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 Re 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 Explorer (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 km and (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 Re and M that are consistent with those found in this work. We show that our measurements of Re and M for PSR J0030+0451 improve the astrophysical constraints on the EoS of cold, catalyzed matter above nuclear saturation density.
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 spectral-timing 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 Req are, respectively, 1.34 − 0.16 + 0.15 M and 12.71 − 1.19 + 1.14 km , while the compactness GM R eq c 2 = 0.156 − 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.
Both the mass and radius of the millisecond pulsar PSR J0030+0451 have been inferred via pulse-profile modeling of X-ray data obtained by NASA's Neutron Star Interior Composition Explorer (NICER) ...mission. In this Letter we study the implications of the mass-radius inference reported for this source by Riley et al. for the dense matter equation of state (EoS), in the context of prior information from nuclear physics at low densities. Using a Bayesian framework we infer central densities and EoS properties for two choices of high-density extensions: a piecewise-polytropic model and a model based on assumptions of the speed of sound in dense matter. Around nuclear saturation density these extensions are matched to an EoS uncertainty band obtained from calculations based on chiral effective field theory interactions, which provide a realistic description of atomic nuclei as well as empirical nuclear matter properties within uncertainties. We further constrain EoS expectations with input from the current highest measured pulsar mass; together, these constraints offer a narrow Bayesian prior informed by theory as well as laboratory and astrophysical measurements. The NICER mass-radius likelihood function derived by Riley et al. using pulse-profile modeling is consistent with the highest-density region of this prior. The present relatively large uncertainties on mass and radius for PSR J0030+0451 offer, however, only a weak posterior information gain over the prior. We explore the sensitivity to the inferred geometry of the heated regions that give rise to the pulsed emission, and find a small increase in posterior gain for an alternative (but less preferred) model. Lastly, we investigate the hypothetical scenario of increasing the NICER exposure time for PSR J0030+0451.
The Neutron Star Interior Composition Explorer collaboration recently published a joint estimate of the mass and the radius of PSR J0030+0451, derived via X-ray pulse-profile modeling. Raaijmakers et ...al. explored the implications of this measurement for the dense matter equation of state (EOS) using two parameterizations of the high-density EOS: a piecewise-polytropic model, and a model based on the speed of sound in neutron stars (NSs). In this work we obtain further constraints on the EOS following this approach, but we also include information about the tidal deformability of NSs from the gravitational wave signal of the compact binary merger GW170817. We compare the constraints on the EOS to those set by the recent measurement of a 2.14 M pulsar, included as a likelihood function approximated by a Gaussian, and find a small increase in information gain. To show the flexibility of our method, we also explore the possibility that GW170817 was a NS-black hole merger, which yields weaker constraints on the EOS.
We report on the first simultaneous Neutron Star Interior Composition Explore (NICER) and Nuclear Spectroscopic Telescope Array (NuSTAR) observations of the neutron star (NS) low-mass X-ray binary 4U ...1735−44, obtained in 2018 August. The source was at a luminosity of ∼1.8 (D/5.6 kpc)2 × 1037 erg s−1 in the 0.4-30 keV band. We account for the continuum emission with two different continuum descriptions that have been used to model the source previously. Despite the choice in continuum model, the combined passband reveals a broad Fe K line indicative of reflection in the spectrum. In order to account for the reflection spectrum we utilize a modified version of the reflection model relxill that is tailored for thermal emission from accreting NSs. Alternatively, we also use the reflection convolution model of rfxconv to model the reflected emission that would arise from a Comptonized thermal component for comparison. We determine that the innermost region of the accretion disk extends close to the innermost stable circular orbit (RISCO) at the 90% confidence level regardless of reflection model. Moreover, the current flux calibration of NICER is within 5% of the NuSTAR/FPMA(B).
We report on a Neutron star Interior Composition Explorer (NICER) observation of the Galactic X-ray binary and stellar-mass black hole candidate, MAXI J1535−571. The source was likely observed in an ..."intermediate" or "very high" state, with important contributions from both an accretion disk and hard X-ray corona. The 2.3-10 keV spectrum shows clear hallmarks of relativistic disk reflection. Fits with a suitable model strongly indicate a near-maximal spin parameter of and a disk that extends close to the innermost stable circular orbit, (1 statistical errors). In addition to the relativistic spectrum from the innermost disk, a relatively narrow Fe K emission line is also required. The resolution of NICER reveals that the narrow line may be asymmetric, indicating a specific range of emission radii. Fits with a relativistic line model suggest an inner radius of for the putative second reflection geometry; full reflection models suggest that radii a few times larger are possible. The origin of the narrow line is uncertain, but a warp likely provides the most physically plausible explanation. We discuss our results in terms of the potential for NICER to reveal new features of the inner and intermediate accretion disk around black holes.
Atoll sources are accreting neutron star (NS) low-mass X-ray binaries. We present a spectral analysis of four persistent atoll sources (GX 3+1, 4U 1702−429, 4U 0614+091, and 4U 1746−371) observed for ...∼20 ks each with NuSTAR to determine the extent of the inner accretion disk. These sources range from an apparent luminosity of 0.006-0.11 of the Eddington limit (assuming the empirical limit of 3.8 × 1038 erg s−1). Broad Fe emission features shaped by Doppler and relativistic effects close to the NS were firmly detected in three of these sources. The position of the disk appears to be close to the innermost stable circular orbit (ISCO) in each case. For GX 3+1, we determine (90% confidence level) and an inclination of 27°-31°. For 4U 1702−429, we find a and inclination of 53°-64°. For 4U 0614+091, the disk has a position of and inclination of 50°-62°. If the disk does not extend to the innermost stable circular orbit, we can place conservative limits on the magnetic field strength in these systems in the event that the disk is truncated at the Alfvén radius. This provides the limit at the poles of B ≤ 6.7 × 108 G, 3.3 × 108 G, and 14.5 × 108 G for GX 3+1, 4U 1702−429, and 4U 0614+091, respectively. For 4U 1746−371, we argue that the most plausible explanation for the lack of reflection features is a combination of source geometry and strong Comptonization. We place these sources among the larger sample of NSs that have been observed with NuSTAR.
We present NuSTAR observations of neutron star (NS) low-mass X-ray binaries: 4U 1636-53, GX 17+2, and 4U 1705-44. We observed 4U 1636-53 in the hard state, with an Eddington fraction, , of 0.01; GX ...17+2 and 4U 1705-44 were in the soft state with fractions of 0.57 and 0.10, respectively. Each spectrum shows evidence for a relativistically broadened Fe K line. Through accretion disk reflection modeling, we constrain the radius of the inner disk in 4U 1636-53 to be ISCO (innermost stable circular orbit), assuming a dimensionless spin parameter , and ISCO for (errors quoted at 1 ). This value proves to be model independent. For and , for example, 1.08 0.06 ISCO translates to a physical radius of km, and the NS would have to be smaller than this radius (other outcomes are possible for allowed spin parameters and masses). For GX 17+2, ISCO for and ISCO for . For and , ISCO translates to km. The inner accretion disk in 4U 1705-44 may be truncated just above the stellar surface, perhaps by a boundary layer or magnetosphere; reflection models give a radius of 1.46-1.64 ISCO for and 1.69-1.93 ISCO for . We discuss the implications our results may have on the equation of state of ultradense, cold matter and our understanding of the innermost accretion flow onto NSs with low surface magnetic fields, and systematic errors related to the reflection models and spacetime metric around less idealized NSs.
We present the discovery of a low-frequency 5.7 Hz quasi-periodic oscillation (QPO) feature in observations of the black hole X-ray binary MAXI J1535-571 in its soft-intermediate state, obtained in ...2017 September-October by the Neutron Star Interior Composition Explorer. The feature is relatively broad (compared to other low-frequency QPOs; quality factor Q 2) and weak (1.9% rms in 3-10 keV), and is accompanied by a weak harmonic and low-amplitude broadband noise. These characteristics identify it as a weak Type A/B QPO, similar to ones previously identified in the soft-intermediate state of the transient black hole X-ray binary XTE J1550-564. The lag-energy spectrum of the QPO shows increasing soft lags toward lower energies, approaching 50 ms at 1 keV (with respect to a 3-10 keV continuum). This large phase shift has similar amplitude but opposite sign to that seen in Rossi X-Ray Timing Explorer data for a Type B QPO from the transient black hole X-ray binary GX 339-4. Previous phase-resolved spectroscopy analysis of the Type B QPO in GX 339-4 pointed toward a precessing jet-like corona illuminating the accretion disk as the origin of the QPO signal. We suggest that this QPO in MAXI J1535-571 may have the same origin, with the different lag sign depending on the scale height of the emitting region and the observer inclination angle.
The Galactic black hole X-ray binary MAXI J1820+070 had a bright outburst in 2018 when it became the second brightest X-ray source in the sky. It was too bright for X-ray CCD instruments such as ...XMM–Newton and Chandra, but was well observed by photon counting instruments such as Neutron star Inner Composition Explorer (NICER) and Nuclear Spectroscopic Telescope Array (NuSTAR). We report here on the discovery of an excess emission component during the soft state. It is best modelled with a blackbody spectrum in addition to the regular disc emission, modelled as either diskbb or kerrbb. Its temperature varies from about 0.9 to 1.1 keV, which is about 30–80 per cent higher than the inner disc temperature of diskbb. Its flux varies between 4 and 12 per cent of the disc flux. Simulations of magnetized accretion discs have predicted the possibility of excess emission associated with a non-zero torque at the innermost stable circular orbit (ISCO) about the black hole, which, from other NuSTAR studies, lies at about 5 gravitational radii or about 60 km (for a black hole, mass is 8Msun). In this case, the emitting region at the ISCO has a width varying between 1.3 and 4.6 km and would encompass the start of the plunge region where matter begins to fall freely into the black hole.
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