arXiv subjects

Stephen R. Taylor

Publications and source records attributed to Stephen R. Taylor.

At least 37 records · Page 2Linked to original sources

arXiv2025

Flexible Spectral Separation of Multiple Isotropic and Anisotropic Stochastic Gravitational Wave Backgrounds in LISA

The Laser Interferometer Space Antenna (LISA) will observe mHz gravitational waves from a wide variety of astrophysical sources. Of these, some will be characterizable as individual deterministic signals; the remainder will overlap to create astrophysical confusion noise. These sources of confusion noise are known as stochastic gravitational wave backgrounds (SGWBs). LISA data is expected to include several such astrophysical SGWBs, including the notable Galactic binary foreground, SGWBs from white dwarf binary populations in satellite galaxies of the Milky Way, and the SGWB from extragalactic stellar-origin binary black holes far from merger. To characterize these astrophysical signals and attempt to seek out possible underlying backgrounds of cosmological origin, it will be necessary to separate the contribution of each SGWB from that of the others. Crucially, several of these SGWBs are expected to be highly anisotropic on the sky, providing a powerful tool for spectral separation. To this end, we present BLIP 2.0: a flexible, GPU-accelerated framework for simulation and Bayesian analysis of arbitrary combinations of isotropic and anisotropic SGWBs. We leverage these capabilities to demonstrate for the first time spectral separation of the Galactic foreground, the Large Magellanic Cloud SGWB, and the SGWB from extragalactic stellar-origin binaries, and show a proof-of-concept for placing upper limits on the detection of an underlying isotropic cosmological SGWB in the presence of multiple astrophysical foregrounds.

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

Solving the PTA Data Analysis Problem with a Global Gibbs Scheme

The announcement in the summer of 2023 about the discovery of evidence for a gravitational wave background (GWB) using pulsar timing arrays (PTAs) has ignited both the PTA and the larger scientific community's interest in the experiment and the scientific implications of its findings. As a result, numerous scientific works have been published analyzing and further developing various aspects of the experiment, from performing tests of gravity to improving the efficiency of the current data analysis techniques. In this regard, we contribute to the recent advancements in the field of PTAs by presenting the most general, agnostic, per-frequency Bayesian search for a low-frequency (red) noise process in these data. Our new method involves the use of a conjugate Jeffrey's-like multivariate prior which allows one to model all unique parameters of the global PTA-level red noise covariance matrix as a separate model parameter for which a marginalized posterior-probability distribution can be found using Gibbs sampling. Even though perfecting the implementation of the Gibbs sampling and mitigating the numerical stability challenges require further development, we show the power of this new method by analyzing realistic and theoretical PTA simulated data sets. We show how our technique is consistent with the more restricted standard techniques in recovering both the auto and the cross-spectrum of pulsars' low-frequency (red) noise. Furthermore, we highlight ways to approximately characterize a GWB (both its auto- and cross-spectrum) using Fourier coefficient estimates from single-pulsar and so-called CURN (common uncorrelated red noise) analyses via analytic draws from a specific Inverse-Wishart distribution.

astro-ph.IM↗

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.

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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

The NANOGrav 15-year Data Set: Search for Gravitational Wave Memory

We present the results of a search for nonlinear gravitational wave memory in the NANOGrav 15-year data set. We find no significant evidence for memory signals in the dataset, with a maximum Bayes factor of 3.1 in favor of a model including memory. We therefore place upper limits on the strain of potential gravitational wave memory events as a function of sky location and observing epoch. We find upper limits that are not always more constraining than previous NANOGrav results. We show that it is likely due to the increase in common red noise between the 12.5-year and 15-year NANOGrav datasets.

gr-qc↗

arXiv2025

Towards robust gravitational wave detections from individual supermassive black hole binaries

The recent discovery of the stochastic gravitational-wave background via pulsar timing arrays will likely be followed by the detection of individual black hole binaries that stand out above the background. However, to confidently claim the detection of an individual binary, we need not only more and better data, but also more sophisticated analysis techniques. In this paper, we develop two new approaches that can help us more robustly ascertain if a candidate found by a search algorithm is indeed an individual supermassive black hole binary. One of these is a coherence test that directly compares the full signal model to an incoherent version of that. The other is a model scrambling approach that builds null distributions of our detection statistic and compares that with the measured value to quantify our confidence in signal coherence. Both of these rely on finding the coherence between pulsars characteristic to gravitational waves from a binary system. We test these methods on simple simulated datasets and find that they work well in correctly identifying both true gravitational waves and false positives. However, as expected for such a flexible and simple signal model, confidently identifying signal coherence is significantly harder than simply finding a candidate in most scenarios. Our analyses also indicate that the confidence with which we can identify a true signal depends not only on the signal-to-noise ratio, but also on the number of contributing pulsars and the amount of frequency evolution shown by the signal.

gr-qc↗

arXiv2025

Spatial and Spectral Characterization of the Gravitational-wave Background with the PTA Optimal Statistic

Pulsar timing arrays (PTAs) have made tremendous progress and are now showing strong evidence for the gravitational-wave background (GWB). Further probing the origin and characteristics of the GWB will require more generalized analysis techniques. Bayesian methods are most often used but can be computationally expensive. On the other hand, frequentist methods, like the PTA Optimal Statistic (OS), are more computationally efficient and can produce results that are complementary to Bayesian methods, allowing for stronger statistical cases to be built from a confluence of different approaches. In this work we expand the capabilities of the OS through a technique we call the Per-Frequency Optimal Statistic (PFOS). The PFOS removes the underlying power-law assumption inherent in previous implementations of the OS, and allows one to estimate the GWB spectrum in a frequency-by-frequency manner. We have also adapted a recent generalization from the OS pipeline into the PFOS, making it capable of accurately characterizing the spectrum in the intermediate and strong GW signal regimes using only a small fraction of the necessary computational resources when compared with fully-correlated Bayesian methods, while also empowering many new types of analyses not possible before. We find that even in the strong GW signal regime, where the GWB dominates over noise in all frequencies, the injected value of the signal lies within the 50th-percentile of the PFOS uncertainty distribution in 41-45% of simulations, remaining 3$σ$-consistent with unbiased estimation.

astro-ph.IM↗

arXiv2025

The NANOGrav 15 yr Data Set: Running of the Spectral Index

The NANOGrav 15-year data provides compelling evidence for a stochastic gravitational-wave (GW) background at nanohertz frequencies. The simplest model-independent approach to characterizing the frequency spectrum of this signal consists in a simple power-law fit involving two parameters: an amplitude A and a spectral index γ. In this paper, we consider the next logical step beyond this minimal spectral model, allowing for a running (i.e., logarithmic frequency dependence) of the spectral index, γ_run(f) = γ+ β\ln(f/f_ref). We fit this running-power-law (RPL) model to the NANOGrav 15-year data and perform a Bayesian model comparison with the minimal constant-power-law (CPL) model, which results in a 95% credible interval for the parameter βconsistent with no running, β\in [-0.80,2.96], and an inconclusive Bayes factor, B(RPL vs. CPL) = 0.69 +- 0.01. We thus conclude that, at present, the minimal CPL model still suffices to adequately describe the NANOGrav signal; however, future data sets may well lead to a measurement of nonzero β. Finally, we interpret the RPL model as a description of primordial GWs generated during cosmic inflation, which allows us to combine our results with upper limits from big-bang nucleosynthesis, the cosmic microwave background, and LIGO-Virgo-KAGRA.

astro-ph.HE↗

arXiv2025

Host Galaxy Demographics Of Individually Detectable Supermassive Black-hole Binaries with Pulsar Timing Arrays

Massive black hole binaries (MBHBs) produce gravitational waves (GWs) that are detectable with pulsar timing arrays. We determine the properties of the host galaxies of simulated MBHBs at the time they are producing detectable GW signals. The population of MBHB systems we evaluate is from the \textit{Illustris} cosmological simulations taken in tandem with post processing semi-analytic models of environmental factors in the evolution of binaries. Upon evolving to the GW frequency regime accessible by pulsar timing arrays, we calculate the detection probability of each system using a variety of different values for pulsar noise characteristics in a plausible near-future International Pulsar Timing Array dataset. We find that detectable systems have host galaxies that are clearly distinct from the overall binary population and from most galaxies in general. With conservative noise factors, we find that host stellar metallicity, for example, peaks at $\sim 2 Z_\odot$ as opposed to the total population of galaxies which peaks at $\sim 0.6 Z_\odot$. Additionally, the most detectable systems are much brighter in magnitude and more red in color than the overall population, indicating their likely identity as large ellipticals with diminished star formation. These results can be used to develop effective search strategies for identifying host galaxies and electromagnetic counterparts following GW detection by pulsar timing arrays.

astro-ph.GA↗

arXiv2024

Identifying Host Galaxies of Supermassive Black Hole Binaries Found by PTAs

Supermassive black hole binaries (SMBHBs) present us with exciting opportunities for multi-messenger science. These systems are thought to form naturally in galaxy mergers and therefore have the potential to produce electromagnetic (EM) radiation as well as gravitational waves (GWs) detectable with pulsar timing arrays (PTAs). Once GWs from individually resolved SMBHBs are detected, the identification of the host galaxy will be a major challenge due to the ambiguity in possible EM signatures and the poor localization capability of PTAs. In order to aid EM observations in choosing which sources to follow up, we attempt to quantify the number of plausible hosts in both realistic and idealistic scenarios. We outline a host galaxy identification pipeline that injects a single-source GW signal into a simulated PTA dataset, uses production-level techniques to recover the signal, quantifies the localization region and number of galaxies contained therein, and finally imposes cuts on the galaxies using the binary parameters estimated from the GW search. In an ideal case, we find that the 90% credible areas span 29 deg^2 to 241 deg^2, containing about 14 to 341 galaxies. After cuts, the number of galaxies remaining ranges from 22 at worst to 1 (the true host) at best. In a more realistic case, if the signal is sufficiently localized, the sky areas range from 287 deg^2 to 530 deg^2 and enclose about 285 to 1238 galaxies. After cuts, the number of galaxies is 397 at worst and 27 at best. While the signal-to-noise ratio is the primary determinant of the localization area of a given source, we find that the size of the area is also influenced by the proximity of nearby pulsars on the sky and the chirp mass of the source.

astro-ph.GA↗

arXiv2024

The NANOGrav 15 yr Data Set: Harmonic Analysis of the Pulsar Angular Correlations

Pulsar timing array observations have found evidence for an isotropic gravitational wave background with the Hellings-Downs angular correlations, expected from general relativity. This interpretation hinges on the measured shape of the angular correlations, which is predominately quadrupolar under general relativity. Here we explore a more flexible parameterization: we expand the angular correlations into a sum of Legendre polynomials and use a Bayesian analysis to constrain their coefficients with the 15-year pulsar timing data set collected by the North American Nanohertz Observatory for Gravitational Waves (NANOGrav). When including Legendre polynomials with multipoles $\ell \geq 2$, we only find a significant signal in the quadrupole with an amplitude consistent with general relativity and non-zero at the $\sim 95\%$ confidence level and a Bayes factor of 200. When we include multipoles $\ell \leq 1$, the Bayes factor evidence for quadrupole correlations decreases by more than an order of magnitude due to evidence for a monopolar signal at approximately 4 nHz which has also been noted in previous analyses of the NANOGrav 15-year data. Further work needs to be done in order to better characterize the properties of this monopolar signal and its effect on the evidence for quadrupolar angular correlations.

astro-ph.HE↗

arXiv2024

The NANOGrav 15 yr Data Set: Looking for Signs of Discreteness in the Gravitational-wave Background

The cosmic merger history of supermassive black hole binaries (SMBHBs) is expected to produce a low-frequency gravitational wave background (GWB). Here we investigate how signs of the discrete nature of this GWB can manifest in pulsar timing arrays through excursions from, and breaks in, the expected $f_{\mathrm{GW}}^{-2/3}$ power-law of the GWB strain spectrum. To do this, we create a semi-analytic SMBHB population model, fit to NANOGrav's 15 yr GWB amplitude, and with 1,000 realizations we study the populations' characteristic strain and residual spectra. Comparing our models to the NANOGrav 15 yr spectrum, we find two interesting excursions from the power-law. The first, at $2 \; \mathrm{nHz}$, is below our GWB realizations with $p$-value significance $p = 0.05$ to $0.06$ ($\approx 1.8 σ- 1.9 σ$). The second, at $16 \; \mathrm{nHz}$, is above our GWB realizations with $p = 0.04$ to $0.15$ ($\approx 1.4 σ- 2.1 σ$). We explore the properties of a loud SMBHB which could cause such an excursion. Our simulations also show that the expected number of SMBHBs decreases by three orders of magnitude, from $\sim 10^6$ to $\sim 10^3$, between $2\; \mathrm{nHz}$ and $20 \; \mathrm{nHz}$. This causes a break in the strain spectrum as the stochasticity of the background breaks down at $26^{+28}_{-19} \; \mathrm{nHz}$, consistent with predictions pre-dating GWB measurements. The diminished GWB signal from SMBHBs at frequencies above the $26~\mathrm{nHz}$ break opens a window for PTAs to detect continuous GWs from individual SMBHBs or GWs from the early universe.

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arXiv2024

Deep Neural Emulation of the Supermassive Black-hole Binary Population

While supermassive black-hole (SMBH)-binaries are not the only viable source for the low-frequency gravitational wave background (GWB) signal evidenced by the most recent pulsar timing array (PTA) data sets, they are expected to be the most likely. Thus, connecting the measured PTA GWB spectrum and the underlying physics governing the demographics and dynamics of SMBH-binaries is extremely important. Previously, Gaussian processes (GPs) and dense neural networks have been used to make such a connection by being built as conditional emulators; their input is some selected evolution or environmental SMBH-binary parameters and their output is the emulated mean and standard deviation of the GWB strain ensemble distribution over many Universes. In this paper, we use a normalizing flow (NF) emulator that is trained on the entirety of the GWB strain ensemble distribution, rather than only mean and standard deviation. As a result, we can predict strain distributions that mirror underlying simulations very closely while also capturing frequency covariances in the strain distributions as well as statistical complexities such as tails, non-Gaussianities, and multimodalities that are otherwise not learnable by existing techniques. In particular, we feature various comparisons between the NF-based emulator and the GP approach used extensively in past efforts. Our analyses conclude that the NF-based emulator not only outperforms GPs in the ease and computational cost of training but also outperforms in the fidelity of the emulated GWB strain ensemble distributions.

astro-ph.IM↗

arXiv2024

Overlap reduction functions for pulsar timing arrays and astrometry

We present an efficient technique for calculating the angular two-point correlation functions (or ``overlap reduction functions'') induced by gravitational waves in both the pulse arrival times of pulsars and in the angular deflections of distant sources. In the most general case, there are six auto- and cross-correlations for the pulse arrival times and the two components of the angular deflection. We provide results for spin-2 (i.e., general-relativistic) gravitational waves as well as the spin-1 modes that may arise in alternative-gravity theories. These calculations can be easily implemented for future analysis or study, and we provide code to do so.

astro-ph.CO↗

arXiv2024

Spectral Variance in a Stochastic Gravitational-Wave Background From a Binary Population

A population of compact object binaries emitting gravitational waves that are not individually resolvable will form a stochastic gravitational wave signal. While the expected spectrum over population realizations is well known from Phinney (2001), its higher order moments have not been fully studied before or computed in the case of arbitrary binary evolution. We calculate analytic scaling relationships as a function of gravitational-wave frequency for the statistical variance, skewness, and kurtosis of a stochastic gravitational-wave signal over population realizations due to finite source effects. If the time derivative of the binary orbital frequency can be expressed as a power-law in frequency, we find that these moment quantities also take the form of power-law relationships. We also develop a numerical population synthesis framework against which we compare our analytic results, finding excellent agreement. These new scaling relationships provide physical context to understanding spectral fluctuations in a gravitational-wave background signal and may provide additional information that can aid in explaining the origin of the nanohertz-frequency signal observed by pulsar timing array campaigns.

gr-qc↗

arXiv2024

An unusual pulse shape change event in PSR J1713+0747 observed with the Green Bank Telescope and CHIME

The millisecond pulsar J1713+0747 underwent a sudden and significant pulse shape change between April 16 and 17, 2021 (MJDs 59320 and 59321). Subsequently, the pulse shape gradually recovered over the course of several months. We report the results of continued multi-frequency radio observations of the pulsar made using the Canadian Hydrogen Intensity Mapping Experiment (CHIME) and the 100-meter Green Bank Telescope (GBT) in a three-year period encompassing the shape change event, between February 2020 and February 2023. As of February 2023, the pulse shape had returned to a state similar to that seen before the event, but with measurable changes remaining. The amplitude of the shape change and the accompanying TOA residuals display a strong non-monotonic dependence on radio frequency, demonstrating that the event is neither a glitch (the effects of which should be independent of radio frequency, $ν$) nor a change in dispersion measure (DM) alone (which would produce a delay proportional to $ν^{-2}$). However, it does bear some resemblance to the two previous "chromatic timing events" observed in J1713+0747 (Demorest et al. 2013; Lam et al. 2016), as well as to a similar event observed in PSR J1643-1224 in 2015 (Shannon et al. 2016).

astro-ph.HE↗