Observational appearance of rapidly rotating neutron stars: X-ray bursts, cooling tail method, and radius determination

Neutron stars (NSs) in low-mass X-ray binaries rotate at frequencies high enough to significantly deviate from sphericity ($\nu_* \sim$ 200--600 Hz). We investigate the effects of rapid rotation on the observational appearance of a NS. We propose analytical formulae relating gravitational mass and equatorial radius of the rapidly rotating NS to the mass $M$ and radius $R$ of a non-rotating NS of the same baryonic mass using accurate fully relativistic computations. We compute spectra from an oblate rotating NS observed at different inclination angles using the modified oblate Schwarzschild (MOS) approximation, where light bending is computed in Schwarzschild metric, but frame dragging and quadrupole moment of a NS are approximately accounted for in the photon redshift calculations. We generalize the cooling tail method to the case of a rapidly rotating NS to obtain the most probable values of $M$ and $R$ of the corresponding non-rotating NS with the same baryonic mass. We approximate the local spectra from the NS surface by a diluted blackbody using previously computed NS atmosphere models. We show that the NS radius could be overestimated by 3--3.5 km for face-on stars of $R\approx 11$ km rotating at $\nu_* =$ 700 Hz if the version of the cooling tail method for a non-rotating NS is used. We apply the method to an X-ray burst observed from the NS rotating at $\nu_* \approx$ 532 Hz in SAX J1810.8$-$2609. The resulting radius of the non-rotating NS (assuming $M=1.5 M_\odot$) becomes $11.8\pm0.5$ km if it is viewed at inclination i=60 deg and $R=11.2\pm0.5$ km for a face-on view, which are smaller by 0.6 and 1.2 km than the radius obtained using standard cooling tail method ignoring rotation. The corresponding equatorial radii of these rapidly rotating NSs are 12.3$\pm 0.6$ km (for i=60 deg) and 11.6$\pm 0.6$\,km (for i=0 deg).Comment: 17 pages, 16 figures, accepted for publication in Astronomy and Astrophysic

On the spreading layer emission in luminous accreting neutron stars

Emission of the neutron star surface potentially contains information about its size and thus of vital importance for high energy astrophysics. In spite of the wealth of data on the emission of luminous accreting neutron stars, the emission of their surfaces is hard to disentangle from their time averaged spectra. A recent X-ray transient source XTE J1701-462 has provided a unique dataset covering the largest ever observed luminosity range for a single source. In this paper, we extract the spectrum of the boundary layer between the inner part of the accretion disc and the neutron star surface with the help of maximally spectral model-independent method. We show compelling evidences that the energy spectrum of the boundary layer stays virtually the same over factor of 20 variations of the source luminosity. It is rather wide and cannot be described by a single temperature blackbody spectrum, probably because of the inhomogeneity of the boundary layer and a spread in the colour temperature. The observed maximum colour temperature of the boundary/spreading layer emission of kT~2.4-2.6 keV is very close to the maximum observed colour temperature in the photospheric radius expansion X-ray bursts, which is set by the limiting Eddington flux at the neutron star surface. Observed stability of the boundary layer spectrum and its maximum colour temperature strongly supports theoretical models of the boundary/spreading layers on surfaces of luminous accreting neutron stars, which assume the presence of a region emitting at the local Eddington limit. Variations in the luminosity in that case lead to changes in the size of this region, but affect less the spectral shape. Elaboration of this model will provide solid theoretical grounds for measurements of the neutron star sizes using the emission of the boundary/spreading layers of luminous accreting neutron stars.Comment: 7 pages, 7 figures, accepted for publication in MNRA

Optically thick envelopes around ULXs powered by accreating neutron stars

Magnetized neutron stars power at least some ultra-luminous X-ray sources. The accretion flow in these cases is interrupted at the magnetospheric radius and then reaches the surface of a neutron star following magnetic field lines. Accreting matter moving along magnetic field lines forms the accretion envelope around the central object. We show that, in case of high mass accretion rates $\gtrsim 10^{19}\,{\rm g\,s^{-1}}$ the envelope becomes closed and optically thick, which influences the dynamics of the accretion flow and the observational manifestation of the neutron star hidden behind the envelope. Particularly, the optically thick accretion envelope results in a multi-color black-body spectrum originating from the magnetospheric surface. The spectrum and photon energy flux vary with the viewing angle, which gives rise to pulsations characterized by high pulsed fraction and typically smooth pulse profiles. The reprocessing of radiation due to interaction with the envelope leads to the disappearance of cyclotron scattering features from the spectrum. We speculate that the super-orbital variability of ultra-luminous X-ray sources powered by accreting neutron stars can be attributed to precession of the neutron star due to interaction of magnetic dipole with the accretion disc.Comment: 8 pages, 6 figures, accepted for publication in MNRA

Expected polarization properties of nonmagnetized CCOs

Central compact objects (CCOs) are neutron stars found close to the center of some supernova remnants. A certain number of them are presumably covered by carbon envelopes. Their unpulsed thermal X-ray emission can originate either from the entire surface covered by a carbon atmosphere or alternatively from a nonuniformly emitting hydrogen atmosphere. However, the latter scenario appears unlikely given the available upper limits on the amplitude of pulsations. Here we explore a possibility to further discriminate between the two scenarios using X-ray polarimetric observations. We compute the polarization degree (PD) for nonmagnetized pure-carbon and pure-hydrogen atmospheres with effective temperatures of between 1 and 6 MK and find that it can reach up to 25% and 40% for hydrogen and carbon atmospheres, respectively, in the photon energy band 1-10 keV. However, given the available constraints on possible inhomogeneities of the temperature distribution deduced from models of the X-ray spectrum of the CCO in HESS J1731-347, the integrated PD appears to be very low for both carbon (<0.25%) and hydrogen (a few percent) compositions in the energy band of 2-8 keV covered by the recently launched Imaging X-ray Polarimetry Explorer. We therefore conclude that polarization from CCOs is not expected to be detectable by current facilities, but future detection would strongly support nonuniform hydrogen composition models.Comment: 10 pages, 16 figures. accepted to be published by A&A, corrected after the language Editor remarks, misprints in some numbers were corrected, a new version of Fig.1

Magnetospheric return-current-heated atmospheres of rotation-powered millisecond pulsars

We computed accurate atmosphere models of rotation-powered millisecond pulsars in which the polar caps of a neutron star (NS) are externally heated by magnetospheric return currents. The external ram pressure, energy losses, and stopping depth of the penetrating charged particles were computed self-consistently with the atmosphere model, instead of assuming a simplified deep-heated atmosphere in radiative equilibrium. We used exact Compton scattering formalism to model the properties of the emergent X-ray radiation. The deep-heating approximation was found to be valid only if most of the heat originates from ultra-relativistic bombarding particles with Lorentz factors of $\gamma \gtrsim 100$. In the opposite regime, the atmosphere attains a distinct two-layer structure with an overheated optically thin skin on top of an optically thick cool plasma. The overheated skin strongly modifies the emergent radiation: it produces a Compton-upscattered high-energy tail in the spectrum and alters the radiation beaming pattern from limb darkening to limb brightening for emitted hard X-rays. This kind of drastic change in the emission properties can have a significant impact on the inferred NS pulse profile parameters as performed, for example, by Neutron star Interior Composition ExploreR. Finally, the connection between the energy distribution of the return current particles and the atmosphere emission properties offers a new tool to probe the exact physics of pulsar magnetospheres.Comment: 13 pages, 10 figures, published in A&

Colors and patterns of black hole X-ray binary GX 339-4

Black hole X-ray binaries show signs of non-thermal emission in the optical/near-infrared range. We analyze the optical/near-infrared SMARTS data on GX339$-$4 over the 2002--2011 period. Using the soft state data, we estimate the interstellar extinction towards the source and characteristic color temperatures of the accretion disk. We show that various spectral states of regular outbursts occupy similar regions on the color-magnitude diagrams, and that transitions between the states proceed along the same tracks despite substantial differences in the observed light curves morphology. We determine the typical duration of the hard-to-soft and soft-to-hard state transitions and the hard state at the decaying stage of the outburst to be one, two and four weeks, respectively. We find that the failed outbursts cannot be easily distinguished from the regular ones at their early stages, but if the source reaches 16 mag in $V$-band, it will transit to the soft state. By subtracting the contribution of the accretion disk, we obtain the spectra of the non-thermal component, which have constant, nearly flat shape during the transitions between the hard and soft states. In contrast to the slowly evolving non-thermal component seen at optical and near-infrared wavelengths, the mid-infrared spectrum is strongly variable on short timescales and sometimes shows a prominent excess with a cutoff below $10^{14}$ Hz. We show that the radio to optical spectrum can be modeled using three components corresponding to the jet, hot flow and irradiated accretion disk.Comment: Accepted for publication in Astronomy & Astrophysics, 19 pages, 6 tables, 18 figure