The final phase of inspiral of strange quark star binaries

We present calculations of the final phase of inspiral of irrotational strange star binaries. Two types of equation of state at zero temperature are used - the MIT bag model and the Dey et al. 1998 model of strange quark matter. We study the precoalescence stage within the Isenberg-Wilson-Mathews approximation of General Relativity using a multidomain spectral method. The gravitational-radiation driven evolution of the binary system is approximated by a sequence of quasi-equilibrium configurations at a fixed baryon number and with decreasing separation. We find that the innermost stable circular orbit (ISCO) is determined always by an orbital instability for binaries consisting of two stars built predominantly of strange quark matter independently on the total mass of a binary system and compactness parameter of each star. In contrast, for neutron stars described by baryonic equation of state without exotic phases the ISCO is given by the mass-shedding limit. The gravitational wave frequency at the ISCO, which marks the end of the inspiral phase, is always higher than 1.1kHz for equal masses irrotational strange quark stars with the total mass-energy of a binary system greater than $2 M_\odot$. We find that the dependence of the frequency of gravitational waves at the ISCO on the compactness parameter for the equal mass binaries can be described by the same simple analytical formulae for broad ranges of masses independently on a strange star model. Detailed comparisons with binary neutrons star models, as well as with the third order Post-Newtonian point-mass binaries are given. The difference in the phase, for two $1.35 M_\odot$ strange stars, between our numerical results and 3PN is $\sim 40 %$ for the last two orbits of inspiral.