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

Title: ON THE CONSISTENCY OF NEUTRON-STAR RADIUS MEASUREMENTS FROM THERMONUCLEAR BURSTS

Abstract

The radius of neutron stars can in principle be measured via the normalization of a blackbody fitted to the X-ray spectrum during thermonuclear (type-I) X-ray bursts, although few previous studies have addressed the reliability of such measurements. Here we examine the apparent radius in a homogeneous sample of long, mixed H/He bursts from the low-mass X-ray binaries GS 1826-24 and KS 1731-26. The measured blackbody normalization (proportional to the emitting area) in these bursts is constant over a period of up to 60 s in the burst tail, even though the flux (blackbody temperature) decreased by a factor of 60%-75% (30%-40%). The typical rms variation in the mean normalization from burst to burst was 3%-5%, although a variation of 17% was found between bursts observed from GS 1826-24 in two epochs. A comparison of the time-resolved spectroscopic measurements during bursts from the two epochs shows that the normalization evolves consistently through the burst rise and peak, but subsequently increases further in the earlier epoch bursts. The elevated normalization values may arise from a change in the anisotropy of the burst emission or alternatively variations in the spectral correction factor, f{sub c} , of order 10%. Since burst samples observed frommore » systems other than GS 1826-24 are more heterogeneous, we expect that systematic uncertainties of at least 10% are likely to apply generally to measurements of neutron-star radii, unless the effects described here can be corrected for.« less

Authors:
;  [1]
  1. School of Physics, Monash University, Clayton, VIC 3800 (Australia)
Publication Date:
OSTI Identifier:
22016282
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; ANISOTROPY; NEUTRON STARS; TIME RESOLUTION; X RADIATION; X-RAY SPECTRA

Citation Formats

Galloway, Duncan K., and Lampe, Nathanael, E-mail: Duncan.Galloway@monash.edu. ON THE CONSISTENCY OF NEUTRON-STAR RADIUS MEASUREMENTS FROM THERMONUCLEAR BURSTS. United States: N. p., 2012. Web. doi:10.1088/0004-637X/747/1/75.
Galloway, Duncan K., & Lampe, Nathanael, E-mail: Duncan.Galloway@monash.edu. ON THE CONSISTENCY OF NEUTRON-STAR RADIUS MEASUREMENTS FROM THERMONUCLEAR BURSTS. United States. doi:10.1088/0004-637X/747/1/75.
Galloway, Duncan K., and Lampe, Nathanael, E-mail: Duncan.Galloway@monash.edu. 2012. "ON THE CONSISTENCY OF NEUTRON-STAR RADIUS MEASUREMENTS FROM THERMONUCLEAR BURSTS". United States. doi:10.1088/0004-637X/747/1/75.
@article{osti_22016282,
title = {ON THE CONSISTENCY OF NEUTRON-STAR RADIUS MEASUREMENTS FROM THERMONUCLEAR BURSTS},
author = {Galloway, Duncan K. and Lampe, Nathanael, E-mail: Duncan.Galloway@monash.edu},
abstractNote = {The radius of neutron stars can in principle be measured via the normalization of a blackbody fitted to the X-ray spectrum during thermonuclear (type-I) X-ray bursts, although few previous studies have addressed the reliability of such measurements. Here we examine the apparent radius in a homogeneous sample of long, mixed H/He bursts from the low-mass X-ray binaries GS 1826-24 and KS 1731-26. The measured blackbody normalization (proportional to the emitting area) in these bursts is constant over a period of up to 60 s in the burst tail, even though the flux (blackbody temperature) decreased by a factor of 60%-75% (30%-40%). The typical rms variation in the mean normalization from burst to burst was 3%-5%, although a variation of 17% was found between bursts observed from GS 1826-24 in two epochs. A comparison of the time-resolved spectroscopic measurements during bursts from the two epochs shows that the normalization evolves consistently through the burst rise and peak, but subsequently increases further in the earlier epoch bursts. The elevated normalization values may arise from a change in the anisotropy of the burst emission or alternatively variations in the spectral correction factor, f{sub c} , of order 10%. Since burst samples observed from systems other than GS 1826-24 are more heterogeneous, we expect that systematic uncertainties of at least 10% are likely to apply generally to measurements of neutron-star radii, unless the effects described here can be corrected for.},
doi = {10.1088/0004-637X/747/1/75},
journal = {Astrophysical Journal},
number = 1,
volume = 747,
place = {United States},
year = 2012,
month = 3
}
  • 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
  • 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. Wemore » 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.« 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 calculate the rotational broadening in the observed thermal spectra of neutron stars spinning at moderate rates in the Hartle-Thorne approximation. These calculations accurately account for the effects of the second-order Doppler boosts as well as for the oblate shapes and the quadrupole moments of the neutron stars. We find that fitting the spectra and inferring the bolometric fluxes under the assumption that a star is not rotating causes an underestimate of the inferred fluxes and, thus, radii. The correction depends on the stellar spin, mass, radius, and the observer's inclination. For a 10 km, 1.4 M {sub ☉} neutron starmore » spinning at 600 Hz, the rotational correction to the flux is ∼1%-4%, while for a 15 km neutron star with the same spin period, the correction ranges from 2% for pole-on sources to 12% for edge-on sources. We calculate the inclination-averaged corrections to inferred radii as a function of the neutron-star radius and mass and provide an empirical formula for the corrections. For realistic neutron-star parameters (1.4 M {sub ☉}, 12 km, 600 Hz), the stellar radius is on the order of 4% larger than the radius inferred under the assumption that the star is not spinning.« less
  • We calculate the effects of spot size on pulse profiles of moderately rotating neutron stars. Specifically, we quantify the bias introduced in radius measurements from the common assumption that spots are infinitesimally small. We find that this assumption is reasonable for spots smaller than 10°–18° and leads to errors that are ≤10% in the radius measurement, depending on the location of the spot and the inclination of the observer. We consider the implications of our results for neutron star radius measurements with the upcoming and planned X-ray missions NICER and LOFT. We calculate the expected spot size for different classesmore » of sources and investigate the circumstances under which the assumption of a small spot is justified.« less