Despite its importance to our understanding of physics at supranuclear densities, the equation of state (EoS) of matter deep within neutron stars remains poorly understood. Millisecond pulsars (MSPs) are among the most useful astrophysical objects in the Universe for testing fundamental physics, and place some of the most stringent constraints on this high-density EoS. Pulsar timing -the process of accounting for every rotation of a pulsar over long time periods -can precisely measure a wide variety of physical phenomena, including those that allow the measurement of the masses of the components of a pulsar binary system [1]. One of these, called relativistic Shapiro delay [2], can yield precise masses for both an MSP and its companion; however, it is only easily observed in a small subset of high-precision, highly inclined (nearly edge-on) binary pulsar systems. By combining data from the North American Nanohertz Observatory for Gravitational Waves (NANOGrav) 12.5-year data set with recent orbital-phase-specific observations using the Green Bank Telescope, we have measured the mass of the MSP J0740+6620 to be 2.14 +0.10 −0.09 solar masses (68.3% credibility interval; 95.4% credibility interval is 2.14 +0.20 −0.18 solar masses). It is highly 1 arXiv:1904.06759v2 [astro-ph.HE] 13 Sep 2019 likely to be the most massive neutron star yet observed, and serves as a strong constraint on the neutron star interior EoS. Relativistic Shapiro delay, which is observable when a pulsar passes behind its stellar companion during orbital conjunction, manifests as a small delay in pulse arrival times induced by the curvature of spacetime in the vicinity of the companion star. For a highly inclined MSP-white dwarf binary, the full delay is of order ∼10 µs. The relativistic effect is characterized by two parameters, "shape" and "range." In general relativity, shape (s) is the sine of the angle of inclination of the binary orbit (i), while range (r) is proportional to the mass of the companion, m c . When combined with the Keplerian mass function, measurements of r and s also constrain the pulsar mass (m p ; [3] provides a detailed overview and an alternate parameterization).Precise neutron star mass measurements are an effective way to constrain the EoS of the ultradense matter in neutron star interiors. Although radio pulsar timing cannot directly determine neutron star radii, the existence of pulsars with masses exceeding the maximum mass allowed by a given model can straightforwardly rule out that EoS.In 2010, Demorest et al. reported the discovery of a 2-solar-mass MSP, J1614−2230 [4] (though the originally reported mass was 1.97 ± 0.04 M , continued timing has led to a more precise mass measurement of 1.928±0.017 M ; Fonseca et al. 2016 [5]). This Shapiro-delay-enabled measurement disproved the plausibility of some hyperon, boson, and free quark models in nuclear-density environments. In 2013, Antoniadis et al. used optical techniques in combination with pulsar timing to yield a mass measurement of 2.01±0.04 M for the pulsar J0...

We search for an isotropic stochastic gravitational-wave background (GWB) in the 12.5 yr pulsar-timing data set collected by the North American Nanohertz Observatory for Gravitational Waves. Our analysis finds strong evidence of a stochastic process, modeled as a power law, with common amplitude and spectral slope across pulsars. Under our fiducial model, the Bayesian posterior of the amplitude for an f −2/3 power-law spectrum, expressed as the characteristic GW strain, has median 1.92 × 10−15 and 5%–95% quantiles of 1.37–2.67 × 10−15 at a reference frequency of f yr = 1 yr − 1 ; the Bayes factor in favor of the common-spectrum process versus independent red-noise processes in each pulsar exceeds 10,000. However, we find no statistically significant evidence that this process has quadrupolar spatial correlations, which we would consider necessary to claim a GWB detection consistent with general relativity. We find that the process has neither monopolar nor dipolar correlations, which may arise from, for example, reference clock or solar system ephemeris systematics, respectively. The amplitude posterior has significant support above previously reported upper limits; we explain this in terms of the Bayesian priors assumed for intrinsic pulsar red noise. We examine potential implications for the supermassive black hole binary population under the hypothesis that the signal is indeed astrophysical in nature.

PSR J0740+6620 has a gravitational mass of 2.08 ± 0.07 M ⊙, which is the highest reliably determined mass of any neutron star. As a result, a measurement of its radius will provide unique insight into the properties of neutron star core matter at high densities. Here we report a radius measurement based on fits of rotating hot spot patterns to Neutron Star Interior Composition Explorer (NICER) and X-ray Multi-Mirror (XMM-Newton) X-ray observations. We find that the equatorial circumferential radius of PSR J0740+6620 is 13.7 − 1.5 + 2.6 km (68%). We apply our measurement, combined with the previous NICER mass and radius measurement of PSR J0030+0451, the masses of two other ∼2 M ⊙ pulsars, and the tidal deformability constraints from two gravitational wave events, to three different frameworks for equation-of-state modeling, and find consistent results at ∼1.5–5 times nuclear saturation density. For a given framework, when all measurements are included, the radius of a 1.4 M ⊙ neutron star is known to ±4% (68% credibility) and the radius of a 2.08 M ⊙ neutron star is known to ±5%. The full radius range that spans the ±1σ credible intervals of all the radius estimates in the three frameworks is 12.45 ± 0.65 km for a 1.4 M ⊙ neutron star and 12.35 ± 0.75 km for a 2.08 M ⊙ neutron star.

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 -+ 10 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. Unified Astronomy Thesaurus concepts: Millisecond pulsars (1062); Rotation powered pulsars (1408); Pulsars (1306); Radio pulsars (1353); X-ray astronomy (1810); Neutron stars (1108)