Observational appearance of rapidly rotating neutron stars
Observational appearance of rapidly rotating neutron stars
复制标题
DOI：
10.1051/0004-6361/202037502
复制
发表时间：
2020-05
影响因子：
6.5
通讯作者：
V. Suleimanov;J. Poutanen;K. Werner
中科院分区：
文献类型：
--
作者：
V. Suleimanov;J. Poutanen;K. Werner
低质量X射线双星中的中子星（NS）以足够高的频率旋转，以显著偏离球度（ν* 200-600 Hz）。首先，我们研究了快速旋转对NS观测外观的影响。我们提出了解析公式的引力质量和赤道半径的快速旋转NS的质量M和半径R的非旋转NS相同的重子质量使用精确的完全相对论计算。我们假设NS表面发射由普朗克函数描述，具有两种不同的发射模式：各向同性强度和对应于电子散射主导的大气。对于这两种情况，我们计算光谱从一个扁圆旋转NS观察到在不同的倾角使用修改后的扁圆史瓦西近似，其中光弯曲计算史瓦西度规，但框架拖曳和四极矩的NS近似占光子红移计算。特别是，我们确定的立体角旋转NS是由一个遥远的观察者，观察到的色温和黑体归一化。然后，我们研究如何快速旋转的影响，使用冷却尾方法应用于X射线暴光谱演化的NS半径测定的结果。我们近似的本地光谱从NS表面的稀释黑体与亮度依赖的稀释因子使用先前计算的NS大气模型。然后将冷尾方法推广到快速旋转NS的情况，得到了具有相同重子质量的相应非旋转NS的M和R的最概然值。我们表明，如果使用非旋转NS的冷却尾方法的版本，则对于以ν*= 700 Hz旋转的R <$11 km的正面恒星，NS半径可能被高估3-3.5 km。我们将该方法应用于在SAXJ1810.8 - 2609中以ν* π 532 Hz旋转的NS观测到的X射线爆发。如果在倾角i = 60°和正面视角R = 11.2 ± 0.5 km的情况下观察，非旋转NS（假设M = 1.5 M）的最终半径为11.8 ± 0.5 km，这比使用忽略旋转的标准冷却尾方法获得的半径小0.6和1.2 km。对应的赤道半径分别为12.3 ± 0.6km（i = 60°）和11.6 ± 0.6km（i = 0°）。
Neutron stars (NSs) in low-mass X-ray binaries rotate at frequencies high enough to significantly deviate from sphericity (ν* ∼ 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 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 ≈ 11 km rotating at ν*= 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 ν* ≈ 532 Hz in SAX J1810.8−2609. The resulting radius of the non-rotating 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 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 ± 0.6 km (for i = 60°) and 11.6 ± 0.6 km (for i = 0°).