arXiv subjects

Rutger van Haasteren

Publications and source records attributed to Rutger van Haasteren.

At least 19 recordsLinked to original sources

arXiv2026

Beyond diagonal approximations: improved covariance modeling for pulsar timing array data analysis

Pulsar Timing Array (PTA) searches for nHz gravitational-wave backgrounds (GWBs) typically model time-correlated noise by assuming a diagonal covariance in Fourier space, neglecting inter-frequency correlations introduced by the finite observation window. We show that this diagonal approximation can produce method-dependent shifts in estimates of spectral parameters, especially for pulsars with shallow intrinsic red noise spectra. To address these limitations, we present a method that (i) computes the time-domain autocorrelation on a coarse grid using a fast Fourier transform (FFT), (ii) interpolates it accurately to the unevenly sampled observation times, and (iii) incorporates it into a low-rank likelihood via the Sherman--Morrison--Woodbury identity. Using both analytic covariance comparisons and end-to-end simulations inspired by the NANOGrav 15-year dataset, we demonstrate that our method captures frequency correlations faithfully, avoids Gibbs ringing, and yields estimates closer to the injected values in the realization studied with modest computational cost. As PTA datasets increase in sensitivity and complexity, our approach offers a practical and scalable path to fully accurate covariance modeling for current and future analyses.

astro-ph.IM↗

arXiv2026

Not just a phase: detecting nanohertz gravitational waves from phase alone

Unambiguously detecting a gravitational-wave background (GWB) in pulsar-timing data requires a robust detection statistic. The pulsar timing community currently relies heavily on the cross-correlation-based "optimal statistic." Its design was motivated to avoid false-positive detections from unmodeled pulsar red noise. However, recent work by van Haasteren (2025) suggests that the optimal statistic is not, in fact, optimal. Moreover, the optimal statistic is still susceptible to false positives from misspecified noise. To guard against this, analysts employ quasi-resampling methods such as phase shifts, in which complex phases are randomly assigned to each pulsar strain measurement, thereby destroying any gravitational-wave-induced correlations. Inspired by the concept of phase shifts, we introduce a formalism in which the GWB is measured entirely from phase measurements. We argue that this approach is robust against false positive detections without the need for ad hoc quasi-resampling methods. We demonstrate the feasibility of this formalism by measuring the amplitude and spectral index of a simulated GWB, injected to a simplified mock representation of a pulsar timing array data set. For this example, we use simulation-based-inference and model the phase-based likelihood using a neural circular spline flow. We show that it is possible to adequately recover the spectral parameters of the gravitational wave background signal using the phase-based likelihood. By comparing our results to ones obtained with the optimal statistic, we show how much resolving power comes from amplitude versus phase.

astro-ph.IM↗

arXiv2026

Hierarchical Inference of the Supermassive Black Hole Binary Merger Rates from Joint Searches using Pulsar Timing Arrays

Gravitational-wave searches do more than identify individual sources - they provide a way to infer the underlying astrophysical populations that produce them. Currently, Pulsar Timing Arrays (PTAs) constrain the supermassive black-hole binary (SMBHB) merger-rate density through both the stochastic gravitational-wave background (SGWB) and searches for individual SMBHB signals. The latter implies converting source upper limits into rate upper limits using detection efficiencies estimated empirically. We instead develop a hierarchical Bayesian framework that places the SMBHB merger-rate density model directly inside the PTA likelihood. The unknown catalog of individual SMBHB merger signals is modeled as a Poisson point process on source-parameter space, so that the number of merger signals is inferred from the data rather than imposed by a detection threshold. We describe two computational routes: a catalog-marginal likelihood based on analyses with fixed numbers of candidate sources, and an explicit transdimensional sampling approach that jointly samples population hyperparameters, latent merger signals, and noise. We validate the method with a toy merger-only population model and then apply it to an astrophysical SMBHB merger-rate density model that jointly predicts the SGWB amplitude and the expected merger-catalog size. In simulations, an individual merger signal adds complementary information to the SGWB and can tighten constraints on the merger-rate population.

astro-ph.HE↗

arXiv2026

JUG: JAX-based Unified pulsar timinG

We present JUG (JAX-based Unified pulsar timinG), a JAX-based, fully independent pulsar timing package emphasising speed and ease of use, designed to confidently handle the increasingly large and complex pulsar timing array datasets that are being created in the pulsar timing field. JUG implements the entire pulsar timing pipeline itself, from data handling and clock corrections through to the timing model and fitting, without relying on other timing software. It enables Pythonic programming at the speed of compiled code, is GPU-capable, and can be operated via a Python API or an interactive GUI. A user of JUG can interactively explore data, fit timing models with complex stochastic noise, model deterministic signals such as continuous gravitational waves, and obtain accurate point estimates of the parameters of the stochastic processes present, thereby bridging frequentist timing and Bayesian noise analysis. JUG is faster than PINT by more than fifty times and is comparably fast to Tempo2, can handle millions of arrival times, agrees with PINT at the picosecond level, and can reliably recover known timing model and noise parameter values. In this paper we describe its design, performance, and validation, and demonstrate its advantages for pulsar timing data analysis.

astro-ph.IM↗

arXiv2026

On the triple nature of the PSR J0435+3233 system

Context. The recent pulsar timing ephemeris of PSR J0435+3233 indicates that this millisecond pulsar (MSP) has a spin-down rate that is much higher than observed in other MSPs and challenges our understanding of the formation and evolution of MSPs. Aims. We propose that this system is a hierarchical triple, and that the high spin-down rate is caused by varying acceleration due to a tertiary in a wide orbit. Methods. We use pulsar timing methods with radio and gamma-ray observations of PSR J0435+3233 to determine the system properties. Results. We find that a hierarchical triple timing model describes the timing observations of PSR J0435+3233 and that this results in the detection of gamma-ray pulsations back to the beginning of the Fermi Large Area Telescope (LAT) data in 2008. The intrinsic spin-down rate remains uncertain as it correlates with the parameters of the outer orbit, but large spin-down rates are excluded and the intrinsic rate is at least two orders of magnitude lower than the observed rate, in line with other Galactic MSPs. We identify a star located 11 mas from the pulsar position as the optical counterpart to the tertiary companion. From the 1.5-2.5 kpc distance and colours, we infer that the tertiary is a 1.2 solar mass F-type main-sequence star. Along with the pulsar binary, it orbits the common centre of mass with an eccentric (e ~ 0.6), wide (~ 70 yr) orbit that is likely seen at a low orbital inclination. Conclusions. We conclude that PSR J0435+3233 is a hierarchical triple system. We discuss the motivation and prospects for the continued study of this system. Spectral measurements of the outer star in addition to continued astrometric measurements will yield mass ratio and inclination estimates, while continued pulsar timing may yield a tighter constraint on violations of the Strong Equivalence Principle than are currently obtained from PSR J0337+1715.

astro-ph.HE↗

arXiv2026

A new framework for lightning-fast gravitational wave analysis of pulsar timing data

Pulsar timing array data analysis is computationally expensive, limiting the complexity of models which can be studied. As pulsar timing datasets and their respective models grow in size and sophistication, faster and scalable inference methods are essential. In this paper, we accelerate pulsar timing analyses by sampling in the space of Fourier coefficients instead of analytically marginalizing over them. Previous studies have shown the Fourier space induces a complex, high-dimensional posterior geometry, from which it is generally difficult to sample. We show that under an appropriate coordinate transformation the Fourier coefficients approximately follow a standard normal distribution, and may be efficiently sampled using a Hamiltonian Monte Carlo scheme. Under this coordinate transformation, for datasets of size and complexity comparable to the NANOGrav 15-year release, the new method produces converged posterior distributions for a range of models which include inter-pulsar correlations, stochastic, and deterministic signals in approximately 15 minutes on an NVIDIA GeForce RTX 3090 GPU. By comparison, the legacy pulsar timing analysis software \texttt{ENTERPRISE} would require months of computation on a CPU cluster to analyze comparable datasets under the same joint stochastic and deterministic models.

gr-qc↗

arXiv2026

Evaluating the Fourier Approximation in Pulsar Timing Array Analysis

Pulsar timing arrays search for stochastic processes such as gravitational waves by comparing pulse time of arrival data for millisecond pulsars to expectations from a background with a given power spectral density (PSD). To make the analysis computationally tractable, the Bayesian likelihood is usually computed using an approximation in which the signal is taken to be a sum of Fourier modes appropriate to the total time of observation, even though the true signal is not periodic. We study the difference between likelihoods computed with this Fourier approximation method for power law spectra and those computed exactly (or using more-closely spaced frequencies as a proxy for the exact result) in the NANOGrav 15-year dataset. We find that the true marginal likelihoods for power-law PSDs are on average about half as large as the likelihoods computed using the Fourier approximation. This could lead to an error of a factor of two in model comparison. However, in the important comparison of uncorrelated vs. Hellings-Downs correlated models, a very similar correction appears in both, so the model comparison is essentially unaffected. We also compare parameter estimation results for power law PSDs, finding little difference between the methods. We briefly discuss spectra with sharper features, for which the approximation could be much worse.

gr-qc↗

arXiv2026

Finding Supermassive Black Hole Binary Mergers in Pulsar Timing Array Data

Galaxy observations suggest that mergers of supermassive black hole binaries (SMBHBs) are rare events, with rates of order one per decade across the observable Universe. We present a framework to search for merging SMBHBs in pulsar timing array (PTA) data using a physically complete waveform model including inspiral, merger, ringdown, and gravitational-wave memory. This enables a unified treatment of continuous emission and the non-oscillatory memory signal. Using simulated PTA datasets, we demonstrate parameter estimation for representative systems with chirp masses of $10^8$ and $10^{10}~M_\odot$ at distances of $3$ Mpc to $100$ Mpc respectively. For sufficiently strong signals, we recover binaries with log Bayes factors >10 and constrain chirp mass and luminosity distance, subject to their characteristic degeneracy. Sky localization uncertainties of a few degrees could potentially enable electromagnetic follow-up and multi-messenger observations of SMBHB mergers. We further demonstrate that commonly used memory burst approximations lead to biased strain amplitudes and inferred source parameters when compared to the full SMBHB waveform, even when optimally tuned. These results establish a pathway for searching for SMBHB mergers with PTAs using complete waveform models.

astro-ph.HE↗

arXiv2026

An updated constraint for the Gravitational Wave Background from the Gamma-ray Pulsar Timing Array

Fermi LAT observations of gamma-ray pulsars can be used to build a pulsar timing array (PTA) experiment to search for gravitational wave (GW) signals at nanohertz frequencies. At those frequencies, the dominant signal is expected to be a stochastic gravitational wave background (GWB) produced by the incoherent superposition of the quasi-monochromatic GW emissions from a population of supermassive black hole binaries. While the radio PTAs have recently announced compelling evidence for a GWB signal with a power law spectrum of strain amplitude $\approx2-3\times10^{-15}$ (at the frequency of $1 {\rm yr}^{-1}$), in 2022 an analysis of $12.5$ years of Fermi data for 35 pulsars led to an upper limit of $1\times10^{-14}$ for the GWB amplitude. The analysis was carried out on times-of-arrival (TOAs) obtained by folding from six months up to one year of photon observations. A photon-by-photon approach was also tested to infer constraints on the GWB amplitude from individual pulsars, but without accounting for the cross-pulsar correlations that a GWB would induce. Here, we reanalyse the same dataset using a regularized likelihood method that correctly models cross-pulsar correlations directly from the photons, while additionally marginalising over the uncertain pulse profile shape. While the two methods are not expected to have significant differences in sensitivity, we prove through simulations of gamma-ray PTA datasets that the photon-by-photon method for GWB recoveries is, statistically, more robust. The resulting upper limit obtained for the GWB strain amplitude is $1.2\times10^{-14}$, indicating that the improved method yields a consistent result with the previous analyses.

astro-ph.HE↗

arXiv2026

A Multimessenger Search for the Supermassive Black Hole Binary in 3C 66B with the Parkes Pulsar Timing Array

A subparsec supermassive black hole binary (SMBHB) at the center of the galaxy 3C 66B is a promising candidate for continuous gravitational-wave searches with pulsar timing arrays (PTAs). In this work, we search for such a signal in the third data release of the Parkes Pulsar Timing Array. Matching our priors to estimates of binary parameters from electromagnetic observations, we find a log Bayes factor $\ln B = - 0.0027(7)$, highlighting that the source can be neither confirmed nor ruled out. We place upper limits at $95\%$ credibility on the chirp mass $M < 6.90 \times 10^{8}\ M_{\odot}$, and on the characteristic strain amplitude $\textrm{log}_{10}(h_0)< -14.44$. This partially rules out the parameter space suggested by electromagnetic (EM) observations of 3C 66B. We also independently reproduce the calculation of the chirp mass with the 3 mm flux monitor data from the unresolved core of 3C 66B. Based on this, we outline a new methodology for constructing a joint likelihood of EM and gravitational-wave data from SMBHBs. Finally, we suggest that targeted searches may allow firmly established SMBHB candidates to be treated as standard sirens, for complementary constraints on the Universe expansion rate.

astro-ph.HE↗

arXiv2026

Timing Gamma-ray Pulsars using Gibbs Sampling

Timing analyses of gamma-ray pulsars in the Fermi Large Area Telescope data set can provide sensitive probes of many astrophysical processes, including timing noise in young pulsars, orbital period variations in redback binaries, and the stochastic gravitational wave background (GWB). These goals can require careful accounting of stochastic noise processes, but existing methods developed to achieve this in radio pulsar timing analyses cannot be immediately applied to the discrete gamma-ray arrival time data. To address this, we have developed a new method for timing gamma-ray pulsars, in which the timing model fit is transformed into a weighted least squares problem by randomly assigning each photon to an individual Gaussian component of a template pulse profile. These random assignments are then numerically marginalised over through a Gibbs sampling scheme. This method allows for efficient estimation of timing and noise model parameters, while taking into account uncertainties in the pulse profile shape. We simulated Fermi-LAT data sets for gamma-ray pulsars with power-law timing noise processes, showing that this method provides robust estimates of timing noise parameters. We also describe a Gaussian-process model for orbital period variations in black-widow and redback binary systems that can be fit using this new timing method. We demonstrate this method on the black-widow binary millisecond pulsar B1957+20, where the orbital period varies significantly over the LAT data, but which provides one of the most stringent gamma-ray upper limits on the GWB.

astro-ph.HE↗

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

Search for Gravitational Wave Memory in PPTA and EPTA Data: A Complete Signal Model

We perform searches for gravitational wave memory in the data of two major Pulsar Timing Array (PTA) experiments located in Europe and Australia. Supermassive black hole binaries (SMBHBs) are the primary sources of gravitational waves in PTA experiments. We develop and carry out the first search for late inspirals and mergers of these sources based on full numerical relativity waveforms with null (nonlinear) gravitational wave memory. Additionally, we search for generic bursts of null gravitational wave memory, exploring possibilities of reducing the computational cost of these searches through kernel density and normalizing flow approximation of the posteriors. We rule out the mergers of SMBHBs with a chirp mass of 10^10 Solar Mass up to 700 Mpc over 18 years of observation at 95% credibility. We rule out the observation of generic displacement memory bursts with strain amplitudes > 10^-14 in brief periods of the observation time but across the sky, or over the whole observation time but for certain preferred sky positions, at 95%$credibility.

gr-qc↗

arXiv2025

On the calculation of p-values for quadratic statistics in Pulsar Timing Arrays

Pulsar Timing Array (PTA) projects have reported various lines of evidence suggesting the presence of a stochastic gravitational wave (GW) background in their data. One key line of evidence involves a detection statistic sensitive to inter-pulsar correlations, such as those induced by GWs. A $p$-value is then calculated to assess how unlikely it is for the observed signal to arise under the null hypothesis $H_0$, purely by chance. However, PTAs cannot empirically draw samples from $H_0$. As a workaround, various techniques are used in the literature to approximate $p$-values under $H_0$. One such technique, which has been heralded as a model-independent method, is the use of "scrambling" transformations that modify the data to cancel out pulsar correlations, thereby simulating realizations from $H_0$. In this work, scrambling methods and the detection statistic are investigated from first principles. The $p$-value methodology that is discussed is general, but the discussions regarding a specific detection statistic apply to the detection of a stochastic background of gravitational waves with PTAs. All methods in the literature to calculate $p$-values for such a detection statistic are rigorously analyzed, and many analytical expressions are derived. All this leads to the conclusion that scrambling methods are not model-independent and thus not completely empirical. Rigorous Bayesian and Frequentist $p$-value calculation methods are advocated, the evaluation of which depend on the generalized $χ^2$ distribution. This view is consistent with the posterior predictive $p$-value approach that is already in the literature. Efficient expressions are derived to evaluate the generalized $χ^2$ distribution of the detection statistic on real data. It is highlighted that no Frequentist $p$-values have been calculated correctly in the PTA literature to date.

astro-ph.IM↗

arXiv2025

Optimal robust detection statistics for pulsar timing arrays

Pulsar timing arrays (PTAs) seek to detect a nano-Hz stochastic gravitational-wave background (GWB) by searching for the characteristic Hellings and Downs angular pattern of timing residual correlations. So far, the evidence remains below the conventional $5$-$σ$ threshold, as assessed using the literature-standard ``optimal cross-correlation detection statistic''. While this quadratic combination of cross-correlated data maximizes the {\em deflection} (signal-to-noise ratio), it does not maximize the detection probability at fixed false-alarm probability (FAP), and therefore is not Neyman-Pearson (NP) optimal for the assumed noise and signal models. The NP-optimal detection statistic is a different quadratic form, but is not used because it also incorporates autocorrelations, making it more susceptible to uncertainties in the modeling of pulsar timing noise. Here, we derive the best compromise: a quadratic detection statistic which is as close as possible to the NP-optimal detection statistic (minimizing the variance of its difference with the NP statistic) subject to the constraint that it only uses cross-correlations, so that it is less affected by pulsar noise modeling errors. We study the performance of this new $\NPMV$ statistic for a simulated PTA whose noise and (putative) signal match those of the NANOGrav 15-year data release: GWB amplitude $A_{\rm gw}=2.1\times 10^{-15}$ and spectral index $γ=13/3$. Compared to the literature-standard ``optimal" cross-correlation detection statistic, the $\NPMV$ statistic increases the detection probability by $47\%$ when operating at a $5$-$σ$ FAP of $α= 2.9 \times 10^{-7}$.

astro-ph.IM↗

arXiv2025

Regularizing the Pulsar Timing Array likelihood: A path towards Fourier Space

The recent announcement of evidence for a stochastic background of gravitational waves (GWB) in pulsar timing array (PTA) data has piqued interest across the scientific community. A combined analysis of all currently available data holds the promise of confirming the announced evidence as a solid detection of a GWB. However, the complexity of individual pulsar noise models and the variety of modeling tools used for different types of pulsars present significant challenges for a truly unified analysis. In this work we propose a novel approach to the analysis of PTA data: first a posterior distribution over Fourier modes is produced for each pulsar individually. Then, in a global analysis of all pulsars these posterior distributions can be re-used for a GWB search, which retains all information regarding the signals of interest without the added complexity of the underlying noise models or implementation differences. This approach facilitates combining radio and gamma-ray pulsar data, while reducing the complexity of the model and of its implementations when carrying out a GWB search with PTA data.

astro-ph.IM↗

arXiv2025

Gaussian process representation of dispersion measure noise in pulsar wideband datasets

The ionized interstellar medium disperses pulsar radio signals, resulting in a stochastic time-variable delay known as the dispersion measure (DM) noise. In the wideband paradigm of pulsar timing, we measure a DM together with a time of arrival from a pulsar observation to handle frequency-dependent profile evolution, interstellar scintillation, and radio frequency interference more robustly, and to reduce data volumes. In this paper, we derive a method to incorporate arbitrary models of DM variation, including Gaussian process models, in pulsar timing and noise analysis and pulsar timing array analysis. This generalizes the existing method for handling DM noise in wideband datasets.

astro-ph.IM↗

arXiv2025

The NANOGrav 15-year Gravitational-Wave Background Methods

Pulsar timing arrays (PTAs) use an array of millisecond pulsars to search for gravitational waves in the nanohertz regime in pulse time of arrival data. This paper presents rigorous tests of PTA methods, examining their consistency across the relevant parameter space. We discuss updates to the 15-year isotropic gravitational-wave background analyses and their corresponding code representations. Descriptions of the internal structure of the flagship algorithms Enterprise and PTMCMCSampler are given to facilitate understanding of the PTA likelihood structure, how models are built, and what methods are currently used in sampling the high-dimensional PTA parameter space. We introduce a novel version of the PTA likelihood that uses a two-step marginalization procedure that performs much faster in gravitational wave searches, reducing the required resources facilitating the computation of Bayes factors via thermodynamic integration and sampling a large number of realizations for computing Bayesian false-alarm probabilities. We perform stringent tests of consistency and correctness of the Bayesian and frequentist analysis methods. For the Bayesian analysis, we test prior recovery, simulation recovery, and Bayes factors. For the frequentist analysis, we test that the optimal statistic, when modified to account for a non-negligible gravitational-wave background, accurately recovers the amplitude of the background. We also summarize recent advances and tests performed on the optimal statistic in the literature from both GWB detection and parameter estimation perspectives. The tests presented here validate current analyses of PTA data.

astro-ph.HE↗