Influence of the Gravitational Darkening Effect on the Spectrum of a Hot, Rapidly Rotating Neutron Star

In this paper, we discuss the influence of the gravitational darkening effect on the emergent spectrum of a fast-rotating, flattened neutron star. Model atmosphere codes always calculate spectra of emergent intensities and fluxes emitted from the unit surface on the star in plane-parallel geometry. Here we took a step beyond that and calculated a small sample grid of theoretical spectra integrated over the distorted surface of a sample rotating neutron star seen by a distant observer at various inclination angles. We assumed parameters like two dimensionless angular velocities ${\bar{{\rm{\Omega }}}}^{2}=0.30$ and 0.60, the effective temperature of a nonrotating star T _eff = 2.20 × 10⁷ K, the logarithm of the surface gravity of a spherical star $\mathrm{log}(g)=14.40$ (cgs), and inclination angles from i = 0° to i = 90° with step Δi = 10°. We assumed that the atmosphere consists of a mixture of hydrogen and helium with M _H = 0.70 and M _He = 0.30. At each point on the neutron star surface, we calculated true intensities for local values of parameters (T _eff and $\mathrm{log}(g)$ ), and these monochromatic intensities are next integrated over the whole surface to obtain the emergent spectrum. In this paper, we compute for the first time theoretical spectra of the fast-rotating neutron star. Our work clearly shows that the gravitational darkening effect strongly influences the spectrum and should be included in realistic models of the atmospheres of rotating neutron stars.