ASTRONOMY AND ASTROPHYSICS Innermost stable circular orbits around strange stars and kHz QPOs in low-mass X-ray binaries

Exact calculations of innermost stable circular orbit (ISCO) around rotating strange stars are performed within the framework of general relativity. Equations of state (EOS) of strange quark matter based on the MIT Bag Model with massive strange quarks and lowest order QCD interactions, are used. The presence of a solid crust of normal matter on rotating, mass accreting strange stars in LMXBs is taken into account. It is found that, contrary to neutron stars, above some minimum mass (which for the considered equations of state ranged from 1.4 M⊙ to 1.6 M⊙) a gap always separates the ISCO and stellar surface, independently of the strange star rotation rate. For a given baryon mass of strange star, we calculate the ISCO frequency as function of stellar rotation frequency, from static to Keplerian configuration. For masses close to the maximum mass of static configurations the ISCO frequencies for static and Keplerian configurations are similar. However, for masses significantly lower than the maximum mass of static configurations, the minimum value of the ISCO frequency is reached in the Keplerian limit. Presence of a solid crust increases the ISCO frequency for the Keplerian configuration by about ten percent compared to that for a bare strange star of the same mass. For standard parameters of strange quark matter EOS, resulting in a maximum static mass of 1.8 M⊙, the ISCO frequency for >∼ 1.4 M⊙ strange stars always exceeds 1.07 kHz (the upper QPO frequency reported for 4U 1820-30). We give an example of strange quark matter model, which yields maximum static mass of 2.3 M⊙, and for which the ISCO frequency of 1.07 kHz is allowed at stellar rotation rates 200-300 Hz, provided the strange star mass exceeds 2.2 M⊙. For this EOS even lower value νISCO ≃ 1 kHz is reached near the Keplerian limit, for a broad range of stellar masses. While reproducing νISCO = 1.07 kHz at slow rotation rates requires tuning of strange quark matter parameters, no such a tuning is required to reproduce orbital frequencies around strange stars equal to highest observed upper QPO frequencies. Send offprint requests to: J.L. Zdunik