We report on Bayesian estimation of the radius, mass, and hot surface regions of the massive millisecond pulsar PSR J0740+6620, conditional on pulse-profile modeling of Neutron Star Interior Composition Explorer X-ray Timing Instrument event data. We condition on informative pulsar mass, distance, and orbital inclination priors derived from the joint North American Nanohertz Observatory for Gravitational Waves and Canadian Hydrogen Intensity Mapping Experiment/Pulsar wideband radio timing measurements of Fonseca et al. We use XMM-Newton European Photon Imaging Camera spectroscopic event data to inform our X-ray likelihood function. The prior support of the pulsar radius is truncated at 16 km to ensure coverage of current dense matter models. We assume conservative priors on instrument calibration uncertainty. We constrain the equatorial radius and mass of PSR J0740+6620 to be 12.39 − 0.98 + 1.30 km and 2.072 − 0.066 + 0.067 M _⊙ respectively, each reported as the posterior credible interval bounded by the 16% and 84% quantiles, conditional on surface hot regions that are non-overlapping spherical caps of fully ionized hydrogen atmosphere with uniform effective temperature; a posteriori, the temperature is log 10 ( T [ K ] ) = 5.99 − 0.06 + 0.05 for each hot region. All software for the X-ray modeling framework is open-source and all data, model, and sample information is publicly available, including analysis notebooks and model modules in the Python language. Our marginal likelihood function of mass and equatorial radius is proportional to the marginal joint posterior density of those parameters (within the prior support) and can thus be computed from the posterior samples.

We report Bayesian inference of the mass, radius, and hot X-ray emitting region properties—using data from the Neutron Star Interior Composition ExploreR (NICER)—for the brightest rotation-powered millisecond X-ray pulsar, PSR J0437−4715. Our modeling is conditional on informative tight priors on mass, distance, and binary inclination obtained from radio pulsar timing using the Parkes Pulsar Timing Array (PPTA; Reardon et al.), and we use NICER background models to constrain the nonsource background, cross-checking with data from XMM-Newton. We assume two distinct hot emitting regions and various parameterized hot region geometries that are defined in terms of overlapping circles; while simplified, these capture many of the possibilities suggested by detailed modeling of return current heating. For the preferred model identified by our analysis, we infer a mass of M = 1.418 ± 0.037 M _⊙ (largely informed by the PPTA mass prior) and an equatorial radius of R = 11.36 − 0.63 + 0.95 km, each reported as the posterior credible interval bounded by the 16% and 84% quantiles. This radius favors softer dense matter equations of state and is highly consistent with constraints derived from gravitational wave measurements of neutron star binary mergers. The hot regions are inferred to be nonantipodal and hence inconsistent with a pure centered dipole magnetic field.

According to recent results of Ho & Heinke, the Cassiopeia A supernova remnant contains a young (≈330-yr-old) neutron star (NS) which has carbon atmosphere and shows notable decline of the effective surface temperature. We report a new (2010 November) Chandra observation which confirms the previously reported decline rate. The decline is naturally explained if neutrons have recently become superfluid (in triplet state) in the NS core, producing a splash of neutrino emission due to Cooper pair formation (CPF) process that currently accelerates the cooling. This scenario puts stringent constraints on poorly known properties of NS cores: on density dependence of the temperature Tcn(ρ) for the onset of neutron superfluidity [Tcn(ρ) should have a wide peak with maximum ≈ (7–9) × 108 K]; on the reduction factor q of CPF process by collective effects in superfluid matter (q > 0.4) and on the intensity of neutrino emission before the onset of neutron superfluidity (30–100 times weaker than the standard modified Urca process). This is serious evidence for nucleon superfluidity in NS cores that comes from observations of cooling NSs.

In 2019 the NICER collaboration published the first mass and radius inferred for PSR J0030+0451, thanks to NICER observations, and consequent constraints on the equation of state characterizing dense matter. Two independent analyses found a mass of ∼1.3–1.4 M _⊙ and a radius of ∼13 km. They also both found that the hot spots were all located on the same hemisphere, opposite to the observer, and that at least one of them had a significantly elongated shape. Here we reanalyze, in greater detail, the same NICER data set, incorporating the effects of an updated NICER response matrix and using an upgraded analysis framework. We expand the adopted models and also jointly analyze XMM-Newton data, which enables us to better constrain the fraction of observed counts coming from PSR J0030+0451. Adopting the same models used in previous publications, we find consistent results, although with more stringent inference requirements. We also find a multimodal structure in the posterior surface. This becomes crucial when XMM-Newton data is accounted for. Including the corresponding constraints disfavors the main solutions found previously, in favor of the new and more complex models. These have inferred masses and radii of ∼[1.4 M _⊙, 11.5 km] and ∼[1.7 M _⊙, 14.5 km], depending on the assumed model. They display configurations that do not require the two hot spots generating the observed X-rays to be on the same hemisphere, nor to show very elongated features, and point instead to the presence of temperature gradients and the need to account for them.

We report an updated analysis of the radius, mass, and heated surface regions of the massive pulsar PSR J0740+6620 using Neutron Star Interior Composition Explorer (NICER) data from 2018 September 21 to 2022 April 21, a substantial increase in data set size compared to previous analyses. Using a tight mass prior from radio-timing measurements and jointly modeling the new NICER data with XMM-Newton data, the inferred equatorial radius and gravitational mass are 12.49 − 0.88 + 1.28 km and 2.073 − 0.069 + 0.069 M _⊙, respectively, each reported as the posterior credible interval bounded by the 16% and 84% quantiles, with an estimated systematic error ≲ 0.1 km. This result was obtained using the best computationally feasible sampler settings providing a strong radius lower limit but a slightly more uncertain radius upper limit. The inferred radius interval is also close to the R = 12.76 − 1.02 + 1.49 km obtained by Dittmann et al., when they require the radius to be less than 16 km as we do. The results continue to disfavor very soft equations of state for dense matter, with R < 11.15 km for this high-mass pulsar excluded at the 95% probability. The results do not depend significantly on the assumed cross-calibration uncertainty between NICER and XMM-Newton. Using simulated data that resemble the actual observations, we also show that our pipeline is capable of recovering parameters for the inferred models reported in this paper.