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: the models and the data are both fit with diluted blackbody functions to yield normalizations and temperatures that are then compared with each other. For the first time, we here fit atmosphere models of X-ray bursting NSs directly to the observed spectra. We present a hierarchical Bayesian fitting framework that uses current 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 M⊙, the distance is 5.1 < D/ kpc < 6.2, and the hydrogen mass fraction is X < 0.09.
The cooling phase of thermonuclear (type-I) X-ray bursts can be used to constrain neutron star (NS) compactness by comparing the observed cooling tracks of bursts to accurate theoretical atmosphere ...model calculations. By applying the so-called cooling tail method, where the information from the whole cooling track is used, we constrain the mass, radius, and distance for three different NSs in low-mass X-ray binaries 4U 1702−429, 4U 1724−307, and SAX J1810.8−260. Care is taken to use only the hard state bursts where it is thought that the NS surface alone is emitting. We then use a Markov chain Monte Carlo algorithm within a Bayesian framework to obtain a parameterized equation of state (EoS) of cold dense matter from our initial mass and radius constraints. This allows us to set limits on various nuclear parameters and to constrain an empirical pressure-density relationship for the dense matter. Our predicted EoS results in NS a radius between 10.5−12.8 km (95% confidence limits) for a mass of 1.4 M⊙, depending slightly on the assumed composition. Because of systematic errors and uncertainty in the composition, these results should be interpreted as lower limits for the radius.
Some thermonuclear (type I) X-ray bursts at the neutron star surfaces in low-mass X-ray binaries take place during hard persistent states of the systems. Spectral evolution of these bursts is well ...described by the atmosphere model of a passively cooling neutron star when the burst luminosity is high enough. The observed spectral evolution deviates from the model predictions when the burst luminosity drops below a critical value of 20–70% of the maximum luminosity. The amplitude of the deviations and the critical luminosity correlate with the persistent luminosity, which leads us to suggest that these deviations are induced by the additional heating of the accreted particles. We present a method for computation of the neutron star atmosphere models heated by accreted particles assuming that their energy is released via Coulomb interactions with electrons. We computed the temperature structures and the emergent spectra of the atmospheres of various chemical compositions and investigate the dependence of the results on the velocity of accreted particles, their temperature and the penetration angle. We show that the heated atmosphere develops two different regions. The upper one is the hot (20–100 keV) corona-like surface layer cooled by Compton scattering, and the deeper, almost isothermal optically thick region with a temperature of a few keV. The emergent spectra correspondingly have two components: a blackbody with the temperature close to that of the isothermal region and a hard Comptonized component (a power law with an exponential decay). Their relative contribution depends on the ratio of the energy dissipation rate of the accreted particles to the intrinsic flux from the neutron star surface. These spectra deviate strongly from those of undisturbed, passively cooling neutron star atmospheres, with the main differences being the presence of a high-energy tail and a strong excess in the low-energy part of the spectrum. They also lack the iron absorption edge, which is visible in the spectra of undisturbed low-luminosity atmospheres with solar chemical composition. Using the computed spectra, we obtained the dependences of the dilution and color-correction factors as functions of relative luminosities for pure helium and solar abundance atmospheres. We show that the helium model atmosphere heated by accretion corresponding to 5% of the Eddington luminosity describes well the late stages of the X-ray bursts in 4U 1820−30.
Aims. The magnetic field of accreting neutron stars determines their overall behavior including the maximum possible luminosity. Some models require an above-average magnetic field strength (≳1013 G) ...in order to explain super-Eddington mass accretion rate in the recently discovered class of pulsating ultraluminous X-ray sources (ULX). The peak luminosity of SMC X-3 during its major outburst in 2016–2017 reached ~2.5 × 1039 erg s-1 comparable to that in ULXs thus making this source the nearest ULX-pulsar. Determination of the magnetic field of SMC X-3 is the main goal of this paper. Methods. SMC X-3 belongs to the class of transient X-ray pulsars with Be optical companions, and exhibited a giant outburst in July 2016–March 2017. The source has been observed over the entire outburst with the Swift/XRT and Fermi/GBM telescopes, as well as the NuSTAR observatory. Collected data allowed us to estimate the magnetic field strength of the neutron star in SMC X-3 using several independent methods. Results. Spin evolution of the source during and between the outbursts, and the luminosity of the transition to the so-called propeller regime in the range of (0.3–7) × 1035 erg s-1 imply a relatively weak dipole field of (1–5) × 1012 G. On the other hand, there is also evidence for a much stronger field in the immediate vicinity of the neutron star surface. In particular, transition from super- to sub-critical accretion regime associated with the cease of the accretion column and very high peak luminosity favor a field that is an order of magnitude stronger. This discrepancy makes SMC X-3 a good candidate for possessing significant non-dipolar components of the field, and an intermediate source between classical X-ray pulsars and accreting magnetars which may constitute an appreciable fraction of ULX population.
Aims. We present the results of the monitoring programmes performed with the Swift/XRT telescope and aimed specifically to detect an abrupt decrease of the observed flux associated with a transition ...to the propeller regime in two well-known X-ray pulsars 4U 0115+63 and V 0332+53. Methods. Both sources form binary systems with Be optical companions and undergo so-called giant outbursts every 3−4 years. The current observational campaigns were performed with the Swift/XRT telescope in the soft X-ray band (0.5−10 keV) during the declining phases of the outbursts exhibited by both sources in 2015. Results. The transitions to the propeller regime were detected at the threshold luminosities of (1.4 ± 0.4) × 1036 erg s-1 and (2.0 ± 0.4) × 1036 erg s-1 for 4U 0115+63 and V 0332+53, respectively. Spectra of the sources are shown to be significantly softer during the low state. In both sources, the accretion at rates close to the aforementioned threshold values briefly resumes during the periastron passage following the transition into the propeller regime. The strength of the dipole component of the magnetic field required to inhibit the accretion agrees well with estimates based on the position of the cyclotron lines in their spectra, thus excluding presence of a strong multipole component of the magnetic field in the vicinity of the neutron star.
We present a Bayesian method to constrain the masses and radii of neutron stars (NSs) using the information encoded in the X-ray pulse profiles of accreting millisecond pulsars. We model the shape of ...the pulses using “oblate Schwarzschild” approximation, which takes into account the deformed shape of the star together with the special and general relativistic corrections to the photon trajectories and angles. The spectrum of the radiation is obtained from an empirical model of Comptonization in a hot slab in which a fraction of seed black-body photons is scattered into a power-law component. By using an affine-invariant Markov chain Monte Carlo ensemble sampling method, we obtain posterior probability distributions for the different model parameters, especially for the mass and the radius. To test the robustness of our method, we first analysed self-generated synthetic data with known model parameters. Similar analysis was then applied for the observations of SAX J1808.4−3658 by the Rossi X-ray Timing Explorer (RXTE). The results show that our method can reproduce the model parameters of the synthetic data, and that accurate constraints for the radius can be obtained using the RXTE pulse profile observations if the mass is a priori known. For a mass in the range 1.5–1.8 M⊙, the radius of the NS in SAX J1808.4−3658 is constrained between 9 and 13 km. If the mass is accurately known, the radius can be determined with an accuracy of 5% (68% credibility). For example, for the mass of 1.7 M⊙ the equatorial radius is Req = 11.9+0.5−0.4Req=11.9−0.4+0.5${R_{{\rm{eq}}} = 11.9_{ - 0.4}^{ + 0.5}$ km. Finally, we show that further improvements can be obtained when the X-ray polarization data from the Imaging X-ray Polarimeter Explorer will become available.
We study the pulse profiles of the accreting X-ray millisecond pulsar SAX J1808.4−3658 at different energies. The two main emission components, the blackbody and the Comptonized tail, which are ...clearly identified in the time-averaged spectrum, show strong variability with the first component lagging the second one. The observed variability can be explained if the emission is produced by Comptonization in a hot slab (radiative shock) of Thomson optical depth ∼0.3–1 at the neutron star surface. The blackbody radiation is strongly beamed along the normal to the slab (a ‘knife’-like or ‘pencil’-like emission pattern), while the Comptonized emission has a broader angular distribution peaking at about 50°–60° from the slab normal (a ‘fan’-like pattern). We construct a detailed model of the X-ray production accounting for the Doppler boosting, relativistic aberration and gravitational light bending in the Schwarzschild space–time. We present also accurate analytical formulae for computations of the light curves from rapidly rotating neutron stars using the formalism recently developed by Beloborodov. Our model reproduces well the pulse profiles at different energies simultaneously, corresponding phase lags, as well as the time-averaged spectrum. We constrain the compact star mass to be bounded between 1.2 and 1.6 M⊙. By fitting the observed profiles, we determine the radius of the compact object to be R∼ 11 km if M= 1.6 M⊙, while for M= 1.2 M⊙ the best-fitting radius is ∼6.5 km, indicating that the compact object in SAX J1808.4−3658 can be a strange star. We obtain a lower limit on the inclination of the system of 65°.
Aims. The aim of this paper is to investigate the transition of a strongly magnetized neutron star into the accretion regime with very low accretion rate. Methods. For this purpose, we monitored the ...Be-transient X-ray pulsar GRO J1008−57 throughout a full orbital cycle. The current observational campaign was performed with the Swift/XRT telescope in the soft X-ray band (0.5–10 keV) between two subsequent Type I outbursts in January and September 2016. Results. The expected transition to the propeller regime was not observed. However, transitions between different regimes of accretion were detected. In particular, after an outburst, the source entered a stable accretion state characterised by an accretion rate of ~ 1014−1015 g s-1. We associate this state with accretion from a cold (low-ionised) disc of temperature below ~6500 K. We argue that a transition to this accretion regime should be observed in all X-ray pulsars that have a certain combination of the rotation frequency and magnetic field strength. The proposed model of accretion from a cold disc is able to explain several puzzling observational properties of X-ray pulsars.
Aims. X-ray bursting neutron stars in low-mass X-ray binaries constitute an appropriate source class for constraining the masses and radii of neutron stars, but a sufficiently extended set of ...corresponding model atmospheres is necessary for these investigations. Methods. We computed such a set of model atmospheres and emergent spectra in a plane-parallel, hydrostatic, and LTE approximation with Compton scattering taken into account. Results. The models were calculated for six different chemical compositions: pure hydrogen, pure helium, and a solar mix of hydrogen and helium with various heavy element abundances Z = 1,0.3,0.1, and 0.01 Z⊙. For each chemical composition the models are computed for three values of surface gravity, log g =14.0, 14.3, and 14.6, and for 20 values of the luminosity in units of the Eddington luminosity, L/LEdd, in the range 0.001–0.98. The emergent spectra of all models are redshifted and fitted by a diluted blackbody in the RXTE/PCA 3–20 keV energy band, and corresponding values of the color correction (hardness factors) fc are presented. Conclusions. Theoretical dependences fc–L/LEdd can be fitted to the observed dependence K −1/4–F of the blackbody normalization K on flux during cooling stages of X-ray bursts to determine the Eddington flux and the ratio of the apparent neutron star radius to the source distance. If the distance is known, these parameters can be transformed to the constraints on neutron star mass and radius. Theoretical atmosphere spectra can also be used for direct comparison with the observed X-ray burst spectra.
Aims. INTEGRAL has been monitoring the Galactic center region for more than a decade. Over this time it has detected hundreds of type-I X-ray bursts from the neutron star low-mass X-ray binary 4U ...1728–34, also known as the slow burster. Our aim is to study the connection between the persistent X-ray spectra and the X-ray burst spectra in a broad spectral range. Methods. We performed spectral modeling of the persistent emission and the X-ray burst emission of 4U 1728–34 using data from the INTEGRAL JEM-X and IBIS/ISGRI instruments. Results. We constructed a hardness intensity diagram to track spectral state variations. In the soft state, the energy spectra are characterized by two thermal components likely coming from the accretion disc and the boundary/spreading layer, together with a weak hard X-ray tail that we detect in 4U 1728–34 for the first time in the ~40 to 80 keV range. In the hard state, the source is detected up to ~200 keV and the spectrum can be described by a thermal Comptonization model plus an additional component: either a powerlaw tail or reflection. By stacking 123 X-ray bursts in the hard state, we detect emission up to 80 keV during the X-ray bursts. We find that during the bursts the emission above 40 keV decreases by a factor of approximately three with respect to the persistent emission level. Conclusions. Our results suggest that the enhanced X-ray burst emission changes the spectral properties of the accretion disc in the hard state. The likely cause is an X-ray burst induced cooling of the electrons in the inner hot flow near the neutron star.
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