Observational appearance of rapidly rotating neutron stars. Xray bursts, cooling tail method, and radius determination
Abstract
Neutron stars (NSs) in lowmass Xray binaries rotate at frequencies high enough to significantly deviate from sphericity (ν_{*} ∼ 200600 Hz). First, 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 nonrotating NS of the same baryonic mass using accurate fully relativistic computations. We assume that the NS surface emission is described by the Planck function with two different emission patterns: the isotropic intensity and that corresponding to the electronscattering dominated atmosphere. For these two cases we compute spectra from an oblate rotating NS observed at different inclination angles using the modified oblate Schwarzschild 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. In particular, we determine the solid angle at which a rotating NS is seen by a distant observer, the observed colour temperature and the blackbody normalization. Then, we investigate how rapid rotation affects the results of NS radius determination using the cooling tail method applied to the Xray burst spectral evolution. We approximate the local spectra from the NS surface by a diluted blackbody with the luminositydependent dilution factor using previously computed NS atmosphere models. We then 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 nonrotating NS with the same baryonic mass. We show that the NS radius could be overestimated by 33.5 km for faceon stars of R ≈ 11 km rotating at ν_{*}= 700 Hz if the version of the cooling tail method for a nonrotating NS is used. We apply the method to an Xray burst observed from the NS rotating at ν_{*} ≈ 532 Hz in SAX J1810.82609. The resulting radius of the nonrotating NS (assuming M = 1.5 M_{⊙}) becomes 11.8 ± 0.5 km if it is viewed at inclination i = 60° and R = 11.2 ± 0.5 km for a faceon 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 ± 0.6 km (for i = 60°) and 11.6 ± 0.6 km (for i = 0°).
 Publication:

Astronomy and Astrophysics
 Pub Date:
 July 2020
 DOI:
 10.1051/00046361/202037502
 arXiv:
 arXiv:2005.09759
 Bibcode:
 2020A&A...639A..33S
 Keywords:

 stars: neutron;
 stars: atmospheres;
 methods: numerical;
 stars: individual: SAX J1810.82609;
 Xrays: binaries;
 Xrays: bursts;
 Astrophysics  High Energy Astrophysical Phenomena;
 Astrophysics  Solar and Stellar Astrophysics;
 Nuclear Theory
 EPrint:
 17 pages, 16 figures, accepted for publication in Astronomy and Astrophysics