Daniel J. Oliver

After two decades of observations, pulsar timing array collaborations have reported strong evidence for a stochastic gravitational wave background, most likely sourced by an inspiraling population of supermassive black hole binaries. Because that population is finite, anisotropy in the background is inevitable, producing hotspots on the sky that track the loudest binaries. Building on the Fisher formalism for anisotropic backgrounds, we recast the directional Fisher information as effective sensitivity curves on the sky, distinguishing the radiometer and full-Fisher estimators, along with a sky-weighted curve that reduces the anisotropic sky to a single spectrum and recovers the standard isotropic curve in the isotropic limit. We implement five sky-decomposition bases: pixel, spherical harmonic, square-root spherical harmonic, radiometer, and principal-map. We demonstrate the framework on a simulated array modeled on the International Pulsar Timing Array: characterizing the angular response, analyzing the Fisher structure, quantifying the detectability of injected anisotropic hotspots, and forecasting future-array sensitivity. The framework is released as an extension to the sensitivity software package hasasia .

The North American Nanohertz Observatory for Gravitational Waves achieves submicrosecond timing precision for several millisecond pulsars in its pulsar timing array (PTA) with the objective of detecting and characterizing nanohertz gravitational waves. PSR J1713+0747 is one of the most precisely timed pulsars in the array, achieving submicrosecond timing precision. However, in 2021 April, PSR J1713+0747 underwent a sudden and unusual change in pulse shape that disrupted its timing stability. As PSR J1713+0747 is a key contributor to PTA sensitivity, variations in its pulse profile significantly affect the array’s sensitivity to nanohertz gravitational waves. We apply frequency-dependent Gaussian component models to decompose the pulse profile and track the evolution of individual components through the event. This component-level method maintains phase-connected timing across the shape-change event. At the L band, the recovered times of arrival (TOAs) have a median uncertainty of ∼0.47 μ s compared to ∼0.70 μ s for standard template matching. At 820 MHz, where profile frequency evolution is stronger, the recovered TOAs have a median uncertainty of ∼1.63 μ s compared to ∼0.67 μ s for standard template matching. The recovered TOAs achieve timing uncertainties comparable to conventional template matching while allowing data affected by profile variability to be retained in PTA gravitational-wave analyses. These results represent an initial step toward profile-domain timing methods capable of accounting for pulse profile evolution while reducing the need for additional timing model parameters.

We quantify pulsar timing array (PTA) sensitivity to anisotropy in the gravitational-wave (GW) 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 _psr in the array, the error δt on the times of arrival, the frequency f _GW of the GWs, and the angular scale ΔΩ of the anisotropy. The sensitivity scales approximately as N psr 0.8 , δt ^−0.08 , and ΔΩ ^1.6 − ΔΩ ^2.1 (depending on the ranges of ℓ and m under consideration). In addition, we use realistic simulations to project the NANOGrav PTA sensitivity to a 30 yr baseline and quantify the growth in sensitivity at several time slices. 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.

The average pulse shape of a pulsar is typically stable over decadal timescales, enabling estimation of pulse times of arrival to better than a small fraction of the pulse width using matched filtering techniques. However, in North American Nanohertz Observatory for Gravitational Waves (NANOGrav) observations of PSR J1713+0747, three discrete timing events that depart from the prevailing timing model have been seen in the last 20 yr. All three correspond to morphological changes in pulse shape. Using principal component analysis, we analyze the pulse profiles of nine NANOGrav pulsars, including seven with profiles from the 15 yr data set and two with additional profiles from the forthcoming 20 yr data set. We recover the three known pulse shape change events in PSR J1713+0747 and another previously known event in PSR J1643−1224. We implement a ranking metric for candidate events and address four highly ranked candidates in this nine-pulsar sample. We also recover known slow pulse shape variations in PSR J1643−1224, PSR J1903+0327, and PSR B1937+21 and report an unexpected recurrence after ∼10 yr of one such variation in PSR B1937+21.

Pulsar timing arrays (PTAs) conduct low-frequency gravitational-wave (GW) searches, which require comprehensive accounting of various noise sources to achieve robust results. Interstellar propagation effects (e.g., dispersion and scattering) are especially complex noise sources, introducing chromatic delays that can reduce sensitivity to GWs and bias their inference if left unmodeled. These delays also strongly depend on the line-of-sight properties to each individual pulsar. To address this, we present customized chromatic noise models for 67 pulsars in the NANOGrav 15 yr dataset. These models are selected from an expanded suite of Gaussian processes to simultaneously characterize multiple types of chromatic delays and are tailored to each pulsar’s dataset. Alongside probing the interstellar medium, we use these models to infer the solar wind electron density over the course of ∼1.5 solar cycles. We also find evidence for nondispersive chromatic delays in 21 out of 67 NANOGrav pulsars. After applying our chromatic models, we observe significant impacts on the inference of achromatic noise in 19 out of 67 pulsars, finding in several cases that a previously significant achromatic noise process can be partially or entirely described as chromatic. These results demonstrate that refined noise modeling is essential to enhance the sensitivity and accuracy of low-frequency GW searches with PTAs.

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 nonstationary chromatic events and the solar wind. As PTAs turn toward high frequency (>1 yr ⁻¹ ) 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.

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.

Scattering events around the center of massive galaxies will occasionally toss a stellar-mass compact object into an orbit around the massive black hole (MBH) at the center, beginning an extreme mass ratio inspiral (EMRI). The early stages of such a highly eccentric orbit are not likely to produce detectable gravitational waves (GWs), as the source will only be in a suitable frequency band briefly when it is close to periapsis during each long-period orbit. This repeated burst of emission, firmly in the millihertz band, is the GW peep. While a single peep is not likely to be detectable, if we consider an ensemble of such subthreshold sources, spread across the Universe, together they may produce an unresolvable background noise that could obscure sources otherwise detectable by the Laser Interferometer Space Antenna. Previous studies of the extreme mass ratio signal confusion background focused either on parabolic orbits near the MBH or events closer to merger. We seek to improve this characterization by implementing numerical kludge waveforms that can calculate highly eccentric orbits with relativistic effects. Our focus is on orbits at the point of capture that are farther away from the MBH. Here we present the waveforms and spectra of peeps generated from recent calculations of EMRIs/extreme mass ratio bursts capture parameters and discuss how these can be used to estimate the signal confusion noise generated by such events. We demonstrate the effects of changing the orbital parameters on the resulting spectra as well as showing direct comparisons to parabolic orbits and why the GW ‘peep’ needs to be studied further. The results of this study will be expanded upon in a further paper that aims to provide an update on the EMRI signal confusion noise problem.