Temperature Profiles of Accretion Disks around Rapidly Rotating Neutron Stars in General Relativity and the Implications for Cygnus X-2

We calculate the temperature profiles of (thin) accretion disks around rapidly rotating neutron stars (with low surface magnetic fields), taking into account the full effects of general relativity. We then consider a model for the spectrum of the X-ray emission from the disk that is parameterized by the mass accretion rate, the color temperature, and the rotation rate of the neutron star. We derive constraints on these parameters for the X-ray source Cygnus X-2 using the estimates of the maximum temperature in the disk along with the disk and boundary layer luminosities, using the spectrum inferred from the EXOSAT data. Our calculations suggest that the neutron star in Cygnus X-2 rotates close to the centrifugal mass-shed limit. Possible constraints on the neutron star equation of state are also discussed.