We report on Bayesian parameter estimation of the mass and equatorial radius of the millisecond pulsar PSRJ0030 +0451, conditional on pulse-profile modeling of Neutron Star Interior Composition Explorer X-ray spectraltiming event data. We perform relativistic ray-tracing of thermal emission from hot regions of the pulsar's surface. We assume two distinct hot regions based on two clear pulsed components in the phase-folded pulse-profile data; we explore a number of forms (morphologies and topologies) for each hot region, inferring their parameters in addition to the stellar mass and radius. For the family of models considered, the evidence (prior predictive probability of the data) strongly favors a model that permits both hot regions to be located in the same rotational hemisphere. Models wherein both hot regions are assumed to be simply connected circular single-temperature spots, in particular those where the spots are assumed to be reflection-symmetric with respect to the stellar origin, are strongly disfavored. For the inferred configuration, one hot region subtends an angular extent of only a few degrees (in spherical coordinates with origin at the stellar center) and we are insensitive to other structural details; the second hot region is far more azimuthally extended in the form of a narrow arc, thus requiring a larger number of parameters to describe. The inferred mass M and equatorial radius R eq are, respectively,-+ eq 2 0.010 0.008 is more tightly constrained; the credible interval bounds reported here are approximately the 16% and 84% quantiles in marginal posterior mass.

Neutron stars are not only of astrophysical interest, but are also of great interest to nuclear physicists because their attributes can be used to determine the properties of the dense matter in their cores. One of the most informative approaches for determining the equation of state (EoS) of this dense matter is to measure both a star's equatorial circumferential radius R e and its gravitational mass M . Here we report estimates of the mass and radius of the isolated 205.53 Hz millisecond pulsar PSR J0030+0451 obtained using a Bayesian inference approach to analyze its energy-dependent thermal X-ray waveform, which was observed using the Neutron Star Interior Composition Ex-Corresponding author: M. C. Miller miller@astro.umd.edu a Einstein Fellow arXiv:1912.05705v1 [astro-ph.HE] 12 Dec 2019 Miller, Lamb, Dittmann, et al. plorer (NICER). This approach is thought to be less subject to systematic errors than other approaches for estimating neutron star radii. We explored a variety of emission patterns on the stellar surface. Our best-fit model has three oval, uniform-temperature emitting spots and provides an excellent description of the pulse waveform observed using NICER. The radius and mass estimates given by this model are R e = 13.02 +1.24 −1.06 km and M = 1.44 +0.15 −0.14 M (68%). The independent analysis reported in the companion paper by Riley et al. explores different emitting spot models, but finds spot shapes and locations and estimates of R e and M that are consistent with those found in this work. We show that our measurements of R e and M for PSR J0030+0451 improve the astrophysical constraints on the EoS of cold, catalyzed matter above nuclear saturation density.

We show that gravitational radiation drives an instability in hot young rapidly rotating neutron stars. This instability occurs primarily in the l = 2 r-mode and will carry away most of the angular momentum of a rapidly rotating star by gravitational radiation. On the timescale needed to cool a young neutron star to about T = 10 9 K (about one year) this instability can reduce the rotation rate of a rapidly rotating star to about 0.076ΩK , where ΩK is the Keplerian angular velocity where mass shedding occurs. In older colder neutron stars this instability is suppressed by viscous effects, allowing older stars to be spun up by accretion to larger angular velocities. (and Friedman and Morsink [2] confirmed more generally) that gravitational radiation tends to drive the r-modes of all rotating stars unstable. In this paper we examine the timescales associated with this instability in some detail. We show that gravitational radiation couples to these modes primarily through the current multipoles, rather than the usual mass multipoles. We also evaluate the effects of internal fluid dissipation which tends to suppress this instability. We find that gravitational radiation is stronger than viscosity in these modes and so this instability severely limits the rotation rates of hot young neutron stars. We show that such stars can spin down by the emission of gravitational radiation to about 7.6% of their maximum rotation rates on the timescale (about one year) needed to cool these stars to 10 9 K.The r-modes of rotating barotropic Newtonian stars are solutions of the perturbed fluid equations having (Eulerian) velocity perturbationswhere R and Ω are the radius and angular velocity of the unperturbed star, α is an arbitrary constant, and Y B l m is the magnetic type vector spherical harmonic defined byPapaloizou and Pringle [3] first showed that the Euler equation for r−modes determines the frequencies asFurther use of the Euler equation (as first noted by Provost, Berthomieu and Rocca [4]) in the barotropic case (a good approximation for neutron stars) determines that only the l = m r-modes exist, and that δ v must have the radial dependence given in Eq. (1). These expressions for the velocity perturbation and frequency are only the lowest order terms in expansions for these quantities in powers of Ω. The exact expressions contain additional terms of order Ω 3 . The lowest order expressions for the (Eulerian) density perturbation δρ can also be deduced from the perturbed fluid equations (Ipser and Lindblom [5]): δρ ρ = αR 2 Ω 2 dρ dp (4) where δΨ(r) is proportional to the gravitational potential δΦ and satisfies d 2 δΨ dr 2 + 2 r dδΨ dr + 4πGρ dρ dp − (l + 1)(l + 2) r 2 δΨ = − 8πGl 2l + 1 l l + 1 ρ dρ dp r R l+1 .Eq. (4) is the complete expression for δρ to order Ω 2 . The next order terms are proportional to Ω 4 . Our interest here is to study the evolution of these modes due to the dissipative influences of viscosity and gravitational radiation. For this purpose it is useful to consider the effects of radiation on t...

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)