Initial Eccentricity Research Articles

Mapping eccentricity evolutions between numerical relativity and effective-one-body gravitational waveforms

Orbital eccentricity in compact binaries is considered to be a key tracer of their astrophysical origin, and can be inferred from gravitational-wave observations due to its imprint on the emitted signal. For a robust measurement, accurate waveform models are needed. However, ambiguities in the definition of eccentricity can obfuscate the physical meaning and result in seemingly discrepant measurements. In this work we present a suite of 28 new numerical relativity simulations of eccentric, aligned-spin binary black holes with mass ratios between 1 and 6 and initial post-Newtonian eccentricities between 0.05 and 0.3. We then develop a robust pipeline for measuring the eccentricity evolution as a function of frequency from gravitational-wave observables that is applicable even to signals that span at least ≳7 orbits. We assess the reliability of our procedure and quantify its robustness under different assumptions on the data. Using the eccentricity measured at the first apastron, we initialize effective-one-body waveforms and quantify how the precision in the eccentricity measurement, and therefore the choice of the initial conditions, impacts the agreement with the numerical data. We find that even small deviations in the initial eccentricity can lead to non-negligible differences in the phase and amplitude of the waveforms. However, we demonstrate that we can reliably map the eccentricities between the simulation data and analytic models, which is crucial for robustly building eccentric hybrid waveforms, and to improve the accuracy of eccentric waveform models in the strong-field regime. Published by the American Physical Society 2024

Horizon fluxes of binary black holes in eccentric orbits

We compute the rate of change of mass and angular momentum of a black hole, namely tidal heating, in an eccentric orbit. The change is caused due to the tidal field of the orbiting companion. We compute the result for both the spinning and non-spinning black holes in the leading order of the mean motion, namely ξ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\xi $$\\end{document}. We demonstrate that the rates get enhanced significantly for nonzero eccentricity. Since eccentricity in a binary evolves with time we also express the results in terms of an initial eccentricity and azimuthal frequency ξϕ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\xi _{\\phi }$$\\end{document}. In the process, we developed a prescription that can be used to compute all physical quantities in a series expansion of initial eccentricity, e0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$e_0$$\\end{document}. These results are computed taking account of the spin of the binary components. The prescription can be used to compute very high-order corrections of initial eccentricity. We use it to find the contribution to eccentricity up to O(e05)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\mathcal {O}}(e_0^5)$$\\end{document} in the spinning binary. Using the computed expression of eccentricity, we derived the rate of change of mass and angular momentum of a black hole, both rotating and non-rotating, in terms of initial eccentricity and azimuthal frequency up to O(e06)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\mathcal {O}}(e_0^6)$$\\end{document}. With the computed fluxes we also compute for the first time the leading order dephasing in both cases analytically up to O(e06)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\mathcal {O}}(e_0^6)$$\\end{document} and study its impact. We argue that for high signal-to-noise ratio sources, these contributions require inclusion in the waveform modeling.

Eccentricity effects on the supermassive black hole gravitational wave background

We studied how eccentricity affects the gravitational wave (GW) spectrum from supermassive black hole (SMBH) binaries. We developed a fast and accurate semi-analytic method for computing the GW spectra, the distribution for the spectral fluctuations and the correlations between different frequencies. As GW emission circularizes binaries, the suppression of the signal strength due to eccentricity is relevant for signals from wider binaries emitting at lower frequencies. Such a feature is present in the signal observed at pulsar timing arrays. We found that when orbital decay of the SMBH binaries is driven by GWs only, the shape of the observed signal preferred highly eccentric binaries $ e nHz $. However, when environmental effects were included, the initial eccentricity could be significantly lowered, yet the scenario with purely circular binaries was still mildly disfavored.

Analysis and Simulation of Spur Gear System Considering Geometric Eccentricity

Geometric eccentricity errors inevitably occur in gear systems, resulting in the center of mass and center of rotation not coinciding. During the gear meshing process, the gear center distance and gear tooth meshing condition will change with time. In this paper, a model considering geometric eccentricity is proposed and a finite element model of the gear pair is developed. Finally, the dynamic response under different eccentricity and initial eccentricity angle is discussed. Based on Ansys, the simulation calculation of the gear pair is carried out, and the equivalent force maps of the dangerous areas of the gear tooth flanks are obtained.

Signatures of circumbinary disc dynamics in multimessenger population studies of massive black hole binaries

ABSTRACT We investigate the effect of the cutting-edge circumbinary disc (CBD) evolution models on massive black hole binary (MBHB) populations and the gravitational wave background (GWB). We show that CBD-driven evolution leaves a tell-tale signature in MBHB populations, by driving binaries towards an equilibrium eccentricity that depends on the binary mass ratio. We find high orbital eccentricities ($e_{\rm b} \sim 0.5$) as MBHBs enter multimessenger observable frequency bands. The CBD-induced eccentricity distribution of MBHB populations in observable bands is independent of the initial eccentricity distribution at binary formation, erasing any memory of eccentricities induced in the large-scale dynamics of merging galaxies. Our results suggest that eccentric MBHBs are the rule rather than the exception in upcoming transient surveys, provided that CBDs regularly form in MBHB systems. We show that the GWB amplitude is sensitive to CBD-driven preferential accretion onto the secondary, resulting in an increase in GWB amplitude $A_{\rm yr^{-1}}$ by over 100 per cent with just 10 per cent Eddington accretion. As we self-consistently allow for binary hardening and softening, we show that CBD-driven orbital expansion does not diminish the GWB amplitude, and instead increases the amplitude by a small amount. We further present detection rates and population statistics of MBHBs with $M_{\rm b} \gtrsim 10^6 \, {\rm M}_{\odot }$ in Laser Interferometer Space Antenna, showing that most binaries have equal mass ratios and can retain residual eccentricities up to $e_{\rm b} \sim 10^{-3}$ due to CBD-driven evolution.

Listening to dark sirens from gravitational waves : Combined effects of fifth force, ultralight particle radiation, and eccentricity

We analyse the orbital period decay in compact binary systems influenced by a fifth force and ultralight particle radiation, considering a general eccentric Keplerian orbit. The analysis provides constraints on the axion decay constant when orbital period decay involves axionic fifth force and axion radiation. The bound on axion coupling improves by an order of magnitude for high eccentricity binaries like the Hulse–Taylor binary. These bounds become stronger when considering both axion mediation and radiation. We also derive constraints on the strengths of the fifth force and radiation from GW170817 by measuring the Chirp mass, which depends on initial eccentricity. The coalescence time increases with higher initial eccentricity compared to the gravity-only scenario, highlighting the importance of accurately selecting initial eccentricity for setting bounds on fifth force searches in precision gravitational wave detection. Additionally, we provide model-independent estimates for dark matter capture by a binary system. The derived constraints can be further strengthened with the use of second and third generation gravitational wave detectors.

The behaviour of eccentric sub-pc massive black hole binaries embedded in massive discs

Using the 3D smoothed-particle hydrodynamics code PHANTOM, we investigated the evolution of the orbital properties of massive black hole binaries embedded in massive discs where gravitational instabilities (GIs) triggered by the disc’s self-gravity are the only significant source of angular momentum transport. In particular, we investigated the evolution of binaries with different initial eccentricities of e0 = 0.05, 0.5, 0.8 and mass ratios of q = 0.1, 0.3, 0.9. Previous studies indicate an equilibrium eccentricity of around 0.6 < e < 0.8, where the binary tidal torques and disc self-gravity torque are in dynamical balance. Our simulations suggest that there might not be a universal value of critical eccentricity. We find that binaries that are initially more eccentric attain higher asymptotic eccentricity than more circular ones do. This implies that there is a range of critical eccentricity values that depend on the initial condition and microphysics (initial eccentricity, mass ratio, cooling) of the system. In particular, we find the width of this range to be narrower for more unequal binaries. We furthermore measured preferential accretion on one of the binary components, only finding more accretion onto the primary for the mass ratio q = 0.3 and eccentricity e = 0.8. We discuss how this might have implications for the amplitude of the gravitational wave background detected by pulsar timing array (PTA) experiments. We finally measure the corresponding value of the viscosity parameter α due to GIs in our simulations and discuss how this depends on the binary properties.

Measuring eccentricity and gas-induced perturbation from gravitational waves of LISA massive black hole binaries

ABSTRACT We assess the possibility of detecting both eccentricity and gas effects (migration and accretion) in the gravitational wave (GW) signal from LISA massive black hole binaries at redshift $z=1$. Gas induces a phase correction to the GW signal with an effective amplitude ($C_{\rm g}$) and a semimajor axis dependence (assumed to follow a power-law with slope $n_{\rm g}$). We use a complete model of the LISA response and employ a gas-corrected post-Newtonian inspiral-only waveform model TaylorF2Ecc. By using the Fisher formalism and Bayesian inference, we constrain $C_{\rm g}$ together with the initial eccentricity $e_0$, the total redshifted mass $M_z$, the primary-to-secondary mass ratio q, the dimensionless spins $\chi _{1,2}$ of both component BHs, and the time of coalescence $t_c$. We find that simultaneously constraining $C_{\rm g}$ and $e_0$ leads to worse constraints on both parameters with respect to when considered individually. For a standard thin viscous accretion disc around $M_z=10^5~{\rm M}_{\odot }$, $q=8$, $\chi _{1,2}=0.9$, and $t_c=4$ years MBHB, we can confidently measure (with a relative error of $\lt 50$ per cent) an Eddington ratio ${\rm f}_{\rm Edd}\sim 0.1$ for a circular binary and ${\rm f}_{\rm Edd}\sim 1$ for an eccentric system assuming $\mathcal {O}(10)$ stronger gas torque near-merger than at the currently explored much-wider binary separations. The minimum measurable eccentricity is $e_0\gtrsim 10^{-2.75}$ in vacuum and $e_0\gtrsim 10^{-2}$ in gas. A weak environmental perturbation (${\rm f}_{\rm Edd}\lesssim 1$) to a circular binary can be mimicked by an orbital eccentricity during inspiral, implying that an electromagnetic counterpart would be required to confirm the presence of an accretion disc.

Dynamical evolution timescales for the triple supermassive black hole system in NGC 6240

Aims. Based on the available observational data from the literature, we analysed the dynamics of the NGC 6240 galaxy central supermassive black hole (SMBH) system. Methods. For the dynamical modelling of this triple SBMH system, we used the massively parallel and GPU accelerated φ-GPU direct summation N-body code. Following a long-timescale modelling of the triple system, we carried out a very detailed time output analysis of the von Zeipel–Lidov–Kozai (ZLK) oscillations for the black holes. Results. According to our Newtonian simulation results, for all models and randomisations, the bound system from S1+S2 components formed at ≈3.6 Myr. The formation of the bound hierarchical triple system S+N occurred at ≈18 Myr. Over the course of these Newtonian simulations of the evolution of the triple SMBH system and the surrounding environment in NGC 6240, ZLK oscillations were detected (in most cases) for the binary components. The inclination angle between the orbital angular momentum of binary components aptly coincides with the theoretical calculations of the ZLK mechanism. Conclusions. In our set of randomised 15 Newtonian N-body dynamical galaxy models in 13 systems, we were able to detect a ZLK mechanism. In contrast, our extra few-body post-Newtonian runs (for one randomisation case) show it is only for the large inner binary initial eccentricity (in our case ≳0.9) that we are able to observe the possibility of the inner binary merging, due to the post-Newtonian energy radiation effects. For the lower eccentricity cases, the test runs show no sign of possible merging or any ZLK oscillations in the system.

Eccentricity evolution of PTA sources from cosmological initial conditions

ABSTRACT Recent results from pulsar timing arrays (PTAs) show evidence for a gravitational wave background (GWB) consistent with a population of unresolved supermassive black hole (SMBH) binaries (BHBs). While the data do not yet constrain the slope of the spectrum, this appears to flatten at the lowest frequencies, deviating from the power-law shape expected for circular binaries evolving solely due to gravitational wave (GW) emission. Interestingly, such flattening can be explained with a population of eccentric rather than circular binaries. The eccentricity of BHBs is notoriously difficult to predict based simply on the parameters of the host galaxies and the initial galactic orbit, as it is subject to stochastic effects. We study the evolution of the eccentricity of BHBs formed in galactic mergers with cosmological initial conditions from pairing to coalescence, with a focus on potential PTA sources. We select galactic mergers from the IllustrisTNG100-1 simulation and re-simulate them at high resolution with the N-body code griffin down to binary separations of the order of a parsec. We then estimate coalescence time-scales with a semi-analytical model of the evolution under the effects of GW emission and stellar hardening. We find that most mergers in IllustrisTNG100-1 occur on highly eccentric orbits, and that the eccentricity of BHBs at binary formation correlates with the initial eccentricity of the merger, if this is no larger than approximately 0.9. For extremely eccentric mergers, the binaries tend to form with modest eccentricities. We discuss the implications of these results on the interpretation of the observed GWB.

Gravitational radiation from eccentric binary black hole system in dynamical Chern-Simons gravity

Dynamical Chern-Simons (DCS) gravity, a typical parity-violating gravitational theory, modifies both the generation and propagation of gravitational waves from general relativity (GR). In this work, we derive the gravitational waveform radiated from a binary slowly-rotating black hole system with eccentric orbits under the spin-aligned assumption in the DCS theory. Compared with GR, DCS modification enters the second-order post-Newtonian (2PN) approximation, affecting the spin-spin coupling and monopole-quadrupole coupling of binary motion. This modification produces an extra precession rate of periastron. This effect modulates the scalar and gravitational waveform through a quite low frequency. Additionally, the dissipation of conserved quantities results in the secular evolution of the semimajor axis and the eccentricity of binary orbits. Finally, the frequency-domain waveform is given in the post-circular scheme, requiring the initial eccentricity to be ≲ 0.3. This ready-to-use template will benefit the signal searches and improve the future constraint on DCS theory.

Individual chaotic behaviour of the S-stars in the Galactic centre

Located at the core of the Galactic centre, the S-star cluster serves as a remarkable illustration of chaos in dynamical systems. The long-term chaotic behaviour of this system can be studied with gravitational N-body simulations. By applying a small perturbation to the initial position of star S5, we can compare the evolution of this system to its unperturbed evolution. This results in two solutions that diverge exponentially, defined by the separation in position space δr, with an average Lyapunov timescale of ∼420 yr, corresponding to the largest positive Lyapunov exponent. Even though the general trend of the chaotic evolution is governed in part by the supermassive black hole Sagittarius A∗ (Sgr A∗), individual differences between the stars can be noted in the behaviour of their phase-space curves. We present an analysis of the individual behaviour of the stars in this Newtonian chaotic dynamical system. The individuality of their behaviour is evident from offsets in the position space separation curves of the S-stars and the black hole. We propose that the offsets originate from the initial orbital elements of the S-stars, where Sgr A∗ is considered in one of the focal points of the Keplerian orbits. Methods were considered to find a relation between these elements and the separation in position space. Symbolic regression provides the clearest diagnostics for finding an interpretable expression for the problem. Our symbolic regression model indicates that ⟨δr⟩ ∝ e2.3, implying that the time-averaged individual separation in position space increases rapidly with the initial eccentricity of the S-stars.

MAGICS I. The First Few Orbits Encode the Fate of Seed Massive Black Hole Pairs

The elusive massive black hole (MBH) seeds stand to be revealed by the Laser Space Antenna Interferometer through mergers. As an aftermath of galaxy mergers, MBH coalescence is a vastly multi-scale process connected to galaxy formation. We introduce the “Massive black hole Assembly in Galaxies Informed by Cosmological Simulations” (MAGICS) suite, with galaxy/MBH properties and orbits recovered from large-volume cosmological simulation ASTRID. The simulations include subgrid star formation, supernovae feedback, and MBH accretion/feedback. In this first suite, we extract fifteen representative galaxy mergers with seed MBHs to examine their dynamics at an improved mass and spatial resolution (by ∼2000 and ∼20) and follow MBH orbits down to ∼10pc. We find that the seed MBH energy loss and orbital decay are largely governed by global torques induced by the galaxy merger process on scales resolvable by cosmological simulations. Specifically, pairs sink quickly if their orbits shrink rapidly below 1kpc during the first ∼200Myr of pairing due to effective energy loss in major galaxy mergers, whereas MBHs gaining energy in minor galaxy mergers with head-on collisions are likely to stall. High initial eccentricities ( einit>0.5) and high stellar densities at kpc scales ( ρstar>0.05M⊙/pc3) also lead to most efficient decays. ∼50% high-redshift seed MBH pairs experience consecutive galaxy mergers and are more likely to stall at ∼1kpc. For a subset of systems, we carry out N-Body re-simulations until binary formation and find that some stalled systems merge at high-z when embedded in sufficient nuclear star clusters.

The eccentricity growth phenomenon for MEO navigation satellites

Lunisolar resonances shape the dynamics in the MEO region and have the effect of increasing an object’s eccentricity possibly up to a value so high that the orbit’s perigee reaches the atmosphere and friction determines the re-entry. The focus of this paper is the eccentricity growth phenomenon observed for navigation satellites. In particular, starting from a secular Hamiltonian model, analytical estimates for the maximum eccentricity reachable along an inclination-only dependent lunisolar resonance are derived as a function of the initial inclination. Also, trajectories that minimize an object’s lifetime are studied, and analytical estimates for such a minimum lifetime are provided as a function of the initial eccentricity of the object. In addition, lifetime cartography maps are presented in the plane of the argument of perigee and the longitude of the ascending node.

Gravitational waves with dark matter minispikes: Fourier-domain waveforms of eccentric intermediate-mass-ratio-inspirals

Abstract An intermediate mass black hole (IMBH) may have a dark matter (DM) minihalo around it and develop a spiky structure called DM minispike. Gravitational waves (GWs) can be produced if a stellar compact object, such as a black hole (BH) or neutron star, inspirals into the IMBH. This kind of systems are known as itermediate-mass-ratio-inspirals (IMRIs) and may be observed by space-based gravitational wave detectors including LISA, Taiji and Tianqin. In this paper, we lay the foundations for the construction of analytic expressions for Fourier-domain gravitational waves produced by eccentric IMRIs with DM minispikes in a post-circular or small-eccentricity approximation (e < 0.4). We take the effect of dynamical friction from the DM as a perturbation, and decompose the dynamical equations into perturbed part and unperturbed part. The equations are solved in a series expansion form about zero initial eccentricity to eighth order. The time-dependent, “plus” and “cross” polarizations are expanded in Bessel functions, which are then self-consistently reexpanded in a power series about zero initial eccentricity. The stationary-phase approximation is then employed to obtain the explicit DM-modified analytic expressions for the Fourier transform of the post-circular expanded, time-domain signal. We exemplify this framework by considering a typical IMRI with a DM minispike and find the GW detectability strongly depends on the radial profile of the DM distribution. When the density of DM is large enough, the signal to noise ratio (SNR) will be degraded significantly and a detection loss may occur if we use a template without the effect of DM to treat a signal including the DM effect. With the Fourier-domain gravitational waveforms we also estimate the accuracy of the measurement of the DM minispike parameters in our reference model. Our framework hold the promise to construct a “ready-to-use” Fourier-domain waveforms for data analysis of eccentric IMRIs with DM minispikes.

The NANOGrav 12.5 yr Data Set: A Computationally Efficient Eccentric Binary Search Pipeline and Constraints on an Eccentric Supermassive Binary Candidate in 3C 66B

The radio galaxy 3C 66B has been hypothesized to host a supermassive black hole binary (SMBHB) at its center based on electromagnetic observations. Its apparent 1.05 yr period and low redshift (∼0.02) make it an interesting testbed to search for low-frequency gravitational waves (GWs) using pulsar timing array (PTA) experiments. This source has been subjected to multiple searches for continuous GWs from a circular SMBHB, resulting in progressively more stringent constraints on its GW amplitude and chirp mass. In this paper, we develop a pipeline for performing Bayesian targeted searches for eccentric SMBHBs in PTA data sets, and test its efficacy by applying it to simulated data sets with varying injected signal strengths. We also search for a realistic eccentric SMBHB source in 3C 66B using the NANOGrav 12.5 yr data set employing PTA signal models containing Earth term-only as well as Earth+pulsar term contributions using this pipeline. Due to limitations in our PTA signal model, we get meaningful results only when the initial eccentricity e 0 < 0.5 and the symmetric mass ratio η > 0.1. We find no evidence for an eccentric SMBHB signal in our data, and therefore place 95% upper limits on the PTA signal amplitude of 88.1 ± 3.7 ns for the Earth term-only and 81.74 ± 0.86 ns for the Earth+pulsar term searches for e 0 < 0.5 and η > 0.1. Similar 95% upper limits on the chirp mass are (1.98 ± 0.05) × 109 and (1.81 ± 0.01) × 109 M ☉. These upper limits, while less stringent than those calculated from a circular binary search in the NANOGrav 12.5 yr data set, are consistent with the SMBHB model of 3C 66B developed from electromagnetic observations.

Experimental Study and Bearing Capacity Calculation of Compression-Reinforced Concrete Columns Strengthened with Ultra-High-Performance Concrete

A total of five ultra-high-performance concrete (UHPC)-strengthened reinforced concrete (RC) columns and one RC column were built and subjected to eccentric compression testing to examine the force performance of UHPC-strengthened eccentrically compressed plain RC columns. This experimental study examined the crack progression, the damage morphology, the deformation ability, the maximum load-carrying capacity, and the ductile properties of the eccentrically compressed columns. It also investigated the impacts of eccentricity, the reinforcement thickness, and the addition of steel fibers on the effectiveness of reinforcement. The cracking load, peak load, and ductility coefficient of the UHPC-reinforced specimens were increased by 100.28%, 172.30%, and 56.30%, respectively, compared with the RC column at an initial eccentricity of 50 mm. As the eccentricity distance increased, the bearing capacity of the UHPC eccentrically compressed specimens decreased, and the deformation capacity increased. Increasing the steel fiber dosage within the appropriate range decreased the crack width of the specimen. The addition of 2% steel fiber resulted in a 24.8% increase in cracking load, an 8.96% increase in peak load, and a 2.60% increase in ductility coefficient compared to the addition of 1% steel fiber. However, the reinforcing effect of UHPC was weakened under high eccentric pressures. Based on the theory of concrete structure and mechanical principles, the formula for calculating the compressive bearing capacity of RC columns strengthened with high-performance concrete was proposed. The results of calculating the positive section bearing capacity of eccentrically compressed RC columns reinforced with high-performance concrete are in good agreement with the test values. The results of this paper provide an experimental basis and theoretical foundation for the cross-sectional design of UHPC eccentrically compressed columns.

“Tidal Peeling Events”: Low-eccentricity Tidal Disruption of a Star by a Stellar-mass Black Hole

Close encounters between stellar-mass black holes (BHs) and stars occur frequently in dense star clusters and in the disks of active galactic nuclei. Recent studies have shown that in highly eccentric close encounters, the star can be tidally disrupted by the BH in a microtidal disruption event (microTDE), resulting in rapid mass accretion and possibly bright electromagnetic signatures. Here we consider a scenario in which the star might approach the stellar-mass BH in a gradual, nearly circular inspiral, under the influence of dynamical friction in a circum-binary gas disk or three-body interactions in a star cluster. We perform hydrodynamics simulations of this scenario using the smoothed particle hydrodynamics code PHANTOM. We find that under certain circumstances (for initial eccentricity e 0 ≳ 0.4 and penetration factor β = 1, or e 0 < 0.4 and β ≲ 0.67), the mass of the star is slowly stripped away by the BH. We call this gradual tidal disruption a “tidal-peeling event.” Additionally, we discover that some low-eccentricity microTDEs (e 0 < 0.4 and β = 1) are a new form of fast luminous transients similar to parabolic microTDEs. Depending on the initial distance and eccentricity of the encounter, these low-eccentricity microTDEs might exhibit significant accretion rates and orbital evolution distinct from those of a typical (eccentric) microTDE.

Fast and Fourier: extreme mass ratio inspiral waveforms in the frequency domain

Extreme Mass Ratio Inspirals (EMRIs) are one of the key sources for future space-based gravitational wave interferometers. Measurements of EMRI gravitational waves are expected to determine the characteristics of their sources with sub-percent precision. However, their waveform generation is challenging due to the long duration of the signal and the high harmonic content. Here, we present the first ready-to-use Schwarzschild eccentric EMRI waveform implementation in the frequency domain for use with either graphics processing units (GPUs) or central processing units (CPUs). We present the overall waveform implementation and test the accuracy and performance of the frequency domain waveforms against the time domain implementation. On GPUs, the frequency domain waveform takes in median 0.044 s to generate and is twice as fast to compute as its time domain counterpart when considering massive black hole masses ≥2×106M⊙ and initial eccentricities e0 &amp;gt; 0.2. On CPUs, the median waveform evaluation time is 5 s, and it is five times faster in the frequency domain than in the time domain. Using a sparser frequency array can further speed up the waveform generation, reaching up to 0.3 s. This enables us to perform, for the first time, EMRI parameter inference with fully relativistic waveforms on CPUs. Future EMRI models, which encompass wider source characteristics (particularly black hole spin and generic orbit geometries), will require significantly more harmonics. Frequency domain models will be essential analysis tools for these astrophysically realistic and important signals.

Stability of coorbital planets around binaries

In previous hydrodynamical simulations, we found a mechanism for nearly circular binary stars, such as Kepler-413, to trap two planets in a stable 1:1 resonance. Therefore, the stability of coorbital configurations becomes a relevant question for planet formation around binary stars. For this work, we investigated the coorbital planet stability using a Kepler-413 analogue as an example and then expanded the parameters to study a general n-body stability of planet pairs in eccentric horseshoe orbits around binaries. The stability was tested by evolving the planet orbits for 105 binary periods with varying initial semi-major axes and planet eccentricities. The unstable region of a single circumbinary planet is used as a comparison to the investigated coorbital configurations in this work. We confirm previous findings on the stability of single planets and find a first order linear relation between the orbit eccentricity ep and pericentre to identify stable orbits for various binary configurations. Such a linear relation is also found for the stability of 1:1 resonant planets around binaries. Stable orbits for eccentric horseshoe configurations exist with a pericentre closer than seven binary separations and, in the case of Kepler-413, the pericentre of the first stable orbit can be approximated by rc,peri = (2.90 ep + 2.46) abin.