Eccentricity Distribution Research Articles

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.

Resonant amplitude distribution of the Hilda asteroids and the free-floating planet flyby scenario

In some recent work, we provided a quantitative explanation for the number asymmetry of Jupiter Trojans by hypothesizing a free-floating planet (FFP) flyby into the Solar System. In support of that explanation, this paper examines the influence of the same FFP flyby on the Hilda asteroids, which orbit stably in the 3:2 mean motion resonance with Jupiter. The observed Hilda population exhibits two distinct resonant patterns: (1) a lack of Hildas with resonant amplitudes <40° at eccentricities <0.1; (2) a nearly complete absence of Hildas with amplitudes <20°, regardless of eccentricity. Previous models of Jupiter migration and resonance capture could account for the eccentricity distribution of Hildas but have failed to replicate the unusual absence of those with the smallest resonant amplitudes, which theoretically should be the most stable. Here we report that the FFP flyby can trigger an extremely rapid outward migration of Jupiter, causing a sudden shift in the 3:2 Jovian resonance. Consequently, Hildas with varying eccentricities would have their resonant amplitudes changed by different degrees, leading to the observed resonant patterns. We additionally show that, in our FFP flyby scenario, these patterns are consistently present across different resonant amplitude distributions of primordial Hildas arising from various formation models. We also place constraints on the potential parameters of the FFP, suggesting it should have an eccentricity of 1-1.3 or larger, an inclination up to 30° or higher, and a minimum mass of about 50 Earth masses.

Disaster mechanism of large-diameter shield tunnel segments under multi-source load coupling: A case study

The deflection squeezing of the shield shell and the eccentric jack thrust significantly impact the segment dislocation and damage. Based on summarizing the derivative relationship between engineering factors and disasters, this study established a 3D numerical calculation model under the multi-source load coupling. Then, this study explored the displacement and dislocation distribution of segments, as well as their derivative relationship with bolt failure. Furthermore, this study analyzed the spatial distribution and evolution characteristics of segment damage. Further revealing the disaster mechanism and proposing the engineering treatment measures. The research results indicate that as the deflection angle increases, the vertical relative compression deformation of the segment that is detaching from the shield tail (segment-DFST) becomes more significant. The plastic strain of the internal bolts inside the two segments in direct contact with the shield shell is mainly related to the radial and longitudinal dislocation. The increase in the deflection angle will lead to a more significant increase in the adjacent dislocation on both sides and the internal dislocation. The plastic strain of the internal bolts of the segment that is completely in the shield shell (segment-CSS) is more influenced by joint opening and longitudinal dislocation under the lower eccentric compression (LEC) state. The plastic strain of the internal bolts in segment-DFST is more influenced by radial dislocation and joint opening under the LEC state. The tension damage of the segments mainly occurs on both sides of the circumferential joint and the lower part of the segment-CSS. The compression damage of the segments is mainly distributed at the top and bottom of the segment-CSS. The eccentric distribution of jack thrust has the most significant impact on the block damage of the lower part of the segment-CSS. With the increase of the deflection angle, the compression damage and distribution range of the blocks at the bottom of the segment-DFST increase sharply. The compression damage and distribution range of the segment-CSS gradually spread from the upper and lower parts to the middle of the segment. The increase in deflection angle will promote the influence of the thrust in LEC state on the compression damage of the lower block of the segment-CSS, and on the tension damage of the upper block of the segment- DFST.

Different Planetary Eccentricity-period (PEP) Distributions of Small and Giant Planets

We used the database of 1040 short-period (1 ≤ P < 200 days) exoplanets radial-velocity orbits to study the planetary eccentricity-period (PEP) distribution. We first divided the sample into low- and high-mass exoplanet subsamples based on the distribution of the (minimum) planetary masses, which displays a clear two-Gaussian distribution, separated at 0.165M J. We then selected 216 orbits, low- and high-mass alike, with eccentricities significantly distinct from circular orbits. The 131 giant-planet eccentric orbits display a clear upper envelope, which we model quantitatively, rises monotonically from zero eccentricity and reaches an eccentricity of 0.8 at P ∼ 100 days. Conversely, the 85 low-mass planetary orbits display a flat eccentricity distribution between 0.1 and 0.5, with almost no dependence on the orbital period. We show that the striking difference between the two PEP distributions is not a result of the detection technique used. The upper envelope of the high-mass planets, also seen in short-period binary stars, is a clear signature of tidal circularization, which probably took place inside the planets, while the small-planet PEP distribution suggests that the circularization was not effective, probably due to dynamical interactions with neighboring planets.

Revisiting the Tertiary-induced Binary Black Hole Mergers: The Role of Superthermal Wide Tertiary Eccentricity Distributions

Recent studies show that the eccentricity distribution of wide binaries (semimajor axis ≳103 au) observed by Gaia tends to favor large eccentricities more strongly than the canonical thermal distribution (P(e) ∝ e)—such distributions are termed “superthermal.” Motivated by this observation, we revisit the formation channel of black hole (BH) binary mergers in triple stellar systems and study the impact of superthermal eccentricity distributions in the outer binaries. We explore the persistence of the highly eccentric outer orbits after each component in a stellar triple has undergone mass loss due to supernova explosions. We find that the outer eccentricity distribution can remain significantly superthermal for modestly hierarchical BH triples satisfying a in/a out ≳ 0.005 (where a in and a out are the semimajor axes of the inner and outer orbits), and are otherwise shaped by mass-loss induced kicks and dynamical instability. We then study the impact of these different outer eccentricity distributions of the remaining BH triples on mergers via the tertiary-induced channel. Of interest, we find that mergers can sometimes be produced even when the initial stellar orbits are near alignment (not subject to the von-Zeipel–Lidov–Kozai effect; ZLK effect) as long as the system is sufficiently hierarchical. On the other hand, although the impact of the octupole-order ZLK effect is much greater when the outer binary is more eccentric, we find that the merger fraction only changes modestly for extreme outer eccentricity distributions because the largest eccentricities tend to lead to dynamical instability.

Giant planet formation in the Solar System

The formation history of Jupiter has been of interest due to its ability to shape the solar system’s history. Yet little attention has been paid to the formation and growth of Saturn and the other giant planets. Here we explore through N-body simulations the implications of the simplest disc and pebble accretion model with steady-state accretion and an assumed ring structure in the disc at 5 AU on the formation of the giant planets in the solar system. We conducted a statistical survey of different disc parameters and initial conditions of the protoplanetary disc to establish which combination best reproduces the present outer solar system. We examined the effect of the initial planetesimal disc mass, the number of planetesimals and their size-frequency distribution slope, pebble accretion prescription and sticking efficiency on the likelihood of forming gas giants and their orbital distribution. The results reveal that the accretion sticking efficiency is the most sensitive parameter to control the final masses and number of giant planets. We have been unable to replicate the formation of all three types of giant planets in the solar system in a single simulation. The probability distribution of the final location of the giant planets is approximately constant in logr, suggesting there is a slight preference for formation closer to the Sun but no preference for more massive planets to form closer. The eccentricity distribution has a higher mean for more massive planets indicating that systems with more massive planets are more violent. We compute the average formation time for proto-Jupiter to reach 10 Earth masses to be 〈tc,J〉=1.1±0.3 Myr and for proto-Saturn 〈tc,S〉=3.3±0.4 Myr, while for the ice giants this increases to 〈tc,I〉=4.9±0.1 Myr. The formation timescales of the cores of the gas giants are distinct at >95% confidence, suggesting that they formed sequentially.

On Binary Formation from Three Initially Unbound Bodies

We explore three-body binary formation (3BBF), the formation of a bound system via gravitational scattering of three initially unbound bodies (3UB), using direct numerical integrations. For the first time, we consider systems with unequal masses, as well as finite-size and post-Newtonian effects. Our analytically derived encounter rates and numerical scattering results reproduce the 3BBF rate predicted by Goodman & Hut for hard binaries in dense star clusters. We find that 3BBF occurs overwhelmingly through nonresonant encounters and that the two most-massive bodies are never the most likely to bind. Instead, 3BBF favors pairing the two least-massive bodies (for wide binaries) or the most- plus least-massive bodies (for hard binaries). 3BBF overwhelmingly favors wide-binary formation with superthermal eccentricities, perhaps helping to explain the eccentric wide binaries observed by Gaia. Hard-binary formation is far rarer, but with a thermal eccentricity distribution. The semimajor axis distribution scales cumulatively as a 3 for hard and slightly wider binaries. Although mergers are rare between black holes when including relativistic effects, direct collisions occur frequently between main-sequence stars—more often than hard 3BBF. Yet, these collisions do not significantly suppress hard 3BBF at the low-velocity dispersions typical of open or globular clusters. Energy dissipation through gravitational radiation leads to a small probability of a bound, hierarchical triple system forming directly from 3UB.

A hot-Jupiter progenitor on a super-eccentric retrograde orbit.

Giant exoplanets orbiting close to their host stars are unlikely to have formed in their present configurations1. These 'hotJupiter' planets are instead thought to have migrated inward from beyond the ice line and several viable migration channels have been proposed, including eccentricity excitation through angular-momentum exchange with a third body followed by tidally driven orbital circularization2,3. The discovery of the extremely eccentric (e = 0.93) giant exoplanet HD 80606 b (ref. 4) provided observational evidence that hot Jupiters may have formed through this high-eccentricity tidal-migration pathway5. However, no similar hot-Jupiter progenitors have been found and simulations predict that one factor affecting the efficacy of this mechanism is exoplanet mass, as low-mass planets are more likely to be tidally disrupted during periastron passage6-8. Here we present spectroscopic and photometric observations of TIC 241249530 b, a high-mass, transiting warm Jupiter with an extreme orbital eccentricity of e = 0.94. The orbit of TIC 241249530 b is consistent with a history of eccentricity oscillations and a future tidal circularization trajectory. Our analysis of the mass and eccentricity distributions of the transiting-warm-Jupiter population further reveals a correlation between high mass and high eccentricity.

Eccentricity dynamics of wide binaries – II. The effect of stellar encounters and constraints on formation channels

ABSTRACT Gaia wide stellar binaries (separations $\sim 10^3{\!-\!}10^{4.5}$ au) are observed to have a superthermal eccentricity distribution function (DF), well-fit by $P(e) \propto e^\alpha$ with $\alpha \sim 1.2$. In a previous paper, we proved that this DF cannot have been produced by Galactic tidal torques starting from any realistic DF that was not already superthermal. Here, we consider the other major dynamical effect on wide binaries: encounters with passing stars. We derive and solve the Fokker–Planck equation governing the evolution of binaries in semimajor axis and eccentricity under many weak, impulsive, penetrative stellar encounters. We show analytically that these encounters drive the eccentricity DF towards thermal on the same time-scale as they drive the semimajor axes a towards disruption, $t_\mathrm{dis}\sim 4\, \mathrm{Gyr}\, (a/10^4\, \mathrm{AU})^{-1}$. We conclude that the observed superthermal DF must derive from an even more superthermal (i.e. higher $\alpha$) birth distribution. This requirement places strong constraints on the dominant binary formation channels. A testable prediction of our theory is that $\alpha$ should be a monotonically decreasing function of binary age.

Wide-binary eccentricity distribution in young star clusters: dependence on the binary separation and mass

ABSTRACT We study the wide-binary eccentricity (e) distribution in young star clusters and the role of turbulence in setting the form of the e distribution using magnetohydrodynamical simulations of star cluster formation. The simulations incorporate gravity, turbulence, magnetic fields, protostellar heating, and jets/outflows. We find that (1) simulations that employ purely compressive turbulence driving produce binaries with a superthermal e distribution [$\alpha \gt 1$ in $p(e) \propto e^\alpha$], while simulations with purely solenoidal driving or natural mixture of driving modes produce subthermal/thermal distributions ($\alpha \le$ 1), (2) the e distribution over the full range of binary separations in our simulations is set at the early stages of the star cluster formation process, (3) while binaries (separation of $r_{\mathrm{pair}} \le 1000\, \mathrm{AU}$) have subthermal to thermal e distributions ($\alpha \sim 0.8$), wide binaries ($r_{\mathrm{pair}} \gt 1000\, \mathrm{AU}$) have a superthermal distribution ($\alpha \sim 1.8$), and (4) low-mass binary systems (system masses of $M_{\mathrm{sys}} \le 0.8\, \mathrm{M_\odot }$) have a highly superthermal distribution ($\alpha \sim 2.4$), whereas high-mass systems ($M_{\mathrm{sys}} \gt 0.8\, \mathrm{M_\odot }$) exhibit a subthermal/thermal distribution ($\alpha \sim 0.8$). The binary eccentricity distribution is often modelled as a thermal distribution. However, our results suggest that the e distribution depends on the range of separation of the sampled binaries, which agrees with the findings from recent Gaia observations. We conclude that the dependence of the e distribution on the binary separation and mass is linked to the binary formation mechanism governed by the turbulent properties of the parent cloud.

Consistent Eccentricities for Gravitational-wave Astronomy: Resolving Discrepancies between Astrophysical Simulations and Waveform Models

Detecting imprints of orbital eccentricity in gravitational-wave (GW) signals promises to shed light on the formation mechanisms of binary black holes. To constrain the formation mechanisms, distributions of eccentricity derived from numerical simulations of astrophysical formation channels are compared to the estimates of eccentricity inferred from GW signals. We report that the definition of eccentricity typically used in astrophysical simulations is inconsistent with the one used while modeling GW signals, with the differences mainly arising due to the choice of reference frequency used in both cases. We also posit a prescription for calculating eccentricity from astrophysical simulations, by evolving ordinary differential equations obtained from post-Newtonian theory and using the dominant (ℓ = m = 2) mode’s frequency as the reference frequency; this ensures consistency in the definitions. On comparing the existing eccentricities of the binaries present in the Cluster Monte Carlo catalog of globular cluster simulations with the eccentricities calculated using the prescription presented here, we find a significant discrepancy at e ≳ 0.2; this discrepancy becomes worse with increasing eccentricity. We note the implications this discrepancy has for existing studies and recommend that care be taken when comparing data-driven constraints on eccentricity to expectations from astrophysical formation channels.

Secular structure of 1:2 and 1:3 mean motion resonances with Neptune

The 1:N mean motion resonances (MMRs) with Neptune are of particular interest in astrophysical research because they have two asymmetric resonance islands, where the distribution of trapped objects may bear important clues to resolving the history of the Solar System. To explore the dynamics of these resonances and to investigate whether the imprints left by the early stage evolution can be preserved in the resonances, we conducted a comprehensive analysis of the 1:2 and 1:3 resonances. By mainly adopting the frequency analysis method, we calculated the proper frequencies of the motion of objects in the resonances and determined the secular mechanisms that influence the dynamics. Using the spectral number (SN) as an indicator of orbital regularity, we constructed dynamical maps on representative planes. After comparing the structures in the maps with the locations of the secular mechanisms, we find that the von-Zeipel-Lidov-Kozai mechanism and the $g=2s$ mechanism destabilize the influenced orbits and thus sculpt the overall structure of the 1:2 and 1:3 resonances. The secular resonance of $2g-s=s_8$ opens a channel for objects to switch between the leading and trailing resonance islands, which can alter the population ratio between these two islands. The secondary resonances associated with the quasi 2:1 resonance between Uranus and Neptune were also detected, likely introducing more chaos to the motion. The fine dynamical structures of the 1:2 and 1:3 resonances revealed in this paper, combined with knowledge of resonant capture, provide a compelling explanation for the eccentricity distribution of observed Twotinos. Furthermore, we anticipate a more complete understanding of the history of planetary migration in the Solar System can be achieved by comparing the results in this paper with the populations in the 1:N resonances, with forthcoming observations offering more objects for study in the future.

Three-body binary formation in clusters: analytical theory

ABSTRACT Binary formation in clusters through triple encounters between three unbound stars, ‘three-body’ binary formation, is one of the main dynamical formation processes of binary systems in dense environments. In this paper, we use an analytical probabilistic approach to study the process for the equal mass case and calculate a probability distribution for the orbital parameters of three-body-formed binaries, as well as their formation rate. For the first time, we give closed-form analytical expressions to the full orbital parameter distribution, accounting for both energy and angular momentum conservation. This calculation relies on the sensitive dependence of the outcomes of three-body scatterings on the initial conditions: here we compute the rate of three-body binaries from ergodic interactions, which allow for an analytical derivation of the distribution of orbital parameters of the binaries thus created. We find that soft binaries are highly favoured in this process and that these binaries have a superthermal eccentricity distribution, while the few hard three-body binaries have an eccentricity distribution much closer to thermal. The analytical results predict and reproduce simulation results of three-body scattering experiments in the literature well.

Abstract 1004: Three-dimensional Characterization Of Sex Differences In Abdominal Aortic Aneurysm Progression Via Vascular Deformation Mapping

Introduction: Although Abdominal Aortic Aneurysms (AAA) are more common in men, women are at greater risk for AAA growth and rupture. Vascular deformation mapping (VDM) is a novel technique that utilizes deformable image registration to qualify and quantify three-dimensions (3D) AAA growth using routing clinical computed tomography angiogram (CTA) images. Hypothesis: We hypothesize that females will have higher rates of focal AAA growth when compared to males. Aims: In this study we aimed to leverage VDM to investigate sex differences in AAA growth. Methods: We identified patients with infra-renal AAA and ≥2 CTA from 2010-2021. Patients with non-contrast CT scans or poor image quality were excluded. Propensity score matching was used to identify a cohort of males and females matched on age, hypertension, and smoking history. AAA were segmented and VDM was conducted using a multi-step image registration of aortic CTA studies to generate a deformation field which is then used to quantify 3D AAA growth rate (GR). Patient characteristics, maximum diameter (Dmax), AAA volume (Vmax), and GR were obtained. Statistical shape modeling was utilized to compare average 3D growth patterns between males and females. Results: Seventeen male and females with AAA were matched. There was no differences between sexes in race, diabetes, symptomatic status, or repair. Males had a trend toward larger Dmax (4.9 ± 0.6 vs 4.5 ± 0.6 cm, p = 0.055) and had Vmax at baseline (118.7 ± 69.9 vs 76.6 ± 35.0 cm 3 , p = 0.034). There was no difference between sexes when looking at change in Dmax or Vmax. Male and female AAA had no difference in average GR (0.11 ± 0.08 vs 0.17 ± 0.22 cm/year, p = 0.293). Shape models demonstrated more diffuse AAA growth for males and more eccentric AAA growth for females (Figure 1). Conclusions: Despite comparable changes in Dmax, Vmax, and GR, women demonstrated a more eccentric distribution of AAA growth, a finding which may contribute to higher rupture risk in women.

Modeling and contact analysis for spur gear pair with modification and localized crack failure

The modified teeth are deliberately manufactured to mitigate the stress concentration generated by offset components, which makes equipment more susceptible to localized failures. Therefore, this paper presents a model aimed at investigating the meshing characteristic of gear pair with modification and crack failure. In this model, the tooth deformation and force transmission are determined based on slice coupling theory. The torsional deformation of teeth produced by eccentric load distribution is considered and complemented to the calculation method. Finally, the approach is proven through the experimental tests and FE model. The result shows that when the equipment is operated in misalignment condition, eccentric load distribution, and stress concentration at tooth edge are generated, the meshing stiffness will be reduced drastically, which can be suppressed by appropriate modification, and the rapid decline of meshing stiffness is weakened by increasing the effective contact length. Although the contact stiffness would be further reduced by the crack failure and the tooth surface deformation is increased, it seems to alleviate the stress concentration and eccentric load effectively.

Mapping the Chemodynamics of the Galactic Disk Using the LAMOST and APOGEE Red Clump Stars

A detailed measurement is made of the metallicity distributions, kinematics, and dynamics of the thin and thick disks across a large disk volume (5.0 ≤ R ≤ 15.0 kpc and ∣Z∣ ≤ 3.0 kpc) by using the LAMOST–APOGEE red clump stars. The metallicity distribution results show that the radial metallicity gradient Δ[Fe/H]/ΔR of the thin disk weakens with ∣Z∣ from −0.06 dex kpc−1 at around ∣Z∣ < 0.25 kpc to −0.02 dex kpc−1 at around ∣Z∣ > 2.75 kpc, while the thick disk displays a global weak positive Δ[Fe/H]/ΔR that is generally weaker than 0.01 dex kpc−1. The vertical metallicity gradient Δ[Fe/H]/Δ∣Z∣ steadily weakened from −0.36 dex kpc−1 at R ∼ 5.5 kpc to −0.05 dex kpc−1 at around R > 11.5 kpc for the thin disk, while the thick disk presents an almost constant value (nearly −0.06∼−0.08 dex kpc−1) for all the R bins. These results indicate the contribution of the radial migration to the disk evolution, and the obvious north–south asymmetry in [Fe/H] may be linked to disk warp and/or disk perturbation events. The oscillations in the corrected Δ[Fe/H]/Δ∣Z∣ with R likely arise from the resonances with the Galactic bar. Our detailed measurements of ΔV ϕ /Δ[Fe/H] indicate an inside-out and upside-down star formation scenario for the thick disk. The results of eccentricity distributions and [α/Fe]–velocity dispersion relations are likely to suggest that thick-disk stars require an obvious contribution from other heating mechanisms, such as mergers and accretion, or are born in the chaotic mergers of gas-rich systems and/or the turbulent interstellar medium.

Neutron star – white dwarf binaries: probing formation pathways and natal kicks with LISA

ABSTRACT Neutron star–white dwarf (NS + WD) binaries offer a unique opportunity for studying NS-specific phenomena with gravitational waves. In this paper, we employ the binary population synthesis technique to study the Galactic population of NS + WD binaries with the future Laser Interferometer Space Antenna (LISA). We anticipate approximately $\mathcal {O}(10^2)$ detectable NS + WD binaries by LISA, encompassing both circular and eccentric ones formed via different pathways. Despite the challenge of distinguishing these binaries from more prevalent double white dwarfs (especially at frequencies below 2 mHz), we show that their eccentricity and chirp mass distributions may provide avenues to explore the NS natal kicks and common envelope evolution. Additionally, we investigate the spatial distribution of detectable NS + WD binaries relative to the Galactic plane and discuss prospects for identifying electromagnetic counterparts at radio wavelengths. Our results emphasise LISA’s capability to detect and characterize NS + WD binaries and to offer insights into the properties of the underlying population. Our conclusions carry significant implications for shaping LISA data analysis strategies and future data interpretation.

A proposed numerical method for absolute efficiency calibration of α-spectrometers and its application for activity calculation

In this work, an absolute method to calibrate an α-spectrometer is proposed taking into account the Source-to-Detector, and lateral distances due to eccentric source distribution. An analytical formula to calibrate an α-spectrometer is derived and the Simpson's integration method was utilized to solve these equations in its integral form numerically using a written C computer code. The general Monte Carlo N-particle code, MCNP as well as experimental measurements for some standard α-emitters are used to benchmark the proposed method. An agreement was found between the efficiency results calculated by MC and the proposed method with a maximum relative difference of about 0.5%. While, experimental measurement of α-emitters activity employing the proposed method differs by about 1.65% from the certified values. Accounting for the man made error allows to accurately quantify the assayed sample. Therefore, the inaccuracy in the efficiency results due to non-accurate inputs pertained to the source, and detector radii, Source–Detector distances, and eccentric source distribution are investigated in the Source-to-Detector distance range of (4 to 44 mm). The results show that a difference of ±1% in the detector radius, and Source-to-Detector distance than the normal values yields a relative difference of about ±2%, while a difference of ±50% in the source radius or source lateral distance from detector symmetry axis could only yields inaccuracy of less than ±3% in the efficiency results.

Formation of Merging Stellar-mass Black Hole Binaries by Gravitational-wave Emission in Active Galactic Nucleus Disks

Many stellar-mass black holes (sBHs) are expected to orbit supermassive black holes at galactic centers. For galaxies with active galactic nuclei, it is likely that the sBHs reside in a disk. We study the formation of sBH binaries via gravitational-wave emission in such disks. We examine analytically the dynamics of two sBHs orbiting a supermassive black hole, estimate the capture cross section, and derive the eccentricity distribution of bound binaries at different frequency bands. We find that the majority of the merging sBH binaries, assembled in this manner, can be measured as highly eccentric, detectable in the LIGO-Virgo-KAGRA (LVK) band from their formation, with (1 − e) ≪ 1, through their circularization and up to their merger; the remaining binaries circularize to small eccentricities (e ≲ 0.3) before entering the LVK band. More eccentric mergers would be observed for sBHs with higher random velocities, closer to the supermassive black hole, or at lower observing frequency bands, as planned in future gravitational-wave detectors such as the Einstein Telescope and LISA.

Eccentricity Distribution beyond the Snow Line and Implications for Planetary Habitability

A fundamental question in the study of planetary system demographics is: how common is the solar system architecture? The primary importance of this question lies in the potential of planetary systems to create habitable environments, and dissecting the various components of solar system evolution that contributed to a sustainable temperate surface for Earth. One important factor in that respect is volatile delivery to the inner system and the dependence on giant planets beyond the snow line as scattering agents, particularly as such cold giant planets are relatively rare. Here, we provide an investigation of the eccentricity distribution for giant planet populations both interior and exterior to their system snow lines. We show that the median eccentricity for cold giants is 0.23, compared with a far more circular orbital regime for inner planets. We further present the results of a dynamical simulation that explores the particle scattering potential for a Jupiter analog in comparison with a Jupiter whose eccentricity matches that of the median cold giant eccentricity. These simulations demonstrate that the capacity for such an eccentric cold giant system to scatter volatiles interior to the snow line is significantly increased compared with the Jupiter analog case, resulting in a far greater volume of Earth-crossing volatiles. Thus, many of the known systems with cold giant planets may harbor water worlds interior to the snow line.