclipsing binary model parameters and the orbital parameters. We identify two groups in the sum of the fractional radii and effective temperature ratio parameter space that may distinguish systems approaching the semidetached limit. Combining Gaia EDR3 with extinction estimates from three-dimensional dust maps, we examine the properties of the systems as a function of their absolute magnitude and evolutionary state. Finally, we present light curves of selected eclipsing binaries that may be of interest for follow-up studies.

Algebraic and machine learning approach to hierarchical triple-star stability

ABSTRACT We present two approaches to determine the dynamical stability of a hierarchical triple-star system. The first is an improvement on the Mardling–Aarseth stability formula from 2001, where we introduce a dependence on inner orbital eccentricity and improve the dependence on mutual orbital inclination. The second involves a machine learning approach, where we use a multilayer perceptron (MLP) to classify triple-star systems as ‘stable’ and ‘unstable’. To achieve this, we generate a large training data set of 106 hierarchical triples using the N-body code MSTAR. Both our approaches perform better than previous stability criteria, with the MLP model performing the best. The improved stability formula and the machine learning model have overall classification accuracies of $93{{\ \rm per\ cent}}$ and $95{{\ \rm per\ cent}}$ respectively. Our MLP model, which accurately predicts the stability of any hierarchical triple-star system within the parameter ranges studied with almost no computation required, is publicly available on Github in the form of an easy-to-use python script.