It has been suggested that the frequency in the co-rotating 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 , \rho _ { 0 } , of self-bound quark matter at zero presure .
For these models , the ISCO frequency is 81.5 \pm 1.5 % of the stellar rotational frequency , whose maximum value \Omega _ { K } = \sqrt { 3.234 G \rho _ { 0 } } is attained for a model close to the maximum-mass model , with M = 2.86 M _ { \odot } ( \rho _ { 0 } / 4.2 \times 10 ^ { 14 } { g cm ^ { -3 } } ) ^ { -1 / 2 } .
In contrast to static models , ISCO frequencies below 1.1 kHz are allowed—in fact , at the canonical value \rho _ { 0 } = 4.2 \times 10 ^ { 14 } { g cm ^ { -3 } } , the ISCO frequencies of rapidly rotating strange stars can be as low as 0.9 kHz for a 1.3 M _ { \odot } strange star .
Hence , the presence of strange stars in low-mass X-ray binaries can not 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 .