Determining Neutron Star Masses and Radii Using Energy-Resolved Waveforms of X-Ray Burst Oscillations

Abstract

Simultaneous, precise measurements of the mass M and radius R of neutron stars can yield uniquely valuable information about the still uncertain properties of cold matter at several times the density of nuclear matter. One method that could be used to measure M and R is to analyze the energy-dependent waveforms of the X-ray flux oscillations seen during some thermonuclear bursts from some neutron stars. These oscillations are thought to be produced by X-ray emission from hot regions on the surface of the star that are rotating at or near the spin frequency of the star. Here we explore how well M and R could be determined by analyzing energy-resolved X-ray data obtained using a future space mission having 2-30 keV energy coverage and an effective area of 10 m 2 , such as the proposed LOFT or AXTAR missions. We do this by generating energy-dependent synthetic observed waveforms for a variety of neutron star and hot spot properties and then using a Bayesian approach and Markov chain Monte Carlo sampling methods to determine the joint posterior probability distributions of the parameters in our waveform model, given each synthetic waveform. We use the resulting posterior distributions to determine Bayesian confidence regions in the M -R plane by marginalizing the other parameters in our model. We explore how the sizes and positions of these confidence regions depend on the inclinations of the hot spot and the observer, the background count rate, and deviations in the actual shape of the hot spot, radiation beaming pattern, and spectrum from those assumed in the waveform model. We also explore the effect on the confidence regions if the distance to the star or the inclination of the observer are known from other measurements, if a resonance scattering line is observed in the burst oscillation spectrum, or if the properties of the background are independently known. We assume that about 10 6 counts are collected from the hot spot and that all sources of background contribute about 0.3 × 10 6 , 10 6 , or 9 × 10 6 counts.We find that the uncertainties in the measured values of M and R depend strongly on the inclination of the hot spot relative to the spin axis. If the hot spot is within 10 • of the rotation equator, both M and R can usually be determined with an uncertainty of about 10%. If instead the spot is within 20 • of the rotation pole, the uncertainties are so large that waveform measurements alone provide no useful constraints on M and R. Observation of an identifiable atomic line in the hot-spot emission always tightly constrains M/R; it can also tightly constrain M and R individually if the spot is within about 30 • of the Following the discovery of thermonuclear X-ray bursts from neutron stars in the mid-1970s (Grindlay et al. 1976Lewin et al. 1976; for a review, see Lewin et al. 1993) and the discovery two decades later that some of these bursts produce X-ray flux oscillations at or near the star's spin frequency (Strohmayer et al. 1996; for a review, see Watts 2012), several approaches have been proposed f...

The Large Observatory for x-ray timing

“…In order to reach the required understanding and thus reducing the systematics in the modeling of the phenomenon, a deep study has been carried out by the LOFT Dense Matter working group. This is reported in Lo et al [5] and Watts et al [6].…”

Improved analytic modeling of neutron star interiors

“…One way to extract internal structure information is to measure the NS mass and radius independently [4][5][6], though current measurements may contain large systematic errors. An X-ray astrophysics payload NICER currently in operation at the International Space Station is expected to measure the stellar radius to ∼ 5% accuracy [7] with less systematics [8,9]. Another way to probe internal structure is to measure tidal deformabilities of neutron stars via gravitational waves.…”

Finite size effects on the light curves of slowly-rotating neutron stars

“…Moreover, they encode information of the spacetime curvature around the star and thereby of the bulk properties of the star. One of the main goals of the ongoing Neutron star Interior Composition ExploreR (NICER) [15][16][17] mission, is to measure light curves from a number of sources with unprecedented time-resolution, constraining their masses and radii within 5−10% accuracy in optimal cases [18][19][20] (see also e.g. [21][22][23]).…”