We present in this paper a first step toward a semi-analytical treatment of the accretion process in wind-fed neutron star supergiant X-ray binaries with eccentric orbits. We consider the case of a spherically symmetric wind for the supergiant star and a simplified model for the accretion onto the compact object. A self-consistent calculation of the photoionization of the stellar wind by the X-rays from the accreting neutron star is included. This effect is convolved with the modulation of the mass accretion rate induced by the eccentric orbit to obtain the expected X-ray luminosity of a system along the orbit. As part of our results, we first show that the bi-modality of low and high X-ray luminosity solutions for supergiant X-ray binaries reported in previous papers is likely to result from the effect of the neutron star approaching first and then moving away from the companion (without coexisting simultaneously). We propose that episodes of strong wind photoionization can give rise to off-states of the sources. Our calculations are applied to the case of a few classical supergiant X-ray binary systems with known eccentricities (Vela X-1, 4U 1907+09, GX 301-2) and to the case of the only supergiant fast X-ray transient with a confirmed eccentric orbit, IGR J08408-4503. The results are compared with observational findings on these sources. We also discuss the next steps needed to expand the calculations toward a more comprehensive treatment in future publications.
We have developed a stellar wind model for OB supergiants to investigate the effects of accretion from a clumpy wind on the luminosity and variability properties of High Mass X-ray Binaries. Assuming that the clumps are confined by ram pressure of the ambient gas and exploring different distributions for their mass and radii, we computed the expected X-ray light curves in the framework of the Bondi-Hoyle accretion theory, modified to take into account the presence of clumps. The resulting variability properties are found to depend not only on the assumed orbital parameters but also on the wind…
The INTEGRAL satellite has revealed a major population of supergiant High Mass X-ray Binaries in our Galaxy, revolutionizing our understanding of binary systems and their evolution. This population, constituted of a compact object orbiting around a massive and luminous supergiant star, exhibits unusual properties, either being extremely absorbed, or showing very short and intense flares. An intensive set of multi-wavelength observations has led us to reveal their nature, and to show that these systems are wind-fed accretors, closely related to massive star-forming regions. In this paper I desc…
Supergiant Fast X-ray Transients (SFXTs) are a new class of High Mass X-ray Binaries, discovered by the INTEGRAL satellite, which display flares lasting from minutes to hours, with peak luminosity of 1E36-1E37 erg/s. Outside the bright outbursts, they show a frequent long-term flaring activity reaching an X-ray luminosity level of 1E33-1E34 erg/s, as recently observed with the Swift satellite. Since a few persistent High Mass X-ray Binaries (HMXBs) with supergiant donors show flares with properties similar to those observed in SFXTs, it has been suggested that the flaring activity in both clas…
It has been proposed multiple times to use the neutron star (NS) in high-mass X-ray binaries (HMXBs) as an orbiting X-ray probe embedded in the wind-fed of its supergiant (SG) companion in order to constrain the stellar line-driven wind from the SG. We demonstrate how to combine various observables of HMXBs from the X-ray accretion luminosity produced by the wind-fed NS, in order to estimate and constrain the age of the donors. This would help us to study the stellar evolution track for each donor model. Since the evolution of massive stars is essentially determined by mass loss, and direct me…
Wind-fed supergiant X-ray binaries are precious laboratories not only to study accretion under extreme gravity and magnetic field conditions, but also to probe still highly debated properties of massive star winds. These includes the so-called clumps, originated from the inherent instability of line driven winds, and larger structures. In this paper, we report on the results of the last (and not yet published) monitoring campaigns that our group has been carrying out since 2007 with both XMM-Newton and the Swift Neil Gehrels observatory. Data collected with the EPIC cameras on-board XMM-Newton…
The long-term X-ray lightcurves of classical supergiant X-ray binaries and supergiant fast X-ray transients show relatively similar super-orbital modulations, which are still lacking a sound interpretation. We propose that these modulations are related to the presence of corotating interaction regions (CIRs) known to thread the winds of OB supergiants. To test this hypothesis, we couple the outcomes of 3-D hydrodynamic models for the formation of CIRs in stellar winds with a simplified recipe for the accretion onto a neutron star. The results show that the synthetic X-ray light curves are inde…
Classical Supergiant X-ray Binaries host a neutron star orbiting a supergiant OB star and display persistent X-ray luminosities of 10$^{35}$ to 10$^{37}$ erg/s. The stellar wind from the massive companion is believed to be the main source of matter accreted by the compact object. With this first paper, we introduce a ballistic model to characterize the structure of the wind at the orbital scale as it accelerates, from the stellar surface to the vicinity of the accretor. Thanks to the parametrization we retained and the numerical pipeline we designed, we can investigate the supersonic flow and …
The usage of cumulative luminosity distributions, constructed thanks to the long-term observations available through wide field hard X-ray imagers, has been recently exploited to study the averaged high energy emission (>17 keV) from Supergiant Fast X-ray Transients (SFXTs) and classical Supergiant High Mass X-ray Binaries (SgXBs). Here, we take advantage of the long term monitorings now available with Swift/XRT to construct for the first time the cumulative luminosity distributions of a number of SFXTs and the classical SgXB IGR J18027-2016 in the soft X-ray domain with a high sensitivity foc…
High Mass X-ray Binaries (HMXB) have been revealed by a wealth of multi-wavelength observations, from X-ray to optical and infrared domain. After describing the 3 different kinds of HMXB, we focus on 3 HMXB hosting supergiant stars: IGR J16320-4751, IGR J16465-4507 and IGR J16318-4848, respectively called "The Good", "The Bad" and "The Ugly". We review in these proceedings what the observations of these sources have brought to light concerning our knowledge of HMXB, and what part still remains in the dark side. Many questions are still pending, related to accretion processes, stellar wind prop…
The accretion of the stellar wind material by a compact object represents the main mechanism powering the X-ray emission in classical supergiant high mass X-ray binaries and supergiant fast X-ray transients. In this work we present the first attempt to simulate the accretion process of a fast and dense massive star wind onto a neutron star, taking into account the effects of the centrifugal and magnetic inhibition of accretion ("gating") due to the spin and magnetic field of the compact object. We made use of a radiative hydrodynamical code to model the non-stationary radiatively driven wind o…
In this review I briefly describe the nature of the three kinds of High-Mass X-ray Binaries (HMXBs), accreting through: (i) Be circumstellar disc, (ii) supergiant stellar wind, and (iii) Roche lobe filling supergiants. A previously unknown population of HMXBs hosting supergiant stars has been revealed in the last years, with multi-wavelength campaigns including high energy (INTEGRAL, Swift, XMM, Chandra) and optical/infrared (mainly ESO) observations. This population is divided between obscured supergiant HMXBs, and supergiant fast X-ray transients (SFXTs), characterized by short and intense X…
Using high-resolution hydrodynamics simulations, we show that equal-mass binaries accreting from a circumbinary disk evolve toward an orbital eccentricity of $e \simeq 0.45$, unless they are initialized on a nearly circular orbit with $e \lesssim 0.08$, in which case they further circularize. The implied bi-modal eccentricity distribution resembles that seen in post-AGB stellar binaries. Large accretion spikes around periapse impart a tell-tale, quasi-periodic, bursty signature on the light curves of eccentric binaries. We predict that intermediate-mass and massive black hole binaries at $z \l…
In young starburst galaxies, the X-ray population is expected to be dominated by the relics of the most massive and short-lived stars, black-hole and neutron-star high mass X-ray binaries (XRBs). In the closest such galaxy, IC 10, we have made a multi-wavelength census of these objects. Employing a novel statistical correlation technique, we have matched our list of 110 X-ray point sources, derived from a decade of Chandra observations, against published photometric data. We report an 8 sigma correlation between the celestial coordinates of the two catalogs, with 42 X-ray sources having an opt…
We have considered the existence of neutron star magnetic field given by the cyclotron lines. We collected the data of 9 sources of high-mass X-ray binaries with supergiant companions as a case of testing our model, to demonstrate their distribution and evolution. The wind velocity, spin period and magnetic field strength are studied under different mass loss rate. In our model, correlations between mass-loss rate and wind velocity are found and can be tested in further observations. We examined the parameter space where wind accretion is allowed, avoiding barrier of rotating magnetic fields, …
We discuss mass transfer in eccentric binaries containing a white dwarf and a neutron star (WD--NS binaries). We show that such binaries are produced from field binaries following a series of mass transfer episodes that allow the white dwarf to form before the neutron star. We predict the orbital properties of binaries similar to the observed WD--NS binary J1141+6545, and show that they will undergo episodic mass transfer from the white dwarf to the neutron star. Furthermore, we describe oil-on-water, a two-phase SPH formalism that we have developed in order to model mass transfer in such bina…
We present a suite of high resolution hydrodynamic simulations of binaries immersed in circumbinary accretion disks (CBDs). For the first time, we investigate the preferential accretion rate as a function of both eccentricity $e_{\rm b}$ and mass ratio $q_{\rm b}$ in a densely sampled parameter space, finding that when compared with circular binaries, mass ratios grow more efficiently in binaries on moderately eccentric orbits ($0.0 \lesssim e_{\rm b} \lesssim 0.4$), and high eccentricities ($e_{\rm b} \gtrsim 0.6 $) suppress mass ratio growth. We suggest that this non-monotonic preferential a…
Massive stars, at least $\sim$ 10 times more massive than the Sun, have two key properties that make them the main drivers of evolution of star clusters, galaxies, and the Universe as a whole. On the one hand, the outer layers of massive stars are so hot that they produce most of the ionizing ultraviolet radiation of galaxies; in fact, the first massive stars helped to re-ionize the Universe after its Dark Ages. Another important property of massive stars are the strong stellar winds and outflows they produce. This mass loss, and finally the explosion of a massive star as a supernova or a gamm…
The INTEGRAL satellite has revealed a major population of supergiant High Mass X-ray Binaries in our Galaxy, revolutionizing our understanding of binary systems and their evolution. This population, constituted of a compact object orbiting around a massive and luminous supergiant star, exhibits unusual properties, either being extremely absorbed, or showing very short and intense flares. An intensive set of multi-wavelength observations has led us to reveal their nature, and to show that these systems are wind-fed accretors, closely related to massive star-forming regions. In this paper I desc…
We describe here the nature, formation and evolution of the supergiant high mass X-ray binary (HMXB) population, i.e. systems accreting the stellar wind of supergiant stars. There are now many new observations, from the high-energy side (mainly from the INTEGRAL satellite), complemented by multi-wavelength observations (mainly in the optical, near and mid-infrared from ESO facilities), showing that a new population of supergiant HMXBs has been recently revealed. We report here on the observational facts about the different categories of HMXBs, allowing to build a consistent scenario explaining…
We report the discovery using data from the Swift Burst Alert Telescope (BAT) of superorbital modulation in the wind-accretion supergiant high-mass X-ray binaries 4U 1909+07 (= X 1908+075), IGR J16418-4532, and IGR J16479-4514. Together with already known superorbital periodicities in 2S 0114+650 and IGR J16493-4348, the systems exhibit a monotonic relationship between superorbital and orbital periods. These systems include both supergiant fast X-ray transients (SFXTs) and classical supergiant systems, and have a range of inclination angles. This suggests an underlying physical mechanism which…
Supergiant High Mass X-ray Binary systems (sgHMXBs) consist of a massive, late type, star and a neutron star. The massive stars exhibits strong, radiatively driven, stellar winds. Wind accretion onto compact object triggers X-ray emission, which alters the stellar wind significantly. Hydrodynamic simulation has been used to study the neutron star - stellar wind interaction it two sgHMXBs: i) A heavily obscured sgHMXB (IGR J17252-3616) discovered by INTEGRAL. To account for observable quantities (i.e., absorbing column density) we have to assume a very slow wind terminal velocity of about 500 k…
The inspiral and merger of eccentric binaries leads to gravitational waveforms distinct from those generated by circularly merging binaries. Dynamical environments can assemble binaries with high eccentricity and peak frequencies within the {\it LIGO} band. In this paper, we study binary-single stellar scatterings occurring in dense stellar systems as a source of eccentrically-inspiraling binaries. Many interactions between compact binaries and single objects are characterized by chaotic resonances in which the binary-single system undergoes many exchanges before reaching a final state. During…
We present preliminary results on Herschel/PACS mid/far-infrared photometric observations of INTEGRAL supergiant High Mass X-ray Binaries (HMXBs), with the aim of detecting the presence and characterizing the nature of absorbing material (dust and/or cold gas), either enshrouding the whole binary systems, or surrounding the sources within their close environment. These unique observations allow us to better characterize the nature of these HMXBs, to constrain the link with their environment (impact and feedback), and finally to get a better understanding of the formation and evolution of such …
In the past fifteen years a new generation of X-ray satellites led to the discovery of a subclass of high-mass X-ray binaries (HMXBs) with supergiant companions and a peculiar transient behaviour: supergiant fast X-ray transients (SFXTs). We calculate the expected number of Galactic SFXTs for the first time, using two different statistical approaches and two sets of data based on Swift and INTEGRAL surveys, with the aim to determine how common the SFXT phenomenon really is. We find that the expected number of SFXTs in the Galaxy is about 37(+53, -22) which shows that SFXTs constitute a large p…
In a recent paper, we determined the measurement accuracy of physical parameters for eccentric, precessing, non-spinning, inspiraling, stellar-mass black hole - black hole (BH-BH) binaries for the upcoming second-generation LIGO/VIRGO/KAGRA detector network at design sensitivity using the Fisher matrix method. Here we extend that study to a wide range of binary masses including neutron star - neutron star (NS-NS), NS-BH, and BH-BH binaries with BH masses up to $110 \, M_{\odot}$. The measurement error of eccentricity $e_{10 \,\rm Hz}$ at a gravitational-wave (GW) frequency of $10 \, {\rm Hz}$ …
Observations with the INTEGRAL satellite have quadrupled the population of supergiant High Mass X-ray Binaries (HMXBs), revealed a previously hidden population of obscured supergiant HMXBs, and allowed the discovery of huge and fast transient flares in supergiant HMXBs. Apart from these 3 observational facts, has INTEGRAL allowed us to better understand these supergiant HMXBs? Do we have now a better understanding of the 3 populations of HMXBs, and of their accretion process, separated in the so-called Corbet diagram? Do we better apprehend the accretion process in the supergiant HMXBs, and wh…
Among the different types of sources shining in the high energy sky, gamma-ray binaries are rapidly becoming the subject of major interest. In fact, in the last few years a number of High Mass X-ray Binaries (HMXBs) have been firmly detected from MeV to TeV energies, providing secure evidences that particles can be efficiently accelerated up to very high energies in such galactic systems. Similarly to this general and emerging class of gamma-ray binaries, in principle Supergiant Fast X-ray Transients (SFXTs) have all the "ingredients" to be transient high energy emitters. In this context, the …
Suzaku observations are presented for the high-mass X-ray binaries IGR J16207-5129 and IGR J17391-3021 (=XTE J1739-302). For IGR J16207-5129, we provide the first X-ray broadband (0.5--60 keV) spectrum from which we confirm a large intrinsic column density (nH = 1.6e23 /cm2), and we constrain the cutoff energy for the first time (Ec = 19 keV). A prolonged (> 30 ks) attenuation of the X-ray flux was observed which we tentatively attribute to an eclipse of the probable neutron star by its massive companion, in a binary system with an orbital period between 4 and 9 days, and inclination angles > …
Binary millisecond pulsars (MSPs) are believed to have descended from low-mass X-ray binaries (LMXBs), which have experienced substantial mass transfer and tidal circularization. Therefore, they should have very circular orbits. However, the discovery of several eccentric binary MSPs (with eccentricity $e\sim 0.01-0.1$) challenges this standard picture. Three models have been proposed thus far based on accretion-induced collapse of massive white dwarfs (WDs), neutron star-strange star transition, and formation of circumbinary disks. All of them are subject to various uncertainties, and are not…
In Supergiant X-ray binaries (SgXB), a compact object captures a fraction of the wind of an O/B supergiant on a close orbit. Proxies exist to evaluate the efficiency of mass and angular momentum accretion but they depend so dramatically on the wind speed that given the current uncertainties, they only set loose constrains. Furthermore, they often bypass the impact of orbital and shock effects on the flow structure. We study the wind dynamics and the angular momentum gained as the flow is accreted. We identify the conditions for the formation of a disc-like structure around the accretor and the…
Distance Estimation and Sky Localization of Eccentric Double White Dwarf Binaries from Gravitational Wave Observations inside Globular Clusters
National Astronomical Observatories, Chinese Academy of Sciences（中国科学院国家天文台）；School of physics and astronomy, Beijing Normal University（北京师范大学物理与天文学院）；Nicolaus Copernicus Astronomical Center, Polish Academy of Sciences（波兰科学院尼古拉·哥白尼天体物理中心）；Department of Physics, Centre for Extragalactic Astronomy, Durham University（杜伦大学系外天文学中心物理系）；School of Astronomy and Space Sciences, University of Chinese Academy of Sciences（中国科学院大学天文与空间科学学院）；International Centre of Supernovae (ICESUN), Yunnan Key Laboratory of Supernova Research, Yunnan Observatories, CAS（中国科学院云南天文台超新星研究云南省重点实验室国际超新星中心）
Evidence for a luminosity-class dichotomy in the supergiant donors of persistent high-mass X-ray binaries and supergiant fast X-ray transients
INAF-IASF Milano, Istituto di Astrofisica Spaziale e Fisica Cosmica（意大利国家天体物理研究所米兰空间天体物理学与宇宙物理学研究所）；INAF-OAS, Osservatorio di Astrofisica e Scienza dello Spazio（意大利国家天体物理研究所太空天体物理学与空间科学观测站）
Supergiant Fast X-ray Transients (SFXTs) represent the most extreme case of X-ray variability in High Mass X-ray Binaries hosting blue supergiant companions. Mainly discovered thanks to the INTEGRAL monitoring of the Galactic plane, these hard X-ray transients display dynamic ranges which can span five orders of magnitude. This intensity variability is associated with accretion onto Galactic compact objects (mostly neutron stars) through a physical mechanism which is still poorly understood. A review of the current status of our understanding on these sources is presented and discussed. Finall…
I present an analytical fit to the duration of the inspiral of two point masses driven by gravitational-wave emission. The fit is accurate to within 3% over the entire range of initial eccentricities from 0 to 0.99999.
Classical Supergiant X-ray Binaries (SGXBs) and Supergiant Fast X-ray Transients (SFXTs) are two types of High-mass X-ray Binaries (HMXBs) that present similar donors but, at the same time, show very different behavior in the X-rays. The reason for this dichotomy of wind-fed HMXBs is still a matter of debate. Among the several explanations that have been proposed, some of them invoke specific stellar wind properties of the donor stars. Only dedicated empiric analysis of the donors' stellar wind can provide the required information to accomplish an adequate test of these theories. However, such…
The Small Magellanic Cloud (SMC) is well known to harbor a large number of High-Mass X-ray Binaries (HMXBs). The identification of their optical counterparts provides information on the nature of the donor stars and can help to constrain the parameters of these systems and their evolution. We obtained optical spectra for a number of HMXBs identified in previous Chandra and XMM-Newton surveys of the SMC using the AAOmega/2dF fiber-fed spectrograph at the Anglo-Australian Telescope. We find 5 new Be/X-ray binaries (BeXRBs; including a tentative one), by identifying the spectral type of their opt…
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…
Compact binaries that emit gravitational waves in the sensitivity band of ground-based detectors can have non-negligible eccentricities just prior to merger, depending on the formation scenario. We develop a purely analytic, frequency-domain model for gravitational waves emitted by compact binaries on orbits with small eccentricity, which reduces to the quasi-circular post-Newtonian approximant TaylorF2 at zero eccentricity and to the post-circular approximation of Yunes et al. (2009) at small eccentricity. Our model uses a spectral approximation to the (post-Newtonian) Kepler problem to model…
We use 2D (axisymmetric) and 3D hydrodynamic simulations to study Bondi-Hoyle-Lyttleton (BHL) accretion with and without transverse upstream gradients. We mainly focus on the regime of high (upstream) Mach number, weak upstream gradients and small accretor size, which is relevant to neutron star (NS) accretion in wind-fed Supergiant X-ray binaries (SgXBs). We present a systematic exploration of the flow in this regime. When there are no upstream gradients, the flow is always stable regardless of accretor size or Mach number. For finite upstream gradients, there are three main types of behavior…
Ultralight bosons can be abundantly produced through superradiance process by a spinning black hole and form a bound state with hydrogen-like spectrum. We show that such a "gravitational atom" typically possesses anomalously large mass quadrupole and leads to significant orbital precession when it forms an eccentric binary with a second compact object. Dynamically formed black hole binaries or pulsar-black hole binaries are typically eccentric during their early inspirals. We show that the large orbital precession can generate distinct and observable signature in their gravitational wave or pu…
In this review I first describe the nature of the three kinds of High-Mass X-ray Binaries (HMXBs), accreting through: (i) Be circumstellar disc, (ii) supergiant stellar wind, and (iii) Roche lobe filling supergiants. I then report on the discovery of two new populations of HMXBs hosting supergiant stars, recently revealed by a wealth of new observations, coming from the high energy side (INTEGRAL, Swift, XMM, Chandra satellites), and complemented by multi-wavelength optical/infrared observations (mainly ESO facilities). The first population is constituted of obscured supergiant HMXBs, the seco…
We investigate how the proximity of supergiant donor stars to the Eddington-limit, and their advanced evolutionary stage, may influence the evolution of massive and ultra-luminous X-ray binaries with supergiant donor stars (SGXBs and ULXs). We construct models of massive stars with different internal hydrogen/helium gradients and different hydrogen-rich envelope masses, and expose them to slow mass loss to probe the response of the stellar radius. In addition, we compute the corresponding Roche-lobe overflow mass-transfer evolution with our detailed binary stellar evolution code, approximating…
Dynamically formed compact object binaries may still be eccentric while in the LIGO/Virgo band. For a neutron star (NS) in an eccentric binary, the fundamental modes (f-modes) are excited at pericenter, transferring energy from the orbit to oscillations in the NS. We model this system by coupling the evolution of the NS f-modes to the orbital evolution of the binary as it circularizes and moves toward coalescence. NS f-mode excitation generally speeds up the orbital decay and advances the phase of the gravitational wave signal from the system. We calculate how this effect changes the timing of…
Mergers of compact binaries, such as binary neutron stars (BNSs), neutron star-black hole binaries (NSBHs), and binary black holes (BBHs), are expected to be the best candidates for the sources of gravitational waves (GWs) and the leading theoretical models for short gamma-ray bursts (SGRBs). Based on the observations of SGRBs, we could derive the merger rates of these compact binaries, and study the stochastic GW backgrounds (SGWBs) or the co-detection rates of GWs associate with SGRBs (GW-SGRBs). But before that, the most important thing is to derive the GW spectrum from a single GW source. …
We determine the ability of Cosmic Explorer, a proposed third-generation gravitational-wave observatory, to detect eccentric binary neutron stars and to measure their eccentricity. We find that for a matched-filter search, template banks constructed using binaries in quasi-circular orbits are effectual for eccentric neutron star binaries with $e_{7} \leq 0.004$ ($e_{7} \leq 0.003$) for CE1 (CE2), where $e_7$ is the binary's eccentricity at a gravitational-wave frequency of 7~Hz. We show that stochastic template placement can be used to construct a matched-filter search for binaries with larger…
We present new numerical-relativity simulations of eccentric merging black holes with initially antiparallel spins lying in the orbital plane (the so-called \emph{superkick} configuration). Binary eccentricity boosts the recoil of the merger remnant by up to $25\%$. The increase in the energy flux is much more modest, and therefore this kick enhancement is mainly due to asymmetry in the binary dynamics. Our findings might have important consequences for the retention of stellar-mass black holes in star clusters and supermassive black holes in galactic hosts.
Due to their small mass, subsolar mass black hole binaries would have to be primordial in origin instead of the result of stellar evolution. Soon after formation in the early universe, primordial black holes can form binaries after decoupling from the cosmic expansion. Alternatively, primordial black holes as dark matter could also form binaries in the late universe due to dynamical encounters and gravitational-wave braking. A significant feature for this channel is the possibility that some sources retain nonzero eccentricity in the LIGO/Virgo band. Assuming all dark matter is primordial blac…
We develop a method to compute low-eccentricity initial data of black hole--neutron star binaries in the puncture framework extending previous work on other types of compact binaries. In addition to adjusting the orbital angular velocity of the binary, the approaching velocity of a neutron star is incorporated by modifying the helical Killing vector used to derive equations of the hydrostationary equilibrium. The approaching velocity of the black hole is then induced by requiring the vanishing of the total linear momentum of the system, differently from the case of binary black holes in the pu…
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…
