If binary intermediate-mass black holes (IMBHs; with masses between 100 and $10^4 \Msun$) form in dense stellar clusters, their inspiral will be detectable with the planned Laser Interferometer Space Antenna (LISA) out to several Gpc. Here we present a study of the dynamical evolution of such binaries using a combination of direct $N$-body techniques (when the binaries are well separated) and three-body relativistic scattering experiments (when the binaries are tight enough that interactions with stars occur one at a time). We find that for reasonable IMBH masses there is only a mild effect on the structure of the surrounding cluster even though the binary binding energy can exceed the binding energy of the cluster. We demonstrate that, contrary to standard assumptions, the eccentricity in the LISA band can be in {\em some} cases as large as $\sim 0.2 - 0.3$ and that it induces a measurable phase difference from circular binaries in the last year before merger. We also show that, even though energy input from the binary decreases the density of the core and slows down interactions, the total time to coalescence is short enough (typically less than a hundred million years) that such mergers will be unique snapshots of clustered star formation.
Distribution of eccentricities of very wide (up to 10 kau) low-mass binaries in the solar neighborhood is studied using the catalog of El-Badry and Rix (2018) based on Gaia. Direction and speed of relative motions in wide pairs contain statistical information on the eccentricity distribution, otherwise inaccessible owing to very long orbital periods. It is found that the eccentricity distribution is close to the linear (thermal) one f(e) = 2e$ However, pairs with projected separations <200 au have less eccentric orbits, while f(e) for very wide pairs appears to be slightly super-thermal, with …
Eccentricity of wide binaries is difficult to measure due to their long orbital periods. With Gaia's high-precision astrometric measurements, eccentricity of a wide binary can be constrained by the angle between the separation vector and the relative velocity vector (the $v$-$r$ angle). In this paper, by using the $v$-$r$ angles of wide binaries in Gaia Early Data Release 3, we develop a Bayesian approach to measure the eccentricity distribution as a function of binary separations. Furthermore, we infer the eccentricities of individual wide binaries and make them publicly available. Our result…
Common envelope evolution (CEE) is believed to be an important stage in the evolution of binary/multiple stellar systems. Following this stage, the CE is thought to be ejected, leaving behind a compact binary (or a merger product). Although extensively studied, the CEE process is still little understood, and although most binaries have non-negligible eccentricity, the effect of initial eccentricity on the CEE has been little explored. Moreover, most studies assume a complete circularization of the orbit by the CE onset, while observationally such eccentricities are detected in many post-CE bin…
Future Gaia and Legacy Survey of Space and Time data releases, together with wide area spectroscopic surveys, will deliver large samples of resolved binary stars with phase space coordinates, albeit with low-cadence. Given an eccentricity law $f(ε)$, we derive properties of (i) the velocity distribution $v/\sqrt{G M/r}$ normalised by the value for a circular orbit at the measured separation $r$; (ii) the astrometric acceleration distributions $a/\left(G M/r^2\right)$ again normalised to the circular orbit value. Our formulation yields analytic predictions for the full statistical distribution …
The eccentricity, periastron angle, orbital inclination, mass ratio, stellar temperatures and relative stellar radii of 12 eclipsing eccentric binaries were determined on the basis of Kepler data. The analysis of their out-of-eclipse variability led to the following results: (i) KIC 10490980 exhibits rotational (spot-type) variability; (ii) Four new heartbeat stars were found: KIC 9344623 and KIC 10296163, which have wide tidally induced light humps and KIC 9119405 and KIC 9673173, which have narrow "W-shape" features; (iii) KIC 4932691 shows oscillations with approximately the 18th harmonic o…
Most, if not all, stars in the field are born in binary configurations or higher multiplicity systems. In dense stellar environment such as the Galactic Center (GC), many stars are expected to be in binary configurations as well. These binaries form hierarchical triple body systems, with the massive black hole (MBH) as the third, distant object. The stellar binaries are expected to undergo large amplitude eccentricity and inclination oscillations via the so-called "eccentric Kozai-Lidov" (EKL) mechanism. These eccentricity excitations, combined with post main sequence stellar evolution, can dr…
About a century ago, Jeans (1919) discovered that if binary stars reach a state approximating energy equipartition, for example through many dynamical encounters that exchange energy, their eccentricity distribution can be described by : dN/de = 2e. This is referred to as the thermal eccentricity distribution, and has been widely used for initial conditions in theoretical investigations of binary stars. However, observations suggest that the eccentricity distributions of most observed binaries, and particularly those with masses < 5 Msun, are flatter than thermal and follow more closely to a u…
We investigate the secular evolution of the orbital semi-major axis and eccentricity due to mass transfer in eccentric binaries, allowing for both mass and angular momentum loss from the system. Adopting a delta function mass transfer rate at the periastron of the binary orbit, we find that, depending on the initial binary properties at the onset of mass transfer, the orbital semi-major axis and eccentricity can either increase or decrease at a rate linearly proportional to the magnitude of the mass transfer rate at periastron. The range of initial binary mass ratios and eccentricities that le…
The Gaia mission recently revealed an excess population of equal-mass "twin" wide binaries, with mass ratio $q\gtrsim 0.95$, extending to separations of at least 1000 AU. The origin of this population is an enigma: twin binaries are thought to form via correlated accretion in circumbinary disks, but the typical observed protostellar disks have radii of $\sim100$ AU, far smaller than the separations of the widest twins. Here, we infer the eccentricity distribution of wide twins from the distribution of their $v$-$r$ angles, i.e., the angle between the components' separation and relative velocit…
Several classes of stellar binaries with post-main sequence (post-MS) components - millisecond pulsars with the white dwarf companions (MSP+WD) and periods P_b~30 d, binaries hosting post-asymptotic giant branch (post-AGB) stars or barium stars with P_b~several yr - feature high eccentricities (up to 0.4) despite the expectation of their efficient tidal circularization during the AGB phase. It was suggested that the eccentricities of these binaries can be naturally excited by their tidal coupling to the circumbinary disk, formed by the material ejected from the binary. Here we critically reass…
We report the very first analysis of 27 eclipsing binary systems with high eccentricities that sometimes reach up to 0.8. The orbital periods for these systems range from 1.4 to 37 days, and the median of the sample is 10.3 days. Star CzeV3392 (= UCAC4 623 022784), for example, currently is the eclipsing system with the highest eccentricity (e = 0.22) of stars with a period shorter than 1.5 days. We analysed the light curves of all 27 systems and obtained the physical parameters of both components, such as relative radii, inclinations, or relative luminosities. The most important parameters ap…
We carried out light curve solutions of ten detached eclipsing eccentric binaries observed by Kepler. The formal errors of the derived parameters from the light curve solutions are below 1%. Our results give indications that the components of the eccentric binaries (especially those with mass ratios below 0.5) do not follow precisely the empirical relations between the stellar parameters derived from the study of circular-orbit binaries. We found the following peculiarities of the targets: (a) the components of KIC 9474969 have almost the same temperatures while their radii and masses differ b…
Hot subdwarf-B stars in long-period binaries are found to be on eccentric orbits, even though current binary-evolution theory predicts those objects to be circularised before the onset of Roche-lobe overflow (RLOF). We aim to find binary-evolution mechanisms that can explain these eccentric long-period orbits, and reproduce the currently observed period-eccentricity diagram. Three different processes are considered; tidally-enhanced wind mass-loss, phase-dependent RLOF on eccentric orbits and the interaction between a circumbinary disk and the binary. The binary module of the stellar-evolution…
Rethinking mass transfer: a unified semianalytical framework for circular and eccentric binaries. II. Orbital evolution due to nonconservative mass transfer
Anton Pannekoek Institute for Astronomy, University of Amsterdam（阿姆斯特丹大学安滕·潘内科克天文研究所）；Institute of Astronomy, KU Leuven（荷鲁文大学天文学研究所）；Leuven Gravity Institute, KU Leuven（荷鲁文大学勒芬引力研究所）；School of Physics and Astronomy, Cardiff University（卡迪夫大学物理与天文学院）
Type I outbursts in Be/X-ray binaries are usually associated with the eccentricity of the binary orbit. The neutron star accretes gas from the outer parts of the decretion disk around the Be star at each periastron passage. However, this mechanism cannot explain type I outbursts that have been observed in nearly circular orbit Be/X-ray binaries. With hydrodynamical simulations and analytic estimates we find that in a circular orbit binary, a nearly coplanar disk around the Be star can become eccentric. The extreme mass ratio of the binary leads to the presence of the 3:1 Lindblad resonance ins…
We have compiled a sample of 16 orbits for very low-mass stellar (<0.1 Msun) and brown dwarf binaries, enabling the first comprehensive study of the eccentricity distribution for such objects. We find that very low-mass binaries span a broad range of eccentricities (0.03<e<0.83), with a median eccentricity of 0.34. We examine potential observational biases in this sample, and for visual binaries we show through Monte Carlo simulations that appropriate selection criteria result in all eccentricities being equally represented (<5% difference between input and output e distributions). The orbits …
Despite numerous efforts to better understand binary star evolution, some aspects of it remain poorly constrained. In particular, the evolution of eccentric binaries has remained elusive mainly because the Roche lobe formalism derived for circular binaries does not apply. Here, we report the results of our Smoothed Particle Hydrodynamics simulations of mass transfer in eccentric binaries using an alternate method in which we model only the outermost layers of the stars with appropriate boundary conditions. Using this technique, along with properly relaxed model stars, we characterize the mass …
We solve the equations of two-dimensional hydrodynamics describing a circumbinary disk accreting onto an eccentric, equal-mass binary. We compute the time rate of change of the binary semimajor axis $a$ and eccentricity $e$ over a continuous range of eccentricities spanning $e=0$ to $e=0.9$. We find that binaries with initial eccentricities $e_0 \lesssim 0.1$ tend to $e=0$, where the binary semimajor axis expands. All others are attracted to $e \approx 0.4$, where the binary semimajor axis decays. The $e \approx 0.4$ attractor is caused by a rapid change in the disk response from a nearly orig…
We determined the orbits and stellar parameters of three eccentric eclipsing binaries by light curve solutions of their Kepler data. KIC 10992733 and KIC 5632781 undergo total eclipses while KIC 10026136 reveals partial eclipses. The components of the targets are G and K stars. KIC 10992733 exhibited variations which were attributed to variable visibility of spot(s) on asynchronously rotating component. KIC 5632781 and KIC 1002613 reveal tidally-induced features at periastron, i.e. they might be considered as eclipsing heartbeat stars. The characteristics of the periastron features (shape, wid…
Tidal evolution of eccentric binary systems containing at least one massive main-sequence (MS) star plays an important role in the formation scenarios of merging compact-object binaries. The dominant dissipation mechanism in such systems involves tidal excitation of outgoing internal gravity waves at the convective-radiative boundary and dissipation of the waves at the stellar envelope/surface. We have derived analytical expressions for the tidal torque and tidal energy transfer rate in such binaries for arbitrary orbital eccentricities and stellar rotation rates. These expressions can be used…
Modelling ellipsoidal variables with known distances can lead to exact determination of the masses of both components, even in the absence of eclipses. We present such modelling using light and radial velocity curves of ellipsoidal red giant binaries in the LMC, where they are also known as sequence E stars. Stars were selected as likely eccentric systems on the basis of light curve shape alone. We have confirmed their eccentric nature and obtained system parameters using the Wilson-Devinney code. Most stars in our sample exhibit unequal light maxima as well as minima, a phenomenon not observe…
To measure the onset of mass transfer in eccentric binaries we have developed a two-phase SPH technique. Mass transfer is important in the evolution of close binaries, and a key issue is to determine the separation at which mass transfer begins. The circular case is well understood and can be treated through the use of the Roche formalism. To treat the eccentric case we use a newly-developed two phase system. The body of the donor star is made up from high-mass "water" particles, whilst the atmosphere is modelled with low-mass "oil" particles. Both sets of particles take part fully in SPH inte…
With 16-month Kepler data, 14 long-period (40 d - 265 d) eclipsing binaries on highly eccentric orbits (minimum e between 0.5 and 0.85) are recognized from their closely separated primary and secondary eclipses (Δt_I,II = 3 d - 10 d). These systems confirm the existence of a previously hinted binary population situated near a constant angular momentum track at P(1-e^2)^(3/2) ~ 15 d, close to the tidal circularization period P_circ. They may be presently migrating due to tidal dissipation and form a steady-state stream (~1% of stars) feeding the close-binary population (few percent of stars). I…
We present an extension of the BEER model for eccentric binaries - eBEER, approximating the BEaming, Ellipsoidal and Reflection effects by harmonic series of the Keplerian elements of their orbit. As such, it can be a tool for fast processing of light curves for detecting non-eclipsing eccentric binary systems. To validate the applicability of the eccentric model and its approximations, we applied eBEER to the Kepler light curves, identified a sample of bright non-eclipsing binary candidates, and followed three of them with the Wise observatory eShel spectrograph. After confirming the three sy…
Next-generation synoptic photometric surveys will yield unprecedented (for the astronomical community) volumes of data and the processes of discovery and rare-object identification are, by necessity, becoming more autonomous. Such autonomous searches can be used to find objects of interest applicable to a wide range of outstanding problems in astronomy, and in this paper we present the methods and results of a largely autonomous search for highly eccentric detached eclipsing binary systems in the Machine-learned ASAS Classification Catalog. 106 detached eclipsing binaries with eccentricities g…
The recent discovery of long-period eccentric binaries hosting a He-WD or a sdB star has been challenging binary-star modelling. Based on accurate determinations of the stellar and orbital parameters for IP Eri, a K0 + He-WD system, we propose an evolutionary path that is able to explain the observational properties of this system and, in particular, to account for its high eccentricity (0.25). Our scenario invokes an enhanced-wind mass loss on the first red giant branch (RGB) in order to avoid mass transfer by Roche-lobe overflow, where tides systematically circularize the orbit. We explore h…
Stellar-mass binary black holes (BBHs) embedded in active galactic nucleus (AGN) discs are possible progenitors of black-hole mergers detected in gravitational waves by LIGO/VIRGO. To better understand the hydrodynamical evolution of BBHs interacting with the disc gas, we perform a suite of high-resolution 2D simulations of binaries in local disc (shearing-box) models, considering various binary mass ratios, eccentricities and background disc properties. We use the $γ$-law equation of state and adopt a robust post-processing treatment to evaluate the mass accretion rate, torque and energy tran…
We carried out light curve solutions of two eclipsing detached binaries on eccentric orbits observed by Kepler. The orbits and fundamental parameters of KIC 11619964 and KIC 7118545 were determined with a high accuracy by modeling of their photometric data. We found that the temperatures of their components differ by around 2000 K while the radii of their secondaries are more than twice smaller than those of the primaries. We detected a strange "brightening" of KIC 11619964 in the narrow phase range (+-0.0005) around the center of the primary eclipse reaching to 0.018 mag in amplitude. This "m…
Most studies of mass transfer in binary systems assume circular orbits at the onset of Roche lobe overflow. However, there are theoretical and observational indications that mass transfer could occur in eccentric orbits. In particular, eccentricity could be produced via sudden mass loss and velocity kicks during supernova explosions, or Lidov-Kozai (LK) oscillations in hierarchical triple systems, or, more generally, secular evolution in multiple-star systems. However, current analytic models of eccentric mass transfer are faced with the problem that they are only well defined in the limit of …
Eclipsing binaries are observed to have a range of eccentricities and spin-orbit misalignments (stellar obliquities). Whether such properties are primordial, or arise from post-formation dynamical interactions remains uncertain. This paper considers the scenario in which the binary is the inner component of a hierarchical triple stellar system, and derives the requirements that the tertiary companion must satisfy in order to raise the eccentricity and obliquity of the inner binary. Through numerical integrations of the secular octupole-order equations of motion of stellar triples, coupled with…
We present the first modern analysis of two young, eclipsing binaries, EK Cep and HS Her, based on new, ground-based, CCD multicolour light curves as well as the TESS observations, radial velocity curves, and eclipse timing measurements. The orbital and stellar parameters of the stars are determined by Roche modelling, and their evolutionary status is examined using a grid of isochrones and evolutionary tracks. We find that HS Her is 25-32 Myr old and its components are on the zero-age main sequence; at the age of 16-20 Myr, the primary of EK Cep is also on the ZAMS, but its secondary is a pre…
We study the orbital stability of a non-zero mass, close-in circular orbit planet around an eccentric orbit binary for various initial values of the binary eccentricity, binary mass fraction, planet mass, planet semi--major axis, and planet inclination by means of numerical simulations that cover $5 \times 10^4$ binary orbits. For small binary eccentricity, the stable orbits that extend closest to the binary (most stable orbits) are nearly retrograde and circulating. For high binary eccentricity, the most stable orbits are highly inclined and librate near the so-called generalised polar orbit …
We present the apsidal motion and light-curve analyses of 21 eccentric eclipsing binaries located in the Small Magellanic Cloud. Most of these systems have never been studied before, hence their orbital and physical properties as well as the apsidal motion parameters are given here for the first time. All the systems are of early spectral type, having orbital periods up to 4 days. The apsidal motion periods were derived to be from 7.2 to 200 yr (OGLE-SMC-ECL-2194 having the shortest apsidal period among known main-sequence systems). The orbital eccentricities are usually rather mild (median of…
We present an analysis of the apsidal motion and light curve parameters of 54 never-before-studied galactic Algol-type binaries. This is the first analysis of such a large sample of eccentric eclipsing binaries in our Galaxy, and has enabled us to identify several systems that are worthy of further study. Bringing together data from various databases and surveys, supplemented with new observations, we have been able to trace the long-term evolution of the eccentric orbit over durations extending back up to several decades. Our present study explores a rather different sample of stars to those …
It is usually thought that viscous torque works to align a circumbinary disk with the binary's orbital plane. However, recent numerical simulations suggest that the disk may evolve to a configuration perpendicular to the binary orbit ("polar alignment") if the binary is eccentric and the initial disk-binary inclination is sufficiently large. We carry out a theoretical study on the long-term evolution of inclined disks around eccentric binaries, calculating the disk warp profile and dissipative torque acting on the disk. For disks with aspect ratio $H/r$ larger than the viscosity parameter $α$,…
Aims: The Danish 1.54-meter telescope at the La Silla observatory was used for photometric monitoring of selected eccentric eclipsing binaries located in the Small Magellanic Cloud. The new times of minima were derived for these systems, which are needed for accurate determination of the apsidal motion. Moreover, many new times of minima were derived from the photometric databases OGLE and MACHO. Eighteen early-type eccentric-orbit eclipsing binaries were studied. Methods: Their (O-C) diagrams of minima timings were analysed and the parameters of the apsidal motion were obtained. The light cur…
R-mode oscillations in a rotating star produce characteristic signatures in a Fourier amplitude spectrum at frequencies related with the rotation frequency, which can be, in turn, used to obtain the surface rotation rate of the star. Some binary stars observed by Kepler indicate the presence of r~modes that are probably excited by the tidal effect. In this paper, we have obtained stellar rotation periods in 20 eccentric (heartbeat) binaries with r-mode signatures. The majority of the rotation periods are found to be comparable to pseudo-synchronous periods, in which the angular velocity of rot…
Binary post-asymptotic giant branch (post-AGB) stars have orbital periods in the range of 100--2500 days in eccentric orbits. They are surrounded by circumbinary dusty discs. They are the immediate result of unconstrained binary interaction processes. Their observed orbital properties do not correspond to model predictions: Neither the periods nor the high eccentricities are expected. Our goal is to investigate if interactions between a binary and its circumbinary disc during the post-AGB phase can result in their eccentric orbits, while simultaneously explaining the chemical anomaly known as …
Among young binary stars whose magnetospheres are expected to collide, only two systems have been observed near periastron in the X-ray band: the low-mass DQ Tau and the older and more massive HD 152404. Both exhibit elevated levels of X-ray emission at periastron. Our goal is to determine whether colliding magnetospheres in young high-eccentricity binaries commonly produce elevated average levels of X-ray activity. This work is based on Chandra snapshots of multiple periastron and non-periastron passages in four nearby young eccentric binaries (Parenago 523, RX J1622.7-2325 Nw, UZ Tau E, and …
Tidal dissipation due to convective turbulent viscosity shapes the evolution of a variety of astrophysical binaries. For example, this type of dissipation determines the rate of orbital circularization in a binary with a post-main sequence star that is evolving toward a common envelope phase. Viscous dissipation can also influence binaries with solar-type stars, or stars with a close-in giant planet. In general, the effective viscosity in a convective stellar envelope depends on the tidal forcing frequency $ω_{\rm tide}$; when $ω_{\rm tide}$ is larger than the turnover frequency of convective …
Although not nearly as numerous as binaries with two white dwarfs, eccentric neutron star-white dwarf (NS-WD) binaries are important gravitational-wave (GW) sources for the next generation of space-based detectors sensitive to low frequency waves. Here we investigate periastron precession in these sources as a result of general relativistic, tidal, and rotational effects; such precession is expected to be detectable for at least some of the detected binaries of this type. Currently, two eccentric NS-WD binaries are known in the galactic field, PSR J1141-6545 and PSR B2303+46, both of which hav…
Eccentricity and Inclination Excitation of Stellar Orbits around merging Black-Hole Binaries
School of Astronomy and Space Science, Nanjing University（南京大学天文与空间科学学院）；Key Laboratory of Modern Astronomy and Astrophysics in Ministry of Education, Nanjing University（南京大学现代天体学与天体物理教育部重点实验室）
