skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: SYSTEMATIC UNCERTAINTIES IN THE SPECTROSCOPIC MEASUREMENTS OF NEUTRON-STAR MASSES AND RADII FROM THERMONUCLEAR X-RAY BURSTS. II. EDDINGTON LIMIT

Abstract

Time-resolved X-ray spectroscopy of thermonuclear bursts observed from low-mass X-ray binaries offer a unique tool to measure neutron-star masses and radii. In this paper, we continue our systematic analysis of all the X-ray bursts observed with Rossi X-ray Timing Explorer from X-ray binaries. We determine the events that show clear evidence for photospheric radius expansion and measure the Eddington limits for these accreting neutron stars using the bolometric fluxes attained at the touchdown moments of each X-ray burst. We employ a Bayesian technique to investigate the degree to which the Eddington limit for each source remains constant between bursts. We find that for sources with a large number of radius expansion bursts, systematic uncertainties are at a 5%-10% level. Moreover, in six sources with only pairs of Eddington-limited bursts, the distribution of fluxes is consistent with a {approx}10% fractional dispersion. This indicates that the spectroscopic measurements of neutron-star masses and radii using thermonuclear X-ray bursts can reach the level of accuracy required to distinguish between different neutron-star equations of state, provided that uncertainties related to the overall flux calibration of X-ray detectors are of comparable magnitude.

Authors:
; ;  [1]
  1. Department of Astronomy, University of Arizona, 933 North Cherry Avenue, Tucson, AZ 85721 (United States)
Publication Date:
OSTI Identifier:
22016284
Resource Type:
Journal Article
Resource Relation:
Journal Name: Astrophysical Journal; Journal Volume: 747; Journal Issue: 1; Other Information: Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
79 ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; ASTROPHYSICS; BOLOMETERS; CALIBRATION; EQUATIONS OF STATE; MASS; NEUTRON STARS; TIME RESOLUTION; X RADIATION; X-RAY SPECTROSCOPY

Citation Formats

Guever, Tolga, Oezel, Feryal, and Psaltis, Dimitrios. SYSTEMATIC UNCERTAINTIES IN THE SPECTROSCOPIC MEASUREMENTS OF NEUTRON-STAR MASSES AND RADII FROM THERMONUCLEAR X-RAY BURSTS. II. EDDINGTON LIMIT. United States: N. p., 2012. Web. doi:10.1088/0004-637X/747/1/77.
Guever, Tolga, Oezel, Feryal, & Psaltis, Dimitrios. SYSTEMATIC UNCERTAINTIES IN THE SPECTROSCOPIC MEASUREMENTS OF NEUTRON-STAR MASSES AND RADII FROM THERMONUCLEAR X-RAY BURSTS. II. EDDINGTON LIMIT. United States. doi:10.1088/0004-637X/747/1/77.
Guever, Tolga, Oezel, Feryal, and Psaltis, Dimitrios. Thu . "SYSTEMATIC UNCERTAINTIES IN THE SPECTROSCOPIC MEASUREMENTS OF NEUTRON-STAR MASSES AND RADII FROM THERMONUCLEAR X-RAY BURSTS. II. EDDINGTON LIMIT". United States. doi:10.1088/0004-637X/747/1/77.
@article{osti_22016284,
title = {SYSTEMATIC UNCERTAINTIES IN THE SPECTROSCOPIC MEASUREMENTS OF NEUTRON-STAR MASSES AND RADII FROM THERMONUCLEAR X-RAY BURSTS. II. EDDINGTON LIMIT},
author = {Guever, Tolga and Oezel, Feryal and Psaltis, Dimitrios},
abstractNote = {Time-resolved X-ray spectroscopy of thermonuclear bursts observed from low-mass X-ray binaries offer a unique tool to measure neutron-star masses and radii. In this paper, we continue our systematic analysis of all the X-ray bursts observed with Rossi X-ray Timing Explorer from X-ray binaries. We determine the events that show clear evidence for photospheric radius expansion and measure the Eddington limits for these accreting neutron stars using the bolometric fluxes attained at the touchdown moments of each X-ray burst. We employ a Bayesian technique to investigate the degree to which the Eddington limit for each source remains constant between bursts. We find that for sources with a large number of radius expansion bursts, systematic uncertainties are at a 5%-10% level. Moreover, in six sources with only pairs of Eddington-limited bursts, the distribution of fluxes is consistent with a {approx}10% fractional dispersion. This indicates that the spectroscopic measurements of neutron-star masses and radii using thermonuclear X-ray bursts can reach the level of accuracy required to distinguish between different neutron-star equations of state, provided that uncertainties related to the overall flux calibration of X-ray detectors are of comparable magnitude.},
doi = {10.1088/0004-637X/747/1/77},
journal = {Astrophysical Journal},
number = 1,
volume = 747,
place = {United States},
year = {Thu Mar 01 00:00:00 EST 2012},
month = {Thu Mar 01 00:00:00 EST 2012}
}
  • The masses and radii of low-magnetic field neutron stars can be measured by combining different observable quantities obtained from their X-ray spectra during thermonuclear X-ray bursts. One of these quantities is the apparent radius of each neutron star as inferred from the X-ray flux and spectral temperature measured during the cooling tails of bursts, when the thermonuclear flash is believed to have engulfed the entire star. In this paper, we analyze 13,095 X-ray spectra of 446 X-ray bursts observed from 12 sources in order to assess possible systematic effects in the measurements of the apparent radii of neutron stars. Wemore » first show that the vast majority of the observed X-ray spectra are consistent with blackbody functions to within a few percent. We find that most X-ray bursts follow a very well determined correlation between X-ray flux and temperature, which is consistent with the whole neutron-star surface emitting uniformly during the cooling tails. We develop a Bayesian Gaussian mixture algorithm to measure the apparent radii of the neutron stars in these sources, while detecting and excluding a small number of X-ray bursts that show irregular cooling behavior. This algorithm also provides us with a quantitative measure of the systematic uncertainties in the measurements. We find that those errors in the spectroscopic determination of neutron-star radii that are introduced by systematic effects in the cooling tails of X-ray bursts are in the range {approx_equal} 3%-8%. Such small errors are adequate to distinguish between different equations of state provided that uncertainties in the distance to each source and the absolute calibration of X-ray detectors do not dominate the error budget.« less
  • Many techniques for measuring neutron star radii rely on absolute flux measurements in the X-rays. As a result, one of the fundamental uncertainties in these spectroscopic measurements arises from the absolute flux calibrations of the detectors being used. Using the stable X-ray burster, GS 1826–238, and its simultaneous observations by Chandra HETG/ACIS-S and RXTE /PCA as well as by XMM-Newton EPIC-pn and RXTE /PCA, we quantify the degree of uncertainty in the flux calibration by assessing the differences between the measured fluxes during bursts. We find that the RXTE /PCA and the Chandra gratings measurements agree with each other withinmore » their formal uncertainties, increasing our confidence in these flux measurements. In contrast, XMM-Newton EPIC-pn measures 14.0 ± 0.3% less flux than the RXTE /PCA. This is consistent with the previously reported discrepancy with the flux measurements of EPIC-pn, compared with EPIC MOS1, MOS2, and ACIS-S detectors. We also show that any intrinsic time-dependent systematic uncertainty that may exist in the calibration of the satellites has already been implicity taken into account in the neutron star radius measurements.« less
  • We investigate the constraints on neutron star mass and radius in GS 1826-24 from models of light curves and spectral evolution of type I X-ray bursts. This source shows remarkable agreement with theoretical calculations of burst energies, recurrence times, and light curves. We first exploit this agreement to set the overall luminosity scale of the observed bursts. When combined with a measured blackbody normalization, this leads to a distance- and anisotropy-independent measurement of the ratio between the redshift 1 + z and color-correction factor f{sub c}. We find 1 + z = 1.19-1.28 for f{sub c} = 1.4-1.5. We thenmore » compare the evolution of the blackbody normalization with flux in the cooling tail of bursts with predictions from spectral models of Suleimanov et al. The observations are well described by the models at luminosities greater than about one-third of the peak luminosity, with deviations emerging at luminosities below that. We show that this comparison leads to distance-independent upper limits on R{sub {infinity}} and neutron star mass of R{sub {infinity}} {approx}< 9.0-13.2 km and M < 1.2-1.7 M{sub Sun }, respectively, for solar abundance of hydrogen at the photosphere and a range of metallicity and surface gravity. The radius limits are low in comparison to previous measurements. This may be indicative of a subsolar hydrogen fraction in the GS 1826-24 photosphere, or of larger color corrections than that predicted by spectral models. Our analysis also gives an upper limit on the distance to GS 1826-24 of d < 4.0-5.5 kpc {xi}{sup -1/2}{sub b}, where {xi}{sub b} is the degree of anisotropy of the burst emission.« less
  • We perform a systematic analysis of neutron star radius constraints from five quiescent low-mass X-ray binaries and examine how they depend on measurements of their distances and amounts of intervening absorbing material, as well as their assumed atmospheric compositions. We construct and calibrate to published results a semi-analytic model of the neutron star atmosphere which approximates these effects for the predicted masses and radii. Starting from mass and radius probability distributions established from hydrogen-atmosphere spectral fits of quiescent sources, we apply this model to compute alternate sets of probability distributions. We perform Bayesian analyses to estimate neutron star mass-radius curvesmore » and equation of state (EOS) parameters that best-fit each set of distributions, assuming the existence of a known low-density neutron star crustal EOS, a simple model for the high-density EOS, causality, and the observation that the neutron star maximum mass exceeds 2 M {sub ☉}. We compute the posterior probabilities for each set of distance measurements and assumptions about absorption and composition. We find that, within the context of our assumptions and our parameterized EOS models, some absorption models are disfavored. We find that neutron stars composed of hadrons are favored relative to those with exotic matter with strong phase transitions. In addition, models in which all five stars have hydrogen atmospheres are found to be weakly disfavored. Our most likely models predict neutron star radii that are consistent with current experimental results concerning the nature of the nucleon-nucleon interaction near the nuclear saturation density.« less
  • 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 hotter regions on the surface of the star that are rotating at or near the spin frequency of the star. Here we explore howmore » well M and R could be determined by generating and analyzing, using Bayesian techniques, synthetic energy-resolved X-ray data that we produce assuming a future space mission having 2-30 keV energy coverage and an effective area of 10 m{sup 2}, such as the proposed Large Observatory for X-Ray Timing or Advanced X-Ray Timing Array missions. We find that waveforms from hot spots within 10° of the rotation equator usually constrain both M and R with an uncertainty of about 10%, if there are 10{sup 6} total counts from the spot, whereas waveforms from spots within 20° of the rotation pole provide no useful constraints. The constraints we report can usually be achieved even if the burst oscillations vary with time and data from multiple bursts must be used to obtain 10{sup 6} counts from the hot spot. This is therefore a promising method to constrain M and R tightly enough to discriminate strongly between competing models of cold, high-density matter.« less