Eccentric Binaries Research Articles

Circumbinary Disk Evolution in the Presence of an Outer Companion Star

Abstract We consider a hierarchical triple system consisting of an inner eccentric binary with an outer companion. A highly misaligned circumbinary disk around the inner binary is subject to two competing effects: (i) nodal precession about the inner binary eccentricity vector that leads to an increase in misalignment (polar alignment) and (ii) Kozai–Lidov (KL) oscillations of eccentricity and inclination driven by the outer companion that leads to a reduction in the misalignment. The outcome depends upon the ratio of the timescales of these effects. If the inner binary torque dominates, then the disk aligns to a polar orientation. If the outer companion torque dominates, then the disk undergoes KL oscillations. In that case, the highly eccentric and misaligned disk is disrupted and accreted by the inner binary, while some mass is transferred to the outer companion. However, when the torques are similar, the outer parts of the circumbinary disk can undergo large eccentricity oscillations while the inclination remains close to polar orientation. The range of initial disk inclinations that evolve to a polar orientation is smaller in the presence of the outer companion. Disk breaking is also more likely, at least temporarily, during the polar alignment process. The stellar orbits in HD 98800 have parameters such that polar alignment of the circumbinary disk is expected. In the absence of gas, solid particles are unstable at much smaller radii than the gas-disk inner tidal truncation radius because KL-driven eccentricity leads to close encounters with the binary.

Effective-one-body multipolar waveforms for eccentric binary black holes with nonprecessing spins

We construct an inspiral-merger-ringdown eccentric gravitational-wave (GW) model for binary black holes with non-precessing spins within the effective-one-body formalism. This waveform model, SEOBNRv4EHM, extends the accurate quasi-circular SEOBNRv4HM model to eccentric binaries by including recently computed eccentric corrections up to 2PN order in the gravitational waveform modes, notably the $(l,|m|)=(2,2),(2,1),(3,3),(4,4),(5,5)$ multipoles. The waveform model reproduces the zero eccentricity limit with an accuracy comparable to the underlying quasi-circular model, with the unfaithfulness of $\lesssim1\%$ against quasi-circular numerical-relativity (NR) simulations. When compared against 28 public eccentric NR simulations from the Simulating eXtreme Spacetimes catalog with initial orbital eccentricities up to $e\simeq0.3$ and dimensionless spin magnitudes up to $+0.7$, the model provides unfaithfulness $<1\%$, showing that both the $(2,|2|)$-modes and the higher-order modes are reliably described without calibration to NR datasets in the eccentric sector. The waveform model SEOBNRv4EHM is able to qualitatively reproduce the phenomenology of dynamical captures, and can be extended to include spin-precession effects. It can be employed for upcoming observing runs with the LIGO-Virgo-KAGRA detectors and used to re-analyze existing GW catalogs to infer the eccentricity parameters for binaries with $e\lesssim0.3$ (at 20 Hz or lower) and spins up to $\lesssim 0.9-0.95$. The latter is a promising region of the parameter space where some astrophysical formation scenarios of binaries predict mild eccentricity in the ground-based detectors' bandwidth. Assessing the accuracy and robustness of the eccentric waveform model SEOBNRv4EHM for larger eccentricities and spins will require comparisons with, and, likely, calibration to eccentric NR waveforms in a larger region of the parameter space.

Eccentricity evolution of massive black hole binaries from formation to coalescence

ABSTRACT Coalescing supermassive black hole binaries (BHBs) are expected to be the loudest sources of gravitational waves (GWs) in the Universe. Detection rates for ground or space-based detectors based on cosmological simulations and semi-analytic models are highly uncertain. A major difficulty stems from the necessity to model the BHB from the scale of the merger to that of inspiral. Of particular relevance to the GW merger time-scale is the binary eccentricity. Here, we present a self-consistent numerical study of the eccentricity of BHBs formed in massive gas-free mergers from the early stages of the merger to the hardening phase, followed by a semi-analytical model down to coalescence. We find that the early eccentricity of the unbound black hole pair is largely determined by the initial orbit. It systematically decreases during the dynamical friction phase. The eccentricity at binary formation is affected by stochasticity and noise owing to encounters with stars, but preserves a strong correlation with the initial orbital eccentricity. Binding of the black holes is a phase characterized by strong perturbations; and we present a quantitative definition of the time of binary formation. During hardening the eccentricity increases in minor mergers, unless the binary is approximately circular, but remains largely unchanged in major mergers, in agreement with predictions from semi-analytical models based on isotropic scattering experiments. Coalescence times due to hardening and GW emission in gas-poor non-rotating ellipticals are ≲ 0.5 Gyr for the large initial eccentricities (0.5 ≤ e ≤ 0.9) typical of galaxy mergers in cosmological simulations.

Stellar rotation rates in Kepler eccentric (heartbeat) binaries obtained from r-mode signatures

ABSTRACT 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 rotation is similar to the angular orbital motion of the companion at periastron. In particular, for the heartbeat stars with orbital periods longer than about 8 d, all but one agree with pseudo-synchronous rotation. In contrast to a previous investigation by Zimmerman et al., our result supports the pseudo-synchronisation theory developed by Hut.

Constraining the orbital eccentricity of inspiralling compact binary systems with Advanced LIGO

The detection of ~50 coalescing compact binaries with the Advanced LIGO and Virgo detectors has allowed us to test general relativity, constrain merger rates, and look for evidence of tidal effects, compact object spins, higher waveform modes, and black hole ringdowns. An effect that has not yet been confidently detected is binary eccentricity, which might be present in a small fraction of binaries formed dynamically. Here we discuss general limits on eccentricity that can, in-principle, be placed on all types of compact object binaries by a detector operating at the design sensitivity of Advanced LIGO. Using a post-Newtonian model for gravitational-wave phasing valid in the small eccentricity regime, we assess the relative measurement error for eccentricity for a variety of spinning and non-spinning binaries. Errors and correlations involving the mass and spin parameters are also investigated. We find that decreasing the low frequency limit of a detector's observational frequency band is one of the key design factors for increasing the odds of measuring binary eccentricity. We also introduce and analytically explore the eccentric chirp mass parameter, which replaces the chirp mass as the key measurable parameter combination in eccentric gravitational waveform models. The eccentric chirp mass parameter explains a degeneracy between the chirp mass and the eccentricity. This degeneracy leads to a bias in the standard chirp mass parameter. We also investigate the systematic parameter bias that arises when eccentric systems are recovered using circular waveform templates. We use both Fisher matrix and Bayesian-inference-based Markov Chain Monte Carlo (MCMC) methods to investigate these parameter estimation issues, and we find good agreement between the two approaches (for both statistical and systematic errors) in the appropriate signal-to-noise ratio regime. (abridged)

Study of 72 Pulsars Discovered in the PALFA Survey: Timing Analysis, Glitch Activity, Emission Variability, and a Pulsar in an Eccentric Binary

Abstract We present new discoveries and results from long-term timing of 72 pulsars discovered in the Pulsar Arecibo L-band Feed Array (PALFA) survey, including precise determination of astrometric and spin parameters, and flux density and scatter broadening measurements at 1.4 GHz. Notable discoveries include two young pulsars (characteristic ages ∼30 kyr) with no apparent supernova remnant associations, three mode-changing, 12 nulling and two intermittent pulsars. We detected eight glitches in five pulsars. Among them is PSR J1939+2609, an apparently old pulsar (characteristic age ∼1 Gy), and PSR J1954+2529, which likely belongs to a newly emerging class of binary pulsars. The latter is the only pulsar among the 72 that is clearly not isolated: a nonrecycled neutron star with a 931 ms spin period in an eccentric (e = 0.114) wide (P b = 82.7 days) orbit with a companion of undetermined nature having a minimum mass of ∼0.6 M ⊙. Since operations at Arecibo ceased in 2020 August, we give a final tally of PALFA sky coverage, and compare its 207 pulsar discoveries to the known population. On average, they are 50% more distant than other Galactic plane radio pulsars; PALFA millisecond pulsars (MSPs) have twice the dispersion measure per unit spin period than the known population of MSP in the plane. The four intermittent pulsars discovered by PALFA more than double the population of such objects, which should help to improve our understanding of pulsar magnetosphere physics. The statistics for these, rotating radio transients, and nulling pulsars suggest that there are many more of these objects in the Galaxy than was previously thought.

An Efficient Signal-to-noise Approximation for Eccentric Inspiraling Binaries

Abstract Eccentricity has emerged as a potentially useful tool for helping to identify the origin of black hole mergers. However, eccentric templates can be computationally very expensive owing to the large number of harmonics, making statistical analyses to distinguish formation channels very challenging. We outline a method for estimating the signal-to-noise ratio (S/N) for inspiraling binaries at lower frequencies such as those proposed for LISA and DECIGO. Our approximation can be useful more generally for any quasi-periodic sources. We argue that surprisingly, the S/N evaluated at or near the peak frequency (of the power) is well approximated by using a constant-noise curve, even if in reality the noise strain has power-law dependence. We furthermore improve this initial estimate over our previous calculation to allow for frequency dependence in the noise to expand the range of eccentricity and frequency over which our approximation applies. We show how to apply this method to get an answer accurate to within a factor of 2 over almost the entire projected observable frequency range. We emphasize this method is not a replacement for detailed signal processing. The utility lies chiefly in identifying theoretically useful discriminators among different populations and providing fairly accurate estimates for how well they should work. This approximation can furthermore be useful for narrowing down parameter ranges in a computationally economical way when events are observed. We furthermore show a distinctive way to identify events with extremely high eccentricity where the signal is enhanced relative to naive expectations on the high-frequency end.

Dynamical tides in eccentric binaries containing massive main-sequence stars: analytical expressions

ABSTRACT 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 to study the spin and orbital evolution of eccentric binaries containing massive MS stars, such as the progenitors of merging neutron star binaries. Applying our results to the PSR J0045-7319 system, which has a massive B-star companion and an observed, rapidly decaying orbit, we find that for the standard radius of convective core based on non-rotating stellar models, the B-star must have a significant retrograde and differential rotation in order to explain the observed orbital decay rate. Alternatively, we suggest that the convective core may be larger as a result of rapid stellar rotation and/or mass transfer to the B-star in the recent past during the post-MS evolution of the pulsar progenitor.

Planet–planet scattering in presence of a companion star

ABSTRACT Planet–planet (P–P) scattering is a leading dynamical mechanism invoked to explain the present orbital distribution of exoplanets. Many stars belong to binary systems; therefore, it is important to understand how this mechanism works in the presence of a companion star. We focus on systems of three planets orbiting the primary star and estimate the time-scale for instability, finding that it scales with the Keplerian period for systems that have the same ratio between inner planet and binary semimajor axes. An empirical formula is also derived from simulations to estimate how the binary eccentricity affects the extent of the stability region. The presence of the secondary star affects the P–P scattering outcomes, causing a broadening of the final distribution in semimajor axis of the inner planet as some of the orbital energy of the planets is absorbed by the companion star. Repeated approaches to the secondary star also cause a significant reduction in the frequency of surviving two-planet systems in particular for larger values of the inner planet semimajor axis. The formation of Kozai states with the companion star increases the number of planets that may be tidally circularized. To predict the possible final distribution of planets in binaries, we have performed a large number of simulations where the initial semimajor axis of the inner planets is chosen randomly. For small values of the binary semimajor axis, the higher frequency of collision alters the final planet orbital distributions that, however, beyond 50 au appear to be scalable to wider binary separations.

Constraints on ultra-low-frequency gravitational waves from an eccentric supermassive black hole binary

ABSTRACT Millisecond pulsars with highly stable periods can be considered as very precise clocks and can be used for pulsar timing arrays (PTAs), which attempt to detect nanohertz gravitational waves (GWs) directly. The main sources of nanohertz GWs are supermassive black hole (SMBH) binaries with sub-parsec-scale orbits. On the other hand, an SMBH binary in an earlier phase with a parsec-scale orbit emits ultra-low-frequency ($\lesssim 10^{-9}\, \mathrm{Hz}$) GWs and cannot be detected with the conventional PTA methodology. Such binaries tend to attain high eccentricity, possibly ∼0.9. In this paper, we develop a formalism for extending the constraints on GW amplitudes from single sources obtained by PTAs toward ultra-low frequencies considering the waveform expected from an eccentric SMBH binary. GWs from eccentric binaries are contributed from higher harmonics and therefore have a different waveform to those from circular binaries. Furthermore, we apply our formalism to several hypothetical SMBH binaries at the centre of nearby galaxies, including M87, using the constraints from NANOGrav’s 11-yr data set. For a hypothetical SMBH binary at the centre of M87, the typical upper limit on the mass ratio is 0.16 for an eccentricity of 0.9 and a semimajor axis of a = 1 pc, assuming the binary phase to be the pericentre.

Effective chirp mass in the inspiral frequency evolution of the nonspinning eccentric compact binary

Compact binary systems with black holes are the primary sources of interferometric advanced gravitational wave detectors. Astrophysical models suggest finite possibility of binary systems with appreciable non-zero eccentricity in the dense stellar environment like globular clusters and galactic nuclei. While most of the compact binary measurements have not shown appreciable eccentricity, constrains on the eccentricity have been placed on few detected events. With increasing sensitivity of the gravitational wave detectors, the eccentric binaries are plausible sources in the gravitational wave window. Nevertheless, the challenges in the waveform modelling for high values of eccentricity constrain both the search methodologies of eccentric system as well as parameter estimation of the eccentricity. Waveform independent approaches are being investigated. In this work, we demonstrate that a new effective chirp mass $\mathcal{M}_e$ parameter can be defined which governs the dynamics of the non-spinning eccentric compact binary system. We obtain the phenomenological model of the same for low to moderate eccentricity values. One direct implication is its application in the unmodelled searches and as an another implication, we demonstrate that this model can be used to constrain the eccentricity of the non-spinning eccentric binaries in the advanced detector era in the waveform model-independent way.

Orbital dynamics of two circumbinary planets around misaligned eccentric binaries

ABSTRACT We investigate the orbital dynamics of circumbinary planetary systems with two planets around a circular or eccentric orbit binary. The orbits of the two planets are initially circular and coplanar to each other, but misaligned with respect to the binary orbital plane. The binary–planet and planet–planet interactions result in complex planet tilt oscillations. We use analytical models and numerical simulations to explore the effects of various values of the planet semimajor axes, binary eccentricity, and initial inclination. Around a circular orbit binary, secular tilt oscillations are driven by planet–planet interactions and are periodic. In that case, planets undergo mutual libration if close together and circulation if far apart with an abrupt transition at a critical separation. Around an eccentric orbit binary, secular tilt oscillations are driven by both planet–planet interactions and binary–planet interactions. These oscillations generally display more than one frequency and are generally not periodic. The transition from mutual planet libration to circulation is not sharp and there is a range of separations for which the planets are on orbits that are sometimes mutually librating and sometimes circulating. In addition, at certain separations, there are resonances for which tilt oscillations are complicated but periodic. For planets that are highly misaligned with respect to an eccentric orbit binary, there are stationary (non-oscillating) tilt configurations that are generalizations of polar configurations for the single planet case. Tilt oscillations of highly inclined planets occur for initial tilts that depart from the stationary configuration.

Probing Ultralight Bosons with Compact Eccentric Binaries

Abstract 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 pulsar timing signals.

An Improved Numerical Fit to the Peak Harmonic Gravitational Wave Frequency Emitted by an Eccentric Binary

Abstract I present a numerical fit to the peak harmonic gravitational wave frequency emitted by an eccentric binary system in the post-Newtonian approximation. This fit significantly improves upon a previous commonly-used fit in population synthesis studies, in particular for eccentricities ≲0.8.

Barrel Instability in Binary Asteroids

Abstract Most close-in planetary satellites are in synchronous rotation, which is usually the stable end-point of tidal despinning. Saturn’s moon Hyperion is a notable exception by having a chaotic rotation. Hyperion’s dynamical state is a consequence of its high eccentricity and its highly prolate shape. As many binary asteroids also have elongated secondaries, chaotic rotation is expected for moons in eccentric binaries, and a minority of asteroidal secondaries may be in that state. The question of secondary rotation is also important for the action of the binary Yarkovsky–O’Keefe–Radzievskii–Paddack (BYORP) effect, which can quickly evolve orbits of synchronous (but not nonsynchronous) secondaries. Here we report results of a large set of short numerical simulations which indicate that, apart from synchronous and classic chaotic rotation, close-in irregularly shaped asteroidal secondaries can occupy an additional, intermediate rotational state. In this “barrel instability” the secondary slowly rolls along its long axis, while the longest axis is staying largely aligned with the primary–secondary line. This behavior may be more difficult to detect through lightcurves than a fully chaotic rotation, but would likewise shut down BYORP. We show that the binary’s eccentricity, separation measured in secondary’s radii and the secondary’s shape are all important for determining whether the system settles in synchronous rotation, chaotic tumbling, or barrel instability. We compare our results for synthetic asteroids with known binary pairs to determine which of these behaviors may be present in the near-Earth asteroid binary population.

Method for detecting highly eccentric binaries with a gravitational wave burst search

Detection of gravitational waves (GW) from highly eccentric binary black hole (BBH) systems can provide insight into their dynamics and formation. To date, all of the LIGO-Virgo BBH detections have been made using quasi-circular templates in their initial discovery. However, recent studies have found some of these systems to be compatible with high eccentricity in the LIGO band, $e_{10 \textrm{Hz}} > 0.1$, possibly pointing to a population of sources that are challenging to detect. Current low-latency search methods used with ground-based GW detector data are not well equipped to detect highly eccentric sources. Template-based, matched-filter searches require accurate eccentric waveform models that are computational expensive. Unmodeled burst searches are designed to detected localized excess power and are unable to identify multiple isolated bursts, as would originate from a single highly eccentric BBH. Therefore, we propose a signal-based prior that can be incorporated into an existing GW burst search to target highly eccentric BBHs. Our eccentric burst prior is based on the Newtonian burst model described by Loutrel & Yunes (2017). As a proof of concept, we test our method on simulated data and find that for intermediate SNR $\sim3-6$ signals using the eccentric burst prior more effectively localizes GW bursts when compared to a uniform prior.

An Accurate Analytical Fit to the Gravitational-wave Inspiral Duration for Eccentric Binaries

Abstract 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.

Dust traffic jams in inclined circumbinary protoplanetary discs – I. Morphology and formation theory

ABSTRACT Gas and dust in inclined orbits around binaries experience precession induced by the binary gravitational torque. The difference in precession between gas and dust alters the radial drift of weakly coupled dust and leads to density enhancements where the radial drift is minimized. We explore this phenomenon using 3D hydrodynamical simulations to investigate the prominence of these ‘dust traffic jams’ and the evolution of the resulting dust sub-structures at different disc inclinations and binary eccentricities. We then derive evolution equations for the angular momentum of warped dust discs and implement them in a 1D code and present calculations to further explain these traffic jams. We find that dust traffic jams in inclined circumbinary discs provide significant dust density enhancements that are long lived and can have important consequences for planetesimal formation.

Formation of Polar Terrestrial Circumbinary Planets

Abstract All circumbinary planets (CBPs) currently detected are in orbits that are almost coplanar to the binary orbit. While misaligned CBPs are more difficult to detect, observations of polar-aligned circumbinary gas and debris disks around eccentric binaries suggest that polar planet formation may be possible. A polar-aligned planet has a stable orbit that is inclined by 90° to the orbital plane of the binary with an angular momentum vector that is aligned to the binary eccentricity vector. With n-body simulations we model polar terrestrial planet formation using hydrodynamic gas disk simulations to motivate the initial particle distribution. Terrestrial planet formation around an eccentric binary is more likely in a polar alignment than in a coplanar alignment. Similar planetary systems form in a polar alignment around an eccentric binary and a coplanar alignment around a circular binary. The polar planetary systems are stable even with the effects of general relativity. Planetary orbits around an eccentric binary exhibit tilt and eccentricity oscillations at all inclinations; however, the oscillations are larger in the coplanar case than the polar case. We suggest that polar-aligned terrestrial planets will be found in the future.

Eccentric binary neutron star search prospects for Cosmic Explorer

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 eccentricities and construct an effectual template bank for binaries with $e_{7} \leq 0.05$. We show that the computational cost of both the search for binaries in quasi-circular orbits and eccentric orbits is not significantly larger for Cosmic Explorer than for Advanced LIGO and is accessible with present-day computational resources. We investigate Cosmic Explorer's ability to distinguish between circular and eccentric binaries. We estimate that for a binary with a signal-to-noise ratio of 8 (800), Cosmic Explorer can distinguish between a circular binary and a binary with eccentricity $e_7 \gtrsim 10^{-2}$ ($10^{-3}$) at 90% confidence.