The mass and the radius of the neutron star in the transient low mass X-ray binary SAX J1748.9−2021

We use time resolved spectroscopy of thermonuclear X-ray bursts observed from SAX J1748.9−2021 to infer the mass and the radius of the neutron star in the binary. Four X-ray bursts observed from the source with RXTE enable us to measure the angular size and the Eddington limit on the neutron star surface. Combined with a distance measurement to the globular cluster NGC 6440, in which SAX J1748.9−2021 resides, we obtain two solutions for the neutron star radius and mass, R = 8.18±1.62 km and M = 1.78±0.3 M_sun or R = 10.93±2.09 km and M = 1.33 ± 0.33 M_sun

Tidal deformability from GW170817 as a direct probe of the neutron star radius

Gravitational waves from the coalescence of two neutron stars were recently detected for the first time by the LIGO-Virgo collaboration, in event GW170817. This detection placed an upper limit on the effective tidal deformability of the two neutron stars and tightly constrained the chirp mass of the system. We report here on a new simplification that arises in the effective tidal deformability of the binary, when the chirp mass is specified. We find that, in this case, the effective tidal deformability of the binary is surprisingly independent of the component masses of the individual neutron stars, and instead depends primarily on the ratio of the chirp mass to the neutron star radius. Thus, a measurement of the effective tidal deformability can be used to directly measure the neutron star radius. We find that the upper limit on the effective tidal deformability from GW170817 implies that the radius cannot be larger than ~13km, at the 90% level, independent of the assumed masses for the component stars. The result can be applied generally, to probe the stellar radii in any neutron star-neutron star merger with a measured chirp mass. The approximate mass-independence disappears for neutron star-black hole mergers. Finally, we discuss a Bayesian inference of the equation of state that uses the measured chirp mass and tidal deformability from GW170817 combined with nuclear and astrophysical priors and discuss possible statistical biases in this inference.Comment: Submitted to ApJ Letter

Confronting Models of Massive Star Evolution and Explosions with Remnant Mass Measurements

The mass distribution of compact objects provides a fossil record that can be studied to uncover information on the late stages of massive star evolution, the supernova explosion mechanism, and the dense matter equation of state. Observations of neutron star masses indicate a bimodal Gaussian distribution, while the observed black hole mass distribution decays exponentially for stellar-mass black holes. We use these observed distributions to directly confront the predictions of stellar evolution models and the neutrino-driven supernova simulations of Sukhbold et al. (2016). We find excellent agreement between the black hole and low-mass neutron star distributions created by these simulations and the observations. We show that a large fraction of the stellar envelope must be ejected, either during the formation of stellar-mass black holes or prior to the implosion through tidal stripping due to a binary companion, in order to reproduce the observed black hole mass distribution. We also determine the origins of the bimodal peaks of the neutron star mass distribution, finding that the low-mass peak (centered at ~1.4 M_sun) originates from progenitors with M_zams ~ 9-18 M_sun. The simulations fail to reproduce the observed peak of high-mass neutron stars (centered at ~1.8 M_sun) and we explore several possible explanations. We argue that the close agreement between the observed and predicted black hole and low-mass neutron star mass distributions provides new promising evidence that these stellar evolution and explosion models are accurately capturing the relevant stellar, nuclear, and explosion physics involved in the formation of compact objects.Comment: Typos in fit coefficients corrected, results unchanged. 13 pages, 10 figures. Submitted to Ap

From Neutron Star Observables to the Equation of State. I. An Optimal Parametrization

The increasing number and precision of measurements of neutron star masses, radii, and, in the near future, moments of inertia offer the possibility of precisely determining the neutron star equation of state. One way to facilitate the mapping of observables to the equation of state is through a parametrization of the latter. We present here a generic method for optimizing the parametrization of any physically allowed EoS. We use mock equations of state that incorporate physically diverse and extreme behavior to test how well our parametrization reproduces the global properties of the stars, by minimizing the errors in the observables mass, radius, and the moment of inertia. We find that using piecewise polytropes and sampling the EoS with five fiducial densities between ~1-8 times the nuclear saturation density results in optimal errors for the smallest number of parameters. Specifically, it recreates the radii of the assumed EoS to within less than 0.5 km for the extreme mock equations of state and to within less than 0.12 km for 95% of a sample of 42 proposed, physically-motivated equations of state. Such a parametrization is also able to reproduce the maximum mass to within 0.04 M_sun and the moment of inertia of a 1.338 M_sun neutron star to within less than 10% for 95% of the proposed sample of equations of state.Comment: Minor changes made to match published ApJ versio

Mapping the Surface of the Magnetar 1E 1048.1-5937 in Outburst and Quiescence Through Phase Resolved X-ray Spectroscopy

We model the pulse profiles and the phase resolved spectra of the anomalous X-ray pulsar 1E 1048.1-5937 obtained with XMM-Newton to map its surface temperature distribution during an active and a quiescent epoch. We develop and apply a model that takes into account the relevant physical and geometrical effects on the neutron star surface, magnetosphere, and spacetime. Using this model, we determine the observables at infinity as a function of pulse phase for different numbers and sizes of hot spots on the surface. We show that the pulse profiles extracted from both observations can be modeled with a single hot spot and an antipodal cool component. The size of the hot spot changes from $\approx 80^{\circ}$ in 2007, 3 months after the onset of a dramatic flux increase, to $\approx 30^{\circ}$ during the quiescent observation in 2011, when the pulsed fraction returned to the pre-outburst $\approx$ 65\% level. For the 2007 observation, we also find that a model consisting of a single 0.4 keV hot spot with a magnetic field strength of $1.8 \times 10^{14}$ G accounts for the spectra obtained at three different pulse phases but under predicts the flux at the pulse minimum, where the contribution to the emission from the cooler component is non-negligible. The inferred temperature of the spot stays approximately constant between different pulse phases, in agreement with a uniform temperature, single hot spot model. These results suggest that the emitting area grows significantly during outbursts but returns to its persistent and significantly smaller size within a few year timescale.Comment: Accepted for publication in The Astrophysical Journa

X-ray Lightcurves from Realistic Polar Cap Models: Inclined Pulsar Magnetospheres and Multipole Fields

Thermal X-ray emission from rotation-powered pulsars is believed to originate from localized "hotspots" on the stellar surface occurring where large-scale currents from the magnetosphere return to heat the atmosphere. Lightcurve modeling has primarily been limited to simple models, such as circular antipodal emitting regions with constant temperature. We calculate more realistic temperature distributions within the polar caps, taking advantage of recent advances in magnetospheric theory, and we consider their effect on the predicted lightcurves. The emitting regions are non-circular even for a pure dipole magnetic field, and the inclusion of an aligned magnetic quadrupole moment introduces a north-south asymmetry. As the aligned quadrupole moment is increased, one hotspot grows in size before becoming a thin ring surrounding the star. For the pure dipole case, moving to the more realistic model changes the lightcurves by $5-10\%$ for millisecond pulsars, helping to quantify the systematic uncertainty present in current dipolar models. Including the quadrupole gives considerable freedom in generating more complex lightcurves. We explore whether these simple dipole+quadrupole models can account for the qualitative features of the lightcurve of PSR J0437$-$4715.Comment: 12 pages, 9 figure

From Neutron Star Observables to the Equation of State. II. Bayesian Inference of Equation of State Pressures

One of the key goals of observing neutron stars is to infer the equation of state (EoS) of the cold, ultradense matter in their interiors. We present here a Bayesian statistical method of inferring the pressures at five fixed densities, from a sample of mock neutron star masses and radii. We show that while five polytropic segments are needed for maximum flexibility in the absence of any prior knowledge of the EoS, regularizers are also necessary to ensure that simple underlying EoS are not over-parametrized. For ideal data with small measurement uncertainties, we show that the pressure at roughly twice the nuclear saturation density, rho_sat, can be inferred to within 0.3 dex for many realizations of potential sources of uncertainties. The pressures of more complicated EoS with significant phase transitions can also be inferred to within ~30%. We also find that marginalizing the multi-dimensional parameter space of pressure to infer a mass-radius relation can lead to biases of nearly 1 km in radius, towards larger radii. Using the full, five-dimensional posterior likelihoods avoids this bias.Comment: Submitted to ApJ. 9 pages, 8 figure

Narrow Atomic Features from Rapidly Spinning Neutron Stars

Neutron stars spinning at moderate rates (~300-600Hz) become oblate in shape and acquire a nonzero quadrupole moment. In this paper, we calculate profiles of atomic features from such neutron stars using a ray-tracing algorithm in the Hartle-Thorne approximation. We show that line profiles acquire cores that are much narrower than the widths expected from pure Doppler effects for a large range of observer inclinations. As a result, the effects of both the oblateness and the quadrupole moments of neutron stars need to be taken into account when aiming to measure neutron star radii from rotationally broadened lines. Moreover, the presence of these narrow cores substantially increases the likelihood of detecting atomic lines from rapidly spinning neutron stars.Comment: 7 pages, 8 figures, accepted to Ap

The Properties of Reconnection Current Sheets in GRMHD Simulations of Radiatively Inefficient Accretion Flows

Non-ideal MHD effects may play a significant role in determining the dynamics, thermal properties, and observational signatures of radiatively inefficient accretion flows onto black holes. In particular, particle acceleration during magnetic reconnection events may influence black hole spectra and flaring properties. We use representative GRMHD simulations of black hole accretion flows to identify and explore the structures and properties of current sheets as potential sites of magnetic reconnection. In the case of standard and normal (SANE) disks, we find that, in the reconnection sites, the plasma beta ranges from $0.1$ to $1000$, the magnetization ranges from $10^{-4}$ to $1$, and the guide fields are weak compared to the reconnecting fields. In magnetically arrested (MAD) disks, we find typical values for plasma beta from $10^{-2}$ to $10^3$, magnetizations from $10^{-3}$ to $10$, and typically stronger guide fields, with strengths comparable to or greater than the reconnecting fields. These are critical parameters that govern the electron energy distribution resulting from magnetic reconnection and can be used in the context of plasma simulations to provide microphysics inputs to global simulations. We also find that ample magnetic energy is available in the reconnection regions to power the fluence of bright X-ray flares observed from the black hole in the center of the Milky Way.Comment: 8 pages, 8 figures, submitted to Ap