Astron. Astrophys. 352, L116-L120 (1999)

1. Introduction

The discovery of millisecond variability in the flux of low-mass X-ray binaries (LMXBs) has raised the prospect of constraining the properties of matter at supranuclear densities, which is thought to make up the compact stellar remnant in these sources. Conventionally, the compact objects is taken to be a neutron star, and it has been shown (Kaaret et al., 1997; Kluzniak, 1998) how the assumption that the highest observed frequency in the X-ray flux is the orbital frequency in the innermost (marginally) stable orbit about the star (Kluzniak and Wagoner, 1985; Syunyaev and Shakura, 1986; Kluzniak et al., 1990) leads to significant constraints on the equation of state of matter at such densities, as very few models of ultra-dense matter admit neutron stars of mass high enough to allow maximum orbital frequencies as low as the observed values in the quasi-periodic oscillations (QPOs) - for instance, the QPO frequency in 4U 1820-30 saturates at 1.07 kHz (Zhang et al., 1998).

Still, the evolutionary status of LMXBs and the nature of the accreting compact object are not clear. It is known that the X-ray bursters cannot be black holes, because their photospheric radius and the temperature during the burst both tend to a definite value, thus showing the presence of a stellar surface, which is also required to explain the (type I) X-ray bursts as thermonuclear explosions of accreted material. The inferred radii (and masses) are consistent with models of neutron stars, but it is possible that the compact object is a "strange", i.e. quark, star (Cheng and Dai, 1996). If it were, at least in the sources 4U 1820-30 and 4U 1636-53, then the energy density of self-bound quark matter at zero pressure would have to have the unusually low value , if the maximum observed frequencies of the kHz QPOs were the orbital frequencies in the ISCO about slowly rotating strange stars; and the observed QPO frequencies could not be the orbital frequencies at the surface of such stars, for any value of (Bulik et al., 1999).

However, it seems likely that in these very old LMXBs, the compact star has been spun up through accretion to very high ¹ frequencies - in the relativistic regime, a neutron star would have to accrete only to attain angular momentum (Lipunov and Postnov, 1984; Kluzniak and Wagoner 1985). A strong magnetic field could prevent rapid rotation, but strange stars may not support such a field (Horvath 1999). Gravitational instabilities could also, in principle, limit the rotation rate, but the stars considered here are likely to be sufficiently cold for the r-mode instability to be inoperative (Andersson et al., 1999). We show that if LMXBs harbour rapidly rotating strange stars, the constraints from kHz QPOs on the stellar mass and on are relaxed to a surprising degree. We also discuss the rotational frequency of "Keplerian" models of strange stars, i.e., ones in which the rotation rate at the stellar equator is equal to the orbital frequency for the star, at the same equatorial radius.

© European Southern Observatory (ESO) 1999

Online publication: December 2, 1999
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