William G. Lamb

William G. Lamb

he/him

Astrophysicist | PhD Candidate | NANOGrav Research Assitant

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A list of all the posts and pages found on the site. For you robots out there, there is an XML version available for digesting as well.

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[The New Federalist] ‘Dafydd Iwan’s Yma o Hyd overtakes Stormzy and Lewis Capaldi to top iTunes chart…’

less than 1 minute read

Published:

This was the headline on the front of the North Welsh local newspaper, The Daily Post, in mid-January. It probably means nothing to you, but to many Welsh language speakers, it was a big deal. For a Welsh-language song to reach the top of a music chart in a mostly English-speaking society, it was an exciting moment for many Welsh speakers. More importantly, it was a big political statement that we are “still here”. Read it on The New Federalist

publications

A parallelized Bayesian approach to accelerated gravitational-wave background characterization

Published in Physics Review D, 2022

The characterization of nanohertz-frequency gravitational waves (GWs) with pulsar-timing arrays requires a continual expansion of datasets and monitored pulsars. Whereas detection of the stochastic GW background is predicated on measuring a distinctive pattern of interpulsar correlations, characterizing the background’s spectrum is driven by information encoded in the power spectra of the individual pulsars’ time series. We propose a new technique for rapid Bayesian characterization of the stochastic GW background that is fully parallelized over pulsar datasets. This factorized likelihood technique empowers a modular approach to parameter estimation of the GW background, multistage model selection of a spectrally-common stochastic process and quadrupolar interpulsar correlations, and statistical cross-validation of measured signals between independent pulsar subarrays. We demonstrate the equivalence of this technique’s efficacy with the full pulsar-timing array likelihood, yet at a fraction of the required time. Our technique is fast, easily implemented, and trivially allows for new data and pulsars to be combined with legacy datasets without reanalysis of the latter.

Recommended citation: Taylor et al. Phys. Rev. D 105, 084049
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The NANOGrav 15 yr Data Set: Constraints on Supermassive Black Hole Binaries from the Gravitational-wave Background

Published in The Astrophysical Journal Letters, 2023

The NANOGrav 15 yr data set shows evidence for the presence of a low-frequency gravitational-wave background (GWB). While many physical processes can source such low-frequency gravitational waves, here we analyze the signal as coming from a population of supermassive black hole (SMBH) binaries distributed throughout the Universe. We show that astrophysically motivated models of SMBH binary populations are able to reproduce both the amplitude and shape of the observed low-frequency gravitational-wave spectrum. While multiple model variations are able to reproduce the GWB spectrum at our current measurement precision, our results highlight the importance of accurately modeling binary evolution for producing realistic GWB spectra. Additionally, while reasonable parameters are able to reproduce the 15 yr observations, the implied GWB amplitude necessitates either a large number of parameters to be at the edges of expected values or a small number of parameters to be notably different from standard expectations. While we are not yet able to definitively establish the origin of the inferred GWB signal, the consistency of the signal with astrophysical expectations offers a tantalizing prospect for confirming that SMBH binaries are able to form, reach subparsec separations, and eventually coalesce. As the significance grows over time, higher-order features of the GWB spectrum will definitively determine the nature of the GWB and allow for novel constraints on SMBH populations.

Recommended citation: Agazie et al 2023 ApJL 952 L37
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The NANOGrav 15 yr Data Set: Evidence for a Gravitational-wave Background

Published in The Astrophysical Journal Letters, 2023

We report multiple lines of evidence for a stochastic signal that is correlated among 67 pulsars from the 15 yr pulsar timing data set collected by the North American Nanohertz Observatory for Gravitational Waves. The correlations follow the Hellings–Downs pattern expected for a stochastic gravitational-wave background. The presence of such a gravitational-wave background with a power-law spectrum is favored over a model with only independent pulsar noises with a Bayes factor in excess of 1014, and this same model is favored over an uncorrelated common power-law spectrum model with Bayes factors of 200–1000, depending on spectral modeling choices. We have built a statistical background distribution for the latter Bayes factors using a method that removes interpulsar correlations from our data set, finding p = 10−3 (≈3σ) for the observed Bayes factors in the null no-correlation scenario. A frequentist test statistic built directly as a weighted sum of interpulsar correlations yields p = 5 × 10−5 to 1.9 × 10−4 (≈3.5σ–4σ). Assuming a fiducial f−2/3 characteristic strain spectrum, as appropriate for an ensemble of binary supermassive black hole inspirals, the strain amplitude is (median + 90% credible interval) at a reference frequency of 1 yr−1. The inferred gravitational-wave background amplitude and spectrum are consistent with astrophysical expectations for a signal from a population of supermassive black hole binaries, although more exotic cosmological and astrophysical sources cannot be excluded. The observation of Hellings–Downs correlations points to the gravitational-wave origin of this signal.

Recommended citation: Agazie et al 2023 ApJL 951 L8
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The NANOGrav 15 yr Data Set: Search for Signals from New Physics

Published in The Astrophysical Journal Letters, 2023

The 15 yr pulsar timing data set collected by the North American Nanohertz Observatory for Gravitational Waves (NANOGrav) shows positive evidence for the presence of a low-frequency gravitational-wave (GW) background. In this paper, we investigate potential cosmological interpretations of this signal, specifically cosmic inflation, scalar-induced GWs, first-order phase transitions, cosmic strings, and domain walls. We find that, with the exception of stable cosmic strings of field theory origin, all these models can reproduce the observed signal. When compared to the standard interpretation in terms of inspiraling supermassive black hole binaries (SMBHBs), many cosmological models seem to provide a better fit resulting in Bayes factors in the range from 10 to 100. However, these results strongly depend on modeling assumptions about the cosmic SMBHB population and, at this stage, should not be regarded as evidence for new physics. Furthermore, we identify excluded parameter regions where the predicted GW signal from cosmological sources significantly exceeds the NANOGrav signal. These parameter constraints are independent of the origin of the NANOGrav signal and illustrate how pulsar timing data provide a new way to constrain the parameter space of these models. Finally, we search for deterministic signals produced by models of ultralight dark matter (ULDM) and dark matter substructures in the Milky Way. We find no evidence for either of these signals and thus report updated constraints on these models. In the case of ULDM, these constraints outperform torsion balance and atomic clock constraints for ULDM coupled to electrons, muons, or gluons.

Recommended citation: Afzal et al 2023 ApJL 951 L117
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Exploring the capabilities of Gibbs sampling in pulsar timing arrays

Published in Physics Review D, 2023

We explore the use of Gibbs sampling in estimating the noise properties of individual pulsars and illustrate its effectiveness using the NANOGrav 11-year dataset. 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.

Recommended citation: Laal et al. Phys. Rev. D 108, 063008
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The NANOGrav 15 yr Data Set: Looking for Signs of Discreteness in the Gravitational-wave Background

Published in The Astrophysical Journal, 2023

The characterization of nanohertz-frequency gravitational waves (GWs) with pulsar-timing arrays requires a continual expansion of datasets and monitored pulsars. Whereas detection of the stochastic GW background is predicated on measuring a distinctive pattern of interpulsar correlations, characterizing the background’s spectrum is driven by information encoded in the power spectra of the individual pulsars’ time series. We propose a new technique for rapid Bayesian characterization of the stochastic GW background that is fully parallelized over pulsar datasets. This factorized likelihood technique empowers a modular approach to parameter estimation of the GW background, multistage model selection of a spectrally-common stochastic process and quadrupolar interpulsar correlations, and statistical cross-validation of measured signals between independent pulsar subarrays. We demonstrate the equivalence of this technique’s efficacy with the full pulsar-timing array likelihood, yet at a fraction of the required time. Our technique is fast, easily implemented, and trivially allows for new data and pulsars to be combined with legacy datasets without reanalysis of the latter.

Recommended citation: Agazie et al 2025 ApJ 978 31
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Comparing Recent Pulsar Timing Array Results on the Nanohertz Stochastic Gravitational-wave Background

Published in The Astrophysical Journal, 2024

The Australian, Chinese, European, Indian, and North American pulsar timing array (PTA) collaborations recently reported, at varying levels, evidence for the presence of a nanohertz gravitational-wave background (GWB). Given that each PTA made different choices in modeling their data, we perform a comparison of the GWB and individual pulsar noise parameters across the results reported from the PTAs that constitute the International Pulsar Timing Array (IPTA). We show that despite making different modeling choices, there is no significant difference in the GWB parameters that are measured by the different PTAs, agreeing within 1σ. The pulsar noise parameters are also consistent between different PTAs for the majority of the pulsars included in these analyses. We bridge the differences in modeling choices by adopting a standardized noise model for all pulsars and PTAs, finding that under this model there is a reduction in the tension in the pulsar noise parameters. As part of this reanalysis, we “extended” each PTA’s data set by adding extra pulsars that were not timed by that PTA. Under these extensions, we find better constraints on the GWB amplitude and a higher signal-to-noise ratio for the Hellings–Downs correlations. These extensions serve as a prelude to the benefits offered by a full combination of data across all pulsars in the IPTA, i.e., the IPTA’s Data Release 3, which will involve not just adding in additional pulsars but also including data from all three PTAs where any given pulsar is timed by more than a single PTA.

Recommended citation: Agazie et al 2024 ApJ 966 105
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Deep Neural Emulation of the Supermassive Black Hole Binary Population

Published in ApJ, 2025

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.

Recommended citation: Nima Laal et al 2025 ApJ 982 55
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Solving the PTA data analysis problem with a global Gibbs scheme

Published in Physics Review D, 2025

The announcement in the summer of 2023 about the discovery of evidence for a gravitational-wave background (GWB) using pulsar timing arrays (PTAs) ignited interest in both the PTA and larger scientific communities about the experiment itself 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 Jeffreys-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 cross spectra of pulsars’ low-frequency (red) noise. Furthermore, we highlight ways to approximately characterize a GWB (both its auto and cross spectra) using Fourier coefficient estimates from single-pulsar and so-called common uncorrelated red-noise analyses via analytic draws from a specific inverse Wishart distribution.

Recommended citation: Laal et al. Phys. Rev. D 111, 063067
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The NANOGrav 15 yr Data Set: Piecewise Power-Law Reconstruction of the Gravitational-Wave Background

Published in arXiv, 2026

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.

Recommended citation: Agazie et al. arXiv:2601.09481 (2026)
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