arXiv subjects

Levi Schult

Publications and source records attributed to Levi Schult.

13 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 $\delta t$ on the times of arrival, the frequency $f_\mathrm{GW}$ of the gravitational waves, and the angular scale $\Delta\Omega$ of the anisotropy. The sensitivity scales approximately as $N_\mathrm{psr}^{0.8}$, $\delta t^{-0.08}$, and $\Delta\Omega^{1.6}-\Delta\Omega^{2.1}$ (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

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

Expectations for the first supermassive black-hole binary resolved by PTAs I: Model efficacy

One of the most promising targets for Pulsar Timing Arrays (PTAs) is identifying an individual supermassive black hole binary (SMBHB) out of the population of binaries theorized to produce a gravitational wave background (GWB). In this work, we emulate realistic PTA datasets, complete with an increasing number of pulsars and timing baseline, in which we inject a single binary on top of a Gaussian GWB. We vary the binary's source parameters, including sky position and frequency, and create ten noise realizations for each source/PTA combination to synthesize an ensemble of datasets to assess current Bayesian binary search techniques. We develop a novel, cross-correlation based model, Spike Pixel (SP), tuned for the frequency-specific anisotropy induced by an individual SMBHB and compare its binary detection and characterization capabilities to two waveform-based template models. We find that a template-based search including the full gravitational-wave signal structure (i.e., both the Earth and pulsar effects of an incident GW) returns the highest Bayes Factors (BF) and the most robust parameter estimation. SP attains a realization-median BF>10 at source strengths (S/N)~7-15. Interestingly, despite being a deterministic model, the Earth-term template struggles to identify and characterize low-frequency binaries (i.e., 5 nHz). These binaries require higher source strengths (S/N)~16-19 to reach the same BF threshold. This is likely due to neglected confusion effects between the pulsar and Earth terms. By contrast, SP shows promise for parameter estimation despite treating a binary's GW signal as excess directional GW power without phase modeling. Sky location and frequency parameter constraints returned by SP are only surpassed by the Earth term template model at (S/N)~12-13. Milestones for a first detection using the full-signal GW model are included in a companion paper Petrov et al. 2026.

astro-ph.IM↗

arXiv2026

Expectations for the first supermassive black-hole binary resolved by PTAs II: Milestones for binary characterization

Following the recent evidence for a gravitational wave (GW) background found by pulsar timing array (PTA) experiments, the next major science milestone is resolving individual supermassive black hole binaries (SMBHBs). The detection of these systems could arise via searches using a power-based GW anisotropy model or a deterministic template model. In Schult et al. 2025, we compared the efficacy of these models in constraining the GW signal from a single SMBHB using realistic, near-future PTA datasets, and found that the full-signal deterministic continuous wave (CW) search may achieve detection and characterization first. Here, we continue our analyses using only the CW model given its better performance, focusing now on characterization milestones. We examine the order in which CW parameters are constrained as PTA data are accumulated and the signal-to-noise ratio (S/N) grows. We also study how these parameter constraints vary across sources of different sky locations and GW frequencies. We find that the GW frequency and strain are generally constrained at the same time (or S/N), closely followed by the sky location, and later the chirp mass (if the source is highly evolving) and inclination angle. At fixed S/N, sources at higher frequencies generally achieve better precision on the GW frequency, chirp mass, and sky location. The time (and S/N) at which the signal becomes constrained is dependent on the sky location and frequency of the source, with the effects of pulsar terms and PTA geometry playing crucial roles in source detection and localization.

astro-ph.IM↗

arXiv2025

FrankenStat I: a New Approach to Pulsar Timing Array Data Combination

In 2023, after more than two decades of searching, pulsar timing array (PTA) collaborations around the world announced evidence for a stochastic gravitational wave background. It was quickly followed by work from the International Pulsar Timing Array (IPTA), demonstrating that the results of regional collaborations were consistent with each other. The combination of these datasets is still ongoing and represents a significant investment of time and expertise. In that IPTA comparison, authors of this letter combined the separate datasets in the standard PTA optimal detection statistic for cross-correlations incoherently, that is, the data was combined without fitting a merged timing model across all PTA datasets, treating datasets of the same pulsar as independent, and neglecting the "same pulsar, different datasets" cross-correlations. This work refines that method by extending its core ideas beyond detection statistics and into a full, general data-combination method. We have demonstrated its efficacy and extreme efficiency on simulated data. This new method, \textit{FrankenStat}, is very similar in sensitivity and parameter-constraining power to traditional data combination methods while completing the full data combination in just a few minutes.

astro-ph.CO↗

arXiv2025

Rapid Construction of Joint Pulsar Timing Array Datasets: The Lite Method

The International Pulsar Timing Array (IPTA)'s second data release (IPTA DR2) combines decades of observations of 65 millisecond pulsars from 7 radio telescopes. IPTA datasets should be the most sensitive datasets to nanohertz gravitational waves (GWs), but take years to assemble, often excluding valuable recent data. To address this, we introduce the IPTA "Lite" analysis, where a Figure of Merit is used to select an optimal PTA dataset to analyze for each pulsar, enabling immediate access to new data and preliminary results prior to full combination. We test the capabilities of the Lite analysis using IPTA DR2, finding that "DR2 Lite" can be used to detect the common red noise process with an amplitude of $A = 4.8^{+1.8}_{-1.8} \times 10^{-15}$ at $γ= 13/3$. This amplitude is slightly large in comparison to the combined analysis, and likely biased high as DR2 Lite is more sensitive to systematic errors from individual pulsars than the full dataset. Furthermore, although there is no strong evidence for Hellings-Downs correlations in IPTA DR2, we still find the full dataset is better at resolving Hellings-Downs correlations than DR2 Lite. Alongside the Lite analysis, we also find that analyzing a subset of pulsars from IPTA DR2, available at a hypothetical "early" stage of combination (EDR2), yields equally competitive results as the full dataset. Looking ahead, the Lite method will enable rapid synthesis of the latest PTA data, offering preliminary GW constraints before the superior full dataset combinations are available.

astro-ph.HE↗

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↗

arXiv2023

The NANOGrav 15-year Data Set: Constraints on Supermassive Black Hole Binaries from the Gravitational Wave Background

The NANOGrav 15-year 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-year 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 sub-parsec 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.

astro-ph.HE↗

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: Evidence for a Gravitational-Wave Background

We report multiple lines of evidence for a stochastic signal that is correlated among 67 pulsars from the 15-year 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 $10^{14}$, 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 these latter Bayes factors using a method that removes inter-pulsar correlations from our data set, finding $p = 10^{-3}$ (approx. $3σ$) for the observed Bayes factors in the null no-correlation scenario. A frequentist test statistic built directly as a weighted sum of inter-pulsar correlations yields $p = 5 \times 10^{-5} - 1.9 \times 10^{-4}$ (approx. $3.5 - 4σ$). Assuming a fiducial $f^{-2/3}$ characteristic-strain spectrum, as appropriate for an ensemble of binary supermassive black-hole inspirals, the strain amplitude is $2.4^{+0.7}_{-0.6} \times 10^{-15}$ (median + 90% credible interval) at a reference frequency of 1/(1 yr). 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.

astro-ph.HE↗

arXiv2023

The NANOGrav 15-year Data Set: Search for Signals from New Physics

The 15-year 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.

astro-ph.HE↗

arXiv2022

Wide-band timing of GMRT discovered millisecond pulsars

Modeling of frequency-dependent effects, contributed by the turbulence in the free electron density of interstellar plasma, is required to enable the detection of the expected imprints from the stochastic gravitational-wave (GW) background in pulsar timing data. In this work, we present an investigation of temporal variations of interstellar medium for a set of millisecond pulsars (MSPs) with the upgraded GMRT aided by large fractional bandwidth at lower observing frequencies. Contrary to the conventional narrow-band analysis using a frequency invariant template profile, we applied $PulsePortraiture$ based wide-band timing analysis while correcting for the evolution of the pulsar profile with frequency. Implementation of $PulsePortraiture$ based wide-band timing method for the GMRT discovered MSPs to probe the DM variations resulted in a DM precision of $10^{-4}\,pc~cm^{-3}$. In general, we achieve similar DM and timing precision from wide-band timing compared to the narrow-band timing with matching temporal variations of DMs. This wide-band timing study of newly discovered MSPs over a wide frequency range highlights the effectiveness of profile-modeling at low frequencies and probes the potential of using them in pulsar timing array.

astro-ph.HE↗

arXiv2022

A Parallelized Bayesian Approach To Accelerated Gravitational-Wave Background Characterization

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 inter-pulsar 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 (FL) technique empowers a modular approach to parameter estimation of the GW background, multi-stage model selection of a spectrally-common stochastic process and quadrupolar inter-pulsar correlations, and statistical cross-validation of measured signals between independent pulsar sub-arrays. 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 re-analysis of the latter.

gr-qc↗