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Journal ArticleDOI

A NICER View of PSR J0030+0451: Millisecond Pulsar Parameter Estimation

TL;DR: In this paper, the mass and equatorial radius of the millisecond pulsar PSR J0030+0451 were estimated based on a relativistic ray-tracing of thermal emission from hot regions of the pulsar surface.
Abstract: 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 R eq are, respectively, and , while the compactness is more tightly constrained; the credible interval bounds reported here are approximately the 16% and 84% quantiles in marginal posterior mass.

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Journal ArticleDOI
Richard J. Abbott1, T. D. Abbott2, Sheelu Abraham3, Fausto Acernese4  +1334 moreInstitutions (150)
TL;DR: In this paper, the authors reported the observation of a compact binary coalescence involving a 222 −243 M ⊙ black hole and a compact object with a mass of 250 −267 M ⋆ (all measurements quoted at the 90% credible level) The gravitational-wave signal, GW190814, was observed during LIGO's and Virgo's third observing run on 2019 August 14 at 21:10:39 UTC and has a signal-to-noise ratio of 25 in the three-detector network.
Abstract: We report the observation of a compact binary coalescence involving a 222–243 M ⊙ black hole and a compact object with a mass of 250–267 M ⊙ (all measurements quoted at the 90% credible level) The gravitational-wave signal, GW190814, was observed during LIGO's and Virgo's third observing run on 2019 August 14 at 21:10:39 UTC and has a signal-to-noise ratio of 25 in the three-detector network The source was localized to 185 deg2 at a distance of ${241}_{-45}^{+41}$ Mpc; no electromagnetic counterpart has been confirmed to date The source has the most unequal mass ratio yet measured with gravitational waves, ${0112}_{-0009}^{+0008}$, and its secondary component is either the lightest black hole or the heaviest neutron star ever discovered in a double compact-object system The dimensionless spin of the primary black hole is tightly constrained to ≤007 Tests of general relativity reveal no measurable deviations from the theory, and its prediction of higher-multipole emission is confirmed at high confidence We estimate a merger rate density of 1–23 Gpc−3 yr−1 for the new class of binary coalescence sources that GW190814 represents Astrophysical models predict that binaries with mass ratios similar to this event can form through several channels, but are unlikely to have formed in globular clusters However, the combination of mass ratio, component masses, and the inferred merger rate for this event challenges all current models of the formation and mass distribution of compact-object binaries

913 citations


Cites background from "A NICER View of PSR J0030+0451: Mil..."

  • ...…et al. (2020b) for discussions about the interpretation of this observation. which may increase the Mmax estimates by a few percent (Landry et al. 2020) because it favors slightly stiffer EOSs than GW170817 (Miller et al. 2019; Raaijmakers et al. 2019; Riley et al. 2019; Jiang et al. 2020)....

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Journal ArticleDOI
TL;DR: In this paper, the mass and radius of the isolated 205.53 Hz millisecond pulsar PSR J0030+0451 were estimated 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).
Abstract: 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 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 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.

758 citations

Journal ArticleDOI
TL;DR: In this article, the mass and radius of the isolated 205.53 Hz millisecond pulsar PSR J0030+0451 were estimated using a Bayesian inference approach to analyze its energy-dependent thermal X-ray waveform.
Abstract: 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 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 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 $R_e = 13.02^{+1.24}_{-1.06}$ km and $M = 1.44^{+0.15}_{-0.14}\ M_\odot$ (68%). The independent analysis reported in the companion paper by Riley et al. (2019) 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 equation of state of cold, catalyzed matter above nuclear saturation density.

586 citations

Journal ArticleDOI
TL;DR: In this article, the authors reported 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) observations.
Abstract: PSR J0740$+$6620 has a gravitational mass of $2.08\pm 0.07~M_\odot$, 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 $13.7^{+2.6}_{-1.5}$ km (68%). We apply our measurement, combined with the previous NICER mass and radius measurement of PSR J0030$+$0451, the masses of two other $\sim 2~M_\odot$ 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 $\sim 1.5-3$ times nuclear saturation density. For a given framework, when all measurements are included the radius of a $1.4~M_\odot$ neutron star is known to $\pm 4$% (68% credibility) and the radius of a $2.08~M_\odot$ neutron star is known to $\pm 5$%. The full radius range that spans the $\pm 1\sigma$ credible intervals of all the radius estimates in the three frameworks is $12.45\pm 0.65$ km for a $1.4~M_\odot$ neutron star and $12.35\pm 0.75$ km for a $2.08~M_\odot$ neutron star.

365 citations

Journal ArticleDOI
TL;DR: In this article, the authors estimate the radius, mass, and hot surface regions of the massive millisecond pulsar PSR J0740$+$6620, conditional on pulse profile modeling of Neutron Star Interior Composition Explorer X-ray Timing Instrument (NICER XTI) event data.
Abstract: We report on Bayesian estimation of the radius, mass, and hot surface regions of the massive millisecond pulsar PSR J0740$+$6620, conditional on pulse-profile modeling of Neutron Star Interior Composition Explorer X-ray Timing Instrument (NICER XTI) event data. We condition on informative pulsar mass, distance, and orbital inclination priors derived from the joint NANOGrav and CHIME/Pulsar wideband radio timing measurements of arXiv:2104.00880. We use XMM European Photon Imaging Camera spectroscopic event data to inform our X-ray likelihood function. The prior support of the pulsar radius is truncated at 16 km to ensure coverage of current dense matter models. We assume conservative priors on instrument calibration uncertainty. We constrain the equatorial radius and mass of PSR J0740$+$6620 to be $12.39_{-0.98}^{+1.30}$ km and $2.072_{-0.066}^{+0.067}$ M$_{\odot}$ 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.

353 citations

References
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Journal ArticleDOI

16,176 citations


"A NICER View of PSR J0030+0451: Mil..." refers methods in this paper

  • ...We apply nestcheck routines to bootstrap re-sample threads and simulate weights for the following: the onedimensional quantiles in posterior mass for each parameter, which are in turn used to report the credible intervals; the global and parameter-by-parameter KL-divergences; and the evidence....

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  • ...The KL-divergence has, as an example, recently been applied by Abbott et al. (2019a) to probe posterior information gain and sensitivity to prior assumptions....

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  • ...Estimating posterior information gain In a Bayesian context, the KL-divergence (Kullback & Leibler 1951) can be applied as a non-negative real scalar98 measure of posterior information gain about a parameter—or jointly about parameters—of a generative model, conditioned on the data set; it is also…...

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  • ...KL-divergence maximization is central to an information-theoretic—but often in practice intractable—definition of a minimally-informative prior via reference to the generative model, but without reference to the data (via data-space marginalization)....

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  • ...Estimating posterior information gain In a Bayesian context, the KL-divergence (Kullback & Leibler 1951) can be applied as a non-negative real scalar98 measure of posterior information gain about a parameter—or jointly about parameters—of a generative model, conditioned on the data set; it is also known via information-theoretic interpretation as relative entropy....

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Journal ArticleDOI
TL;DR: In this article, the authors show how to improve the performance of NumPy arrays through vectorizing calculations, avoiding copying data in memory, and minimizing operation counts, which is a technique similar to the one described in this paper.
Abstract: In the Python world, NumPy arrays are the standard representation for numerical data and enable efficient implementation of numerical computations in a high-level language. As this effort shows, NumPy performance can be improved through three techniques: vectorizing calculations, avoiding copying data in memory, and minimizing operation counts.

9,149 citations

Journal ArticleDOI
B. P. Abbott1, Richard J. Abbott1, T. D. Abbott2, Fausto Acernese3  +1131 moreInstitutions (123)
TL;DR: The association of GRB 170817A, detected by Fermi-GBM 1.7 s after the coalescence, corroborates the hypothesis of a neutron star merger and provides the first direct evidence of a link between these mergers and short γ-ray bursts.
Abstract: On August 17, 2017 at 12∶41:04 UTC the Advanced LIGO and Advanced Virgo gravitational-wave detectors made their first observation of a binary neutron star inspiral. The signal, GW170817, was detected with a combined signal-to-noise ratio of 32.4 and a false-alarm-rate estimate of less than one per 8.0×10^{4} years. We infer the component masses of the binary to be between 0.86 and 2.26 M_{⊙}, in agreement with masses of known neutron stars. Restricting the component spins to the range inferred in binary neutron stars, we find the component masses to be in the range 1.17-1.60 M_{⊙}, with the total mass of the system 2.74_{-0.01}^{+0.04}M_{⊙}. The source was localized within a sky region of 28 deg^{2} (90% probability) and had a luminosity distance of 40_{-14}^{+8} Mpc, the closest and most precisely localized gravitational-wave signal yet. The association with the γ-ray burst GRB 170817A, detected by Fermi-GBM 1.7 s after the coalescence, corroborates the hypothesis of a neutron star merger and provides the first direct evidence of a link between these mergers and short γ-ray bursts. Subsequent identification of transient counterparts across the electromagnetic spectrum in the same location further supports the interpretation of this event as a neutron star merger. This unprecedented joint gravitational and electromagnetic observation provides insight into astrophysics, dense matter, gravitation, and cosmology.

7,327 citations


"A NICER View of PSR J0030+0451: Mil..." refers background in this paper

  • ...It follows that if the three stars have nearly the same radius, and if the mass ratio of GW170817 was near its lower limit of 0.7, the common radius should be at the lower end of the NICER range....

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  • ...In such cases, we would expect to find NSs whose radii differ by several km , reinforcing the importance of jointly estimating both the radius and the mass of each member of a population of NSs. Constraints on NS masses and tidal deformabilities are now also being reported based on the first binary NS merger gravitational wave event, GW170817 (Abbott et al. 2018, 2019b)....

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  • ...Let us make the assumption that PSR J0030+0415 also has the same radius as the binary members to well within the posterior uncertainty on each star: the radius reported in this Letter, inferred from NICER data, is more consistent with values in the upper ranges emerging from the gravitational wave analysis of GW170817....

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  • ...NS mass and tidal deformability estimates are now also being reported based on the first binary NS merger gravitational wave event, GW170817 (Abbott et al. 2017, 2018; De et al. 2018)....

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  • ...Moreover, studies have utilized mass and tidal deformability constraints derived from analysis of the NS binary merger event GW170817 (Abbott et al. 2018; Annala et al. 2018; Most et al. 2018; Tews et al. 2018b; Lim & Holt 2018; Malik et al. 2018; Carson et al. 2019; Li & Sedrakian 2019; Montaña et al. 2019), and consideration is already being given to combining constraints from electromagnetic and gravitational wave analysis (Kumar & Landry 2019; Forbes et al. 2019; Weih et al. 2019)....

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Journal ArticleDOI
01 May 2007
TL;DR: The IPython project as mentioned in this paper provides an enhanced interactive environment that includes, among other features, support for data visualization and facilities for distributed and parallel computation for interactive work and a comprehensive library on top of which more sophisticated systems can be built.
Abstract: Python offers basic facilities for interactive work and a comprehensive library on top of which more sophisticated systems can be built. The IPython project provides on enhanced interactive environment that includes, among other features, support for data visualization and facilities for distributed and parallel computation

3,355 citations

Journal ArticleDOI
28 Oct 2010-Nature
TL;DR: Radio timing observations of the binary millisecond pulsar J1614-2230 that show a strong Shapiro delay signature are presented and the pulsar mass is calculated to be (1.97 ± 0.04)M⊙, which rules out almost all currently proposed hyperon or boson condensate equations of state.
Abstract: Neutron stars comprise the densest form of matter known to exist in our Universe, but their composition and properties are uncertain. Measurements of their masses and radii can constrain theoretical predictions of their composition, but so far it has not been possible to rule out many predictions of 'exotic' non-nucleonic components. Here, radio timing observations of the binary millisecond pulsar J1614-2230 are presented, allowing almost all currently proposed hyperon or boson condensate equations of state to be ruled out.

3,338 citations


"A NICER View of PSR J0030+0451: Mil..." refers methods in this paper

  • ...4 Note that PSR J1614−2230 was initially reported as having mass 1.97 ± 0.04 (Demorest et al. 2010); the inferences have since been updated via analysis of newly acquired data. both NSs have the same EOS, it is found that their radii are nearly equal and (for the 68% credible interval) have the…...

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