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Paul S. Ray

Publications and source records attributed to Paul S. Ray.

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.

astro-ph.HE

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

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

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 $3.16\sigma$ to $3.32\sigma$ 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 $\gamma_{\rm GWB} = 13/3$. In a varied-$\gamma$ analysis, the spectral index increases to $\gamma_{\rm GWB}=3.5^{+0.7}_{-0.6}$. 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

The NANOGrav 15 yr Data Set: Customized Chromatic Noise Models

Pulsar timing arrays conduct low-frequency gravitational wave 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 gravitational waves 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 $\sim 1.5$ solar cycles. We also find evidence for non-dispersive 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 gravitational wave searches with pulsar timing arrays.

astro-ph.HE

The NANOGrav 15 yr and 20 yr Datasets: Timing Events and Pulse Shape Changes

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 dataset and two with additional profiles from the forthcoming 20 yr dataset. 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.

astro-ph.HE

Photon-Count Statistics of Crab X-ray Pulses: Skellam Behavior and Excess Variance in the Main Pulse

The Crab pulsar (PSR B0531+21) provides an unusually rich test bed for statistical studies of high-energy photon-counting data, owing to its extreme brightness and the contrasting behavior of its main pulse (MP) and interpulse (IP) components. Using 78.8 ks of Neutron star Interior Composition Explorer (NICER; Gendreau and Arzoumanian 2017) data-over two million individual X-ray pulses- we construct the single-pulse photon-count distributions of the MP and IP at keV energies. We find that the IP is well described by the Skellam distribution expected for the difference of two Poisson processes, providing a rare, high-statistics empirical demonstration of Skellam behavior in an astrophysical photon-counting context. The MP also shows pulse-by-pulse variability best described by a Skellam framework when compared to Gaussian alternatives, but exhibits a significant excess variance driven by high-count events. When photon counts are summed over successive pulses, this excess averages out and the MP distribution becomes consistent with Skellam expectations, indicating that the enhanced variability does not persist across rotations. We further search for short-lag (memory) correlations between successive X-ray pulses and find no statistically significant lag-1 correlation. Although giant radio pulses occur in the MP phase window, their contribution is insufficient to account for the observed excess variability. Together, these results highlight a clear statistical distinction between the MP and IP and underscore the importance of using statistically appropriate models for high-energy photon-counting analyses. The distributional fits and memory limits reported here provide quantitative constraints on pulsar emission models and illustrate the broader utility of Skellam-based approaches.

astro-ph.HE

Gravitational Wave Measurement of the $M_\mathrm{BH}$-$M_\mathrm{bulge}$ Intrinsic Scatter at High Redshift

The observed GWB spectrum is higher in amplitude than model predictions by a factor of 2-3. Using a semi-analytic model, we evaluate the effect of a high-scatter supermassive black hole (SMBH) scaling relation ($M_\mathrm{BH}$-$M_\mathrm{bulge}$) on models of the nanohertz gravitational wave background (GWB). By implementing an intrinsic scatter of the $M_\mathrm{BH}$-$M_\mathrm{bulge}$ relation, which is larger at higher redshift, but matches local observations, we find that the amplitude of GWB models increases to be consistent with the low-frequency end of the GWB spectrum. This amplitude increase is not uniform across frequencies, a strongly evolving scatter preferentially increases the number density of the most massive SMBHs which, in the GWB spectrum, minimizes the strength of the low-frequency turnover. Our models with positively evolving intrinsic scatter can reproduce the electromagnetically observed overmassive SMBHs at $4 < z < 6$ without changing the $M_\mathrm{BH}$-$M_\mathrm{bulge}$ normalization though we find that including moderate normalization evolution marginally improves fits to the GWB data. We conclude that the $M_\mathrm{BH}$-$M_\mathrm{bulge}$ relation which best describes the available GWB and electromagnetic data sets has intrinsic scatter that evolves as $\varepsilon(z) = \varepsilon_0 + (0.56 \pm 0.4) \log_{10}(1 + z)$ and normalization that evolves as $\alpha(z) = \alpha_0 (1 + z)^{0.84 \pm 0.35}$. The results of this work imply that the $M_\mathrm{BH}$-$M_\mathrm{bulge}$ relation we see today is not universal throughout cosmic time and that a diversity of seeding models and growth mechanisms may be at play in the early stages of SMBH-galaxy evolution.

astro-ph.HE

A NICER View of PSR J0030+0451: Updated Constraints from Six Years of NICER Observations

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--radius was 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 significantly reduces the discrepancy between the hot spot models. The inferred mass and radius are $M = 1.43^{+0.20}_{-0.17}\,M_\odot$ and $R_{\rm eq} = 12.68^{+1.31}_{-1.04}$ km (68% credible intervals), reducing the tension with the results from other sources. In addition, the inferred hot spot configurations suggest the presence of intra-spot temperature gradients.

astro-ph.HE

The NANOGrav 15 yr Data Set: Piecewise Power-Law Reconstruction of the Gravitational-Wave Background

The NANOGrav 15-year (NG15) data set provides evidence for a gravitational-wave background (GWB) signal at nanohertz 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 paper, 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 gamma. 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.) that 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.

astro-ph.HE

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.

astro-ph.IM

Shapiro Delay Measurements from Fifteen Years of PSR J1231$-$1411 Radio Observations

We present 15 years of Nan\c{c}ay and Green Bank radio telescope timing observations for PSR J1231$-$1411. This millisecond pulsar is a primary science target for the Neutron Star Interior Composition Explorer telescope (NICER, which discovered its X-ray pulsations), has accumulated near-continuous $\gamma$-ray data since the Fermi-Large Area Telescope's launch, and has been studied extensively with the Green Bank and Nan\c{c}ay radio telescopes. We have undertaken a campaign with the Green Bank Telescope targeting specific orbital phases designed to improve our constraint on the pulsar's mass through the detection of a relativistic Shapiro delay. Both frequentist and Bayesian techniques -- the latter incorporating priors from white dwarf binary evolution models -- are applied to fifteen years of radio observations, yielding relatively weak constraints on the companion and pulsar masses of $0.23^{+0.09}_{-0.06}$ M$_{\odot}$ and $1.87^{+1.11}_{-0.67}$ M$_{\odot}$, respectively (68.3% CI from Bayesian fits); however, the orbital inclination is measured to better relative precision ($79.80^{+3.47}_{-4.70}$ degrees). Restricting the maximum allowed pulsar mass to 3 M$_{\odot}$ improves the constraint and lowers the measured mass to $1.71^{+0.70}_{-0.56}$ M$_{\odot}$. A fully-generalized Bayesian fit that simultaneously samples the noise and timing models yields a pulsar mass in close agreement with this value. While our radio-derived inclination result has informed recent NICER X-ray studies of PSR J1231$-$1411, the lessons learned from this troublesome pulsar will also bolster future high-precision mass measurement campaigns and resulting constraints on the neutron star interior equation of state.

astro-ph.HE

CHIME-o-Grav: Wideband Timing of Four Millisecond Pulsars from the NANOGrav 15-yr dataset

Wideband timing of the North American Nanohertz Observatory for Gravitational Waves (NANOGrav) datasets, where a single time-of-arrival (TOA) and a single dispersion measure (DM) are measured using the entire bandwidth of each observation, was first done for the 12.5-year dataset, and proved to be invaluable for characterizing the time-varying dispersion measure, reducing the data volume, and for improving the overall timing precision. The Canadian Hydrogen Intensity Mapping Experiment (CHIME) Telescope has been observing most NANOGrav millisecond pulsars (MSPs) at nearly daily cadence (compared to roughly monthly cadence for other NANOGrav observations) since 2019 with the objective of integration into future pulsar timing array (PTA) datasets. In this paper, we show the results of integration of high-cadence, low-observing-frequency CHIME data with data from the NANOGrav experiment for an isolated MSP PSR J0645$+$5158 and three binary MSPs PSR J1012$+$5307, PSR J2145$-$0750, and PSR J2302$+$4442. Using a wideband timing pipeline which we also describe, we present updated timing results for all four sources, including improvements in measurements of relativistic post-Keplerian parameters for the three binary pulsars in this analysis. For PSR J2302$+$4442, we report an updated strong detection of Shapiro delay from which we measured a companion mass of $0.35^{+0.05}_{-0.04}\ M_{\odot}$, a pulsar mass of $1.8^{+0.3}_{-0.3}\ M_{\odot}$, and an orbital inclination of ${80^{\circ}}^{+1}_{-2}$. We also report updated constraints on the reflex motion for PSR J2145$-$0750 using a combination of Very Long Baseline Array astrometry and our updated measurement of the time derivative of the projected semi-major axis of the pulsar orbit as a prior.

astro-ph.HE

Searching for Exotrojans in Pulsar Systems

Trojan asteroids are found in the equilateral triangle Lagrange points of the Sun-Jupiter system in great number, though they also exist less prolifically in other parts of the Solar System. Despite up to planetary mass Trojans being predicted in extrasolar systems (i.e. exotrojans), they remain unconfirmed, although strong candidate evidence has emerged recently. For the first time, we extend the search for exotrojans to radio pulsars with low-mass ($\sim0.01\,\rm{M}_\odot$) companions using accurately measured pulse times of arrival. With techniques developed for detecting the reflex motion of a star due to a librating Trojan, we place $\sim 1\,\rm{M}_\oplus$ upper mass constraints on potential exotrojans around eight pulsars observed in the NANOGrav 15-year data set. We find weak evidence consistent with $\sim2$--4$\,\rm{M}_{\rm J}$ exotrojans in the PSR~J0023+0923 and PSR~J1705$-$1903 binary systems, though the signals likely have a different, unknown source. We also place a libration-independent upper mass constraint of $\sim8$\,M$_{\rm J}$ on exotrojans in the PSR~J1641+8049 system by looking for an inconsistency between the times of superior conjunction as measured by optical light curves and those predicted by radio timing. These results offer initial observational constraints on the existence of exotrojans around pulsars, while their possible formation mechanisms remain unexplored.

astro-ph.HE

The NANOGrav 15-Year Data Set: Improved Timing Precision With VLBI Astrometric Priors

Accurate pulsar astrometric estimates play an essential role in almost all high-precision pulsar timing experiments. Traditional pulsar timing techniques refine these estimates by including them as free parameters when fitting a model to observed pulse time-of-arrival measurements. However, reliable sub-milliarcsecond astrometric estimations require years of observations and, even then, power from red noise can be inadvertently absorbed into astrometric parameter fits, biasing the resulting estimations and reducing our sensitivity to red noise processes, including gravitational waves (GWs). In this work, we seek to mitigate these shortcomings by using pulsar astrometric estimates derived from Very Long Baseline Interferometry (VLBI) as priors for the timing fit. First, we calibrated a frame tie to account for the offsets between the reference frames used in VLBI and timing. Then, we used the VLBI-informed priors and timing-based likelihoods of several astrometric solutions consistent with both techniques to obtain a maximum-posterior astrometric solution. We found offsets between our results and the timing-based astrometric solutions, which, if real, would lead to absorption of spectral power at frequencies of interest for single-source GW searches. However, we do not find significant power absorption due to astrometric fitting at the low-frequency domain of the GW background.

astro-ph.HE

The NANOGrav 15 yr Data Set: Targeted Searches for Supermassive Black Hole Binaries

We present the first targeted searches for continuous gravitational waves (CWs) from 114 active galactic nuclei (AGN) that may host supermassive black hole binaries, using the NANOGrav 15 yr data set. By incorporating electromagnetic priors on sky location, distance, redshift, and CW frequency, our strain and chirp mass upper limits are typically improved by a factor of $\sim 2$ (median 2.2) relative to all-sky limits at the same frequency. Bayesian comparisons against a model including only a Hellings-Downs correlated background disfavors a CW signal for all targets, with a mean Bayes factor of $0.73 \pm 0.32$. Two targets have Bayes factors slightly above unity, but coherence tests, random targeting experiments, and a conservative accounting of the 114-target trials factor all indicate that they are consistent with noise. We use these two candidates as worked examples to illustrate an end-to-end targeted CW search analysis and a suite of follow up tests that future promising candidates would need to pass. We find that the electromagnetic interpretations of both candidates are ambiguous, and we update the constraints on a putative binary in 3C 66B, ruling out part of its previously allowed parameter space. Ultimately, our results demonstrate the current sensitivity of targeted pulsar timing array searches for CWs and define a roadmap for future multimessenger CW detections.

astro-ph.HE

The NANOGrav 15-year Data Set: Search for Gravitational Scattering of Pulsars by Free-Floating Objects in Interstellar Space

Free-floating objects (FFOs) in interstellar space$-$rogue planets, brown dwarfs, and large asteroids that are not gravitationally bound to any star$-$are expected to be ubiquitous throughout the Milky Way. Recent microlensing surveys have discovered several free-floating planets that are not bound to any known stellar systems. Additionally, three interstellar objects, namely 1I/'Oumuamua, 2I/Borisov, and 3I/ATLAS, have been detected passing through our solar system on hyperbolic trajectories. In this work, we search for FFOs on hyperbolic orbits that pass near millisecond pulsars (MSPs), where their gravitational influence can induce detectable perturbations in pulse arrival times. Using the NANOGrav 15-year narrowband dataset, which contains high-precision timing data for 68 MSPs, we conduct a search for such hyperbolic scattering events between FFOs and pulsars. Although no statistically significant events were detected, this non-detection enables us to place upper limits on the number density of FFOs as a function of their mass within our local region of the Galaxy. For example, the upper limit on the number density for Jupiter-mass FFOs ($\sim 10^{-2.5} - 10^{-3.5}~M_{\odot}$) obtained from different pulsars ranges from $5.25\times10^{6}~\text{pc}^{-3}$ to $5.37\times10^{9}~\text{pc}^{-3}$, while the upper limit calculated by combining results from all the pulsars is $6.03\times10^{5}~\text{pc}^{-3}$. These results represent the first constraints on FFO population derived from pulsar timing data.

astro-ph.HE

A NICER view of the 1.4 solar-mass edge-on pulsar PSR J0614-3329

Four neutron star radius measurements have already been obtained by modeling the X-ray pulses of rotation-powered millisecond pulsars observed by the Neutron Star Interior Composition ExploreR (NICER). We report here the radius measurement of PSR J0614-3329 employing the same method with NICER and XMM-Newton data using Bayesian Inference. For all different models tested, including one with unrestricted inclination prior, we retrieve very similar non-antipodal hot regions geometries and radii. For the preferred model, we infer an equatorial radius of $R_{\rm eq}=10.29^{+1.01}_{-0.86}\,$km for a mass of $M=1.44^{+0.06}_{-0.07} \, M_{\odot}$ (median values with equal-tailed $68\%$ credible interval), the latter being essentially constrained from radio timing priors obtained by MeerKAT. A more complex model, fitting the data equally well, resulted in a consistent inferred radius. We find that, for all different models, the pulse emission originates from two hot regions, one at the pole and the other at the equator. The resulting radius constraint is consistent with previous X-ray and gravitational wave measurements of neutron stars in the same mass range. Equation of state inferences, including previous NICER and gravitational wave results, slightly soften the equation of state with PSR J0614$-$3329 included and shift the allowed mass-radius region toward lower radii by $\sim 300\,$m, which is compatible with previous analyses to within less than one standard deviation.

astro-ph.HE