Neutron stars ( NSs ) in low-mass X-ray binaries rotate at frequencies high enough to significantly deviate from sphericity ( \nu _ { * } \sim 200–600 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 non-rotating 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 electron-scattering dominated atmosphere .
For these two cases 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 .
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 X-ray burst spectral evolution .
We approximate the local spectra from the NS surface by a diluted blackbody with the luminosity-dependent 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 non-rotating NS with the same baryonic mass .
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 \pm 0.5 km if it is viewed at inclination i = 60 \degr and R = 11.2 \pm 0.5 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 \degr ) and 11.6 \pm 0.6 km ( for i = 0 \degr ) .