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Register a new userThe direct cooling tail method for X-ray burst analysis to constrain neutron star masses and radii
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Determining neutron star (NS) radii and masses can help to understand the properties of matter at supra-nuclear densities. Thermal emission during thermonuclear X-ray bursts from NSs in low-mass X-ray binaries provides a unique opportunity to study NS parameters, because of the high fluxes, large luminosity variations and the related changes in the spectral properties. The standard cooling tail method uses hot NS atmosphere models to convert the observed spectral evolution during cooling stages of X-ray bursts to the Eddington flux F_Edd and the stellar angular size Omega. These are then translated to the constraints on the NS mass M and radius R. Here we present the improved, direct cooling tail method that generalises the standard approach. First, we adjust the cooling tail method to account for the bolometric correction to the flux. Then, we fit the observed dependence of the blackbody normalization on flux with a theoretical model directly on the M-R plane by interpolating theoretical dependences to a given gravity, hence ensuring only weakly informative priors for M and R instead of F_Edd and Omega. The direct cooling method is demonstrated using a photospheric radius expansion burst from SAX J1810.8--2609, which has happened when the system was in the hard state. Comparing to the standard cooling tail method, the confidence regions are shifted by 1 sigma towards larger radii, giving R=11.5-13.0 km at M=1.3-1.8 M_sun for this NS.
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Observations of thermonuclear X-ray bursts from accreting neutron stars (NSs) in low-mass X-ray binary systems can be used to constrain NS masses and radii. Most previous work of this type has set these constraints using Planck function fits as a proxy: both the models and the data are fit with diluted blackbody functions to yield normalizations and temperatures which are then compared against each other. Here, for the first time, we fit atmosphere models of X-ray bursting NSs directly to the observed spectra. We present a hierarchical Bayesian fitting framework that uses state-of-the-art X-ray bursting NS atmosphere models with realistic opacities and relativistic exact Compton scattering kernels as a model for the surface emission. We test our approach against synthetic data, and find that for data that are well-described by our model we can obtain robust radius, mass, distance, and composition measurements. We then apply our technique to Rossi X-ray Timing Explorer observations of five hard-state X-ray bursts from 4U 1702-429. Our joint fit to all five bursts shows that the theoretical atmosphere models describe the data well but there are still some unmodeled features in the spectrum corresponding to a relative error of 1-5% of the energy flux. After marginalizing over this intrinsic scatter, we find that at 68% credibility the circumferential radius of the NS in 4U 1702-429 is R = 12.4+-0.4 km, the gravitational mass is M=1.9+-0.3 Msun, the distance is 5.1 < D/kpc < 6.2, and the hydrogen mass fraction is X < 0.09.
Precise and reliable measurements of the masses and radii of neutron stars with a variety of masses would provide valuable guidance for improving models of the properties of cold matter with densities above the saturation density of nuclear matter. Several different approaches for measuring the masses and radii of neutron stars have been tried or proposed, including analyzing the X-ray fluxes and spectra of the emission from neutron stars in quiescent low-mass X-ray binary systems and thermonuclear burst sources; fitting the energy-dependent X-ray waveforms of rotation-powered millisecond pulsars, burst oscillations with millisecond periods, and accretion-powered millisecond pulsars; and modeling the gravitational radiation waveforms of coalescing double neutron star and neutron star -- black hole binary systems. We describe the strengths and weaknesses of these approaches, most of which currently have substantial systematic errors, and discuss the prospects for decreasing the systematic errors in each method.
Neutron star X-ray binaries emit a compact, optically thick, relativistic radio jet during low-luminosity, usually hard states, as Galactic black-hole X-ray binaries do. When radio emission is bright, a hard power-law tail without evidence for an exponential cutoff is observed in most systems. We have developed a jet model that explains many spectral and timing properties of black-hole binaries in the states where a jet is present. Our goal is to investigate whether our jet model can reproduce the hard tail, with the correct range of photon index and the absence of a high-energy cutoff, in neutron-star X-ray binaries. We have performed Monte Carlo simulations of the Compton upscattering of soft, accretion-disk or boundary layer photons, in the jet and computed the emergent energy spectra, as well as the time lag of hard photons with respect to softer ones as a function of Fourier frequency. We demonstrate that our jet model explains the observed power-law distribution with photon index in the range 1.8-3. With an appropriate choice of the parameters, the cutoff expected from Comptonization is shifted to energies above ~300 keV, producing a pure power law without any evidence for a rollover, in agreement with the observations. Our results reinforce the idea that the link between the outflow (jet) and inflow (disk) in X-ray binaries does not depend on the nature of the compact object, but on the process of accretion. Furthermore, we address the differences of jets in black-hole and neutron-star X-ray binaries and predict that the break frequency in the spectral energy distribution of neutron-star X-ray binaries, as a class, will be lower than that of black-hole binaries.
When the upper layer of an accreting neutron star experiences a thermonuclear runaway of helium and hydrogen, it exhibits an X-ray burst of a few keV with a cool-down phase of typically 1~minute. When there is a surplus of hydrogen, hydrogen fusion is expected to simmer during that same minute due to the rp process, which consists of rapid proton captures and slow beta-decays of proton-rich isotopes. We have analyzed the high-quality light curves of 1254 X-ray bursts, obtained with the Proportional Counter Array on the Rossi X-ray Timing Explorer between 1996 and 2012, to systematically study the cooling and rp process. This is a follow-up of a study on a selection of 37 bursts from systems that lack hydrogen and show only cooling during the bursts. We find that the bolometric light curves are well described by the combination of a power law and a one-sided Gaussian. The power-law decay index is between 1.3 and 2.1 and similar to that for the 37-bursts sample. There are individual bursters with a narrower range. The Gaussian is detected in half of all bursts, with a typical standard deviation of 50~s and a fluence ranging up to 60% of the total fluence. The Gaussian appears consistent with being due to the rp process. The Gaussian fluence fraction suggests that the layer where the rp process is active is underabundant in H by a factor of at least five with respect to cosmic abundances. Ninety-four percent of all bursts from ultracompact X-ray binaries lack the Gaussian component, and the remaining 6% are marginal detections. This is consistent with a hydrogen deficiency in these binaries. We find no clear correlation between the power law and Gaussian light-curve components.
We develop a new method to measure neutron star parameters and derive constraints on the equation of state of dense matter by fitting the frequencies of simultaneous Quasi Periodic Oscillation modes observed in the X-ray flux of accreting neutron stars in low mass X-ray binaries. To this aim we calculate the fundamental frequencies of geodesic motion around rotating neutron stars based on an accurate general-relativistic approximation for their external spacetime. Once the fundamental frequencies are related to the observed frequencies through a QPO model, they can be fit to the data to obtain estimates of the three parameters describing the spacetime, namely the neutron star mass, angular momentum and quadrupole moment. From these parameters we derive information on the neutron star structure and equation of state. We present a proof of principle of our method applied to pairs of kHz QPO frequencies observed from three systems (4U1608-52, 4U0614+09 and 4U1728-34). We identify the kHz QPOs with the azimuthal and the periastron precession frequencies of matter orbiting the neutron star, and via our Bayesian inference technique we derive constraints on the neutrons stars masses and radii. This method is applicable to other geodesic-frequency-based QPO models.
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