Extreme Mass Ratio Research Articles

On-shell approach to black hole mergers

We develop an on-shell approach to study black hole mergers. Since, asymptotically, the initial and final states can be described by point-like spinning particles, we propose a massive three-point amplitude for the merger of two Schwarzschild black holes into a Kerr black hole. This three-point amplitude and the spectral function of the final state are fully determined by kinematics and the model-independent input about the black hole merger which is described by a complete absorption process. Using the Kosower-Maybee-O’Connell (KMOC) formalism, we then reproduce the classical conservation laws for momentum and angular momentum after the merger. As an application, we use the proposed three-point to compute the graviton emission amplitude, from which we extract the merger waveform to all orders in spin but leading in gravitational coupling. Up to sub-subleading order in spin, this matches the classical soft graviton theorem. We conclude with a comparison to black hole perturbation theory, which gives complementary amplitudes which are non-perturbative in the gravitational coupling but to leading order in the extreme mass ratio limit. This also highlights how boundary conditions on a Schwarzschild background can be used to rederive the proposed on-shell amplitudes for merger processes.

Detection of a Highly Ionized Outflow in the Quasiperiodically Erupting Source GSN 069

Quasiperiodic eruptions (QPEs) are high-amplitude, soft X-ray bursts recurring every few hours, associated with supermassive black holes. Many interpretations for QPEs were proposed since their recent discovery in 2019, including extreme mass ratio inspirals and accretion disk instabilities. But, as of today, their nature still remains debated. We perform the first high-resolution X-ray spectral study of a QPE source using the Reflection Grating Spectrometers' gratings on board XMM-Newton, leveraging nearly 2 Ms of exposure on GSN 069, the first discovered source of this class. We resolve several absorption and emission lines including a strong line pair near the N vii rest-frame energy, resembling the P-Cygni profile. We apply photoionization spectral models and identify the absorption lines as an outflow blueshifted by 1700−2900 km s−1, with a column density of about 1022 cm−2 and an ionization parameter log(ξ /erg cm s−1) of 3.9−4.6. The emission lines are instead redshifted by up to 2900 km s−1, and likely originate from the same outflow that imprints the absorption features, and covers the full 4π sky from the point of view of GSN 069. The column density and ionization are comparable to the outflows detected in some tidal disruption events, but this outflow is significantly faster and has a strong emission component. The outflow is more highly ionized when the system is in the phase during which QPEs are present, and from the limits, we derive on its location, we conclude that the outflow is connected to the recent complex, transient activity of GSN 069, which began around 2010.

Are all models wrong? Falsifying binary formation models in gravitational-wave astronomy using exceptional events

Abstract As the catalogue of gravitational-wave transients grows, several entries appear ‘exceptional’ within the population. Tipping the scales with a total mass of ∼150M⊙, GW190521 likely contained black holes in the pair-instability mass gap. The event GW190814, meanwhile, is unusual for its extreme mass ratio and the mass of its secondary component. A growing model-building industry has emerged to provide explanations for such exceptional events, and Bayesian model selection is frequently used to determine the most informative model. However, Bayesian methods can only take us so far. They provide no answer to the question: does our model provide an adequate explanation for exceptional events in the data? If none of the models we are testing provide an adequate explanation, then it is not enough to simply rank our existing models—we need new ones. In this paper, we introduce a method to answer this question with a frequentist p-value. We apply the method to different models that have been suggested to explain the unusually massive event GW190521: hierarchical mergers in active galactic nuclei and globular clusters. We show that some (but not all) of these models provide adequate explanations for exceptionally massive events like GW190521.

Prograde and retrograde stars in nuclear cluster merger. Evolution of the supermassive black hole binary and the host galactic nucleus

Nuclear star cluster (NSC) mergers, involving the fusion of dense stellar clusters near the centres of galaxies, play a pivotal role in shaping galactic structures. The distribution of stellar orbits has significant effects on the formation and characteristics of extreme mass ratio inspirals (EMRIs). In this study, we address the orbital distribution of stars in merging NSCs and the subsequent effects on supermassive black hole binary (SMBHB) evolution. We ran dedicated direct-summation $N$-body simulations with different initial conditions to do a detailed study of the resulting NSC after their progenitors had merged. Our findings reveal that prograde stars form a flattened structure, while retrograde stars have a more spherical distribution. The axial ratios of the prograde component vary based on the presence and mass ratio of the SMBHs. The fraction of prograde and retrograde stars depends on the merger orbital properties and the SMBH mass ratio. The interactions of retrograde stars with the SMBHB affect the eccentricity and separation evolution of the binary. Our analysis reveals a strong correlation between the angular momentum and eccentricity of the SMBH binary. This relationship could serve as a means to infer information about the stellar dynamics surrounding the binary. We find that prograde orbits are particularly close to the binary of SMBHs, a promising fact regarding EMRI production. Moreover, prograde and retrograde stars have different kinematic structures, with the prograde stars typically rotating faster than the retrograde ones. The line-of-sight velocity and velocity dispersion, as well as the velocity anisotropy of each NSC, depend on the initial merger orbital properties and SMBH mass ratios. The prograde and retrograde stars always show different behaviours. The distribution of stellar orbits and the dynamical properties of each kinematic population can potentially be used as a way to tell the properties of the parent nuclei apart, and has an important impact on expected rates of EMRIs, which will be detected by future gravitational wave observatories such as the Laser Interferometer Space Antenna (LISA).

Low-mass contact binaries: orbital stability at extreme low mass ratios

ABSTRACT With the ever-increasing number of light-curve solutions of contact binary systems, an increasing number of potential bright red nova progenitors are being reported. There remains, however, only one confirmed event. In this study, we undertake a comprehensive review of the orbital stability of contact binary systems, considering the effects of the stellar internal composition (metallicity) and age on the evolution of the gyration radius and its effect on the instability mass ratio of contact binaries. We find that both metallicity and age have an independent effect on orbital stability, with metal-poor and older systems being more stable. The combined effects of age and metallicity are quite profound, such that for most systems with primaries of solar mass or greater, which are halfway or more through the main-sequence lifespans have instability mass ratios at levels where the secondary component would be below the hydrogen fusion mass limit. We find that from the currently available solutions we cannot confidently assign any system as unstable. Although we identify eight potential red nova progenitors, all have methodological or astrophysical concerns, which lowers our confidence in designating any of them as potential merger candidates.

Post-Newtonian expansions of extreme mass ratio inspirals of spinning bodies into Schwarzschild black holes

Post-Newtonian expansions of extreme mass ratio inspirals of spinning bodies into Schwarzschild black holes

Enhanced Extreme Mass Ratio Inspiral Rates and Intermediate Mass Black Holes.

Extreme mass ratio inspirals (EMRIs) occur when stellar-mass compact objects begin a gravitational wave (GW) driven inspiral into massive black holes. EMRI waveforms can precisely map the surrounding spacetime, making them a key target for future space-based GW interferometers such as LISA, but their event rates and parameters are massively uncertain. One of the largest uncertainties is the ratio of true EMRIs (which spend at least thousands of orbits in the LISA band) and direct plunges, which are in-band for at most a handful of orbits and are not detectable in practice. In this Letter, we show that the traditional dichotomy between EMRIs and plunges-EMRIs originate from small semimajor axes, plunges from large-does not hold for intermediate-mass black holes with masses M_{•}≲10^{5}M_{⊙}. In this low-mass regime, a plunge always has an O(1) probability of failing and transitioning into a novel "cliffhanger" EMRI. Cliffhanger EMRIs are more easily produced for larger stellar-mass compact objects, and are less likely for smaller ones. This new EMRI production channel can dominate volumetric EMRI rates n[over ˙]_{EMRI} if intermediate-mass black holes are common in dwarf galactic nuclei, potentially increasing n[over ˙]_{EMRI} by an order of magnitude.

Gravitational scattering and beyond from extreme mass ratio effective field theory

We explore a recently proposed effective field theory describing electromagnetically or gravitationally interacting massive particles in an expansion about their mass ratio, also known as the self-force (SF) expansion. By integrating out the deviation of the heavy particle about its inertial trajectory, we obtain an effective action whose only degrees of freedom are the lighter particle together with the photon or graviton, all propagating in a Coulomb or Schwarzschild background. The 0SF dynamics are described by the usual background field method, which at 1SF is supplemented by a “recoil operator” that encodes the wobble of the heavy particle, and similarly computable corrections appearing at 2SF and higher. Our formalism exploits the fact that the analytic expressions for classical backgrounds and particle trajectories encode dynamical information to all orders in the couplings, and from them we extract multiloop integrands for perturbative scattering. As a check, we study the two-loop classical scattering of scalar particles in electromagnetism and gravity, verifying known results. We then present new calculations for the two-loop classical scattering of dyons, and of particles interacting with an additional scalar or vector field coupling directly to the lighter particle but only gravitationally to the heavier particle.

Gravitational waves for eccentric extreme mass ratio inspirals of self-dual spacetime

In this paper, we calculate the frequencies of geodesic orbits in self-dual spacetime on the equatorial plane and obtain the leading-order effects of loop quantum parameters P on the energy flux and angular momentum flux in eccentric extreme mass ratio inspirals. The gravitational waveform under different eccentricity is carried out by improved “analytic-kludge” method. We calculate the waveform mismatches for the LISA detector and the measurement error on loop quantum parameters. The constraint capability on P will be improved by a factor of 3 to 10, compared to the weak field experiments in the solar system.

Coupled Disk-star Evolution in Galactic Nuclei and the Lifetimes of QPE Sources

A modest fraction of the stars in galactic nuclei fed toward the central supermassive black hole (SMBH) approach on low-eccentricity orbits driven by gravitational-wave radiation (extreme mass ratio inspiral (EMRI)). In the likely event that a gaseous accretion disk is created in the nucleus during this slow inspiral (e.g., via an independent tidal disruption event (TDE)), star–disk collisions generate regular short-lived flares consistent with the observed quasiperiodic eruption (QPE) sources. We present a model for the coupled star-disk evolution, which self-consistently accounts for mass and thermal energy injected into the disk from stellar collisions and associated mass ablation. For weak collision/ablation heating, the disk is thermally unstable and undergoes limit-cycle oscillations, which modulate its properties and lead to accretion-powered outbursts on timescales of years to decades, with a time-averaged accretion rate ∼0.1Ṁ Edd. Stronger collision/ablation heating acts to stabilize the disk, enabling roughly steady accretion at the EMRI-stripping rate. In either case, the stellar destruction time through ablation, and hence the maximum QPE lifetime, is ∼102–103 yr, far longer than fallback accretion after a TDE. The quiescent accretion disks in QPE sources may at the present epoch be self-sustaining and fed primarily by EMRI ablation. Indeed, the observed range of secular variability broadly matches those predicted for collision-fed disks. Changes in the QPE recurrence pattern following such outbursts, similar to that observed in GSN 069, could arise from temporary misalignment between the EMRI-fed disk and the SMBH equatorial plane as the former regrows its mass after a state transition.

Fast inspirals and the treatment of orbital resonances

Abstract Extreme mass ratio inspirals (EMRIs), where a compact object orbits a massive black hole, are a key source of gravitational waves for the future Laser Interferometer Space Antenna (LISA). Due to their small mass ratio, ε ~ 10-4 -- 10-7 , the binary evolves slowly and EMRI signals will be in-band for years. Additionally, astrophysical EMRIs are expected to have complex dynamics featuring both spin-precession and eccentricity. A standard approach to modelling these inspirals is via the method of osculating geodesics (OG) which we employ along with a toy model for the gravitational self-force. Using this method requires resolving tens of thousands radial and polar orbital librations over the long duration of the signal which makes the inspiral trajectory expensive to compute.In this work we accelerate these calculations by employing Near-Identity (averaging) Transformations. 
However, this averaging technique breaks down at orbital resonances where the radial and polar frequencies are an integer ratio of each other. Thus, we switch to a partial averaging transformation in the vicinity of the resonance where the dynamics are characterised by the slow evolution of the so-called ``resonant phase". Additionally, we develop an optimal switching criterion to minimise the computation time while maximising accuracy. We find the error in the waveform phase is improved from O(ε-1/2) in the fully averaged scheme to O(ε4/7) in the switching scheme. At the same time, this scheme improves the scaling of the computation time from being inversely proportional to ε using OG, to a very weak scaling with ε. This results in a speed-up of at least two orders of magnitude for LISA EMRIs with room for further optimisation.

Exploring dark forces with multimessenger studies of extreme mass ratio inspirals

The exploration of dark sector interactions via gravitational waves (GWs) from binary inspirals has been a subject of recent interest. We study dark forces using extreme mass ratio inspirals (EMRIs), pointing out two issues of interest. Firstly, the innermost stable circular orbit (ISCO) of the EMRI, which sets the characteristic length scale of the system and hence the dark force range to which it exhibits enhanced sensitivity, probes force mediator masses that complement those studied with supermassive black hole (SMBH) or neutron star binaries. The LISA mission (the proposed μAres detector) will probe mediators with masses m V ∼ 10-16 eV (m V ∼ 10-18 eV), corresponding to ISCOs of 106 M ⊙ (108 M ⊙) central SMBHs. Secondly, while the sensitivity to dark couplings is typically limited by the uncertainty in the binary component masses, independent mass measurements of the central SMBH through reverberation mapping campaigns or the motion of dynamical tracers enable one to break this degeneracy. Our results therefore highlight the necessity for coordinated studies, loosely referred to as “multimessenger”, between future μHz- mHz GW observatories and ongoing and forthcoming SMBH mass measurement campaigns, including OzDES-RM, SDSS-RM, and SDSS-V Black Hole Mapper.

Photometric and Spectroscopic Study of Ten Low Mass Ratio Contact Binary Systems: Orbital Stability, O’Connell Effect and Infrared Calcium Line Filling

Low mass ratio contact binary systems are more likely to have unstable orbits and potentially merge. In addition, such systems exhibit characteristics such as starspots and high energy emissions (UV) suggestive of chromospheric and magnetic activity. Light curve modeling of ten contact binary systems is reported. All were found to be of extreme low mass ratio ranging from 0.122 to 0.24 and three were found to be potentially unstable and possible merger candidates. Filling of the infrared calcium absorption lines is a marker of increased chromospheric activity. We use the available Large Sky Area Multi-Object Fiber Spectroscopic Telescope spectra along with matched standard spectra (broadened for rotation) to measure the excess filling of the central core depression flux of the two main infrared calcium absorption lines λ8542 and λ8662. We find that all reported contact binaries have excess filling of the core flux in the infrared calcium lines. Three of the systems reported were also observed by the Galaxy Evolution Explorer mission and we find that all three have features of excess ultraviolet emissions further adding evidence for increased chromospheric activity in low mass ratio contact binaries. Analysis of both orbital stability and absorption line filling is dependent on the determination of geometric and absolute parameters from light curve modeling. Not an insignificant number of contact binary light curves exhibit the O’Connell effect, usually attributed to starspots. We discuss the inclusion of starspots in light curve solutions and how they influence the geometric and absolute parameters.

Investigation of the stability of the extreme low mass ratio contact binaries SX Crv and XX Sex, which are analysed photometrically

The photometric analyses of the extreme low mass ratio contact binaries SX Crv and XX Sex were conducted in detail. Light curves of SX Crv and XX Sex were retrieved from TESS, and light curve analyses were performed simultaneously with radial velocities. The mass ratios for SX Crv and XX Sex were calculated as 0.077(1) and 0.099(2). The masses of the primary components account for about 90% of the total masses of the systems and were determined to be 1.256(48) M⊙ and 1.337(37) M⊙ for SX Crv and XX Sex, respectively. It has been observed that the orbital periods of both systems have increased. The orbital period change rate of SX Crv has been calculated to be 0.39 s per century, while that of XX Sex has been calculated to be 2.68 s per century. The orbital angular momentum (Jo) determined for both systems is more than 3 times the spin angular momentum (Js), and it can be said that the SX Crv and XX Sex systems are stable. The calculated instability separation (ains.) and instability mass ratio (qins.) values for both systems are smaller than those obtained in the analyses, which supports the stability. The estimated ages of the systems are 7.4 Gyr for SX Crv and 3.9 Gyr for XX Sex. logMtot – logJ and logTeff – logL diagrams were also interpreted to better understand the evolution of the extreme low mass ratio contact binaries.

Tidal heating as a discriminator for horizons in equatorial eccentric extreme mass ratio inspirals

Tidal heating in a binary black hole system is driven by the absorption of energy and angular momentum by the black hole’s horizon. Previous works have shown that this phenomenon becomes particularly significant during the late stages of an extreme mass ratio inspiral (EMRI) into a rapidly spinning massive black hole, a key focus for future low-frequency gravitational-wave observations by (for instance) the Laser Interferometer Space Antenna mission. Past analyses have largely focused on quasicircular inspiral geometry, with some of the most detailed studies looking at equatorial cases. Though useful for illustrating the physical principles, this limit is not very realistic astrophysically, since the population of EMRI events is expected to arise from compact objects scattered onto relativistic orbits in galactic centers through many-body events. In this work, we extend those results by studying the importance of tidal heating in equatorial EMRIs with generic eccentricities. Our results suggest that accurate modeling of tidal heating is crucial to prevent significant dephasing and systematic errors in EMRI parameter estimation. We examine a phenomenological model for EMRIs around exotic compact objects by parametrizing deviations from the black hole (BH) picture in terms of the fraction of radiation absorbed compared to the BH case. Based on a mismatch calculation, we find that reflectivities as small as |R|2∼O(10−5) are distinguishable from the BH case, irrespective of the value of the eccentricity. We stress, however, that this finding should be corroborated by future parameter estimation studies. Published by the American Physical Society 2024

A Study of Nine Extremely Low Mass Ratio-contact Binary Systems

Low-mass ratio systems (LMR) are a very interesting class of contact eclipsing binaries challenging the theoretical models of stability. These systems are also considered possible progenitors of the rare low-mass optical transients called red novae. In this study, we present the identification of 7 new totally eclipsing LMR systems from Catalina Sky Surveys (CSS) and 77 LMR candidates from the All Sky Automated Survey. Using the available CSS light curves and new multiband observations for CSS_J210228.3-031048 and CSS_J231513.3+345335 with the 2.3 m Aristarchos telescope at Helmos Observatory, we estimate their physical and absolute parameters and investigate their stability and their progenitors. The light curves are analyzed by performing a two-dimensional scan on the mass–ratio inclination plane with Phoebe-0.31 scripter, while the errors are estimated using Monte Carlo simulations and heuristic scanning of the parameter space. Our analysis revealed that all 9 CSS systems have extreme mass ratios from 0.09 to 0.16. Our statistical analysis of well-studied LMR contact binaries shows that LMR systems tend to have warmer and more massive primaries. The investigation of the progenitors of both low and higher-mass-ratio systems reveals a trend for the former to originate from higher-mass ancestors. Finally, we investigate the stability condition by calculating the ratio of spin angular momentum to orbital angular momentum and other stability indicators in the context of the reliability of the solutions.

X-Ray Quasi-periodic Eruptions and Tidal Disruption Events Prefer Similar Host Galaxies

In the past 5 yr, six X-ray quasi-periodic eruption (QPE) sources have been discovered in the nuclei of nearby galaxies. Their origin remains an open question. We present Multi Unit Spectroscopic Explorer integral field spectroscopy of five QPE host galaxies to characterize their properties. We find that 3/5 galaxies host extended emission-line regions (EELRs) up to 10 kpc in size. The EELRs are photoionized by a nonstellar continuum, but the current nuclear luminosity is insufficient to power the observed emission lines. The EELRs are decoupled from the stars both kinematically and in projected sky position, and the low velocities and velocity dispersions (<100 km s−1 and ≲75 km s−1, respectively) are inconsistent with being driven by active galactic nuclei (AGNs) or shocks. The origin of the EELRs is likely a previous phase of nuclear activity. QPE host galaxies share several similarities with tidal disruption event (TDE) hosts, including an overrepresentation of galaxies with strong Balmer absorption and little ongoing star formation, as well as a preference for a short-lived (the typical EELR lifetime is ∼15,000 yr), gas-rich phase where the nucleus has recently faded significantly. This suggests that QPEs and TDEs may share a common formation channel, disfavoring AGN accretion disk instabilities as the origin of QPEs. If QPEs are related to extreme mass ratio inspiral systems (EMRIs), e.g., stellar-mass objects on bound orbits about massive black holes, the high incidence of EELRs and recently faded nuclei could be used to localize the hosts of EMRIs discovered by low-frequency gravitational-wave observatories.

Viscous torque in turbulent magnetized active galactic nucleus accretion disks and its effects on the gravitational waves of extreme mass ratio inspirals

The merger of supermassive black holes produces millihertz gravitational waves (GWs), which are potentially detectable by the future Laser Interferometer Space Antenna (LISA). Such binary systems are usually embedded in an accretion disk environment at the center of an active galactic nucleus (AGN). Recent studies suggest the plasma environment imposes measurable imprints on the GW signal if the mass ratio of the binary is around q ∼ 10−4 − 10−3. The effect of the gaseous environment on the GW signal is strongly dependent on the disk’s parameters; therefore, it is believed that future low-frequency GW detections will provide us with precious information about the physics of AGN accretion disks. We investigated this effect by measuring the viscous torque via modeling of the evolution of magnetized tori around the primary massive black hole. Using the general relativistic magnetohydrodynamic HARM-COOL code, we performed 2D and 3D simulations of weakly magnetized, thin accretion disks, with a possible truncation and transition to advection-dominated accretion flow. We studied the angular momentum transport and turbulence generated by the magnetorotational instability. We quantified the disk’s effective alpha viscosity and its evolution over time. We applied our numerical results to quantify the relativistic viscous torque on a hypothetical low-mass secondary black hole via a 1D analytical approach, and we estimated the GW phase shift due to the gas environment.

Repeating nuclear transients as candidate electromagnetic counterparts of LISA extreme mass ratio inspirals

ABSTRACT Extreme mass ratio inspirals (EMRIs) are one of the primary targets for the recently adopted millihertz gravitational-wave observatory LISA. Some previous studies have argued that a fraction of all EMRIs form in matter-rich environments, and can potentially explain the dozens of soft X-ray band ($\sim 10^{-1}\,\rm keV$), low-frequency ($\sim 0.1$ mHz) periodic phenomena known as quasi-periodic eruptions (QPEs) and quasi-periodic oscillations (QPOs). Here, using a representative EMRI population retrofitted with cutoffs on LISA-band SNRs and luminosity distances to account for the sensitivity of current instruments, we estimate the mean frequency band in which QPEs and QPOs originating from detectable LISA EMRIs may be emitting an X-ray signal ‘today’ (i.e. in 2024) to be $0.46 \pm 0.22$ mHz. We also model the well-known QPO source, RE J1034+396, which falls in this frequency band, as an EMRI assuming its primary black hole mass to be $10^6{-}10^7 \,{\rm M}_\odot$. Through a prior-predictive analysis, we estimate the orbiting compact object’s mass to be $46^{+ 10}_{-40} \,{\rm M}_\odot$ and the source’s LISA-band SNR as $\approx 14$, highlighting it as a candidate multimessenger EMRI target. We also highlight the role of current and near-future X-ray and UV observatories in enabling multimessenger observations of EMRIs in conjunction with LISA, and conclude with a discussion of caveats of the current analysis, such as the exclusion of eccentricity and inclination from the model, and the measurability of subsolar mass compact object EMRIs.

Discovering Love numbers through resonance excitation during extreme mass ratio inspirals

General Relativity predicts that black holes (BHs) do not possess an internal structure and consequently cannot be excited. This leads to a specific prediction about the waveform of gravitational waves (GWs) which they emit during a binary BH inspiral and to the vanishing of their Love numbers. However, if astrophysical BHs do possess an internal structure, their Love numbers would no longer vanish, and they could be excited during an inspiral by the transfer of orbital energy. This would affect the orbital period and lead to an observable imprint on the emitted GWs waveform. The effect is enhanced if one of the binary companions is resonantly excited. We discuss the conditions for resonant excitation of a hypothetical internal structure of BHs and calculate the phase change of the GWs waveform that is induced due to such resonant excitation during intermediate- and extreme-mass-ratio inspirals. We then relate the phase change to the electric quadrupolar Love number of the larger companion, which is resonantly excited by its smaller companion. We discuss the statistical error on measuring the Love number by LISA and show that, because of this phase change, the statistical error is small even for values of the Love number as small as 10−4 for moderate values of the spin parameter. Our results indicate that, for extreme-mass-ratio inspirals with moderate spin parameter, the Love number could be detected by LISA with an accuracy which is higher by up to two orders of magnitude than what can be achieved via tidal deformation effects. Thus, our results indicate that resonant excitation of the central BH during an extreme- or intermediate-mass-ratio inspirals is the most promising effect for putting bounds on, or detecting, non-vanishing tidal Love numbers of BHs.