Letter to the Editor Keplerian frequencies and innermost stable circular orbits of rapidly rotating strange stars

It has been suggested that the frequency in the corotating innermost stable circular orbit (ISCO) about a compact stellar remnant can be determined through X-ray observations of low-mass X-ray binaries, and that its value can be used to constrain the equation of state of ultradense matter. Upon constructing numerical models of rapidly rotating strange (quark) stars in general relativity, we find that for stars rotating at the equatorial mass-shedding limit, the ISCO is indeed above the stellar surface, for a wide range of central energy densities at a height equal to 11% of the circumferential stellar radius, which scales inversely with the square root of the energy density, ρ0c, of self-bound quark matter at zero presure. For these models, the ISCO frequency is 81.5 ± 1.5% of the stellar rotational frequency, whose maximum value ΩK = √ 3.234Gρ0 is attained for a model close to the maximum-mass model, with M = 2.86M (ρ0/4.2×10 g cm−3)−1/2. In contrast to static models, ISCO frequencies below 1.1 kHz are allowed – in fact, at the canonical value ρ0 = 4.2×1014 g cm−3, the ISCO frequencies of rapidly rotating strange stars can be as low as 0.9 kHz for a 1.3M strange star. Hence, the presence of strange stars in low-mass X-ray binaries cannot be excluded on the basis of the currently observed frequencies of kHz QPOs, such as the cut-off frequency of 1066 Hz in 4U 1820-30.