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.

Fast Radio Bursts are millisecond-duration astronomical radio pulses of unknown physical origin that appear to come from extragalactic distances [1][2][3][4][5][6][7][8] . Previous follow-up observations have failed to find additional bursts at the same dispersion measures (i.e. integrated column density of free electrons between source and telescope) and sky position as the original detections 9 . The apparent non-repeating nature of the fast radio bursts has led several authors to hypothesise that they originate in cataclysmic astrophysical events 10 . Here we report the detection of ten additional bursts from the direction of FRB 121102, using the 305-m Arecibo telescope. These new bursts have dispersion measures and sky positions consistent with the original burst 4 . This unambiguously identifies FRB 121102 as repeating and demonstrates that its source survives the energetic events that cause the bursts. Additionally, the bursts from FRB 121102 show a wide range of spectral shapes that appear to be predominantly intrinsic to the source and which vary on timescales of minutes or shorter. While there may be multiple physical origins for the population of fast radio bursts, the repeat bursts with high dispersion measure and variable spectra specifically seen from FRB 121102 support models that propose an origin in a young, highly magnetised, extragalactic neutron star 11,12 .2 FRB 121102 was discovered 4 in the PALFA survey, a deep search of the Galactic plane at 1.4 GHz for radio pulsars and fast radio bursts (FRBs) using the 305-m William E. Gordon Telescope at the Arecibo Observatory and the 7-beam Arecibo L-band Feed Array (ALFA) 13,14 . The observed dispersion measure (DM) of the burst is roughly three times the maximum value expected along this line of sight in the NE2001 model 15 of Galactic electron density, i.e. β DM ≡ DM FRB /DM Gal Max ∼ 3, suggesting an extragalactic origin.Initial Arecibo follow-up observations were limited in both dwell time and sky coverage and resulted in no detection of additional bursts 4 . In 2015 May and June we carried out more extensive follow-up using Arecibo, covering a ∼ 9 radius with a grid of six ALFA pointings around the then-best sky position of FRB 121102 (Figure 1 and Extended Data Table 1 and 2). As described in the Methods, high-time-resolution, total intensity spectra were recorded, and the data were processed using standard radio-frequency interference (RFI) excision, dispersion removal, and single-pulse-search algorithms implemented in the PRESTO software suite and associated data reduction pipelines 14,16,17 .We detected 10 additional bursts from FRB 121102 in these observations. The burst properties, and those of the initial FRB 121102 burst, are listed in Table 1. The burst intensities are shown in Figure 2. No other periodic or single-pulse signals of a plausible astrophysical origin were detected at any other DM. Until the source's physical nature is clear, we continue to refer to it as FRB 121102 and label each burst chronologically starting with the o...

The precise localization of the repeating fast radio burst (FRB 121102) has provided the first unambiguous association (chance coincidence probability p3×10 −4 ) of an FRB with an optical and persistent radio counterpart. We report on optical imaging and spectroscopy of the counterpart and find that it is an extended (0 6-0 8) object displaying prominent Balmer and [O III] emission lines. Based on the spectrum and emission line ratios, we classify the counterpart as a low-metallicity, star-forming, m r′ = 25.1 AB mag dwarf galaxy at a redshift of z = 0.19273(8), corresponding to a luminosity distance of 972 Mpc. From the angular size, the redshift, and luminosity, we estimate the host galaxy to have a diameter 4 kpc and a stellar mass of M * ∼(4-7)×107 M e , assuming a mass-to-light ratio between 2 to 3 M e L e −1 . Based on the Hα flux, we estimate the star formation rate of the host to be 0.4 M e yr −1 and a substantial host dispersion measure (DM) depth 324 pc cm −3 . The net DM contribution of the host galaxy to FRB 121102 is likely to be lower than this value depending on geometrical factors. We show that the persistent radio source at FRB 121102's location reported by Marcote et al. is offset from the galaxy's center of light by ∼200 mas and the host galaxy does not show optical signatures for AGN activity. If FRB 121102 is typical of the wider FRB population and if future interferometric localizations preferentially find them in dwarf galaxies with low metallicities and prominent emission lines, they would share such a preference with long gamma-ray bursts and superluminous supernovae.

Fast radio bursts 1,2 are astronomical radio flashes of unknown physical nature with durations of milliseconds. Their dispersive arrival times suggest an extragalactic origin and imply radio luminosities that are orders of magnitude larger than those of all known short-duration radio transients 3 . So far all fast radio bursts have been detected with large single-dish telescopes with arcminute localizations, and attempts to identify their counterparts (source or host galaxy) have relied on the contemporaneous variability of field sources 4 or the presence of peculiar field stars 5 or galaxies 4 . These attempts have not resulted in an unambiguous association 6,7 with a host or multi-wavelength counterpart. Here we report the subarcsecond localization of the fast radio burst FRB 121102, the only known repeating burst source 8-11 , using high-time-resolution radio interferometric observations that directly image the bursts. Our precise localization reveals that FRB 121102 originates within 100 milliarcseconds of a faint 180-microJansky persistent radio source with a continuum spectrum that is consistent with nonthermal emission, and a faint (twenty-fifth magnitude) optical counterpart. The flux density of the persistent radio source varies by around ten per cent on day timescales, and very long baseline radio interferometry yields an angular size of less than 1.7 milliarcseconds. Our observations are inconsistent with the fast radio burst having a Galactic origin or its source being located within a prominent star-forming galaxy. Instead, the source appears to be co-located with a low-luminosity active galactic nucleus or a previously unknown type of extragalactic source. Localization and identification of a host or counterpart has been essential to understanding the origins and physics of other kinds of transient events, including gamma-ray bursts 12,13 and tidal disruption events 14 . However, if other fast radio bursts have similarly faint radio and optical counterparts, our findings imply that direct subarcsecond localizations may be the only way to provide reliable associations.The repetition of bursts from FRB 121102 9,10 enabled a targeted interferometric localization campaign with the Karl G. Jansky Very Large Array (VLA) in concert with single-dish observations using the 305-m William E. Gordon Telescope at the Arecibo Observatory. We searched for bursts in VLA data with 5-ms sampling using both beam-forming and imaging techniques 15 (see Methods). In over 83 h of VLA observations distributed over six months, we detected nine bursts from FRB 121102 in the 2.5-3.5-GHz band with signalto-noise ratios ranging from 10 to 150, all at a consistent sky position.

Fast radio bursts (FRBs) are millisecond-duration, extragalactic radio flashes of unknown physical origin [1][2][3] . FRB 121102, the only known repeating FRB source [4][5][6] , has been localized to a star-forming region in a dwarf galaxy 7-9 at redshift z = 0.193, and is spatially coincident with a compact, persistent radio source 7,10 . The origin of the bursts, the nature of the persistent source, and the properties of the local environment are still debated. Here we present bursts that show ∼100% linearly polarized emission at a very high and variable Faraday rotation measure in the source frame: RM src = +1.46 × 10 5 rad m −2 and +1.33 × 10 5 rad m −2 at epochs separated by 7 months, in addition to narrow ( 30 µs) temporal structure. The large and variable rotation measure demonstrates that FRB 121102 is in an extreme and dynamic magneto-ionic environment, while the short burst durations argue for a neutron star origin. Such large rotation measures have, until now, only been observed 11,12 in the vicinities of massive black holes (M BH 10 4 M ). Indeed, the properties of the persistent radio source are compatible with those of a low-luminosity, accreting massive black hole 10 . The bursts may thus come from a neutron star in such an environment. However, the observed properties may also be explainable in other models, such as a highly magnetized wind nebula 13 or supernova remnant 14 surrounding a young neutron star. 2Using the 305-m William E. Gordon Telescope at the Arecibo Observatory, we detected 16 bursts from FRB 121102 at radio frequencies from 4.1 − 4.9 GHz (Table 1). The data recorder provided complete polarization parameters with 10.24-µs time resolution. See Methods and Extended Data Figs. 1-6 for observation and analysis details.The 4.5-GHz bursts have typical widths 1 ms, which are narrower than the 2 to 9-ms bursts previously detected at lower frequencies 5,15 . In some cases they show multiple components and structure close to the sampling time of the data. Burst #6 is particularly striking, with a width of 30 µs, which constrains the size of the emitting region to 10 km, modulo geometric and relativistic effects. Evolution in burst morphology with frequency complicates the determination 5 of dispersion measure (DM = d 0 n e (l) dl), but aligning the narrow component in Burst #6 results in DM= 559.7 ± 0.1 pc cm −3 , which is consistent 4,5,15,16 with other bursts detected since 2012, and suggests that any bona fide dispersion measure variations are at the 1% level.After correcting for Faraday rotation, and accounting for ∼2% depolarization from the finite channel widths, the bursts are consistently ∼100% linearly polarized (Fig. 1). The polarization angles PA = PA ∞ + θ (where PA ∞ is a reference angle at infinite frequency, θ = RMλ 2 is the rotation angle of the electric field vector and λ is the observing wavelength) are flat across the observed frequency range and burst envelopes (∆PA 5 • ms −1 ). This could mean that the burst durations reflect the timescale of the emission process and n...

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)