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

TL;DR

This work measures the radius of PSR J0614-3329 by applying Bayesian pulse-profile modeling to joint NICER and XMM-Newton data, using X-PSI to simulate surface emission from two hot regions and constraining $R_{ m eq}$ under tight radio timing priors on $M$ and $i$. Across multiple hotspot geometries (ST-U, ST+PDT, PDT-U), the radius remains robust, with the Headline ST+PDT result yielding $R_{ m eq}=10.29^{+1.01}_{-0.86}$ km for $M=1.44^{+0.06}_{-0.07}\,M_\\odot$, and a background treatment anchored by XMM phase-averaged spectra. The radius constraint, together with prior NICER and GW data, mildly softens the dense-matter EOS, shifting the allowed mass–radius region toward lower radii by about $\sim300$ m, while leaving the maximum mass largely unchanged. Overall, the findings demonstrate a stable, geometry-consistent radius estimate for an edge-on MSP and illustrate how incorporating multi-instrument data and strong priors improves EOS inferences in neutron-star interiors.

Abstract

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.

Figures (12)

• Figure 1: Reduced and phase-folded NICER event data for PSR J0614$-$3329 duplicated over two rotational cycles for visualization purpose. The top panel displays the $0.3-2.0$ keV bolometric pulse profile with its associated Poisson uncertainty. The bottom panel shows the energy resolved pulse profile. Phases are separated into $32$ regular sized bins and energy by registered PI channel, as used for the inference. Energy resolved pulse profiles in previous publications had their number of counts per bin divided by the number of cycles shown, which is not the case here.
• Figure 2: Extracted source (blue) and background (green) spectra from all EPIC instruments used for inference. The green shaded area represents the uniform prior range for the background ($\pm 3 \sigma$, see Section \ref{['subsec:priors']}). Backgrounds are rescaled using the source and background backscal values. For visualization purpose only, the rescaled source and background spectra grouped in 13 uniformly sized bins are shown, respectively, in purple and orange.
• Figure 3: Posterior distributions of the mass, radius, and compactness for the runs presented in Section \ref{['sec:inference']}. Dash-dotted black lines on the diagonal plots show the marginalized prior distributions, shared across all runs. The shaded vertical bands show the $68.3\%$ credible intervals. The contours in the 2D posteriors show the $68.3\%$, $95.4\%$, and $99.7\%$ credible regions, which are filled for the Headline result.
• Figure 4: Representation of the best fit geometries, as seen from Earth, for the two main modes uncovered by the Headline ST+PDT run. The pulsar is represented without gravitational or relativistic effects at phase zero of the data. The hotspots located behind the star are plotted with dimmed colors. The hotspot color changes from blue to red, from the hottest to the coldest temperatures. The equatorial ST hotspot can be seen at phase $\phi \sim 0.4$ (behind the star) for both modes. The polar PDT hotspot has two possible configurations, where the smaller and hotter components can be either ceding or superseding components (see Section \ref{['subsec:ST+PDT']}). The right geometry is the overall best fit geometry. These representations do not capture the full posterior distributions of the geometric parameters and should be considered with care.
• Figure 5: Posterior predictive distribution and best fit model of the bolometric pulse on the left panel and of the phase-averaged spectrum on the right panel. The posterior predictive distribution represents the posterior probability distribution of the observables. The contribution of the individual model components are shown in orange for ST, blue for PDT (left panel only) and purple for the background (BKG). The combined model components are in green for ST+PDT, and in light blue for the total (Expected, i.e., ST+PDT+BKG). The shaded regions, from darker to lighter, represent, respectively, the $68\%$, $95\%$ (and $99\%$ for the right panel only) credible interval computed over $5000$ samples. The solid lines represent the maximum likelihood model and the black dashed line the data. The left panel has a discontinuous y-axis and the horizontal line at $\sim13,000$ counts represent the phase-independent maximum likelihood background. On the right panel, the expected distribution, maximum likelihood and data all overlap. Note that the sampling procedure does not fit individually the ST, PDT, or BKG components but their sum (see Section \ref{['subsec:Headline']} for details).