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Sarah J. Vigeland

Publications and source records attributed to Sarah J. Vigeland.

At least 19 recordsLinked to original sources

Generalized Non-linear Bayesian Pulsar Timing with Enterprise

In this study, we use the Bayesian methods in the Enterprise package to examine the fully general parameterization of pulsar timing models in tandem with noise. We investigate four pulsars, PSR J1600$-$3053, PSR J2043+1711, PSR J0740+6620, and PSR J1640+2224, through the lens of Bayesian timing. These four are selected as they are well-studied, but exhibit interesting characteristics under the lens of Bayesian timing. Our new pulsar mass constraints (medians and 68\% confidence intervals) for our fully general non-linear Bayesian timing models are $m_{\mathrm{p}}=1.6(1)~\mathrm{M}_{\odot}$ for PSR J2043+1711 and $m_{\mathrm{p}}=2.3^{+0.9}_{-0.7}~\mathrm{M}_{\odot}$ for PSR J1600$-$3053 both using the NANOGrav 12.5-yr data release, and $m_{\mathrm{p}}=2.06(6)~\mathrm{M}_{\odot}$ for PSR J0740+6620 using the data from Fonseca, et al., 2021. We investigate the effects on placing physical priors on timing model parameters, including restricting the upper limit on the pulsar mass for PSR J1640+2224, which has a mass often estimated to be greater than $3~\mathrm{M}_{\odot}$. We find \ark{that restricting the allowed sampling space of the pulsar mass for PSR J1640+2224 to} $m_{\mathrm{p}}<3~\mathrm{M}_{\odot}$ results in a pulsar mass of $m_{\mathrm{p}}=2.2(5)~\mathrm{M}_{\odot}$ for PSR J1640+2224 using the NANOGrav 12.5-yr data release. For the first time, we find evidence for intrinsic red noise in PSR J2043+1711. We show how fully general Bayesian timing can better model the interplay of the intrinsic noise and the timing parameters.

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The NANOGrav 12.5-year Data Set: Chromatic Noise Characterization & Mitigation with Time-Domain Kernels

Pulsar timing arrays (PTAs) have recently entered the detection era, quickly moving beyond the goal of simply improving sensitivity at the lowest frequencies for the sake of observing the stochastic gravitational wave background (GWB), and focusing on its accurate spectral characterization. While all PTA collaborations around the world use Fourier-domain Gaussian processes to model the GWB and intrinsic long time-correlated (red) noise, techniques to model the time-correlated radio frequency-dependent (chromatic) processes have varied from collaboration to collaboration. Here we test a new class of models for PTA data, Gaussian processes based on time-domain kernels that model the statistics of the chromatic processes starting from the covariance matrix. As we will show, these models can be effectively equivalent to Fourier-domain models in mitigating chromatic noise. This work presents a method for Bayesian model selection across the various choices of kernel as well as deterministic chromatic models for non-stationary chromatic events and the solar wind. As PTAs turn towards high frequency (>1/yr) sensitivity, the size of the basis used to model these processes will need to increase, and these time-domain models present some computational efficiencies compared to Fourier-domain models.

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Optimal strategies for continuous wave detection in pulsar timing arrays: Realistic pulsar noise and a gravitational wave background

Pulsar timing arrays are sensitive to low-frequency gravitational waves (GWs), such as those produced by supermassive binary black holes at subparsec separations. The incoherent superposition of GWs emitted by a cosmological population of these sources produces a gravitational wave background (GWB), while some individual sources may be resolvable as deterministic signals with slowly varying GW frequencies, which are often referred to as "continuous waves" (CWs). The Fp-statistic is a frequentist method of detecting these CWs. In this paper, we study how the presence of pulsar red noise and a GWB affect the Fp-statistic. We compare results when marginalizing over the red noise and using the maximum-likelihood values of the red noise, and find little difference between the two. We also present results of using the Fp-statistic to analyze the NANOGrav 12.5-year data set, where we find no evidence for CWs in agreement with the previously published Bayesian results.

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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.

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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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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.

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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.

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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.

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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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The NANOGrav 12.5-Year Data Set: Probing Interstellar Turbulence and Precision Pulsar Timing with PSR J1903+0327

Free electrons in the interstellar medium refract and diffract radio waves along multiple paths, resulting in angular and temporal broadening of radio pulses that limits pulsar timing precision. We determine multifrequency, multi-epoch scattering times for the large dispersion measure millisecond pulsar J1903+0327 by developing a three component model for the emitted pulse shape that is convolved with a best fit pulse broadening function (PBF) identified from a family of thin-screen and extended-media PBFs. We show that the scattering time, $τ$, at a fiducial frequency of 1500 MHz changes by approximately 10% over a 5.5yr span with a characteristic timescale of approximately 100 days. We also constrain the spectral index and inner scale of the wavenumber spectrum of electron density variations along this line of sight. We find that the scaling law for $τ$ vs. radio frequency is strongly affected by any mismatch between the true and assumed PBF or between the true and assumed intrinsic pulse shape. We show using simulations that refraction is a plausible cause of the epoch dependence of $τ$, manifesting as changes in the PBF shape and $1/e$ time scale. Finally, we discuss the implications of our scattering results on pulsar timing including time of arrival delays and dispersion measure misestimation.

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Characterizing the nanohertz gravitational wave background using a $t$-process power spectral density

Pulsar timing arrays are sensitive to low-frequency gravitational waves (GWs), which induce correlated changes in millisecond pulsars' timing residuals. PTA collaborations around the world have recently announced evidence of a nanohertz gravitational wave background (GWB), which may be produced by a population of supermassive black hole binaries (SMBHBs). The GWB is often modeled as following a power-law power spectral density (PSD); however, a GWB produced by a cosmological population of SMBHBs is expected to have a more complex power spectrum due to the discrete nature of the sources. In this paper, we investigate using a $t$-process PSD to model the GWB, which allows us to fit for both the underlying power-law amplitude and spectral index as well as deviations from that power law, which may be produced by individual nearby binaries. We create simulated data sets based on the properties of the NANOGrav 15-year data set, and we demonstrate that the $t$-process PSD can accurately recover the PSD when deviations from a power-law are present. With longer timed datasets and more pulsars, we expect the sensitivity of our PTAs to improve, which will allow us to precisely measure the PSD of the GWB and study the sources producing it.

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An efficient pipeline for joint gravitational wave searches from individual binaries and a gravitational wave background with Hamiltonian sampling

The pulsar timing array community has recently reported the first evidence of a low-frequency stochastic gravitational wave background. With longer observational timespans we expect to be able to resolve individual gravitational wave sources in our data alongside the background signal. The statistical modeling and Bayesian searches for such individual signals is a computationally taxing task that is the focus of many different avenues of methods development. We present a pipeline for performing efficient joint searches for gravitational waves originating from individual supermassive black hole binaries as well as a gravitational wave background using a Hamiltonian Monte Carlo sampling scheme. Hamiltonian sampling proposes samples based on the gradients of the model likelihood, and can both converge faster to more complicated and high-dimensional distributions as well as efficiently explore highly covariant parameter spaces such as the joint gravitational wave background and individual binary model. We show the effectiveness of our scheme by demonstrating accurate parameter estimation for simulated datasets containing low- (6 nHz) or high- (60 nHz) frequency binary sources. Additionally we show that our method is capable at more efficiently generating skymaps for individual binary sources -- maps displaying the upper limits on the gravitational wave strain of the source, $h_{0}$, as a function of sky location -- by sampling over larger portions of the full sky. Comparing against results for the NANOGrav 12.5-year dataset, we find similar reconstructed upper limits on the gravitational wave strain while simultaneously reducing the number of required analyses from 72 independent binned searches down to a single run.

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Status Report on Global Pulsar-Timing-Array Efforts to Detect Gravitational Waves

The stability of the spin of pulsars and the precision with which these spins can be determined, allows many unique tests of interest to physics and astrophysics. Perhaps the most challenging and revolutionary of these, is the detection of nanohertz gravitational waves. An increasing number of efforts to detect and study long-period gravitational waves by timing an array of pulsars have been ongoing for several decades and the field is moving ever closer to actual gravitational-wave science. In this review article, we summarise the state of this field by presenting the current sensitivity to gravitational waves and by reviewing recent progress along the multiple lines of research that are part of the continuous push towards greater sensitivity. We also briefly review some of the most recent efforts at astrophysical interpretation of the most recent GW estimates derived from pulsar timing.

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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).

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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.

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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.

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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.

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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.

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