arXiv subjects

Michael Kesden

Publications and source records attributed to Michael Kesden.

At least 19 recordsLinked to original sources

arXiv2026

Distinguishing lensing and precessional modulation in binary black-hole inspiral waveforms

Binary black holes (BBHs) emit gravitational waves (GWs) as they inspiral towards merger. These GWs can be gravitationally lensed by large-scale structure along the line of sight, potentially creating multiple images of the same source with fixed time delays determined by the lensing geometry. As the BBHs inspiral, the GW frequency increases, leading to successive constructive and destructive interference between the multiple images. BBHs also have spins $\mathbf{S}_i$ that may be misaligned with their orbital angular momentum $\mathbf{L}$. As the BBHs inspiral, these misaligned spins cause $\mathbf{L}$ to precess about the total angular momentum $\mathbf{J}$, modulating the GW emission similar to pulsar emission resulting from a misaligned jet rotating in and out of the line of sight. We investigate the ability of a single L-shaped GW detector to distinguish between these two sources of modulation. We find that precessional modulation can mimic the lensing modulation between two images with comparable magnifications when the time delay between the images is short enough that fewer than three interference fringes occur during the time the GW signal spends in the sensitivity band of the detector. As strong lensing is rare for GW sources at moderate redshift while misaligned spins are common for BBHs produced in certain formation channels, ruling out precessional modulation is essential to identifying genuinely lensed systems.

gr-qc↗

arXiv2025

Detecting regular precession using a new gravitational waveform model directly parameterized by both precession amplitude and frequency

Nearly 210 binary black hole (BBH) mergers have been observed by the LIGO-Virgo-KAGRA network during its four observing runs. Generic BBHs are spinning, and their spins are misaligned with the orbital angular momentum $\vec{L}$. These misaligned spins cause $\vec{L}$ to precess in a cone with dimensionless precession amplitude $\tilde{\theta}$ and frequency $\tilde{\Omega}$ about the nearly constant direction of the total angular momentum. This precession modulates the observed GWs. We propose a model of regularly precessing (RP) waveforms that incorporates $\tilde{\theta}$ and $\tilde{\Omega}$ directly as parameters. We investigate how these waveforms vary as functions of these precessional parameters, as well as binary orientation and sky location. We use the Lindblom criterion to estimate that precession can be detected in a RP source with signal-to-noise ratio $\rho$ when the mismatch $\epsilon$ with a non-precessing (NP) source with otherwise identical parameters exceeds $1/2\rho^2$. Precession is most detectable when $\vec{L}$ precesses through configurations we call +~nulls during the inspiral. At +~nulls, a NP source only emits +-polarization to which the GW detector is insensitive. The large mismatch between a RP source and this vanishing NP signal enhances the detectability of precession. We also explore the detectability of precession as a function of redshift $z$ for different BBH populations. We find that for BBHs with isotropically oriented maximal spins, precession is detectable in a majority of systems out to $z \approx 0.3$ for chirp masses $10 \lesssim M_c/M_\odot \lesssim 40$ and mass ratios $q \gtrsim 0.5$. Reduced spin magnitudes or greater alignment between the spins and $\vec{L}$ make it difficult to observe beyond $z \approx 0.1$. (abridged)

gr-qc↗

arXiv2025

Identifying multiple images of gravitational-wave sources lensed by elliptical lensing potentials

Real astrophysical lenses typically lack axisymmetry, necessitating the study of gravitational-wave (GW) lensing by elliptical mass distributions to accurately assess detectability and waveform interpretation. We investigate strong lensing using the singular isothermal ellipsoid (SIE) model, which produces two or four images depending on the source's position relative to lens caustics. Employing a quasi-geometrical optics framework, we determine that the geometrical-optics approximation holds reliably for lens masses above approximately $10^5 \, M_\odot$ at GW frequencies relevant for ground-based detectors $(\sim 10^2 \,\text{Hz})$, though wave-optics effects become significant for lower masses or sources near caustics. Our waveform mismatch analysis demonstrates that the use of three-image templates significantly improves our ability to distinguish source signals, reducing mismatches from $O(10^{-1})$ to $O(10^{-2})$, typically by factors between 1.5 and 5 compared to the standard two-image template model. At lens masses above $10^7 \, M_\odot$, diffraction effects become negligible for ground-based detectors, resulting in an additional mismatch reduction by a factor of approximately three. These findings highlight the critical need for multi-image templates in GW searches to enhance detection efficiency and accuracy.

gr-qc↗

arXiv2023

Distribution of orbital inclinations for tidal disruption events by Kerr black holes

The Kerr metric that describes the spacetime of a spinning supermassive black hole (SMBH) is axisymmetric, implying that the nearly parabolic geodesics on which stars approach the SMBH depend on the inclination angle $\iota$ of the orbital angular momentum with respect to the SMBH spin. This inclination affects both the geodesic deviation that determines whether a star is tidally disrupted and whether the tidal debris survives direct capture by the event horizon to produce an observable tidal disruption event (TDE). The steady-state TDE rate is the rate at which stars are scattered into the loss cone determined by these spin- and inclination-dependent effects. As the anisotropy of this loss-cone refilling is highly uncertain, we consider the two extreme limits in which stellar inclination is preserved (IP) or isotropized (ISO). We calculate the inclination distribution in these two limits and find a prograde bias in the IP limit because of the strong retrograde bias for direct capture. However, we find a retrograde bias in the ISO limit for intermediate SMBH masses when the empty loss cone suppresses capture and allows the weaker retrograde bias of geodesic deviation to dominate. Partially empty loss cones lead to steeper distributions of the penetration factor $\beta$ than for a full loss cone, with this effect even more pronounced in the ISO limit. We also calculate the total TDE rates and maximum SMBH mass $M_{\rm \bullet, max}$ for tidal disruption in these two limits. In the IP limit, we find a highly spin-dependent capture cutoff in the TDE rate and $M_{\rm \bullet, max} \approx 10^{8.45} M_\odot$ for maximal SMBH spin. In the ISO limit, we find a strong spin-dependent enhancement in the TDE rate at intermediate SMBH masses, a weakly spin-dependent capture cutoff above $M_\bullet \approx 10^{7.5} M_\odot$, and $M_{\rm \bullet, max} \approx 10^{7.95} M_\odot$ for maximal SMBH spin.

astro-ph.HE↗

arXiv2023

Constraining black-hole binary spin precession and nutation with sequential prior conditioning

We investigate the detectability of sub-dominant spin effects in merging black-hole binaries using current gravitational-wave data. Using a phenomenological model that separates the spin dynamics into precession (azimuthal motion) and nutation (polar motion), we present constraints on the resulting amplitudes and frequencies. We also explore current constraints on the spin morphologies, indicating if binaries are trapped near spin-orbit resonances. We dissect such weak effects from the signals using a sequential prior conditioning approach, where parameters are progressively re-sampled from their posterior distribution. This allows us to investigate whether the data contain additional information beyond what is already provided by quantities that are better measured, namely the masses and the effective spin. For the current catalog of events, we find no significant measurements of weak spin effects such as nutation and spin-orbit locking. We synthesize a source with a high nutational amplitude and show that near-future detections will allow us to place powerful constraints, hinting that we may be at the cusp of detecting spin nutations in gravitational-wave data.

gr-qc↗

arXiv2023

Pathways for producing binary black holes with large misaligned spins in the isolated formation channel

Binary black holes (BBHs) can form from the collapsed cores of isolated high-mass binary stars. The masses and spins of these BBHs are determined by the complicated interplay of phenomena such as tides, winds, accretion, common-envelope evolution (CEE), supernova natal kicks, and stellar core-envelope coupling. The gravitational waves emitted during the mergers of BBHs depend on their masses and spins and can thus constrain these phenomena. We present a simplified model of binary stellar evolution and identify regions of the parameter space that produce BBHs with large spins misaligned with their orbital angular momentum. In Scenario A (B) of our model, stable mass transfer (SMT) occurs after Roche-lobe overflow (RLOF) of the more (less) massive star, while CEE follows RLOF of the less (more) massive star. Each scenario is further divided into Pathways 1 and 2 depending on whether the core of the more massive star collapses before or after RLOF of the less massive star, respectively. If the stellar cores are coupled weakly to their envelopes, highly spinning BBHs can be produced if natal spins greater than $10\%$ of the breakup value are inherited from the stellar progenitors. BBHs can alternatively acquire large spins by tidal synchronization during the Wolf-Rayet stage in Scenario A or by accretion onto the initially more massive star during SMT in Scenario B. BBH spins can be highly misaligned if the kicks are comparable to the orbital velocity, which is more easily achieved in Pathway A1 where the kick of the more massive star precedes CEE.

astro-ph.HE↗

arXiv2023

Signatures of spin precession and nutation in isolated black-hole binaries

The spin precession of binary black holes (BBHs) that originate from isolated high-mass binary stars is determined by the interplay of phenomena such as tides, winds, accretion, common-envelope evolution, natal kicks, and stellar core-envelope coupling. In previous work, we identified regions of the parameter space that may produce BBHs with large misalignments from natal kicks and high spin magnitudes from three mechanisms - tides, accretion, or inheritance via minimal core-envelope coupling. Here, we explore the spin precession of such BBHs using five parameters that describe the amplitude and frequency with which the orbital angular momentum precesses and nutates about the total angular momentum, modulating the gravitational-wave emission. Precession is generally possible for sufficiently strong natal kicks provided at least one of the black holes is spinning. Nutation is a consequence of spin-spin coupling and depends on the three spin-up mechanisms. Tidal synchronization can leave a distinct correlation between the aligned effective spin and the nutation frequency, but does not produce large nutations. When a black hole accretes $\gtrsim 20\%$ of its companion's envelope, the precession frequency and amplitude are large. A much smaller amount of accretion, e.g., $\approx 2\%$, is needed to provide a large precession frequency and amplitude when the accretor is a Wolf-Rayet (WR) star. The inheritance of high natal WR spins ($\gtrsim 5\%$ of their maximum breakup value) via minimal core-envelope coupling is the most promising mechanism for producing nutating BBHs, implying that a measurement of nutation from gravitational-wave observations may suggest isolated-binary origin with minimal core-envelope coupling.

astro-ph.HE↗

arXiv2022

Detectability of strongly lensed gravitational waves using model-independent image parameters

Strong gravitational lensing of gravitational waves (GWs) occurs when the GWs from a compact binary system travel near a massive object. The mismatch between a lensed signal and unlensed templates determines whether lensing can be identified in a particular GW event. For axisymmetric lens models, the lensed signal is traditionally calculated in terms of model-dependent lens parameters such as the lens mass $M_L$ and source position $y$. We propose that it is useful to parameterize this signal instead in terms of model-independent image parameters: the flux ratio $I$ and time delay $Δt_d$ between images. The functional dependence of the lensed signal on these image parameters is far simpler, facilitating data analysis for events with modest signal-to-noise ratios. In the geometrical-optics approximation, constraints on $I$ and $Δt_d$ can be inverted to constrain $M_L$ and $y$ for any lens model including the point mass (PM) and singular isothermal sphere (SIS) that we consider. We use our model-independent image parameters to determine the detectability of gravitational lensing in GW signals and find that for GW events with signal-to-noise ratios $ρ$ and total mass $M$, lensing should in principle be identifiable for flux ratios $I \gtrsim 2ρ^{-2}$ and time delays $Δt_d \gtrsim M^{-1}$.

gr-qc↗

arXiv2021

Two regimes of tidal-stream circularization by supermassive black holes

Stars that approach a supermassive black hole (SMBH) too closely can be disrupted by the tidal gravitational field of the SMBH. The resulting debris forms a tidal stream orbiting the SMBH which can collide with itself due to relativistic apsidal precession. These self-collisions dissipate energy, causing the stream to circularize. We perform kinematic simulations of these stream self-collisions to estimate the efficiency of this circularization as a function of SMBH mass $M_\bullet$ and penetration factor $β$, the ratio of the tidal radius to the pericenter distance. We uncover two distinct regimes depending on whether the time $t_c$ at which the most tightly bound debris circularizes is greater or less than the time $t_{\rm fb}$ at which the mass fallback rate peaks. The bolometric light curve of energy dissipated in the stream self-collisions has a single peak at $t > t_{\rm fb}$ in the slow circularization regime ($t_c > t_{\rm fb}$), but two peaks (one at $t < t_{\rm fb}$ and a second at $t_{\rm fb}$) in the fast circularization regime ($t_c < t_{\rm fb}$). Tidal streams will circularize in the slow (fast) regime for apsidal precession angles less (greater) than 0.2 radians which occur for $β\lesssim (\gtrsim) (M_\bullet/10^6M_\odot)^{-2/3}$. The observation of prominent double peaks in bolometric TDE light curves near the transition between these two regimes would strongly support our model of tidal-stream kinematics.

astro-ph.HE↗

arXiv2021

A taxonomy of black-hole binary spin precession and nutation

Binary black holes with misaligned spins will generically induce both precession and nutation of the orbital angular momentum $\bf{L}$ about the total angular momentum $\bf{J}$. These phenomena modulate the phase and amplitude of the gravitational waves emitted as the binary inspirals to merger. We introduce a "taxonomy" of binary black-hole spin precession that encompasses all the known phenomenology, then present five new phenomenological parameters that describe generic precession and constitute potential building blocks for future gravitational waveform models. These are the precession amplitude $\langleθ_L\rangle$, the precession frequency $\langle Ω_L\rangle$, the nutation amplitude $Δθ_L$, the nutation frequency $ω$, and the precession-frequency variation $ΔΩ_L$. We investigate the evolution of these five parameters during the inspiral and explore their statistical properties for sources with isotropic spins. In particular, we find that nutation of $\bf{L}$ is most prominent for binaries with high spins ($χ\gtrsim 0.5$) and moderate mass ratios ($q \sim 0.6$).

gr-qc↗

arXiv2021

Massive black hole binary inspiral and spin evolution in a cosmological framework

Massive black hole (MBH) binary inspiral time scales are uncertain, and their spins are even more poorly constrained. Spin misalignment, along with unequal mass ratios and spin magnitudes, introduces asymmetry in the gravitational radiation, which imparts a recoil kick to the merged MBH. Understanding how MBH binary spins evolve is crucial for determining their recoil velocities, their gravitational wave (GW) waveforms detectable with LISA, as well as their post-merger retention rate in galaxies and thus their subsequent merger rate. Here we present a novel study that introduces a sub-resolution model for gas- and GW-driven MBH binary spin evolution using a population of accreting MBHs from the Illustris cosmological hydrodynamics simulations. We also model sub-resolution binary inspiral via dynamical friction, stellar scattering, viscous gas drag, and GW emission. Our model assumes differential accretion, which causes greater alignment of the secondary MBH spin in unequal-mass mergers. We find that 47% of the MBHs in our population merge by $z=0$. Of these, 19% have misaligned primaries and 10% have misaligned secondaries at the time of merger in our (conservative) fiducial model. The MBH misalignment fraction depends strongly on the accretion disc parameters, however. Reducing accretion rates by a factor of 100, in a thicker disc, yields 79% and 42% misalignment for primaries and secondaries, respectively. Even in the fiducial model, more than 12% of binaries experience recoils of $>500$ km s$^{-1}$, which could displace them at least temporarily from galactic nuclei. We additionally find that a significant number of systems experience strong precession.

astro-ph.GA↗

arXiv2020

Rates of Stellar Tidal Disruption

Tidal disruption events occur rarely in any individual galaxy. Over the last decade, however, time-domain surveys have begun to accumulate statistical samples of these flares. What dynamical processes are responsible for feeding stars to supermassive black holes? At what rate are stars tidally disrupted in realistic galactic nuclei? What may we learn about supermassive black holes and broader astrophysical questions by estimating tidal disruption event rates from observational samples of flares? These are the questions we aim to address in this Chapter, which summarizes current theoretical knowledge about rates of stellar tidal disruption, and compares theoretical predictions to the current state of observations.

astro-ph.HE↗

arXiv2019

Wide nutation: binary black-hole spins repeatedly oscillating from full alignment to full anti-alignment

Within the framework of 2PN black-hole binary spin precession, we explore configurations where one of the two spins oscillates from being completely aligned with the orbital angular momentum to being completely anti-aligned with it during a single precession cycle. This "wide nutation" is the extreme limit of the generic phenomenon of spin nutation in black-hole binaries. Crucially, wide nutation happens on the short precession time scale and it is not a secular effect due to gravitational-wave radiation reaction. The spins of these binaries, therefore, flip repeatedly as one of these special configurations is entered. Binaries with total mass $M$, mass ratio $q$, and dimensionless spin $χ_1$ ($χ_2$) of the more (less) massive black hole are allowed to undergo wide nutation at binary separations $r \leq r_{\rm wide} \equiv [(q χ_2 - χ_1)/(1-q)]^2 M$. Sources that are more likely to nutate widely have similar masses and effective spins close to zero.

gr-qc↗

arXiv2018

Spin orientations of merging black holes formed from the evolution of stellar binaries

We study the expected spin misalignments of merging binary black holes (BHs) formed in isolation by combining state-of-the-art population-synthesis models with efficient post-Newtonian evolutions, thus tracking sources from stellar formation to gravitational-wave detection. We present extensive predictions of the properties of sources detectable by both current and future interferometers. We account for the fact that detectors are more sensitive to spinning BH binaries with suitable spin orientations and find that this significantly impacts the population of sources detectable by LIGO, while this is not the case for 3rd-generation detectors. We find that three formation pathways, differentiated by the order of core collapse and common-envelope phases, dominate the observed population, and that their relative importance critically depends on the recoils imparted to BHs at birth. Our models suggest that measurements of the "effective-spin" parameter $χ_{\rm eff}$ will allow for powerful constraints. For instance, we find that the role of spin magnitudes and spin directions in $χ_{\rm eff}$ can be largely disentangled, and that the symmetry of the effective-spin distribution is a robust indicator of the binary's formation history. Our predictions for individual spin directions and their precessional morphologies confirm and extend early toy models, while exploring substantially more realistic and broader sets of initial conditions. Our main conclusion is that specific subpopulations of BH binaries will exhibit distinctive precessional dynamics: these classes include (but are not limited to) sources where stellar tidal interactions act on sufficiently short timescales, and massive binaries produced in pulsational pair-instability supernovae. Measurements of BH spin orientations have enormous potential to constrain specific evolutionary processes in the lives of massive binary stars.

astro-ph.HE↗

arXiv2018

Stellar Tidal Disruption Events in General Relativity

A tidal disruption event (TDE) ensues when a star passes too close to the supermassive black hole (SMBH) in a galactic center and is ripped apart by the tidal field of the SMBH. The gaseous debris produced in a TDE can power a bright electromagnetic flare as it is accreted by the SMBH; so far, several dozen TDE candidates have been observed. For SMBHs with masses above $\sim 10^7 M_\odot$, the tidal disruption of solar-type stars occurs within ten gravitational radii of the SMBH, implying that general relativity (GR) is needed to describe gravity. Three promising signatures of GR in TDEs are: (1) a super-exponential cutoff in the volumetric TDE rate for SMBH masses above $\sim 10^8 M_\odot$ due to direct capture of tidal debris by the event horizon, (2) delays in accretion disk formation (and a consequent alteration of the early-time light curve) caused by the effects of relativistic precession on stream circularization, and (3) quasi-periodic modulation of X-ray emission due to global precession of misaligned accretion disks and the jets they launch. We review theoretical models and simulations of TDEs in Newtonian gravity, then describe how relativistic modifications give rise to these proposed observational signatures, as well as more speculative effects of GR. We conclude with a brief summary of TDE observations and the extent to which they show indications of these predicted relativistic signatures.

astro-ph.HE↗

arXiv2017

PRECESSION: Dynamics of spinning black-hole binaries with python

We present the numerical code PRECESSION: a new open-source python module to study the dynamics of precessing black-hole binaries in the post-Newtonian regime. The code provides a comprehensive toolbox to (i) study the evolution of the black-hole spins along their precession cycles, (ii) perform gravitational-wave driven binary inspirals using both orbit-averaged and precession-averaged integrations, and (iii) predict the properties of the merger remnant through fitting formulae obtained from numerical-relativity simulations. PRECESSION is a ready-to-use tool to add the black-hole spin dynamics to larger-scale numerical studies such as gravitational-wave parameter estimation codes, population synthesis models to predict gravitational-wave event rates, galaxy merger trees and cosmological simulations of structure formation. PRECESSION provides fast and reliable integration methods to propagate statistical samples of black-hole binaries from/to large separations where they form to/from small separations where they become detectable, thus linking gravitational-wave observations of spinning black-hole binaries to their astrophysical formation history. The code is also a useful tool to compute initial parameters for numerical-relativity simulations targeting specific precessing systems. PRECESSION can be installed from the Python Package Index and it is freely distributed under version control on Github, where further documentation is provided.

astro-ph.HE↗

arXiv2017

Nutational resonances, transitional precession, and precession-averaged evolution in binary black-hole systems

In the post-Newtonian (PN) regime, the timescale on which the spins of binary black holes precess is much shorter than the radiation-reaction timescale on which the black holes inspiral to smaller separations. On the precession timescale, the angle between the total and orbital angular momenta oscillates with nutation period $τ$, during which the orbital angular momentum precesses about the total angular momentum by an angle $α$. This defines two distinct frequencies that vary on the radiation-reaction timescale: the nutation frequency $ω\equiv 2π/τ$ and the precession frequency $Ω\equiv α/τ$. We use analytic solutions for generic spin precession at 2PN order to derive Fourier series for the total and orbital angular momenta in which each term is a sinusoid with frequency $Ω- nω$ for integer $n$. As black holes inspiral, they can pass through nutational resonances ($Ω= nω$) at which the total angular momentum tilts. We derive an approximate expression for this tilt angle and show that it is usually less than $10^{-3}$ radians for nutational resonances at binary separations $r > 10M$. The large tilts occurring during transitional precession (near zero total angular momentum) are a consequence of such states being approximate $n=0$ nutational resonances. Our new Fourier series for the total and orbital angular momenta converge rapidly with $n$ providing an intuitive and computationally efficient approach to understanding generic precession that may facilitate future calculations of gravitational waveforms in the PN regime.

gr-qc↗

arXiv2017

Detecting binarity of GW150914-like lenses in gravitational microlensing events

The recent discovery of gravitational waves (GWs) from stellar-mass binary black holes (BBHs) provided direct evidence of the existence of these systems. BBH lenses would have gravitational microlensing signatures that are distinct from single-lens signals. We apply Bayesian statistics to examine the distinguishability of BBH microlensing events from single-lens events under ideal observing conditions, using the photometric capabilities of the Korean Microlensing Telescope Network. Given one year of observations, a source star at the Galactic Centre, a GW150914-like BBH lens (total mass 65M$_\odot$, mass ratio 0.8) at half that distance, and an impact parameter of 0.4 Einstein radii, we find that binarity is detectable for BBHs with separations down to 0.0250 Einstein radii, which is nearly 3.5 times greater than the maximum separation for which such BBHs would merge within the age of the Universe. Microlensing searches are thus sensitive to more widely separated BBHs than GW searches, perhaps allowing the discovery of BBH populations produced in different channels of binary formation.

astro-ph.HE↗