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

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3. Keplerian models of strange stars

We have computed exact numerical models of strange stars in general relativity using the Stergioulas and Friedman (1995) code (see Stergioulas 1998 for a description). In this code, the equilibrium models are obtained following the KEH (Komatsu et al. 1989) method, in which the field equations are converted to integral equations using appropriate Green's functions.

The detailed expected properties of strange stars depend on the adopted theory of interactions. All models presented here were constructed using Eq. (1) for the equation of state. For our models of rotating stars, we find that mass and radial quantities (e.g., the stellar radius and the height of the ISCO above it) accurately scale as [FORMULA], just as for the static stars, while the frequencies scale as [FORMULA]. For the more general e.o.s. [FORMULA], we also confirm the approximate scalings with a, discovered by Lattimer et al. (1990) - to within 9% we find that for our Keplerian models, the maximum stellar mass scales as [FORMULA], the stelar radius scales as [FORMULA], and the rotation rate of the star scales as [FORMULA]. Thus, between the scalings with [FORMULA] and with a, the numerical results presented in Table 1 can at once be extended to the general e.o.s. of strange matter.


Table 1. Keplerian models of strange stars, for [FORMULA].

In Figs. 1 through 3, we present the mass, radius and the ISCO frequencies in our Keplerian models, for three values of [FORMULA], and compare them with the static models. In Fig. 4 we present the ISCO angular frequencies as a function of the central energy density of the strange star, and also exhibit the (larger) angular frequency of the star itself. The maximal rotation rate of a strange star is very close to the rotation rate of the maximum-mass model, i.e., 9522 s-1 for [FORMULA]. Note, that because of the scalings with energy density it is described by the simple formula [FORMULA], where G is the gravitational constant. The dimensional form of this formula was anticipated by Prakash et al. (1990) and Glendenning (1990).

[FIGURE] Fig. 1. Radius vs. mass for strange stars (near their maximum mass). Models of both non-rotating stars (thin lines) and maximally rotating stars (thick lines, i.e., upper three curves) are shown for three values of the energy density of quark matter at zero pressure, [FORMULA]: [FORMULA] (continuous lines), [FORMULA] (long-dashed lines), [FORMULA] (dashed lines). The maximum-mass models for these values of [FORMULA] are indicated by a filled circle, an open circle and a star, respectively. Note that the radius and mass scale as [FORMULA]. A large increase of the radius and maximum mass is evident as the stellar rotation rate increases from zero to the equatorial mass-shedding limit.

[FIGURE] Fig. 2. Mass vs. central energy density for the same models as in Fig. 1. For each sequence, a star is stable only at values of [FORMULA] smaller than, approximately, the one corresponding to the maximum mass.

[FIGURE] Fig. 3. The frequency of the co-rotating innermost stable circular orbit as a function of mass for static models (thin, continuous line) and for strange stars rotating at the equatorial mass-shedding limit (thick lines, in the style of Fig. 1). For the static models, this frequency is given by the keplerian value at [FORMULA], i.e., by [FORMULA], and the minimum ISCO frequency corresponds to the maximum mass, denoted by a filled circle, an empty circle, and a star, respectively for [FORMULA] 4.2, 5.3, and 6.5. Note that the ISCO frequencies for rapidly rotating strange stars can have much lower values, and [FORMULA]kHz can be achieved for strange stars of fairly modest mass, e.g. [FORMULA], if the star rotates close to the equatorial mass-shedding limit.

[FIGURE] Fig. 4. The angular frequency of strange stars (the upper three, thick, lines) rotating at the equatorial mass-shedding limit, and of their co-rotating ISCOs (thin lines), as a function of central energy density. The symbols have the same meaning as in Fig. 1.

Table 1 presents in detail, the various stellar parameters obtained in our calculation for Keplerian strange stars, modeled with Eq. (1) for the value [FORMULA]. In addition to the central density, gravitational mass of the star, its radius and maximal rotation rate, the successive columns list the angular frequency ([FORMULA]) in the co-rotating ISCO (at height [FORMULA] above the surface), the height of the retrograde ISCO, the stellar angular momentum, the moment of inertia, the ratio of the polar to equatorial radii, and the polar and the equatorial (forward and backward) redshifts. The ratio of kinetic to potential energy [FORMULA] is much larger for these models than for neutron stars. Note that in all cases, the co-rotating ISCO is above the stellar surface and, as exhibited in Fig. 3, the ISCO frequencies are much lower for the Keplerian models than for static models (at fixed stellar mass) and differ considerably from their lowest-order slow-rotation approximation. The significant departure from the slow-rotation result is explained by the unusually large oblateness of rapidly rotating strange stars, and the fact that the ISCO frequency and height depend not only on the angular momentum, but also on the stationary quadrupole moment, in rapidly rotating stars (Shibata and Sasaki, 1998; Sibgatullin and Sunayev, 1998).

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© European Southern Observatory (ESO) 1999

Online publication: December 2, 1999