Paul. S. Ray

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, PSRs J1600–3053, J2043+1711, J0740+6620, and J1640+2224, through the lens of Bayesian timing. We selected these pulsars as they are well studied but exhibit interesting characteristics through the lens of Bayesian timing. We generally find good agreement between best-fit and maximum a posteriori values, and in many cases more constrained parameter estimations, when comparing our method to various other Bayesian and frequentist generalized timing methods. We find tighter constraints on the estimated pulsar mass for three pulsars when using NANOGrav 12.5 yr data releases as compared to their published results. These constraints (medians and 68% confidence intervals) for our fully general nonlinear Bayesian timing models are m _p = 1.6(1) M _⊙ for PSR J2043+1711 and m p = 2 . 3 − 0.7 + 0.9 M ⊙ for PSR J1600–3053 both using the NANOGrav 12.5 yr data release, and m _p = 2.06(6) M _⊙ for PSR J0740+6620 using the data from E. Fonseca et al. We investigate the effects of 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 M _⊙ . We find that this results in a pulsar mass of m _p = 2.2(5) M _⊙ 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.

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.

In the published article, we presented inferences about the population of supermassive black hole (SMBH) binaries emitting at nanohertz gravitational-wave (GW) frequencies based on the 15 yr dataset from the North American Nanohertz Observatory for Gravitational Waves (NANOGrav). Here, we report two bugs in the astrophysical analysis software used for the published article. While parameter posteriors of our inference can be seen to have slight differences on close inspection, none of the conclusions from the original publication have changed, including the finding that the measured GW background is dominated by the most massive, high-mass-ratio SMBH binaries. Our corrected results show slightly less evidence for environmental interactions with SMBH binaries and indicate that the population of SMBH binaries contributing to the GW background occurs at slightly higher mass ratios and redshifts than indicated in the published article. Correcting these errors does not change the central conclusion that astrophysically motivated models of SMBH binary populations are able to reproduce both the amplitude and shape of the observed low-frequency GW spectrum. These errors did not affect any other analyses of the NANOGrav 15 yr dataset, including the evidence for a GW background presented in another of our published articles.

We report the discovery of giant pulse (GP) emission from the transitional millisecond pulsar PSR J1227−4853, using 174 hr of single-pulse data from the upgraded Giant Metrewave Radio Telescope. This marks the first detection of GPs from a transitional millisecond pulsar and adds to the small number of millisecond pulsars known to exhibit such extreme variability. A total of 235 GPs were detected across observations at 550–750 MHz, with widths as narrow as 1.28 μ s and flux densities up to ∼10 ⁴ times the pulsar’s mean flux density. The GPs are strongly localized in pulse phase, originating predominantly from the second and third main-pulse components, and are absent in the interpulse region. Their cumulative fluence distribution follows a power law above the completeness threshold, consistent with a defining characteristic of GP emission. The arrival times of the GPs deviate significantly from Poisson statistics, with the waiting-time distribution well described by a Weibull model having a shape parameter of k = 0.30, indicative of strong temporal clustering. During an epoch of enhanced activity, the GP rate increased by nearly 2 orders of magnitude to 124 hr ⁻¹ , with a corresponding shape parameter of k = 0.47. This value is similar to that reported for a burst storm from the repeating fast radio burst (FRB) FRB 20200120E, suggesting possible phenomenological parallels between GPs from compact binary systems and repeating FRBs.

Pulse-profile modeling of rotation-powered millisecond pulsars targeted by NICER has enabled mass–radius constraints of several neutron star sources, with implications for the dense-matter equation of state. For the bright isolated pulsar PSR J0030+0451, the inferred mass and radius were previously found to depend strongly on the assumed hot-spot model. These hot-spot models yielded different mass–radius constraints, with the statistically preferred model exhibiting some mild tension with results inferred for PSR J0437−4715, PSR J0614−3329, and GW170817. We present an updated pulse-profile analysis of PSR J0030+0451 using new NICER observations obtained between 2017 July to 2023 January, increasing the number of X-ray counts by about 50% compared to previous analyses. We jointly analyze the NICER data with archival XMM-Newton observations to better constrain the source spectrum and background. The new analysis, using more conservative nested-sampling settings together with the new NICER observations, significantly reduces the discrepancy between the hot-spot models. The inferred mass and radius are M = 1.4 3 − 0.17 + 0.20 M ⊙ and R eq = 12.6 8 − 1.04 + 1.31 km (68% credible intervals), reducing the tension with the results from other sources. In addition, the inferred hot-spot configurations suggest the presence of intraspot temperature gradients.

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.

The NANOGrav 15 yr (NG15) data set provides evidence for a gravitational-wave background (GWB) signal at nHz 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 Letter, 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 γ . 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.), which 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.

Evidence for a low-frequency gravitational-wave background using pulsar timing arrays has generated recent interest in its underlying contributing sources. However, multiple investigations have seen that the significance of the evidence does not change with the choice of pulsar modeling techniques, but the resulting parameters from the gravitational wave searches do. PSR J1455−3330 is one of the longest-observed pulsars in the array monitored by the North American Nanohertz Observatory for Gravitational Waves (NANOGrav), but showed no evidence for long-timescale red noise, either intrinsic or the common signal found among many pulsars in the array. In this work, we argue that NANOGrav’s piecewise-constant function used to model variations in radio-frequency-dependent dispersive delay should not be used for this pulsar, and a much simpler physical model of a fixed solar wind density plus a linear or quadratic trend in dispersion measure is preferred. When the original model is replaced, (i) the pulsar’s timing parallax signal changes from an upper limit to a significant detection, (ii) red noise becomes significant, and (iii) the red noise is consistent with the common signal found for the other pulsars. Neither of these signals is radio-frequency dependent. While the same physical motivation will not apply to many of the pulsars currently used in pulsar timing arrays, we argue for careful, physically motivated timing and noise modeling of pulsars used in precision timing experiments.