arXiv subjects

Michael L. Katz

Publications and source records attributed to Michael L. Katz.

At least 19 recordsLinked to original sources

arXiv2026

Learned proposals in trans-dimensional inference are optimal at equilibrium, not during assembly

Inferring the dimension of a model - the number of components needed to explain data - jointly with the parameters is a pervasive problem, from counting sources in an image to mixture modeling, and reversible-jump Markov chain Monte Carlo solves it exactly but mixes slowly. Learned proposals are well established at fixed dimension, but whether they can accelerate the dimension-changing moves themselves has remained largely untested. We show that the answer has a structural origin: the optimal proposal for the dimension-changing birth move is a different object in different phases of the run. While the fit is being assembled it must match the current residual - a state-dependent quantity no state-independent network can represent - but at equilibrium it degenerates to the posterior's single-component marginal, which is exactly the distribution an adaptive normalizing flow learns from the sampler's own history. A learned state-independent birth proposal is therefore useless in one phase and optimal in the other. Controlled experiments confirm the attribution: applied with an exact Metropolis--Hastings correction that leaves the target invariant for any network, the learned births leave acceptance rates unchanged yet accelerate model-order mixing - in a ten-seed benchmark they meet a pre-specified stopping rule in six of ten runs, typically several times sooner, where a strong hand-tuned baseline meets it in one (one-sided p=0.03) - and an isolation experiment shows the same flow deployed within-model buys nothing. Making no domain-specific assumptions, the same sampler counts sources in a noisy image and reconstructs signals across scientific domains, including gravitational waves from ground- and space-based detectors and a scalp EEG recording. We release the method as HyperWave, an open-source package.

physics.data-an↗

arXiv2026

Eccentric Stellar-mass Binary Black Holes: Population, Detectability, and Waveform Analysis in the LISA and LIGO Era

Eccentric binary black holes (BBHs) formed through dynamical interactions can significantly contribute to gravitational wave (GW) detections. In this work, we present a simulated catalog of dynamically-formed, stellar-mass BBHs in the local universe, incorporating contributions from the Galactic field (flyby interactions), Galactic nucleus (eccentric Kozai-Lidov evolution), and globular clusters (N-body interactions). Our results predict a wide, highly eccentric BBH population in the Milky Way (MW), with source counts of $\sim 36, 13, 4.7, 2.3, 1.0$ (for $\mathrm{SNR} > 1, 3, 8, 20, 50$, respectively) during a 10-yr LISA observation. Extending this model to cosmological populations, we show that different dynamical channels can produce distinct eccentricity distributions in the LVK band and can contribute hundreds of additional low-SNR mHz sources. Specifically, our model yields a merger rate of $Γ\sim 9 \mathrm{Gpc}^{-3}\mathrm{yr}^{-1}$ and $\sim 490$ extragalactic mHz BBHs with $\mathrm{SNR} > 1$. However, due to the lower mass and weaker GW signals of stellar-mass BBHs, this number declines sharply at higher detection thresholds (e.g., $\sim 1$ for $\mathrm{SNR} > 8$). We further highlight the impact of eccentric BBH signals on the LISA global fit, showing that their individual harmonics can be independently detected in the Milky Way, and may mimic circular binaries with systematically biased chirp masses. Lastly, we show that post-Newtonian waveforms converge reliably for eccentric BBHs with masses of $\lesssim 10^3 M_\odot$ in the mHz band. Overall, eccentric BBHs represent a prevalent and promising target for future space-based GW observatories. The simulated catalog and the LISA Eccentricity Astrophysics Package (LEAP) developed in this work are publicly available at https://github.com/zeyuanxuan/lisa-leap/.

astro-ph.HE↗

arXiv2026

Waveform Modelling for the Laser Interferometer Space Antenna

LISA, the Laser Interferometer Space Antenna, will usher in a new era in gravitational-wave astronomy. As the first anticipated space-based gravitational-wave detector, it will expand our view to the millihertz gravitational-wave sky, where a spectacular variety of interesting new sources abound: from millions of ultra-compact binaries in our Galaxy, to mergers of massive black holes at cosmological distances; from the beginnings of inspirals that will venture into the ground-based detectors' view to the death spiral of compact objects into massive black holes, and many sources in between. Central to realising LISA's discovery potential are waveform models, the theoretical and phenomenological predictions of the pattern of gravitational waves that these sources emit. This white paper is presented on behalf of the Waveform Working Group for the LISA Consortium. It provides a review of the current state of waveform models for LISA sources, and describes the significant challenges that must yet be overcome.

gr-qc↗

arXiv2025

The Fast and the Frame-Dragging: Efficient waveforms for asymmetric-mass eccentric equatorial inspirals into rapidly-spinning black holes

Observations of gravitational-wave signals emitted by compact binary inspirals provide unique insights into their properties, but their analysis requires accurate and efficient waveform models. Intermediate- and extreme-mass-ratio inspirals (I/EMRIs), with mass ratios $q \gtrsim 10^2$, are promising sources for future detectors such as the Laser Interferometer Space Antenna (LISA). Modelling waveforms for these asymmetric-mass binaries is challenging, entailing the tracking of many harmonic modes over thousands to millions of cycles. The FastEMRIWaveforms (FEW) modelling framework addresses this need, leveraging precomputation of mode data and interpolation to rapidly compute adiabatic waveforms for eccentric inspirals into zero-spin black holes. In this work, we extend FEW to model eccentric equatorial inspirals into black holes with spin magnitudes $|a| \leq 0.999$. Our model supports eccentricities $e < 0.9$ and semi-latus recta $p < 200$, enabling the generation of long-duration IMRI waveforms, and produces waveforms in $\sim 100$ ms with hardware acceleration. Characterising systematic errors, we estimate that our model attains mismatches of $\sim 10^{-5}$ (for LISA sensitivity) with respect to error-free adiabatic waveforms over most of parameter space. We find that kludge models introduce errors in signal-to-noise ratios (SNRs) as great as $^{+60\%}_{-40\%}$ and induce marginal biases of up to $\sim 1σ$ in parameter estimation. We show LISA's horizon redshift for I/EMRI signals varies significantly with $a$, reaching a redshift of $3$ ($15$) for EMRIs (IMRIs) with only minor $(\sim10\%)$ dependence on $e$ for an SNR threshold of 20. For signals with SNR $\sim 50$, spin and eccentricity-at-plunge are measured with uncertainties of $δa \sim 10^{-7}$ and $δe_f \sim 10^{-5}$. This work advances the state-of-the-art in waveform generation for asymmetric-mass binaries.

gr-qc↗

arXiv2025

A pipeline for searching and fitting instrumental glitches in LISA data

Instrumental artefacts, such as glitches, can significantly compromise the scientific output of LISA. Our methodology employs advanced Bayesian techniques, including Reversible Jump Markov Chain Monte Carlo and parallel tempering to find and characterize glitches and astrophysical signals. The robustness of the pipeline is demonstrated through its ability to simultaneously handle diverse glitch morphologies and it is validated with a 'Spritz'-type data set from the LISA Data Challenge. Our approach enables accurate inference on Massive Black Hole Binaries, while simultaneously characterizing both instrumental artefacts and noise. These results present a significant development in strategies for differentiating between instrumental noise and astrophysical signals, which will ultimately improve the accuracy and reliability of source population analyses with LISA.

gr-qc↗

arXiv2025

Mind the gap: addressing data gaps and assessing noise mismodeling in LISA

Due to the sheer complexity of the Laser Interferometer Space Antenna (LISA) space mission, data gaps arising from instrumental irregularities and/or scheduled maintenance are unavoidable. Focusing on merger-dominated massive black hole binary signals, we test the appropriateness of the Whittle-likelihood on gapped data in a variety of cases. From first principles, we derive the likelihood valid for gapped data in both the time and frequency domains. Cheap-to-evaluate proxies to p-p plots are derived based on a Fisher-based formalism, and verified through Bayesian techniques. Our tools allow to predict the altered variance in the parameter estimates that arises from noise mismodeling, as well as the information loss represented by the broadening of the posteriors. The result of noise mismodeling with gaps is sensitive to the characteristics of the noise model, with strong low-frequency (red) noise and strong high-frequency (blue) noise giving statistically significant fluctuations in recovered parameters. We demonstrate that the introduction of a tapering window reduces statistical inconsistency errors, at the cost of less precise parameter estimates. We also show that the assumption of independence between inter-gap segments appears to be a fair approximation even if the data set is inherently coherent. However, if one instead assumes fictitious correlations in the data stream, when the data segments are actually independent, then the resultant parameter recoveries could be inconsistent with the true parameters. The theoretical and numerical practices that are presented in this work could readily be incorporated into global-fit pipelines operating on gapped data.

gr-qc↗

arXiv2024

An efficient GPU-accelerated multi-source global fit pipeline for LISA data analysis

The large-scale analysis task of deciphering gravitational wave signals in the LISA data stream will be difficult, requiring a large amount of computational resources and extensive development of computational methods. Its high dimensionality, multiple model types, and complicated noise profile require a global fit to all parameters and input models simultaneously. In this work, we detail our global fit algorithm, called ``Erebor,'' designed to accomplish this challenging task. It is capable of analysing current state-of-the-art datasets and then growing into the future as more pieces of the pipeline are completed and added. We describe our pipeline strategy, the algorithmic setup, and the results from our analysis of the LDC2A Sangria dataset, which contains Massive Black Hole Binaries, compact Galactic Binaries, and a parameterized noise spectrum whose parameters are unknown to the user. The Erebor algorithm includes three unique and very useful contributions: GPU acceleration for enhanced computational efficiency; ensemble MCMC sampling with multiple MCMC walkers per temperature for better mixing and parallelized sample creation; and special online updates to reversible-jump (or trans-dimensional) sampling distributions to ensure sampler mixing and accurate initial estimates for detectable sources in the data. We recover posterior distributions for all 15 (6) of the injected MBHBs in the LDC2A training (hidden) dataset. We catalog $\sim12000$ Galactic Binaries ($\sim8000$ as high confidence detections) for both the training and hidden datasets. All of the sources and their posterior distributions are provided in publicly available catalogs.

gr-qc↗

arXiv2024

Measuring source properties and quasi-normal-mode frequencies of heavy massive black-hole binaries with LISA

The laser-interferometer space antenna (LISA) will be launched in the mid 2030s. It promises to observe the coalescence of massive black-hole (BH) binaries with signal-to-noise ratios (SNRs) reaching thousands. Crucially, it will detect some of these binaries with high SNR both in the inspiral and the merger-ringdown stages. Such signals are ideal for tests of General Relativity (GR) using information from the whole waveform. Here, we consider astrophysically motivated binary systems at the high-mass end of the population observable by LISA, and simulate their signals using the newly developed multipolar effective-one-body model: \texttt{pSEOBNRv5HM}. The merger-ringdown signal in this model depends on the binary properties, and also on parameters that describe fractional deviations from the GR quasi-normal-mode (complex) frequencies of the remnant BH. Performing full Bayesian analyses, we assess to which accuracy LISA will be able to constrain deviations from GR in the ringdown signal when using information from the whole signal. We find that these deviations can typically be constrained to within $10\%$ and in the best cases to within $1\%$. We also show that with this model we can measure the binary masses and spins with great accuracy even for very massive BH systems with low SNR in the inspiral. We also probe the accuracy of the \texttt{SEOBNRv5HM} waveform family by performing synthetic injections of GR numerical-relativity waveforms. Using a novel method that we develop here to quantify the impact of systematic errors, we show that already for sources with SNR $\mathcal{O}(100)$, we would measure erroneous deviations from GR due to waveform model inaccuracies. One of the main sources of error is the mismodelling of the relative alignment between harmonics. Our results confirm the need for improving waveform models to perform tests of GR with high SNR binary BHs observed by LISA.

gr-qc↗

arXiv2024

Adiabatic waveforms for extreme mass-ratio inspirals via multivoice decomposition in time and frequency

We compute adiabatic waveforms for extreme mass-ratio inspirals (EMRIs) by "stitching" together a long inspiral waveform from a sequence of waveform snapshots, each of which corresponds to a particular geodesic orbit. We show that the complicated total waveform can be regarded as a sum of "voices." Each voice evolves in a simple way on long timescales, a property which can be exploited to efficiently produce waveform models that faithfully encode the properties of EMRI systems. We look at examples for a range of different orbital geometries: spherical orbits, equatorial eccentric orbits, and one example of generic (inclined and eccentric) orbits. To our knowledge, this is the first calculation of a generic EMRI waveform that uses strong-field radiation reaction. We examine waveforms in both the time and frequency domains. Although EMRIs evolve slowly enough that the stationary phase approximation (SPA) to the Fourier transform is valid, the SPA calculation must be done to higher order for some voices, since their instantaneous frequency can change from chirping forward ($\dot f > 0$) to chirping backward ($\dot f < 0$). The approach we develop can eventually be extended to more complete EMRI waveform models, for example to include effects neglected by the adiabatic approximation such as the conservative self force and spin-curvature coupling.

gr-qc↗

arXiv2024

Neural density estimation for Galactic Binaries in LISA data analysis

The future space based gravitational wave detector LISA (Laser Interferometer Space Antenna) will observe millions of Galactic binaries constantly present in the data stream. A small fraction of this population (of the order of several thousand) will be individually resolved. One of the challenging tasks from the data analysis point of view will be to estimate the parameters of resolvable galactic binaries while disentangling them from each other and from other gravitational wave sources present in the data. This problem is quite often referred to as a global fit in the field of LISA data analysis. A Bayesian framework is often used to infer the parameters of the sources and their number. The efficiency of the sampling techniques strongly depends on the proposals, especially in the multi-dimensional parameter space. In this paper we demonstrate how we can use neural density estimators, and in particular Normalising flows, in order to build proposals which significantly improve the convergence of sampling. We also demonstrate how these methods could help in building priors based on physical models and provide an alternative way to represent the catalogue of identified gravitational wave sources.

gr-qc↗

arXiv2024

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 $0.044$ seconds to generate and is twice as fast to compute as its time domain counterpart when considering massive black hole masses $\geq 2 \times 10^6 \,{\rm M_\odot}$ and initial eccentricities $e_0 > 0.2$. On CPUs, the median waveform evaluation time is $5$ seconds, 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$ seconds. 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.

gr-qc↗

arXiv2023

Eryn : A multi-purpose sampler for Bayesian inference

In recent years, methods for Bayesian inference have been widely used in many different problems in physics where detection and characterization are necessary. Data analysis in gravitational-wave astronomy is a prime example of such a case. Bayesian inference has been very successful because this technique provides a representation of the parameters as a posterior probability distribution, with uncertainties informed by the precision of the experimental measurements. During the last couple of decades, many specific advances have been proposed and employed in order to solve a large variety of different problems. In this work, we present a Markov Chain Monte Carlo (MCMC) algorithm that integrates many of those concepts into a single MCMC package. For this purpose, we have built {\tt Eryn}, a user-friendly and multipurpose toolbox for Bayesian inference, which can be utilized for solving parameter estimation and model selection problems, ranging from simple inference questions, to those with large-scale model variation requiring trans-dimensional MCMC methods, like the LISA global fit problem. In this paper, we describe this sampler package and illustrate its capabilities on a variety of use cases.

astro-ph.IM↗

arXiv2023

Is there an excess of black holes around $20 M_{\odot}$? Optimising the complexity of population models with the use of reversible jump MCMC

Some analyses of the third gravitational wave catalogue released by the LIGO-Virgo-KAGRA collaboration (LVK) suggest an excess of black holes around $15-20 M_{\odot}$. In order to investigate this feature, we introduce two flexible population models, a semi-parametric one and a non-parametric one. Both make use of reversible jump Markov chain Monte-Carlo to optimise their complexity. We also illustrate how the latter can be used to efficiently perform model selection. Our parametric model broadly agrees with the fiducial analysis of the LVK, but finds a peak of events at slightly larger masses. Our non-parametric model shows this same displacement. Moreover, it also suggests the existence of an excess of black holes around $20 M_{\odot}$. We assess the robustness of this prediction by performing mock injections and running hierarchical analyses on those. We find that such a feature might be due to statistical fluctuations, given the small number of events observed so far, with a $5\%$ probability. We estimate that with a few hundreds of observations, as expected for O4, our non-parametric model will, be able to robustly determine the presence of this excess. It will then allow for an efficient agnostic inference of the properties of black holes.

gr-qc↗

arXiv2023

Probing Accretion Physics with Gravitational Waves

Gravitational-wave observations of extreme mass ratio inspirals (EMRIs) offer the opportunity to probe the environments of active galactic nuclei (AGN) through the torques that accretion disks induce on the binary. Within a Bayesian framework, we study how well such environmental effects can be measured using gravitational wave observations from the Laser Interferometer Space Antenna (LISA). We focus on the torque induced by planetary-type migration on quasicircular inspirals, and use different prescriptions for geometrically thin and radiatively efficient disks. We find that LISA could detect migration for a wide range of disk viscosities and accretion rates, for both $α$ and $β$ disk prescriptions. For a typical EMRI with masses $50M_\odot+10^6M_\odot$, we find that LISA could distinguish between migration in $α$ and $β$ disks and measure the torque amplitude with $\sim 20\%$ relative precision. Provided an accurate torque model, we also show how to turn gravitational-wave measurements of the torque into constraints on the disk properties. Furthermore, we show that, if an electromagnetic counterpart is identified, the multimessenger observations of the AGN EMRI system will yield direct measurements of the disk viscosity. Finally, we investigate the impact of neglecting environmental effects in the analysis of the gravitational-wave signal, finding 3$σ$ biases in the primary mass and spin, and showing that ignoring such effects can lead to false detection of a deviation from general relativity. This work demonstrates the scientific potential of gravitational observations as probes of accretion-disk physics, accessible so far through electromagnetic observations only.

gr-qc↗

arXiv2023

Merging Black Holes in Dwarf Galaxies: Calculating Binary Black Hole Coalescence Timescales from Simulations for LISA Detection

Supermassive black holes (SMBHs) merging in dwarf galaxies will be detectable by the Laser Interferometer Space Antenna (LISA) in the mid-2030s. Previous cosmological hydrodynamic simulations have shown the prediction of massive black holes merging in dwarf galaxies, but these simulations are limited by their resolution and cannot follow black hole pairs all the way to coalescence. We calculate the delay time between black hole pairing and merger based on the properties of the black holes and their host galaxies, and use these properties to calculate gravitational wave strains for eleven different binary black holes that merge inside dwarf galaxies from eight cosmological simulations. This delay time calculation accounts for dynamical friction due to gas and stars, loss-cone scattering, and hardening of the binary due to gravitational radiation. Out of the eleven black hole mergers in the simulations, five black hole pairs will merge within 0.8 - 8 Gyr of forming a close pair and could be observed by LISA, and the remaining six are unresolved due to resolution limitations of the simulation. As all five of the resolved close pairs merge within a Hubble time, we make the broad estimate that close SMBH pairs in dwarf galaxies will merge and be detectable by LISA, but this estimate depends on either the presence of gas during orbital decay or a solution to the dynamical buoyancy problem in cored potentials.

astro-ph.GA↗

arXiv2022

Observing the inspiral of coalescing massive black hole binaries with LISA in the era of Multi-Messenger Astrophysics

Massive black hole binaries (MBHBs) of $10^5 \, \rm M_\odot - 3 \times 10^7 \, \rm M_\odot $ merging in low redshift galaxies ($z\le4$) are sufficiently loud to be detected weeks before coalescence with the Laser Interferometer Space Antenna (LISA). This allows us to perform the parameter estimation $on$ $the$ $fly$, i.e. as a function of the time to coalescence during the inspiral phase, relevant for early warning of the planned LISA protected periods and for searches of electromagnetic signals. In this work, we study the evolution of the sky position, luminosity distance, chirp mass and mass ratio uncertainties as function of time left before merger. Overall, light systems with total intrinsic mass $\rm M_{\rm tot} = 3 \times 10^5 \, \rm M_\odot$ are characterized by smaller uncertainties than heavy ones ($\rm M_{\rm tot} = 10^7 \, \rm M_\odot$) during the inspiral. Luminosity distance, chirp mass and mass ratio are well constrained at the end of the inspiral. Concerning sky position, at $z=1$, MBHBs with $\rm M_{\rm tot} = 3 \times 10^5 \, \rm M_\odot$ can be localized with a median precision of $\simeq 10^2 \, \rm deg^2 (\simeq 1 \, \rm deg^2)$ at 1 month (1 hour) from merger, while the sky position of heavy MBHBs can be determined to $10 \, \rm deg^2$ only 1 hour before merger. However the uncertainty around the median values broadens with time, ranging in between 0.04 -- 20 $\rm deg^2$ (0.3 -- 3 $\times 10^3 \, \rm deg^2$) for light (heavy) systems at 1 hour before merger. At merger the sky localization improves down to $\simeq 10^{-1} \, \rm deg^2$ for all masses. For the benefit of the observer community, we provide the full set of data from our simulations and simple and ready-to-use analytical fits to describe the time evolution of uncertainties in the aforementioned parameters, valid for systems with total mass between $10^5$--$10^7 \, \rm M_\odot$ and redshift $0.3$--$3$.

astro-ph.HE↗

arXiv2022

Assessing the data-analysis impact of LISA orbit approximations using a GPU-accelerated response model

The analysis of gravitational wave (GW) datasets is based on the comparison of measured time series with theoretical templates of the detector's response to a variety of source parameters. For LISA, the main scientific observables will be the so-called time-delay interferometry (TDI) combinations, which suppress the otherwise overwhelming laser noise. Computing the TDI response to GW involves projecting the GW polarizations onto the LISA constellation arms, and then combining projections delayed by a multiple of the light propagation time along the arms. Both computations are difficult to perform efficiently for generic LISA orbits and GW signals. Various approximations are currently used in practice, e.g., assuming constant and equal armlengths, which yields analytical TDI expressions. In this article, we present 'fastlisaresponse', a new efficient GPU-accelerated code that implements the generic TDI response to GWs in the time domain. We use it to characterize the parameter-estimation bias incurred by analyzing loud Galactic-binary signals using the equal-armlength approximation. We conclude that equal-armlength parameter-estimation codes should be upgraded to the generic response if they are to achieve optimal accuracy for high (but reasonable) SNR sources within the actual LISA data.

gr-qc↗

arXiv2022

Bayesian Characterisation of Circumbinary Exoplanets with LISA

The Laser Interferometer Space Antenna (LISA) will detect and characterize $\sim10^4$ Galactic Binaries consisting predominantly of two White Dwarfs (WD). An interesting prospect within this population is a third object--another WD star, a Circumbinary Exoplanet (CBP), or a Brown Dwarf (BD)--in orbit about the inner WD pair. We present the first fully Bayesian detection and posterior analysis of sub-stellar objects with LISA, focusing on the characterization of CBPs. We used an optimistic astrophysically motivated catalogue of these CBP third-body sources, including their orbital eccentricity around the inner binary for the first time. We examined Bayesian Evidence computations for detectability, as well as the effects on the posterior distributions for both the inner binary parameters and the third-body parameters. We find that the posterior behavior bifurcates based on whether the third-body period is above or below half the observation time. Additionally, we find that undetectable third-body sources can bias the inner binary parameters whether or not the correct template is used. We used the information retrieved from the study of the CBP population to make an initial conservative prediction for the number of detectable BD systems in the original catalogue. We end with commentary on the predicted qualitative effects on LISA global fitting and Galactic Binary population analysis. The procedure used in this work is generic and can be directly applied to other astrophysical effects expected within the Galactic Binary population.

astro-ph.EP↗