arXiv subjects

Patrick M. Meyers

Publications and source records attributed to Patrick M. Meyers.

At least 19 recordsLinked to original sources

arXiv2026

Pulsar Timing Array Sensitivity to Anisotropy: Empirical Sensitivity Curves, Scaling Relations, and the Multi-Resolution Pixel Basis

We quantify pulsar timing array (PTA) sensitivity to anisotropy in the gravitational wave background using the cross-correlation based Fisher information matrix in the pixel and spherical harmonic bases. We use a set of simulations to empirically determine scaling relations of a PTA's sensitivity to anisotropy with the number of pulsars $N_\mathrm{psr}$ in the array, the error $δt$ on the times of arrival, the frequency $f_\mathrm{GW}$ of the gravitational waves, and the angular scale $ΔΩ$ of the anisotropy. The sensitivity scales approximately as $N_\mathrm{psr}^{0.8}$, $δt^{-0.08}$, and $ΔΩ^{1.6}-ΔΩ^{2.1}$ (depending on the ranges of $\ell$ and $m$ under consideration). In addition, we use realistic simulations to project the NANOGrav PTA sensitivity to a 30-year baseline and quantify the growth in sensitivity at several timeslices. Except at the lowest frequencies, we find negligible effect on sensitivity through increasing the observation duration only. Finally, we introduce a multi-resolution pixel basis motivated by the large dependence of the sensitivity on sky location, and demonstrate the operation of the basis through a set of injections and recoveries.

astro-ph.IM↗

arXiv2026

Mitigating the Timing Impact of Anomalous Pulse Profile Shape Variability in PSR J1713+0747 with Gaussian Component Modeling

The North American Nanohertz Observatory for Gravitational Waves (NANOGrav) achieves sub-microsecond timing precision for several millisecond pulsars in its pulsar timing array (PTA) with the objective of detecting and characterizing nanohertz gravitational waves. PSR J1713+0747 is one of the most precisely timed pulsars in the array, achieving sub-microsecond timing precision. However, in April 2021, PSR J1713+0747 underwent a sudden and unusual change in pulse shape that disrupted its timing stability. As PSR J1713+0747 is a key contributor to PTA sensitivity, variations in its pulse profile significantly affect the array's sensitivity to nanohertz gravitational waves. We apply frequency-dependent Gaussian component models to decompose the pulse profile and track the evolution of individual components through the event. This component-level method maintains phase-connected timing across the shape-change event. At L-band, the recovered TOAs have a median uncertainty of ~0.47 microseconds compared to ~0.69 microseconds for standard template matching. At 820 MHz, where profile evolution is stronger, the recovered TOAs have a median uncertainty of ~1.63 microseconds compared to ~0.67 microseconds for standard template matching. The recovered TOAs achieve timing uncertainties comparable to conventional template matching while allowing data affected by profile variability to be retained in PTA gravitational-wave analyses. These results represent an initial step toward profile-domain timing methods capable of accounting for pulse-profile evolution while reducing the need for additional timing model parameters.

astro-ph.HE↗

arXiv2026

A new framework for lightning-fast gravitational wave analysis of pulsar timing data

Pulsar timing array data analysis is computationally expensive, limiting the complexity of models which can be studied. As pulsar timing datasets and their respective models grow in size and sophistication, faster and scalable inference methods are essential. In this paper, we accelerate pulsar timing analyses by sampling in the space of Fourier coefficients instead of analytically marginalizing over them. Previous studies have shown the Fourier space induces a complex, high-dimensional posterior geometry, from which it is generally difficult to sample. We show that under an appropriate coordinate transformation the Fourier coefficients approximately follow a standard normal distribution, and may be efficiently sampled using a Hamiltonian Monte Carlo scheme. Under this coordinate transformation, for datasets of size and complexity comparable to the NANOGrav 15-year release, the new method produces converged posterior distributions for a range of models which include inter-pulsar correlations, stochastic, and deterministic signals in approximately 15 minutes on an NVIDIA GeForce RTX 3090 GPU. By comparison, the legacy pulsar timing analysis software \texttt{ENTERPRISE} would require months of computation on a CPU cluster to analyze comparable datasets under the same joint stochastic and deterministic models.

gr-qc↗

arXiv2026

The NANOGrav 15 yr Data Set: Impacts of Customized Chromatic Noise Models on Gravitational Wave Analyses

We report updated nHz gravitational wave (GW) significance, characterization, and interpretations using the customized chromatic-noise models (CNMs) developed in Larsen, Baier et al. (2026). for the NANOGrav 15-year data set. We find increased evidence for the Hellings-Downs (HD) correlation signature of the stochastic gravitational wave background (GWB), with a Bayes factor of $1571\pm14$ for HD-correlations over a common uncorrelated red-noise process using a power-law model with $14$ Fourier modes. We find this $\sim8\times$ increase in Bayes factor from Agazie et al. (2023a) is a result of improved noise mitigation. Assuming an analytic null distribution for the frequentist interpulsar correlation statistic, this corresponds to a slightly more significant measurement from $3.16σ$ to $3.32σ$ against the no-correlation scenario. Spectral inference with CNMs brings the power-law GWB amplitude down to $A_{\rm GWB} = 2.1^{+0.6}_{-0.5}\times10^{-15}$ at fixed $γ_{\rm GWB} = 13/3$. In a varied-$γ$ analysis, the spectral index increases to $γ_{\rm GWB}=3.5^{+0.7}_{-0.6}$. We report updates on an all-sky continuous gravitational wave (CW) search as well as select targeted searches and calculate a $3.2\times$ larger detection volume for the NANOGrav detector. With CNMs, we find reduced evidence for a non-Einsteinian, scalar-transverse mode of gravity. Finally, we reinterpret the GWB first with the assumption of an astrophysical background sourced by SMBHBs and then assuming the more exotic origins of cosmic inflation, a first-order cosmological phase transition, and stable cosmic strings. Under both the SMBHB hypothesis and the cosmological hypotheses, we see only marginal shifts in model parameter posteriors which are consistent with the slightly quieter and steeper power-law GWB spectrum.

astro-ph.CO↗

arXiv2026

Gravitational Wave Measurement of the $M_\mathrm{BH}$-$M_\mathrm{bulge}$ Intrinsic Scatter at High Redshift

The observed GWB spectrum is higher in amplitude than model predictions by a factor of 2-3. Using a semi-analytic model, we evaluate the effect of a high-scatter supermassive black hole (SMBH) scaling relation ($M_\mathrm{BH}$-$M_\mathrm{bulge}$) on models of the nanohertz gravitational wave background (GWB). By implementing an intrinsic scatter of the $M_\mathrm{BH}$-$M_\mathrm{bulge}$ relation, which is larger at higher redshift, but matches local observations, we find that the amplitude of GWB models increases to be consistent with the low-frequency end of the GWB spectrum. This amplitude increase is not uniform across frequencies, a strongly evolving scatter preferentially increases the number density of the most massive SMBHs which, in the GWB spectrum, minimizes the strength of the low-frequency turnover. Our models with positively evolving intrinsic scatter can reproduce the electromagnetically observed overmassive SMBHs at $4 < z < 6$ without changing the $M_\mathrm{BH}$-$M_\mathrm{bulge}$ normalization though we find that including moderate normalization evolution marginally improves fits to the GWB data. We conclude that the $M_\mathrm{BH}$-$M_\mathrm{bulge}$ relation which best describes the available GWB and electromagnetic data sets has intrinsic scatter that evolves as $\varepsilon(z) = \varepsilon_0 + (0.56 \pm 0.4) \log_{10}(1 + z)$ and normalization that evolves as $α(z) = α_0 (1 + z)^{0.84 \pm 0.35}$. The results of this work imply that the $M_\mathrm{BH}$-$M_\mathrm{bulge}$ relation we see today is not universal throughout cosmic time and that a diversity of seeding models and growth mechanisms may be at play in the early stages of SMBH-galaxy evolution.

astro-ph.HE↗

arXiv2026

Posterior Predictive Checks for Gravitational-wave Populations: Limitations and Improvements

When selecting a model to characterize an astrophysical population, it is crucial to assess whether that model fits the data and, if not, how it can be improved. To this end, posterior predictive checks (PPCs) are a widely-used statistical test of model fit when inferring gravitational-wave source populations. However, PPCs exhibit limitations when assessing single-event parameters with large measurement uncertainty, like the spin tilt angles of the binary black holes (BBHs) observable with the LIGO-Virgo-KAGRA (LVK) detectors. When single-event inference is prior-dominated, traditional PPCs fail to flag even very poor model fits. In this work, we assess the efficacy of various alternative PPCs on poorly-constrained parameters. We compare PPCs conducted on event- vs. data-level parameters (e.g. posterior samples vs. maximum likelihood points), and explore two additional event-level PPCs: partial predictive checks and split predictive checks. Independent of measurement uncertainty, we find that PPCs on maximum likelihood parameters are always more discerning of model misspecification than any event-level PPC. However, when investigating simulated GWTC-3.0-like catalogs, none of the alternative PPCs show significant improvement over those traditionally used, indicating that at that sensitivity, any limited information in the data about spin tilts is insufficient to diagnose model misspecification. Finally, we apply our suite of PPCs to the spin magnitude and tilt distributions inferred in the most recent LVK catalog, GWTC-4.0. We conclude that the Gaussian Component Spins model used therein under-predicts BBHs with large spin magnitudes and over-predicts those with perfectly anti-aligned tilts.

gr-qc↗

arXiv2026

The NANOGrav 15 yr and 20 yr Datasets: Timing Events and Pulse Shape Changes

The average pulse shape of a pulsar is typically stable over decadal timescales, enabling estimation of pulse times of arrival to better than a small fraction of the pulse width using matched filtering techniques. However, in North American Nanohertz Observatory for Gravitational Waves (NANOGrav) observations of PSR J1713+0747, three discrete timing events that depart from the prevailing timing model have been seen in the last 20 yr. All three correspond to morphological changes in pulse shape. Using principal component analysis, we analyze the pulse profiles of nine NANOGrav pulsars, including seven with profiles from the 15 yr dataset and two with additional profiles from the forthcoming 20 yr dataset. We recover the three known pulse shape change events in PSR J1713+0747 and another previously known event in PSR J1643$-$1224. We implement a ranking metric for candidate events and address four highly ranked candidates in this nine-pulsar sample. We also recover known slow pulse shape variations in PSR J1643$-$1224, PSR J1903+0327, and PSR B1937+21 and report an unexpected recurrence after ~10 yr of one such variation in PSR B1937+21.

astro-ph.HE↗

arXiv2026

Inference on inner galaxy structure via gravitational waves from supermassive binaries

The detection of a stochastic gravitational wave background by pulsar-timing arrays indicates the presence of a population of supermassive black hole binaries. Although the observed spectrum generally matches predictions for orbital evolution driven by gravitational-wave emission in circular orbits, there is a preference for a spectral turnover at the lowest observed frequencies, which may point to substantial hardening during a transition from early environmental influences to later stages dominated by emission. In the vicinity of these binaries, the ejection of stars or dark matter particles through gravitational three-body slingshots efficiently extracts orbital energy, leading to a low-frequency turnover in the spectrum. Here we model how the gravitational-wave spectrum depends on the initial inner galactic profile before scouring by binary ejections while accounting for a range of initial binary eccentricities. By analysing the NANOGrav 15-year data, we find that a parsec-scale galactic-centre density of around $10^6 M_{\odot} \mathrm{pc}^{-3}$ is favoured across most of the parameter space, thus shedding light on the environmental effects that shape black hole evolution and the combined matter density near galaxy centres.

astro-ph.HE↗

arXiv2026

The NANOGrav 15 yr Data Set: Piecewise Power-Law Reconstruction of the Gravitational-Wave Background

The NANOGrav 15-year (NG15) data set provides evidence for a gravitational-wave background (GWB) signal at nanohertz frequencies, which is expected to originate either from a cosmic population of inspiraling supermassive black-hole binaries or new particle physics in the early Universe. A firm identification of the source of the NG15 signal requires an accurate reconstruction of its frequency spectrum. In this paper, we provide such a spectral characterization of the NG15 signal based on a piecewise power-law (PPL) ansatz that strikes a balance between existing alternatives in the literature. Our PPL reconstruction is more flexible than the standard constant-power-law model, which describes the GWB spectrum in terms of only two parameters: an amplitude A and a spectral index gamma. Concurrently, it better approximates physically realistic GWB spectra -- especially those of cosmological origin -- than the free spectral model, since the latter allows for arbitrary variations in the GWB amplitude from one frequency bin to the next. Our PPL reconstruction of the NG15 signal relies on individual PPL models with a fixed number of internal nodes (i.e., constant power law, broken power law, doubly broken power law, etc.) that are ultimately combined in a Bayesian model average. The data products resulting from our analysis provide the basis for fast refits of spectral GWB models.

astro-ph.HE↗

arXiv2026

The NANOGrav 15 yr Data Set: Targeted Searches for Supermassive Black Hole Binaries

We present the first targeted searches for continuous gravitational waves (CWs) from 114 active galactic nuclei (AGN) that may host supermassive black hole binaries, using the NANOGrav 15 yr data set. By incorporating electromagnetic priors on sky location, distance, redshift, and CW frequency, our strain and chirp mass upper limits are typically improved by a factor of $\sim 2$ (median 2.2) relative to all-sky limits at the same frequency. Bayesian comparisons against a model including only a Hellings-Downs correlated background disfavors a CW signal for all targets, with a mean Bayes factor of $0.73 \pm 0.32$. Two targets have Bayes factors slightly above unity, but coherence tests, random targeting experiments, and a conservative accounting of the 114-target trials factor all indicate that they are consistent with noise. We use these two candidates as worked examples to illustrate an end-to-end targeted CW search analysis and a suite of follow up tests that future promising candidates would need to pass. We find that the electromagnetic interpretations of both candidates are ambiguous, and we update the constraints on a putative binary in 3C 66B, ruling out part of its previously allowed parameter space. Ultimately, our results demonstrate the current sensitivity of targeted pulsar timing array searches for CWs and define a roadmap for future multimessenger CW detections.

astro-ph.HE↗

arXiv2025

Model-agnostic gravitational-wave background characterization algorithm

As ground-based gravitational-wave (GW) detectors improve in sensitivity, gravitational-wave background (GWB) signals will progressively become detectable. Currently, searches for the GWB model the signal as a power law; however, deviations from this model will be relevant at increased sensitivity. Therefore, to prepare for the range of potentially detectable GWB signals, we propose an interpolation model implemented through a transdimensional reversible-jump Markov chain Monte Carlo algorithm. This interpolation model foregoes a specific physics-informed model (of which there are a great many) in favor of a flexible model that can accurately recover a broad range of potential signals. In this paper, we employ this framework for an array of GWB applications. We present three dimensionless fractional GW energy density injections and recoveries as examples of the capabilities of this spline interpolation model. We further demonstrate how our model can be implemented for hierarchical GW analysis on $Ω_{\rm GW}$.

gr-qc↗

arXiv2025

Is there a retrograde accretion disk around 4U 1626$-$67? Tracking torque reversals with a state-space model

X-ray timing studies of the persistent, Galactic, accretion-powered pulsar 4U 1626$-$67 reveal torque reversals, during which the pulse frequency $ν(t)$ alternates between multiyear episodes of secular acceleration and deceleration, separated by transitions lasting $\lesssim 150 \, \rm{days}$. Here an unscented Kalman filter is applied to track the $ν(t)$ fluctuations observed in 22.7 years (3340 samples) of publicly available Compton Gamma-Ray Observatory and Fermi Gamma-Ray Space Telescope data to test the canonical picture of magnetocentrifugal accretion for consistency with prograde-prograde and retrograde-prograde accretion disk configurations on either side of the 2008 torque reversal. It is found that the retrograde-prograde model is preferred, with a log Bayes factor equal to 0.44 and maximum a posteriori log likelihood ratio equal to 2.5. The mass accretion rate $Q(t)$ and magnetocentrifugal fastness $ω(t)$ transition smoothly between episodes of deceleration and acceleration; $Q(t)$ shifts by $\leq 0.34 \, {\rm dex}$ across the reversal, and one measures $ω(t) \approx 0.25$ and $ω(t) \approx 0.30$ during deceleration and acceleration, respectively. The angular acceleration $\dotΩ(t)$ satisfies $-9 \lesssim \dotΩ(t)/(10^{-12} \, \rm{rad \, s^{-2}}) \lesssim -5$ and $2 \lesssim \dotΩ(t)/(10^{-12} \, \rm{rad \, s^{-2}}) \lesssim 9$ before and after the 2008 reversal, respectively, compared to $\dotΩ \approx -3.0 \times 10^{-12} \, \rm{rad \, s^{-2}}$ before reversal and $\dotΩ \approx 2.5 \times 10^{-12} \, \rm{rad \, s^{-2}}$ after reversal, as inferred from previous long-term X-ray timing and spectral analysis of 4U 1626$-$67.

astro-ph.HE↗

arXiv2025

Measuring the crust-superfluid coupling time-scale for 105 UTMOST pulsars with a Kalman filter

Crust-superfluid coupling plays an important role in neutron star rotation, particularly with respect to timing noise and glitches. Here, we present new timing-noise-based estimates of the crust-superfluid coupling time-scale $τ$ for 105 radio pulsars in the UTMOST dataset, by Kalman filtering the pulse times of arrival. The 105 objects are selected because they favor a two-component, crust-superfluid model over a one-component model with log Bayes factor $\ln \mathfrak{B}_{\rm BF} \geq 5$. The median estimate of $τ$ ranges from $10^{4.6\pm0.4}$\,s for PSR J2241$-$5236 to $10^{7.7^{+0.7}_{-0.4}}$\,s for PSR J1644$-$4559 among 28 out of 105 objects with sharply peaked $τ$ posteriors. A hierarchical Bayesian analysis is performed on 101 out of 105 objects that are canonical (i.e.\ neither recycled nor magnetars) and reside in the populous core of the $Ω_{\rm c}$-$\dotΩ_{\rm c}$ plane. It returns the population-level scaling $τ\propto Ω_{\rm c}^{0.19^{+0.50}_{-0.52}} |\dotΩ_{\rm c}|^{0.18^{+0.18}_{-0.19}}$, where $Ω_{\rm c}$ and $\dotΩ_{\rm c}$ are the angular velocity and spin-down rate of the crust respectively. The variances of the stochastic crust and superfluid torques are also estimated hierarchically, with $Q_{\rm c} \propto Ω_{\rm c}^{1.23^{+0.80}_{-0.75}} |\dotΩ_{\rm c}|^{0.49^{+0.27}_{-0.32}}$ and $Q_{\rm s} \propto Ω_{\rm c}^{0.71^{+0.76}_{-0.78}} |\dotΩ_{\rm c}|^{1.27^{+0.30}_{-0.28}}$ respectively. Implications for the physical origin of crust-superfluid coupling, e.g.\ through mutual friction, are discussed briefly.

astro-ph.HE↗

arXiv2025

Argus: JAX state-space filtering for gravitational wave detection with a pulsar timing array

Argus is a high-performance Python package for detecting and characterising nanohertz gravitational waves in pulsar timing array data. The package provides a complete Bayesian inference framework based on state-space models, using Kalman filtering for efficient likelihood evaluation. Argus leverages JAX for just-in-time compilation, GPU acceleration, and automatic differentiation, facilitating rapid Bayesian inference with gradient-based samplers. The state-space approach provides a computationally efficient alternative to traditional frequency-domain methods, offering linear scaling with the number of pulse times-of-arrival, and natural handling of non-stationary processes.

astro-ph.IM↗

arXiv2025

Beyond diagonal approximations: improved covariance modeling for pulsar timing array data analysis

Pulsar Timing Array (PTA) searches for nHz gravitational-wave backgrounds (GWBs) typically model time-correlated noise by assuming a diagonal covariance in Fourier space, neglecting inter-frequency correlations introduced by the finite observation window. We show that this diagonal approximation can lead to biased estimates of spectral parameters, especially for the common red process that represents the GWB. To address these limitations, we present a method that (i) computes the time-domain autocorrelation on a coarse grid using a fast Fourier transform (FFT), (ii) interpolates it accurately to the unevenly sampled observation times, and (iii) incorporates it into a low-rank likelihood via the Sherman--Morrison--Woodbury identity. Using both analytic covariance comparisons and end-to-end simulations inspired by the NANOGrav 15-year dataset, we demonstrate that our method captures frequency correlations faithfully, avoids Gibbs ringing, and recovers unbiased spectral parameters with modest computational cost. As PTA datasets increase in sensitivity and complexity, our approach offers a practical and scalable path to fully accurate covariance modeling for current and future analyses.

astro-ph.IM↗

arXiv2025

The NANOGrav 15 Yr Data Set: Removing Pulsars One by One from the Pulsar Timing Array

Evidence has emerged for a stochastic signal correlated among 67 pulsars within the 15-year pulsar-timing data set compiled by the NANOGrav collaboration. Similar signals have been found in data from the European, Indian, Parkes, and Chinese PTAs. This signal has been interpreted as indicative of the presence of a nanohertz stochastic gravitational wave background. To explore the internal consistency of this result we investigate how the recovered signal strength changes as we remove the pulsars one by one from the data set. We calculate the signal strength using the (noise-marginalized) optimal statistic, a frequentist metric designed to measure correlated excess power in the residuals of the arrival times of the radio pulses. We identify several features emerging from this analysis that were initially unexpected. The significance of these features, however, can only be assessed by comparing the real data to synthetic data sets. After conducting identical analyses on simulated data sets, we do not find anything inconsistent with the presence of a stochastic gravitational wave background in the NANOGrav 15-year data. The methodologies developed here can offer additional tools for application to future, more sensitive data sets. While this analysis provides an internal consistency check of the NANOGrav results, it does not eliminate the necessity for additional investigations that could identify potential systematics or uncover unmodeled physical phenomena in the data.

astro-ph.HE↗

arXiv2025

The NANOGrav 15-year Gravitational-Wave Background Methods

Pulsar timing arrays (PTAs) use an array of millisecond pulsars to search for gravitational waves in the nanohertz regime in pulse time of arrival data. This paper presents rigorous tests of PTA methods, examining their consistency across the relevant parameter space. We discuss updates to the 15-year isotropic gravitational-wave background analyses and their corresponding code representations. Descriptions of the internal structure of the flagship algorithms Enterprise and PTMCMCSampler are given to facilitate understanding of the PTA likelihood structure, how models are built, and what methods are currently used in sampling the high-dimensional PTA parameter space. We introduce a novel version of the PTA likelihood that uses a two-step marginalization procedure that performs much faster in gravitational wave searches, reducing the required resources facilitating the computation of Bayes factors via thermodynamic integration and sampling a large number of realizations for computing Bayesian false-alarm probabilities. We perform stringent tests of consistency and correctness of the Bayesian and frequentist analysis methods. For the Bayesian analysis, we test prior recovery, simulation recovery, and Bayes factors. For the frequentist analysis, we test that the optimal statistic, when modified to account for a non-negligible gravitational-wave background, accurately recovers the amplitude of the background. We also summarize recent advances and tests performed on the optimal statistic in the literature from both GWB detection and parameter estimation perspectives. The tests presented here validate current analyses of PTA data.

astro-ph.HE↗

arXiv2025

The NANOGrav 15 yr data set: Posterior predictive checks for gravitational-wave detection with pulsar timing arrays

Pulsar-timing-array experiments have reported evidence for a stochastic background of nanohertz gravitational waves consistent with the signal expected from a population of supermassive--black-hole binaries. Their analyses assume power-law spectra for intrinsic pulsar noise and for the background, as well as a Hellings--Downs cross-correlation pattern among the gravitational-wave--induced residuals across pulsars. These assumptions may not be realized in actuality. We test them in the NANOGrav 15 yr data set using Bayesian posterior predictive checks. After fitting our fiducial model to real data, we generate a population of simulated data-set replications. We use the replications to assess whether the optimal-statistic significance, inter-pulsar correlations, and spectral coefficients are extreme. We recover Hellings--Downs correlations in simulated data sets at significance levels consistent with the correlations measured in the NANOGrav 15 yr data set. A similar test on spectral coefficients shows that their values in real data are not extreme compared to their distributions across replications. We also evaluate the evidence for the stochastic background using posterior-predictive versions of the frequentist optimal statistic and of Bayesian model comparison, and find comparable significance (3.2 $σ$ and 3 $σ$ respectively) to what was previously reported for the standard statistics. We conclude with novel visualizations of the reconstructed gravitational waveforms that enter the residuals for each pulsar. Our analysis strengthens confidence in the identification and characterization of the gravitational-wave background.

astro-ph.HE↗