arXiv subjects

Matthew Mould

Publications and source records attributed to Matthew Mould.

36 records · Page 2Linked to original sources

arXiv2025

Reconstructing parametric gravitational-wave population fits from non-parametric results without refitting the data

Combining multiple events into population analyses is a cornerstone of gravitational-wave astronomy. A critical component of such studies is the assumed population model, which can range from astrophysically motivated functional forms to non-parametric treatments that are flexible but difficult to interpret. In practice, the current approach is to fit the data multiple times with different population models to identify robust features. We propose an alternative strategy: assuming the data have already been fit with a flexible model, we present a practical recipe to reconstruct the population distribution of a different model. As our procedure postprocesses existing results, it avoids the need to access the underlying gravitational-wave data again and handle selection effects. Additionally, our reconstruction metric provides a goodness-of-fit measure to compare multiple models. We apply this method to the mass distribution of black-hole binaries detected by LIGO/Virgo/KAGRA. Our work paves the way for streamlined gravitational-wave population analyses by fitting the data once and for all with advanced non-parametric methods and careful handling of selection effects, while the astrophysical interpretation is then made accessible using our reconstruction procedure on targeted models. The key principle is that of conceptually separating data description from data interpretation.

astro-ph.HE↗

arXiv2025

Constraining Population III stellar demographics with next-generation gravitational-wave observatories

Next-generation gravitational-wave observatories will reach farther into the universe than currently possible, revealing black-hole mergers from early stellar binary systems such as Population III stars, whose properties are currently poorly constrained. We develop a method to infer the properties of their progenitor populations from gravitational-wave catalogs. Using Bayesian deep learning, we train an emulator for population-synthesis predictions of black-hole merger properties across redshift as a function of the initial stellar mass function, crucially accounting for systematic uncertainty due to the finite number of training simulations. Combined with a nonparametric model for star formation history, we analyze catalogs containing both Population I/II and III sources simulated with full Bayesian parameter estimation for a detector network of Cosmic Explorer and Einstein Telescope with one year of observing time. We demonstrate our ability to separate these two populations at high redshifts where both make comparable contributions to the black-hole merger rate, excluding a Population III merger rate of zero at nearly 100% credibility. Moreover, we can place meaningful constraints on the Population III progenitor distributions; in particular, we constrain the spectral index of the initial mass function to within roughly +/-0.5 of the true value and the log of the star formation rate density to within ~25% over redshifts 10 to 20. By leveraging astrophysics-informed and astrophysics-agnostic models, we demonstrate the discriminative power of our combined inference approach and highlight the potential of next-generation gravitational-wave observatories to uncover the details of high-redshift stellar populations.

gr-qc↗

arXiv2024

Calibrating signal-to-noise ratio detection thresholds using gravitational-wave catalogs

Searching for gravitational-wave signals is a challenging and computationally intensive endeavor undertaken by multiple independent analysis pipelines. While detection depends only on observed noisy data, it is sometimes inconsistently defined in terms of source parameters that in reality are unknown, e.g., by placing a threshold on the optimal signal-to-noise ratio (SNR). We present a method to calibrate unphysical thresholds to search results by performing Bayesian inference on real observations using a model that simultaneously parametrizes the intrinsic network optimal SNR distribution and the effect of search sensitivity on it. We find consistency with a fourth-order power law and detection thresholds of $10.5_{-2.4}^{+2.1}$, $11.2_{-1.4}^{+1.2}$, and $9.1_{-0.5}^{+0.5}$ (medians and $90\%$ credible intervals) for events with false-alarm rates less than $1\,\mathrm{yr}^{-1}$ in the first, second, and third LIGO-Virgo-KAGRA observing runs, respectively. Though event selection can only be self-consistently reproduced by physical searches, employing our inferred thresholds allows approximate observation-calibrated selection criteria to be applied when efficiency is required and injection campaigns are infeasible.

gr-qc↗

arXiv2023

QLUSTER: quick clusters of merging binary black holes

This short document illustrates QLUSTER: a toy model for populations of binary black holes in dense astrophysical environments. QLUSTER is a simple tool to investigate the occurrence and properties of hierarchical black-hole mergers detectable by gravitational-wave interferometers. QLUSTER is not meant to rival the complexity of state-of-the-art population synthesis and N-body codes but rather provide a fast, approximate, and easy-to-interpret framework to investigate some of the key ingredients of the problem. These include the binary pairing probability, the escape speed of the host environment, and the merger generation. We also introduce the "hierarchical-merger efficiency" -- an estimator that quantifies the relevance of hierarchical black-hole mergers in a given astrophysical environment.

astro-ph.HE↗

arXiv2023

One to many: comparing single gravitational-wave events to astrophysical populations

Gravitational-wave observations have revealed sources whose unusual properties challenge our understanding of compact-binary formation. Inferring the formation processes that are best able to reproduce such events may therefore yield key astrophysical insights. A common approach is to count the fraction of synthetic events from a simulated population that are consistent with some real event. Though appealing owing to its simplicity, this approach is flawed because it neglects the full posterior information, depends on an ad-hoc region that defines consistency, and fails for high signal-to-noise detections. We point out that a statistically consistent solution is to compute the posterior odds between two simulated populations, which crucially is a relative measure, and show how to include the effect of observational biases by conditioning on source detectability. Applying the approach to several gravitational-wave events and simulated populations, we assess the degree to which we can conclude model preference not just between distinct formation pathways but also between subpopulations within a given pathway.

astro-ph.HE↗

arXiv2023

Parameter estimation of binary black holes in the endpoint of the up-down instability

Black-hole binary spin precession admits equilibrium solutions corresponding to systems with (anti-) aligned spins. Among these, binaries in the up-down configuration, where the spin of the heavier (lighter) black hole is co- (counter-) aligned with the orbital angular momentum, might be unstable to small perturbations of the spin directions. The occurrence of the up-down instability leads to gravitational-wave sources that formed with aligned spins but are detected with precessing spins. We present a Bayesian procedure based on the Savage-Dickey density ratio to test the up-down origin of gravitational-wave events. This is applied to both simulated signals, which indicate that achieving strong evidence is within the reach of current experiments, and the LIGO/Virgo events released to date, which indicate that current data are not informative enough.

gr-qc↗

arXiv2023

Efficient multi-timescale dynamics of precessing black-hole binaries

We present analytical and numerical progress on black-hole binary spin precession at second post-Newtonian order using multi-timescale methods. In addition to the commonly used effective spin which acts as a constant of motion, we exploit the weighted spin difference and show that such reparametrization cures the coordinate singularity that affected the previous formulation for the case of equal-mass binaries. The dynamics on the precession timescale is written down in closed form in both coprecessing and inertial frames. Radiation reaction can then be introduced in a quasi-adiabatic fashion such that, at least for binaries on quasi-circular orbits, gravitational inspirals reduce to solving a single ordinary differential equation. We provide a broad review of the resulting phenomenology and rewrite the relevant physics in terms of the newly adopted parametrization. This includes the spin-orbit resonances, the up-down instability, spin propagation at past time infinity, and new precession estimators to be used in gravitational-wave astronomy. Our findings are implemented in version 2 of the public Python module PRECESSION. Performing a precession-averaged post-Newtonian evolution from/to arbitrarily large separation takes $\lesssim 0.1$ s on a single off-the-shelf processor - a 50x speedup compared to our previous implementation. This allows for a wide variety of applications including propagating gravitational-wave posterior samples as well as population-synthesis predictions of astrophysical nature.

gr-qc↗

arXiv2022

Deep learning and Bayesian inference of gravitational-wave populations: Hierarchical black-hole mergers

The catalog of gravitational-wave events is growing, and so are our hopes of constraining the underlying astrophysics of stellar-mass black-hole mergers by inferring the distributions of, e.g., masses and spins. While conventional analyses parametrize this population with simple phenomenological models, we propose an emulation-based approach that can compare astrophysical simulations against gravitational-wave data. We combine state-of-the-art deep-learning techniques with hierarchical Bayesian inference and exploit our approach to constrain the properties of repeated black-hole mergers from the gravitational-wave events in the most recent LIGO/Virgo catalog. Deep neural networks allow us to (i) construct a flexible single-channel population model that accurately emulates simple parametrized numerical simulations of hierarchical mergers, (ii) estimate selection effects, and (iii) recover the branching ratios of repeated-merger generations. Among our results, we find the following: The distribution of host-environment escape speeds favors values less than $100~\mathrm{km\,s^{-1}}$ but is relatively flat, with around $37\%$ of first-generation mergers retained in their host environments; first-generation black holes are born with a maximum mass that is compatible with current estimates from pair-instability supernovae; there is multimodal substructure in both the mass and spin distributions, which, in our model, can be explained by repeated mergers; and binaries with a higher-generation component make up at least $14\%$ of the underlying population. Though these results are inferred through emulation of a simplified model, the deep-learning pipeline we present is readily applicable to realistic astrophysical simulations

astro-ph.HE↗

arXiv2022

Characterization of merging black holes with two precessing spins

Spin precession in merging black-hole binaries is a treasure trove for both astrophysics and fundamental physics. There are now well-established strategies to infer from gravitational-wave data whether at least one of the two black holes is precessing. In this paper we tackle the next-in-line target, namely the statistical assessment that the observed system has two precessing spins. We find that the recently developed generalization of the effective precession spin parameter $χ_\mathrm{p}$ is a well-suited estimator to this task. With this estimator, the occurrence of two precessing spins is a necessary (though not sufficient) condition to obtain values $1<χ_\mathrm{p}\leq 2$. Confident measurements of gravitational-wave sources with $χ_\mathrm{p}$ values in this range can be taken as a conservative assessment that the binary presents two precessing spins. We investigate this argument using a large set of >100 software injections assuming anticipated LIGO/Virgo sensitivities for the upcoming fourth observing run, O4. Our results are very encouraging, suggesting that, if such binaries exist in nature and merge at a sufficient rate, current interferometers are likely to deliver the first confident detection of merging black holes with two precessing spins. We investigate prior effects and waveform systematics and, though these need to be better investigated, did not find any confident false-positive case among all the configurations we tested. Our assessment should thus be taken as conservative.

gr-qc↗

arXiv2022

Which black hole formed first? Mass-ratio reversal in massive binary stars from gravitational-wave data

Population inference of gravitational-wave catalogues is a useful tool to translate observations of black-hole mergers into constraints on compact-binary formation. Different formation channels predict identifiable signatures in the astrophysical distributions of source parameters, such as masses and spins. One example within the scenario of isolated binary evolution is mass-ratio reversal: even assuming efficient core-envelope coupling in massive stars and tidal spin-up of the stellar companion by the first-born black hole, a compact binary with a lighter, non-spinning first-born black hole and a heavier, spinning second-born black hole can still form through mass transfer from the initially more to less massive progenitor. Using current LIGO/Virgo observations, we measure the fraction of sources in the underlying population with this mass-spin combination and interpret it as a constraint on the occurrence of mass-ratio reversal in massive binary stars. We modify commonly used population models by including negligible-spin subpopulations and, most crucially, non-identical component spin distributions. We do not find evidence for subpopulations of black holes with negligible spins and measure the fraction of massive binary stars undergoing mass-ratio reversal to be consistent with zero and $<32\%$ ($99\%$ confidence). The dimensionless spin peaks around $0.2\unicode{x2013}0.3$ appear robust, however, and are yet to be explained by progenitor formation scenarios.

astro-ph.HE↗

arXiv2022

Gravitational-wave population inference at past time infinity

Population studies of stellar-mass black-hole binaries have become major players in gravitational-wave astronomy. The underlying assumptions are that the targeted source parameters refer to the same quantities for all events in the catalog and are included when modeling selection effects. Both these points have so far been neglected when estimating the orientations of the black-hole spins. In particular, the detector-frame gravitational-wave frequency used to define frequency-dependent quantities (e.g., 20 Hz) introduces an inconsistent reference between events at the population level. We solve both issues by modeling binary black-hole populations and selection effects at past time infinity, corresponding to the well-defined reference frequency of 0 Hz. We show that, while current gravitational-wave measurement uncertainties obfuscate the influence of reference frequency in population inference, ignoring spins when estimating selection effects leads to an over-prediction of spin alignment in the underlying astrophysical distribution of merging black holes.

astro-ph.HE↗

arXiv2021

Looking for the parents of LIGO's black holes

Solutions to the two-body problem in general relativity allow us to predict the mass, spin and recoil velocity of a black-hole merger remnant given the masses and spins of its binary progenitors. In this paper we address the inverse problem: given a binary black-hole merger, can we use the parameters measured by gravitational-wave interferometers to tell if the binary components are of hierarchical origin, i.e. if they are themselves remnants of previous mergers? If so, can we determine at least some of the properties of their parents? This inverse problem is in general overdetermined. We show that hierarchical mergers occupy a characteristic region in the plane composed of the effective spin parameters $χ_{\rm eff}$ and $χ_{\rm p}$, and therefore a measurement of these parameters can add weight to the hierarchical-merger interpretation of some gravitational-wave events, including GW190521. If one of the binary components has hierarchical origin and its spin magnitude is well measured, we derive exclusion regions on the properties of its parents: for example we infer that the parents of GW190412 (if hierarchical) must have had unequal masses and low spins. Our formalism is quite general, and it can be used to infer constraints on the astrophysical environment producing hierarchical mergers.

gr-qc↗

arXiv2021

Unstable binary black-hole spins: post-Newtonian theory and numerical relativity

Spin precession occurs in binary black holes whose spins are misaligned with the orbital angular momentum. Otherwise, the spin configuration is constant and the subsequent binary dynamics and gravitational-wave emission are much simpler. We summarize a series of works which has shown that, while three of the aligned configurations are stable equilibria, the `up-down' configuration, in which the heavier (lighter) black hole is (anti) aligned with the orbital angular momentum, is unstable when perturbed; at a critical point in the inspiral the black hole spins begin to tilt wildly as precession takes over. We present two equivalent approaches to derive the instability onset based on multitimescale post-Newtonian techniques, and point out that the instability has a predictable endpoint. Finally, we demonstrate the presence of this precessional instability in the strong-field regime of numerical relativity with simulations of aligned-spin binaries lasting $\sim100$ orbits before merger. The spins of up-down systems can tilt by $\sim90^\circ$, leaving a notable imprint in the emitted gravitational-wave signals and providing a possible mechanism to form precessing systems in astrophysical environments from which sources are preferentially born with (anti) aligned spins.

gr-qc↗

arXiv2021

A generalized precession parameter $χ_\mathrm{p}$ to interpret gravitational-wave data

Originally designed for waveform approximants, the effective precession parameter $χ_\mathrm{p}$ is the most commonly used quantity to characterize spin-precession effects in gravitational-wave observations of black-hole binary coalescences. We point out that the current definition of $χ_\mathrm{p}$ retains some, but not all, variations taking place on the precession timescale. We rectify this inconsistency and propose more general definitions that either fully consider or fully average those oscillations. Our generalized parameter $χ_\mathrm{p}\in[0,2]$ presents an exclusive region $χ_\mathrm{p}>1$ that can only be populated by binaries with two precessing spins. We apply our prescriptions to current LIGO/Virgo events and find that posterior distributions of $χ_\mathrm{p}$ tend to show longer tails at larger values. This appears to be a generic feature, implying that (i) current $χ_\mathrm{p}$ measurement errors might be underestimated, but also that (ii) evidence for spin precession in current data might be stronger than previously inferred. Among the gravitational-wave events released to date, that which shows the most striking behavior is GW190521.

gr-qc↗

arXiv2021

Up-down instability of binary black holes in numerical relativity

Binary black holes with spins that are aligned with the orbital angular momentum do not precess. However, post-Newtonian calculations predict that "up-down" binaries, in which the spin of the heavier (lighter) black hole is aligned (antialigned) with the orbital angular momentum, are unstable when the spins are slightly perturbed from perfect alignment. This instability provides a possible mechanism for the formation of precessing binaries in environments where sources are preferentially formed with (anti) aligned spins. In this paper, we present the first full numerical relativity simulations capturing this instability. These simulations span $\sim 100$ orbits and $\sim 3$-$5$ precession cycles before merger, making them some of the longest numerical relativity simulations to date. Initialized with a small perturbation of $1^{\circ}$-$10^{\circ}$, the instability causes a dramatic growth of the spin misalignments, which can reach $\sim 90^{\circ}$ near merger. We show that this leaves a strong imprint on the subdominant modes of the gravitational wave signal, which can potentially be used to distinguish up-down binaries from other sources. Finally, we show that post-Newtonian and effective-one-body approximants are able to reproduce the unstable dynamics of up-down binaries extracted from numerical relativity.

gr-qc↗

arXiv2020

Mapping the asymptotic inspiral of precessing binary black holes to their merger remnants

Multiple approaches are required to study the evolution of black-hole binaries. While the post-Newtonian approximation is sufficient to describe the early inspiral (even from infinitely large orbital separation), only numerical relativity can capture the full complexity of the dynamics near merger. We combine multi-timescale post-Newtonian integrations with numerical-relativity surrogate models, thus mapping the entire history of the binary from its asymptotic configuration at past-time infinity to the post-merger remnant. This approach naturally allows us to assess the impact of the precessional and orbital phase on the properties - mass, spin, and kick - of the merger remnant. These phases introduce a fundamental uncertainty when connecting the two extrema of the binary evolution.

gr-qc↗

arXiv2020

The mass gap, the spin gap, and the origin of merging binary black holes

Two of the dominant channels to produce the black-hole binary mergers observed by LIGO and Virgo are believed to be the isolated evolution of stellar binaries in the field and dynamical formation in star clusters. Their relative efficiency can be characterized by a "mixing fraction." Pair instabilities prevent stellar collapse from generating black holes more massive than about $45 M_\odot$. This "mass gap" only applies to the field formation scenario, and it can be filled by repeated mergers in clusters. A similar reasoning applies to the binary's effective spin. If black holes are born slowly rotating, the high-spin portion of the parameter space (the "spin gap") can only be populated by black hole binaries that were assembled dynamically. Using a semianalytical cluster model, we show that future gravitational-wave events in either the mass gap, the spin gap, or both can be leveraged to infer the mixing fraction between the field and cluster formation channels.

astro-ph.HE↗

arXiv2020

Endpoint of the up-down instability in precessing binary black holes

Binary black holes in which both spins are aligned with the binary's orbital angular momentum do not precess. However, the up-down configuration, in which the spin of the heavier (lighter) black hole is aligned (anti-aligned) with the orbital angular momentum, is unstable to spin precession at small orbital separations. We first cast the spin precession problem in terms of a simple harmonic oscillator and provide a cleaner derivation of the instability onset. Surprisingly, we find that following the instability, up-down binaries do not disperse in the available parameter space but evolve toward precise endpoints. We then present an analytic scheme to locate these final configurations and confirm them with numerical integrations. Namely, unstable up-down binaries approach mergers with the two spins coaligned with each other and equally misaligned with the orbital angular momentum. Merging up-down binaries relevant to LIGO/Virgo and LISA may be detected in these endpoint configurations if the instability onset occurs prior to the sensitivity threshold of the detector. As a by-product, we obtain new generic results on binary black hole spin-orbit resonances at 2nd~post-Newtonian order. We finally apply these findings to a simple astrophysical population of binary black holes where a formation mechanism aligns the spins without preference for co- or counteralignment, as might be the case for stellar-mass black holes embedded in the accretion disk of a supermassive black hole.

gr-qc↗