arXiv subjects

Will M. Farr

Publications and source records attributed to Will M. Farr.

At least 19 recordsLinked to original sources

arXiv2026

Constraining Gravitational Wave Memory with Hierarchical Inference

With the multitude of gravitational wave observations that have been made in the past ten years, probing the dynamical and nonlinear nature of strong gravity is becoming more and more feasible. One promising way to test the nonlinear nature of Einstein's theory of general relativity (GR) is through the gravitational wave null memory effect: a nonlinear prediction of GR which corresponds to initially comoving observers being permanently displaced due to a burst of gravitational radiation. Previous studies have shown that, while it is unlikely that the memory effect will be observed in a single event by the LIGO-Virgo-KAGRA (LVK) detectors, evidence for memory in the population of LVK events should be attainable after $\sim$2,000 gravitational wave detections. These works, however, largely relied on Bayes factors to perform their memory analyses: an approach that can depend sensitively on the analysis priors and, when naively multiplied across many events, can even favor incorrect conclusions. In this work, using the GWTC-5.0 catalog of binary black hole observations, we instead perform hierarchical Bayesian inference -- which is not subject to the issues associated with Bayes factors -- to measure the evidence for memory in current LVK observations. We find that we can constrain what we call the memory enhancement factor -- the constant appearing in front of the contribution to the strain from the supermomentum flux -- to $0.26_{-4.08}^{+4.09}$ (with $\pm$ values denoting the 68\% credible interval), consistent with its GR value of 1. We also forecast that $\sim$2,000 detections will be needed to constrain the memory enhancement factor away from zero at the $1\sigma$ level.

gr-qc↗

arXiv2026

Scalable Gaussian Processes for Integrated and Overlapping Measurements Via Augmented State Space Models

Astronomical measurements are often integrated over finite exposures, which can obscure latent variability on comparable timescales. Correctly accounting for exposure integration with Gaussian Processes (GPs) in such scenarios is essential but computationally challenging: once exposure times vary or overlap across measurements, the covariance matrix forfeits any quasiseparability, forcing O($N^2$) memory and O($N^3$) runtime costs. Linear Gaussian state space models (SSMs) are equivalent to GPs and have well-known O($N$) solutions via the Kalman filter and RTS smoother. In this work, we extend the GP-SSM equivalence to handle integrated measurements while maintaining scalability by augmenting the SSM with an integral state that resets at exposure start times and is observed at exposure end times. This construction yields exactly the same posterior as a fully integrated GP but in O($N$) time on a CPU, and is parallelizable down to O($N/T + \log T$) on a GPU with $T$ parallel workers. We present smolgp (State space Model for O(Linear/log) GPs), an open-source Python/JAX package offering drop-in compatibiltiy with tinygp while supporting both standard and exposure-aware GP modeling. As SSMs provide a framework for representing general GP kernels via their series expansion, smolgp also brings scalable performance to many commonly used covariance kernels in astronomy that lack quasiseparability, such as the quasiperiodic kernel. The substantial performance boosts at large $N$ will enable massive multi-instrument cross-comparisons where exposure overlap is ubiquitous, and unlocks the potential for analyses with more complex models and/or higher dimensional datasets.

astro-ph.IM↗

arXiv2025

Polka-dotted Stars II: Starspots and obliquities of Kepler-17 and Kepler-63

Starspots trace stellar magnetic activity and influence both stellar evolution and exoplanet characterization. While occultation-based spot analyses have been applied to individual systems, comparative studies remain limited. We apply the StarryStarryProcess Bayesian surface-mapping framework to archival Kepler light curves of two planet hosts, Kepler-63 and Kepler-17, extending the validation established on TOI-3884 (Paper I). Across both systems, we infer characteristic spot radii smaller than 10 degrees. The latitudinal spot distributions of these G dwarfs show active latitudes: Kepler-63 near 30 degrees and Kepler-17 near 15 degrees. Our analysis yields stellar obliquity measurements in excellent agreement with previous studies, validating our methodology and demonstrating that transit-based surface mapping can simultaneously recover planetary parameters, stellar orientations, and magnetic morphologies. Together, these results reveal a range of stellar geometries from nearly aligned (Kepler-17) to highly misaligned (Kepler-63).

astro-ph.EP↗

arXiv2025

Surprisingly Similar: The Mass Function of Gaia Neutron Stars and First-Born Double Neutron Stars

The mass distribution of neutron stars encodes information about their formation and binary evolution. We compare the masses of two distinct populations: I) the recently identified Gaia neutron stars in wide orbits with solar-like companions and, II) the assumed first-born recycled pulsar in Galactic double neutron star systems. Naively, one would expect their masses to differ due to both the presumed differences in their evolutionary histories, as well as astrophysical selection effects that can filter out configurations that would merge or be disrupted. Yet, we find that their mass distributions are strikingly similar. Using a two-component Gaussian model, we find that both populations exhibit a narrow component centred near $1.3 \text{ M}_\odot$, accompanied by a broader, higher-mass component that extends the distribution toward larger masses. The highest density regions of their fitted parameter posteriors coincide by over 91.6%. Statistical tests further confirm the agreement between these distributions with a Jensen-Shannon divergence $JS < 0.08$ and an earth mover's distance of $W <0.063 \text{ M}_\odot$ at 90% credibility. This finding seems to imply that both mass functions reflect the natal mass distribution of first-born neutron stars in binary systems, supporting the hypothesis that neutron stars can be born with high masses. Consequently and perhaps surprisingly, binary evolutionary processes need not impart features on the NS mass distribution.

astro-ph.SR↗

arXiv2025

A Mid-Thirties Crisis: Dissecting the Properties of Gravitational Wave Sources Near the 35 Solar Mass Peak

One striking feature of binary black hole (BBH) mergers observed in the first decade of gravitational-wave astronomy is an excess of events with component masses around $35\,\mathrm{M}_{\odot}$. Multiple formation channels have been proposed to explain this excess. To distinguish among these channels, it is essential to examine their predicted population-level distributions across additional parameters. In this work, we focus on BBH mergers near the $35\,\mathrm{M}_{\odot}$ peak and infer the population distributions of primary mass ($m_1$), mass ratio ($q$), effective spin ($χ_{\rm eff}$), and redshift ($z$). We observe a gradual increase in the merger rate with $m_1$, rising by a factor of $3$ from $20\,\mathrm{M}_{\odot}$ to a peak around $34\,\mathrm{M}_{\odot}$, followed by a sharp, order-of-magnitude decline by $50\,\mathrm{M}_{\odot}$. This population also shows a weak preference for equal-mass mergers and has a $χ_{\rm eff}$ distribution skewed toward positive values, with a median of zero excluded at approximately $90\%$ confidence. We find no significant $q-χ_{\rm eff}$ correlation in the $35\, \mathrm{M}_{\odot}$ peak population, suggesting that lower-mass systems ($m_1<20\,\mathrm{M}_{\odot}$) likely drive the $q-χ_{\rm eff}$ anti-correlation observed in the full BBH merger catalog. The redshift evolution of the merger rate is consistent with the cosmic star formation rate. We compare our findings with predictions from a wide range of formation channels. We find that common variants of the pair-instability supernova scenario, as well as hierarchical mergers, are incompatible with the observed features of the $35\,\mathrm{M}_{\odot}$ population. Ultimately, none of the formation channels we consider can explain all or even most of the features observed in this population. The ''mid-thirties'' of black hole mergers are in crisis.

astro-ph.HE↗

arXiv2025

GW231123 ringdown: interpretation as multimodal Kerr signal

GW231123 is a short-duration, low-frequency gravitational wave signal consistent with a binary black hole coalescence and dominated by the merger-ringdown regime due to the high mass of the source. We demonstrate that fits of this ringdown signal using two quasinormal modes are statistically preferred over single-mode fits, for a broad range of fit start times. We also find that two-mode fits give remnant mass and spin measurements consistent with those of the inspiral-merger-ringdown model NRSur7dq4, whereas one-mode fits struggle to do so. Agreement of our fits with those of NRSur7dq4 is achieved by labeling the two quasinormal modes as the ${(\ell,m)=(2,2)}$ and ${(2,0)}$ Kerr prograde fundamental modes. However, we find some indications that fits with the ${(2,1)}$ quasinormal mode instead of the ${(2,0)}$ mode may describe the data better, hinting at possible NRSur7dq4 error or other systematics. When fitting at early times near the estimated peak strain, we find that the inclusion of a third mode, an ${(\ell,m,n)=(2,2,1)}$ prograde overtone, improves consistency with fits at later times. Finally, we perform a test of general relativity by searching for deviations from the Kerr frequency spectrum. Setting issues of systematics aside, we validate the Kerr frequency and damping rate spectrum to within $\pm10\%$ at the 90$\%$ credible level using a fundamental mode fit, and we also report $\pm8\%$ constraints using a model with fundamental modes and an overtone fit at times near the peak strain. Understanding the systematic errors that may be affecting the most accurate analyses of GW231123 is crucial in the context of population and binary formation studies -- our ${(2,1)}$ mode fits return a significantly higher remnant mass and spin than all available inspiral-merger-ringdown models including NRSur7dq4, and this difference in parameter estimates may have astrophysical implications.

gr-qc↗

arXiv2025

Rotation Periods for Stars in Open Cluster NGC 6819 From Kepler IRIS Light Curves

We present an updated catalog of stellar rotation periods for the 2.5 Gyr open cluster NGC 6819 using the Kepler IRIS light curves from superstamp data. Our analysis uses Gaussian Process modeling to extract robust rotation signals from image subtraction light curves, allowing us unprecedented data access and measurement precision in the crowded cluster field. After applying stringent quality and contamination cuts, we identify 271 reliable rotation periods, representing by far the largest sample of rotators measured in a single intermediate-age cluster. Compared to previous work, which relied on only ~30 stars, our catalog extends the gyrochronological sequence of NGC 6819 with an order of magnitude more measurements and improved precision. The expanded dataset reveals both the expected temperature-dependent spin-down trend and substantial scatter at fixed effective temperature, including a bimodal distribution of fast and slow rotators. We also identify a distinct ``pile-up'' sequence consistent with predictions of weakened magnetic braking at critical Rossby numbers. These results strengthen this cluster's role as a benchmark for stellar spin evolution, while also highlighting the limitations of traditional gyrochronology at older ages. The final catalog and the model implementations are all available on Zenodo.

astro-ph.SR↗

arXiv2025

Inference with finite time series II: the window strikes back

Smooth window functions are often applied to strain data when inferring the parameters describing the astrophysical sources of gravitational-wave transients. Within the LIGO-Virgo-KAGRA collaboration, it is conventional to include a term to account for power loss due to this window in the likelihood function. We show that the inclusion of this factor leads to biased inference. The simplest solution to this, omitting the factor, leads to unbiased posteriors and Bayes factor estimates provided the window does not suppress the signal for signal-to-noise ratios $\lesssim O(100)$, but unreliable estimates of the absolute likelihood. Instead, we propose a multi-stage method that yields consistent estimates for the absolute likelihood in addition to unbiased posterior distributions and Bayes factors for signal-to-noise ratios $\lesssim O(1000)$. Additionally, we demonstrate that the commonly held wisdom that using rectangular windows necessarily leads to biased inference is incorrect.

gr-qc↗

arXiv2025

Polka-dotted Stars: a Hierarchical Model for Mapping Stellar Surfaces Using Occultation Light Curves and the Case of TOI-3884

We present StarryStarryProcess, a novel hierarchical Bayesian framework for mapping stellar surfaces using exoplanet transit light curves. While previous methods relied solely on stellar rotational light curves -- which contain limited information about spot properties -- our approach leverages planetary transits as probes of stellar surfaces. When a planet crosses a spot during transit, it creates a distinctive change in the light curve that directly reveals spot properties. Our model integrates planetary transit modeling with stellar variability analysis by combining the spherical harmonic surface map representation from starry, the probabilistic approach to spot properties of StarryProcess, and a comprehensive transit model that accounts for spot-crossing events during transits. We demonstrate through synthetic data experiments that our model successfully recovers spot distributions, stellar orientation, and spot physical properties. We extend the framework to handle evolving stellar surfaces through time-dependent modeling. Applying our method to TESS observations of TOI-3884, we find evidence for high-latitude spot concentrations and significant spin-orbit misalignment. The transit-based approach overcomes fundamental limitations of previous models by providing constraints on spot properties that would remain hidden in the null space of rotational light curves alone. This methodology enables more accurate exoplanet characterization by disentangling stellar activity due to starspots from planetary signals while simultaneously providing insights into stellar magnetic activity patterns. The whole paper is reproducible, and can be found by clicking the GitHub icon.

astro-ph.EP↗

arXiv2025

Identifying Compact Chirping SMBHBs in LSST using Bayesian Analysis

The Legacy Survey of Space and Time (LSST) is expected to observe up to ${\sim}100$ million quasars in the next decade. In this work, we show that it is possible to use such data to measure the characteristic frequency evolution of a "chirp" induced by gravitational waves, which can serve as robust evidence for the presence of a compact supermassive black-hole binary. Following the LSST specifications, we generate mock lightcurves consisting of (i) a post-Newtonian chirp produced by orbital motion through, e.g., relativistic Doppler boosting, (ii) a damped random walk representing intrinsic quasar variability, and (iii) Gaussian photometric errors, while assuming non-uniform observations with extended gaps over a period of 10 yr. Through a fully-Bayesian analysis, we show that we can simultaneously measure the chirp and noise parameters with little degeneracy between the two. For chirp signals with an amplitude of $A = 0.5$ mag and a range of times to merger ($t_m = 15{-}10^4$ yr), we can typically measure a non-zero amplitude and positive frequency derivative with over $5σ$ credibility. For binaries with $t_m = 50$ yr, we achieve $3σ$ ($5σ$) confidence that the signal is chirping for $A \gtrsim 0.1$ ($A > 0.2$). Our analysis can take as little as 35 s (and typically $<$ 10 min) to run, making it scalable to a large number of lightcurves. This implies that LSST could, on its own, establish the presence of a compact supermassive black-hole binary, and thus discover gravitational wave sources detectable by LISA and by Pulsar Timing Arrays.

astro-ph.HE↗

arXiv2025

Black hole spectroscopy: from theory to experiment

The "ringdown" radiation emitted by oscillating black holes has great scientific potential. By carefully predicting the frequencies and amplitudes of black hole quasinormal modes and comparing them with gravitational-wave data from compact binary mergers we can advance our understanding of the two-body problem in general relativity, verify the predictions of the theory in the regime of strong and dynamical gravitational fields, and search for physics beyond the Standard Model or new gravitational degrees of freedom. We summarize the state of the art in our understanding of black hole quasinormal modes in general relativity and modified gravity, their excitation, and the modeling of ringdown waveforms. We also review the status of LIGO-Virgo-KAGRA ringdown observations, data analysis techniques, and the bright prospects of the field in the era of LISA and next-generation ground-based gravitational-wave detectors.

gr-qc↗

arXiv2025

Cosmology with Binary Neutron Stars: Does Mass-Redshift Correlation Matter?

Next-generation gravitational wave detectors are expected to detect millions of compact binary mergers across cosmological distances. The features of the mass distribution of these mergers, combined with gravitational wave distance measurements, will enable precise cosmological inferences, even without the need for electromagnetic counterparts. However, achieving accurate results requires modeling the mass spectrum, particularly considering possible redshift evolution. Binary neutron star (BNS) mergers are thought to be less influenced by changes in metallicity compared to binary black holes (BBH) or neutron star-black hole (NSBH) mergers. This stability in their mass spectrum over cosmic time reduces the chances of introducing biases in cosmological parameters caused by redshift evolution. In this study, we use the population synthesis code COMPAS to generate astrophysically motivated catalogs of BNS mergers and explore whether assuming a non-evolving BNS mass distribution with redshift could introduce biases in cosmological parameter inference. Our findings show that despite significant variations in the BNS mass distribution across binary physics assumptions and initial conditions in COMPAS, the joint mass-redshift population can be expressed as the product of the mass distribution marginalized over redshift and the redshift distribution marginalized over masses. This enables a 2% unbiased constraint on the Hubble constant-sufficient to address the Hubble tension. Additionally, we show that in the fiducial COMPAS setup, the bias from a non-evolving BNS mass model is less than 0.5% for the Hubble parameter measured at redshift 0.4. These results establish BNS mergers as strong candidates for spectral siren cosmology in the era of next-generation gravitational wave detectors.

astro-ph.CO↗

arXiv2025

Black Hole Spectroscopy for Precessing Binary Black Hole Coalescences

The spectroscopic study of black hole quasinormal modes in gravitational-wave ringdown observations is hindered by our ignorance of which modes should dominate astrophysical signals for different binary configurations, limiting tests of general relativity and astrophysics. In this work, we present a description of the quasinormal modes that are excited in the ringdowns of comparable mass, quasi-circular precessing binary black hole coalescences -- a key region of parameter space that has yet to be fully explored within the framework of black hole spectroscopy. We suggest that the remnant perturbation for precessing and non-precessing systems is approximately the same up to a rotation, which implies that the relative amplitudes of the quasinormal modes in both systems are also related by a rotation. We present evidence for this by analyzing an extensive catalog of numerical relativity simulations. Additional structure in the amplitudes is connected to the system's kick velocity and other asymmetries in the orbital dynamics. We find that the ringdowns of precessing systems need not be dominated by the ${(\ell,m)=(2,\pm 2)}$ quasinormal modes, and that instead the $(2,\pm 1)$~or~$(2,0)$ quasinormal modes can dominate. Our results are consistent with a ringdown analysis of the LIGO-Virgo gravitational wave signal GW190521, and may also help in understanding phenomenological inspiral-merger-ringdown waveform model systematics.

gr-qc↗

arXiv2025

Understanding $Ω_\mathrm{gw}(f)$ in Gravitational Wave Experiments

In this paper we provide a comprehensive derivation of the energy density in the stochastic gravitational-wave background $Ω_\mathrm{gw}(f)$, and show how this quantity is measured in ground-based detectors such as Laser Interferometer Gravitational-Wave Observatory (LIGO), space-based Laser Interferometer Space Antenna (LISA), and Pulsar Timing Arrays. By definition $Ω_\mathrm{gw}(f) \propto S_h(f)$ -- the power spectral density (PSD) of the Fourier modes of the gravitational-wave background. However, this is often confused with the PSD of the strain signal, which we call $S_\mathrm{gw}(f)$, and is a detector-dependent quantity. This has led to confusing definitions of $Ω_\mathrm{gw}(f)$ in the literature which differ by factors of up to 5 when written in a detector-dependent way. In addition to clarifying this confusion, formulas presented in this paper facilitate easy comparison of results from different detector groups, and how to convert from one measure of the strength of the background (or an upper limit) to another. Our codes are public and on GitHub.

gr-qc↗

arXiv2025

Analyzing black-hole ringdowns II: data conditioning

Time series data from observations of black hole ringdown gravitational waves are often analyzed in the time domain by using damped sinusoid models with acyclic boundary conditions. Data conditioning operations, including downsampling, filtering, and the choice of data segment duration, reduce the computational cost of such analyses and can improve numerical stability. Here we analyze simulated damped sinsuoid signals to illustrate how data conditioning operations, if not carefully applied, can undesirably alter the analysis' posterior distributions. We discuss how currently implemented downsampling and filtering methods, if applied too aggressively, can introduce systematic errors and skew tests of general relativity. These issues arise because current downsampling and filtering methods do not operate identically on the data and model. Alternative downsampling and filtering methods which identically operate on the data and model may be achievable, but we argue that the current operations can still be implemented safely. We also show that our preferred anti-alias filtering technique, which has an instantaneous frequency-domain response at its roll-off frequency, preserves the structure of posterior distributions better than other commonly used filters with transient frequency-domain responses. Lastly, we highlight that exceptionally long data segments may need to be analyzed in cases where thin lines in the noise power spectral density overlap with central signal frequencies. Our findings may be broadly applicable to any analysis of truncated time domain data with acyclic boundary conditions.

gr-qc↗

arXiv2024

The curvature dependence of gravitational-wave tests of General Relativity

High-energy extensions to General Relativity modify the Einstein-Hilbert action with higher-order curvature corrections and theory-specific coupling constants. The order of these corrections imprints a universal curvature dependence on observations while the coupling constant controls the deviation strength. In this Letter, we leverage the theory-independent expectation that modifications to the action of a given order in spacetime curvature (Riemann tensor and contractions) lead to observational deviations that scale with the system length-scale to a corresponding power. Focusing on gravitational wave observations, the relevant scale is the binary total mass, and deviations scale as a power of mass $p$ related to the action order. For example, $p=4,6$ arise in effective field theory for cubic and quartic theories respectively. We incorporate this universal scaling into theory-agnostic tests of General Relativity with current gravitational-wave observations, thus enabling constraints on the curvature scaling without compromising the agnostic nature of these tests. This introduces a flexible yet highly interpretable new paradigm for tests of General Relativity with gravitational-wave catalogs.

gr-qc↗

arXiv2024

Extracting Astrophysical Information of Highly-Eccentric Binaries in the Millihertz Gravitational Wave Band

Wide, highly eccentric ($e>0.9$) compact binaries can naturally arise as progenitors of gravitational wave (GW) mergers. These systems are expected to have a significant population in the mHz band (e.g., $\sim 3-45$ detectable stellar-mass binary black holes with $e>0.9$ in the Milky Way), with their GW signals characterized by "repeated bursts" emitted upon each pericenter passage. In this study, we show that the detection of mHz GW signals from highly eccentric stellar mass binaries in the local universe can strongly constrain their orbital parameters. Specifically, it can achieve a relative measurement error of $\sim 10^{-6}$ for orbital frequency and $\sim 1\%$ for eccentricity (as $1-e$) in most of the detectable cases. On the other hand, the binary's mass ratio, distance, and intrinsic orbital orientation may be less precisely determined due to degeneracies in the GW waveform. We also perform mock LISA data analysis to evaluate the realistic detectability of highly eccentric compact binaries. Our results show that highly eccentric systems could be efficiently identified when multiple GW sources and stationary Gaussian instrumental noise are present in the detector output. This work highlights the potential of extracting the signal of "bursting'' LISA sources to provide valuable insights into their orbital evolution, surrounding environment, and formation channels.

astro-ph.HE↗

arXiv2024

Background information: a study on the sensitivity of astrophysical gravitational-wave background searches

The vast majority of gravitational-wave signals from stellar-mass compact binary mergers are too weak to be individually detected with present-day instruments and instead contribute to a faint, persistent background. This astrophysical background is targeted by searches that model the gravitational-wave ensemble collectively with a small set of parameters. The traditional search models the background as a stochastic field and estimates its amplitude by cross-correlating data from multiple interferometers. A different search uses gravitational-wave templates to marginalize over all individual event parameters and measure the duty cycle and population properties of binary mergers. Both searches ultimately estimate the total merger rate of compact binaries and are expected to yield a detection in the coming years. Given the conceptual and methodological differences between them, though, it is not well understood how their results should be mutually interpreted. In this paper, we use the Fisher information to study the implications of a background detection in terms of which region of the Universe each approach probes. Specifically, we quantify how information about the compact binary merger rate is accumulated by each search as a function of the event redshift. For the LIGO Design sensitivity and a uniform-in-comoving-volume distribution of equal-mass 30M_sol binaries, the traditional cross-correlation search obtains 99% of its information from binaries up to redshift 2.5 (average signal-to-noise-ratio <8), and the template-based search from binaries up to redshift 1.0 (average signal-to-noise-ratio ~8). While we do not calculate the total information accumulated by each search, our analysis emphasizes the need to pair any claimed detection of the stochastic background with an assessment of which binaries contribute to said detection.

astro-ph.HE↗