Numerical study on the hydrodynamic instability of binary stars in the first post Newtonian approximation of general relativity

We present numerical results on the hydrodynamic stability of coalescing binary stars in the first post Newtonian (1PN) approximation of general relativity. We pay particular attention to the hydrodynamic instability of corotating binary stars in equilibrium states assuming a stiff polytropic equation of state with the adiabatic constant Gamma = 3. In previous 1PN numerical studies on corotating binary stars in equilibrium states, it was found that along the sequence of binary stars as a function of the orbital separation, they have the energy and/or angular nominatum minima where the secular instability sets in, and that with increase of the IPN correction, the orbital separation at this minimum decreases while the angular velocity there increases. In this paper, to determine the location of the innermost stable circular orbit (ISCO), we perform numerical simulations and find where the hydrodynamic instability along the corotating sequences of the binary sets in. From these numerical results, we found that the dynamical stability Limit seems to exist near the energy and/or angular momentum minima not only in the Newtonian, but also in the 1PN cases. This means that the 1PN effect of general relativity increases the angular frequency of gravitational waves at the ISCO.