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Stephen R. Taylor

Publications and source records attributed to Stephen R. Taylor.

At least 55 records · Page 3Linked to original sources
arXiv2024

Generalized optimal statistic for characterizing multiple correlated signals in pulsar timing arrays

The optimal statistic (OS) is a frequentist estimator for the amplitude and significance of a spatially-correlated signal in pulsar timing array (PTA) data, and it is widely used to search for the gravitational wave background (GWB). However, the OS cannot perfectly distinguish between different spatial correlations. In this paper, we introduce the multiple component optimal statistic (MCOS): a generalization of the OS that allows for multiple correlations to be simultaneously fit to the data. We use simulated data to show that this method more accurately recovers injected spatially correlated signals, and in particular reduces the risk of a false detection of a signal with the wrong spatial correlation. We also demonstrate that this method can be used to recover multiple correlated signals.

astro-ph.IM↗
arXiv2024

The NANOGrav 12.5-year data set: A computationally efficient eccentric binary search pipeline and constraints on an eccentric supermassive binary candidate in 3C 66B

The radio galaxy 3C 66B has been hypothesized to host a supermassive black hole binary (SMBHB) at its center based on electromagnetic observations. Its apparent 1.05-year period and low redshift ($\sim0.02$) make it an interesting testbed to search for low-frequency gravitational waves (GWs) using Pulsar Timing Array (PTA) experiments. This source has been subjected to multiple searches for continuous GWs from a circular SMBHB, resulting in progressively more stringent constraints on its GW amplitude and chirp mass. In this paper, we develop a pipeline for performing Bayesian targeted searches for eccentric SMBHBs in PTA data sets, and test its efficacy by applying it on simulated data sets with varying injected signal strengths. We also search for a realistic eccentric SMBHB source in 3C 66B using the NANOGrav 12.5-year data set employing PTA signal models containing Earth term-only as well as Earth+Pulsar term contributions using this pipeline. Due to limitations in our PTA signal model, we get meaningful results only when the initial eccentricity $e_0<0.5$ and the symmetric mass ratio $η>0.1$. We find no evidence for an eccentric SMBHB signal in our data, and therefore place 95% upper limits on the PTA signal amplitude of $88.1\pm3.7$ ns for the Earth term-only and $81.74\pm0.86$ ns for the Earth+Pulsar term searches for $e_0<0.5$ and $η>0.1$. Similar 95% upper limits on the chirp mass are $(1.98 \pm 0.05) \times 10^9\,M_{\odot}$ and $(1.81 \pm 0.01) \times 10^9\,M_{\odot}$. These upper limits, while less stringent than those calculated from a circular binary search in the NANOGrav 12.5-year data set, are consistent with the SMBHB model of 3C 66B developed from electromagnetic observations.

astro-ph.HE↗
arXiv2023

How to Detect an Astrophysical Nanohertz Gravitational-Wave Background

Analysis of pulsar timing data have provided evidence for a stochastic gravitational wave background in the nHz frequency band. The most plausible source of such a background is the superposition of signals from millions of supermassive black hole binaries. The standard statistical techniques used to search for such a background and assess its significance make several simplifying assumptions, namely: i) Gaussianity; ii) isotropy; and most often iii) a power-law spectrum. However, a stochastic background from a finite collection of binaries does not exactly satisfy any of these assumptions. To understand the effect of these assumptions, we test standard analysis techniques on a large collection of realistic simulated datasets. The dataset length, observing schedule, and noise levels were chosen to emulate the NANOGrav 15-year dataset. Simulated signals from millions of binaries drawn from models based on the Illustris cosmological hydrodynamical simulation were added to the data. We find that the standard statistical methods perform remarkably well on these simulated datasets, despite their fundamental assumptions not being strictly met. They are able to achieve a confident detection of the background. However, even for a fixed set of astrophysical parameters, different realizations of the universe result in a large variance in the significance and recovered parameters of the background. We also find that the presence of loud individual binaries can bias the spectral recovery of the background if we do not account for them.

gr-qc↗
arXiv2023

The NANOGrav 15-year data set: Search for Transverse Polarization Modes in the Gravitational-Wave Background

Recently we found compelling evidence for a gravitational wave background with Hellings and Downs (HD) correlations in our 15-year data set. These correlations describe gravitational waves as predicted by general relativity, which has two transverse polarization modes. However, more general metric theories of gravity can have additional polarization modes which produce different interpulsar correlations. In this work we search the NANOGrav 15-year data set for evidence of a gravitational wave background with quadrupolar Hellings and Downs (HD) and Scalar Transverse (ST) correlations. We find that HD correlations are the best fit to the data, and no significant evidence in favor of ST correlations. While Bayes factors show strong evidence for a correlated signal, the data does not strongly prefer either correlation signature, with Bayes factors $\sim 2$ when comparing HD to ST correlations, and $\sim 1$ for HD plus ST correlations to HD correlations alone. However, when modeled alongside HD correlations, the amplitude and spectral index posteriors for ST correlations are uninformative, with the HD process accounting for the vast majority of the total signal. Using the optimal statistic, a frequentist technique that focuses on the pulsar-pair cross-correlations, we find median signal-to-noise-ratios of 5.0 for HD and 4.6 for ST correlations when fit for separately, and median signal-to-noise-ratios of 3.5 for HD and 3.0 for ST correlations when fit for simultaneously. While the signal-to-noise-ratios for each of the correlations are comparable, the estimated amplitude and spectral index for HD are a significantly better fit to the total signal, in agreement with our Bayesian analysis.

gr-qc↗
arXiv2023

Fast Parameter Inference on Pulsar Timing Arrays with Normalizing Flows

Pulsar timing arrays (PTAs) perform Bayesian posterior inference with expensive MCMC methods. Given a dataset of ~10-100 pulsars and O(10^3) timing residuals each, producing a posterior distribution for the stochastic gravitational wave background (SGWB) can take days to a week. The computational bottleneck arises because the likelihood evaluation required for MCMC is extremely costly when considering the dimensionality of the search space. Fortunately, generating simulated data is fast, so modern simulation-based inference techniques can be brought to bear on the problem. In this paper, we demonstrate how conditional normalizing flows trained on simulated data can be used for extremely fast and accurate estimation of the SGWB posteriors, reducing the sampling time from weeks to a matter of seconds.

astro-ph.IM↗
arXiv2023

The Need For Speed: Rapid Refitting Techniques for Bayesian Spectral Characterization of the Gravitational Wave Background Using PTAs

Pulsar timing arrays (PTAs) have recently found evidence for a nanohertz-frequency stochastic gravitational-wave background (SGWB). Constraining its spectral characteristics will reveal its origins. To achieve this, we must understand how data and modeling conditions in each pulsar influence the precision and accuracy of SGWB spectral recovery, typically requiring many Bayesian analyses on real data sets and large-scale simulations that are slow and computationally taxing. To combat this, we have developed several new rapid approaches that operate on intermediate SGWB analysis products. These techniques refit SGWB spectral models to previously computed Bayesian posterior estimates of the timing power spectra. We test our new techniques on simulated PTA data sets and the NANOGrav 12.5-year data set, where in the latter our refit posterior achieves a Hellinger distance -- bounded between 0 for identical distributions and 1 for zero overlap -- from the current full production-level pipeline that is < 0.1. Our techniques are ~ $10^2$--$10^4$ times faster than the production-level likelihood and scale much more favorably (sub-linearly) as a PTA is expanded with new pulsars or observations. Our techniques also allow us to demonstrate conclusively that SGWB spectral characterization in PTA data sets is driven by the longest-timed pulsars and the best-measured power spectral densities. Indeed, the common-process spectral properties found in the NANOGrav 12.5-year data set are given by analyzing only the ~14 longest-timed pulsars out of the full 45 pulsar array, and we find that the 'shallowing' of the common-process power-law model occurs when gravitational-wave frequencies higher than ~50 nanohertz are included. The implementation of our techniques is openly available as a software suite to allow fast and flexible PTA SGWB spectral characterization and model selection.

astro-ph.HE↗
arXiv2023

Exploring the Capabilities of Gibbs Sampling in Pulsar Timing Arrays

We explore the use of Gibbs sampling in estimating the noise properties of individual pulsars and illustrate its effectiveness using the NANOGrav 11-year data set. We find that Gibbs sampling noise modeling (GM) is more efficient than the current standard Bayesian techniques (SM) for single pulsar analyses by yielding model parameter posteriors with average effective-sample-size ratio (GM/SM) of 6 across all parameters and pulsars. Furthermore, the output of GM contains posteriors for the Fourier coefficients that can be used to characterize the underlying red noise process of any pulsar's timing residuals, which are absent in current implementations of SM. Through simulations, we demonstrate the potential for such coefficients to measure the spatial cross-correlations between pulsar pairs produced by a gravitational wave background.

astro-ph.IM↗
arXiv2023

The NANOGrav 12.5-year Data Set: Search for Gravitational Wave Memory

We present the results of a Bayesian search for gravitational wave (GW) memory in the NANOGrav 12.5-yr data set. We find no convincing evidence for any gravitational wave memory signals in this data set (Bayes factor = 2.8). As such, we go on to place upper limits on the strain amplitude of GW memory events as a function of sky location and event epoch. These upper limits are computed using a signal model that assumes the existence of a common, spatially uncorrelated red noise in addition to a GW memory signal. The median strain upper limit as a function of sky position is approximately $3.3 \times 10^{-14}$. We also find that there are some differences in the upper limits as a function of sky position centered around PSR J0613$-$0200. This suggests that this pulsar has some excess noise which can be confounded with GW memory. Finally, the upper limits as a function of burst epoch continue to improve at later epochs. This improvement is attributable to the continued growth of the pulsar timing array.

gr-qc↗
arXiv2023

The NANOGrav 15-year Data Set: Search for Anisotropy in the Gravitational-Wave Background

The North American Nanohertz Observatory for Gravitational Waves (NANOGrav) has reported evidence for the presence of an isotropic nanohertz gravitational wave background (GWB) in its 15 yr dataset. However, if the GWB is produced by a population of inspiraling supermassive black hole binary (SMBHB) systems, then the background is predicted to be anisotropic, depending on the distribution of these systems in the local Universe and the statistical properties of the SMBHB population. In this work, we search for anisotropy in the GWB using multiple methods and bases to describe the distribution of the GWB power on the sky. We do not find significant evidence of anisotropy, and place a Bayesian $95\%$ upper limit on the level of broadband anisotropy such that $(C_{l>0} / C_{l=0}) < 20\%$. We also derive conservative estimates on the anisotropy expected from a random distribution of SMBHB systems using astrophysical simulations conditioned on the isotropic GWB inferred in the 15-yr dataset, and show that this dataset has sufficient sensitivity to probe a large fraction of the predicted level of anisotropy. We end by highlighting the opportunities and challenges in searching for anisotropy in pulsar timing array data.

astro-ph.HE↗
arXiv2023

The NANOGrav 15-Year Data Set: Detector Characterization and Noise Budget

Pulsar timing arrays (PTAs) are galactic-scale gravitational wave detectors. Each individual arm, composed of a millisecond pulsar, a radio telescope, and a kiloparsecs-long path, differs in its properties but, in aggregate, can be used to extract low-frequency gravitational wave (GW) signals. We present a noise and sensitivity analysis to accompany the NANOGrav 15-year data release and associated papers, along with an in-depth introduction to PTA noise models. As a first step in our analysis, we characterize each individual pulsar data set with three types of white noise parameters and two red noise parameters. These parameters, along with the timing model and, particularly, a piecewise-constant model for the time-variable dispersion measure, determine the sensitivity curve over the low-frequency GW band we are searching. We tabulate information for all of the pulsars in this data release and present some representative sensitivity curves. We then combine the individual pulsar sensitivities using a signal-to-noise-ratio statistic to calculate the global sensitivity of the PTA to a stochastic background of GWs, obtaining a minimum noise characteristic strain of $7\times 10^{-15}$ at 5 nHz. A power law-integrated analysis shows rough agreement with the amplitudes recovered in NANOGrav's 15-year GW background analysis. While our phenomenological noise model does not model all known physical effects explicitly, it provides an accurate characterization of the noise in the data while preserving sensitivity to multiple classes of GW signals.

astro-ph.HE↗
arXiv2023

The NANOGrav 15-year Data Set: Observations and Timing of 68 Millisecond Pulsars

We present observations and timing analyses of 68 millisecond pulsars (MSPs) comprising the 15-year data set of the North American Nanohertz Observatory for Gravitational Waves (NANOGrav). NANOGrav is a pulsar timing array (PTA) experiment that is sensitive to low-frequency gravitational waves. This is NANOGrav's fifth public data release, including both "narrowband" and "wideband" time-of-arrival (TOA) measurements and corresponding pulsar timing models. We have added 21 MSPs and extended our timing baselines by three years, now spanning nearly 16 years for some of our sources. The data were collected using the Arecibo Observatory, the Green Bank Telescope, and the Very Large Array between frequencies of 327 MHz and 3 GHz, with most sources observed approximately monthly. A number of notable methodological and procedural changes were made compared to our previous data sets. These improve the overall quality of the TOA data set and are part of the transition to new pulsar timing and PTA analysis software packages. For the first time, our data products are accompanied by a full suite of software to reproduce data reduction, analysis, and results. Our timing models include a variety of newly detected astrometric and binary pulsar parameters, including several significant improvements to pulsar mass constraints. We find that the time series of 23 pulsars contain detectable levels of red noise, 10 of which are new measurements. In this data set, we find evidence for a stochastic gravitational-wave background.

astro-ph.HE↗
arXiv2023

The NANOGrav 12.5-year Data Set: Bayesian Limits on Gravitational Waves from Individual Supermassive Black Hole Binaries

Pulsar timing array collaborations, such as the North American Nanohertz Observatory for Gravitational Waves (NANOGrav), are seeking to detect nanohertz gravitational waves emitted by supermassive black hole binaries formed in the aftermath of galaxy mergers. We have searched for continuous waves from individual circular supermassive black hole binaries using the NANOGrav's recent 12.5-year data set. We created new methods to accurately model the uncertainties on pulsar distances in our analysis, and we implemented new techniques to account for a common red noise process in pulsar timing array data sets while searching for deterministic gravitational wave signals, including continuous waves. As we found no evidence for continuous waves in our data, we placed 95\% upper limits on the strain amplitude of continuous waves emitted by these sources. At our most sensitive frequency of 7.65 nanohertz, we placed a sky-averaged limit of $h_0 < $ $(6.82 \pm 0.35) \times 10^{-15}$, and $h_0 <$ $(2.66 \pm 0.15) \times 10^{-15}$ in our most sensitive sky location. Finally, we placed a multi-messenger limit of $\mathcal{M} <$ $(1.41 \pm 0.02) \times 10^9 M_\odot$ on the chirp mass of the supermassive black hole binary candidate 3C~66B.

astro-ph.GA↗
arXiv2023

Efficient large-scale, targeted gravitational-wave probes of supermassive black-hole binaries

Supermassive black hole binaries are promising sources of low-frequency gravitational waves (GWs) and bright electromagnetic emission. Pulsar timing array searches for resolved binaries are complex and computationally expensive and so far limited to only a few sources. We present an efficient approximation that empowers large-scale targeted multi-messenger searches by neglecting GW signal components from the pulsar term. This Earth-term approximation provides similar constraints on the total mass and GW frequency of the binary, yet is $>100$ times more efficient.

gr-qc↗
arXiv2022

Quality over Quantity: Optimizing pulsar timing array analysis for stochastic and continuous gravitational wave signals

The search for gravitational waves using Pulsar Timing Arrays (PTAs) is a computationally expensive complex analysis that involves source-specific noise studies. As more pulsars are added to the arrays, this stage of PTA analysis will become increasingly challenging. Therefore, optimizing the number of included pulsars is crucial to reduce the computational burden of data analysis. Here, we present a suite of methods to rank pulsars for use within the scope of PTA analysis. First, we use the maximization of the signal-to-noise ratio as a proxy to select pulsars. With this method, we target the detection of stochastic and continuous gravitational wave signals. Next, we present a ranking that minimizes the coupling between spatial correlation signatures, namely monopolar, dipolar, and Hellings & Downs correlations. Finally, we also explore how to combine these two methods. We test these approaches against mock data using frequentist and Bayesian hypothesis testing. For equal-noise pulsars, we find that an optimal selection leads to an increase in the log-Bayes factor two times steeper than a random selection for the hypothesis test of a gravitational wave background versus a common uncorrelated red noise process. For the same test but for a realistic EPTA dataset, a subset of 25 pulsars selected out of 40 can provide a log-likelihood ratio that is $89\%$ of the total, implying that an optimally selected subset of pulsars can yield results comparable to those obtained from the whole array. We expect these selection methods to play a crucial role in future PTA data combinations.

astro-ph.HE↗
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

Controlling Outlier Contamination In Multimessenger Time-domain Searches For Supermasssive Binary Black Holes

Time-domain datasets of many varieties can be prone to statistical outliers that result from instrumental or astrophysical anomalies. These can impair searches for signals within the time series and lead to biased parameter estimation. Versatile outlier mitigation methods tuned toward multimessenger time-domain searches for supermassive binary black holes have yet to be fully explored. In an effort to perform robust outlier isolation with low computational costs, we propose a Gibbs sampling scheme. This provides structural simplicity to outlier modeling and isolation, as it requires minimal modifications to adapt to time-domain modeling scenarios with pulsar-timing array or photometric data. We robustly diagnose outliers present in simulated pulsar-timing datasets, and then further apply our methods to pulsar J$1909$$-$$3744$ from the NANOGrav 9-yr Dataset. We also explore the periodic binary-AGN candidate PG$1302$$-$$102$ using datasets from the Catalina Real-time Transient Survey, All-Sky Automated Survey for Supernovae, and the Lincoln Near-Earth Asteroid Research. We present our findings and outline future work that could improve outlier modeling and isolation for multimessenger time-domain searches.

astro-ph.IM↗
arXiv2022

Quasars with Periodic Variability: Capabilities and Limitations of Bayesian Searches for Supermassive Black Hole Binaries in Time-Domain Surveys

Supermassive black hole binaries (SMBHBs) are an inevitable consequence of galaxy mergers. At subparsec separations, they are practically impossible to resolve, and the most promising technique is to search for quasars with periodic variability. However, searches for quasar periodicity in time-domain data are challenging due to the stochastic variability of quasars. In this paper, we used Bayesian methods to disentangle periodic SMBHB signals from intrinsic damped random walk (DRW) variability in active galactic nuclei light curves. We simulated a wide variety of realistic DRW and DRW+sine light curves. Their observed properties are modeled after the Catalina Real-time Transient Survey (CRTS) and expected properties of the upcoming Legacy Survey of Space and Time (LSST) from the Vera C. Rubin Observatory. Through a careful analysis of parameter estimation and Bayesian model selection, we investigated the range of parameter space for which binary systems can be detected. We also examined which DRW signals can mimic periodicity and be falsely classified as binary candidates. We found that periodic signals are more easily detectable if the period is short or the amplitude of the signal is large compared to the contribution of the DRW noise. We saw similar detection rates both in the CRTS and LSST-like simulations, while the false-detection rate depends on the quality of the data and is minimal in LSST. Our idealized simulations provide an excellent way to uncover the intrinsic limitations in quasar periodicity searches and set the stage for future searches for SMBHBs.

astro-ph.GA↗
arXiv2022

Disentangling Multiple Stochastic Gravitational Wave Background Sources in PTA Datasets

With strong evidence of a common-spectrum stochastic process in the most recent datasets from the NANOGrav Collaboration, the European Pulsar Timing Array (PTA), Parkes PTA, and the International PTA, it is crucial to assess the effects of the several astrophysical and cosmological sources that could contribute to the stochastic gravitational wave background (GWB). Using the same dataset creation and injection techniques as in Pol et al. (2021), we assess the separability of multiple GWBs by creating single and multiple GWB source datasets. We search for these injected sources using Bayesian PTA analysis techniques to assess recovery and separability of multiple astrophysical and cosmological backgrounds. For a GWB due to supermassive black hole binaries and an underlying weaker background due to primordial gravitational waves with a GW energy density ratio of $Ω_{\mathrm{PGW}}/Ω_{\mathrm{SMBHB}} = 0.5$, the Bayes' factor for a second process exceeds unity at 17 years, and increases with additional data. At 20 years of data, we are able to constrain the spectral index and amplitude of the weaker GWB at this density ratio to a fractional uncertainty of 64% and 110%, respectively, using current PTA methods and techniques. Using these methods and findings, we outline a basic protocol to search for multiple backgrounds in future PTA datasets.

astro-ph.CO↗