Astron. Astrophys. 363, 1005-1012 (2000)

2. Equation of state and static strange star models

In the present paper we describe strange quark matter using the model presented by Dey et al. (1998). In this model quarks of the density dependent mass are confined at zero pressure and deconfined at high density. The quark interaction is described by an interquark vector potential originating from gluon exchange, and by a density dependent scalar potential which restores the chiral symmetry at high densities.

We start our calculation by noticing that the equations of state SS1 and SS2 can be very well approximated by a linear function - see Fig. 1:

with resulting from first law of thermodynamics . We find it very interesting that the equation of state based on rather complicated physics can have a simple form like that of Eq. (1). In general, the equation of the type (1) corresponds to self-bound matter at the density (mass-energy) at zero pressure and with a fixed sound velocity (). Thus equations of state SS1 and SS2 are physical realizations of linear equations of state considered previously, see e.g. Glendenning (1997). Such a parametrization is very convenient - we not only can calculate the stellar structure for stars described by equations of state SS1 and SS2 but also can use the scaling relations to extend the results to stars described by the EOS of the form given by Eq. (1). All stellar parameters are subject to the scaling relations with appropriate powers of for a fixed value of a (see e.g. Witten 1984; Zdunik 2000).

Fig. 1. Equations of state (the dependence of pressure in the units of dyne cm-2 on the density in the units of g cm-3) considered in this work; top panel - SS1, bottom panel - SS2. The thick solid line is the tabulated equation of state, and the dotted line is the linear approximation.

To calculate parameters a, and we use a least squares fit method taking into account the region of the densities, which is relevant to the interior of stable stellar configurations, i.e we neglect in the fitting the part of the EOS for densities larger than the central density in the last stable configuration (maximum mass in the non-rotating case). For the case of SS1 we obtained the values of , , and for the case SS2 the values are , , , see Fig. 1.

We have calculated the static stellar configurations using both the tabulated equation of state of Dey et al. (1998) and its linear approximation. The linear approximation agrees very well with calculations of stellar parameters of non-rotating configurations using the tabulated form of the EOS. The difference in the range of masses and radii is smaller than 2%, and the maximum mass point agrees within 0.2%.

We present the physical parameters for the maximum mass static strange stars described by Eqs. SS1, SS2 in the left columns of Table 1. The stars described by EOS SS1 and SS2 are very compact i.e. the gravitational redshifts z for the maximum mass configurations are much larger than those for SS within the MIT bag model (also larger than z for most models of neutron stars), for which z varies from 0.432 to 0.477 for a massive strange quark with MeV and for massless quarks respectively. The maximal baryon mass in the case of static strange stars described by the SS1 and SS2 is relatively low (most of the neutron star models have a maximum baryon mass close to ). In the case considered here the difference between the baryon mass and the gravitational mass is much higher ( and ) than in the case of neutron stars (up to ) (for the MIT bag stars it is ). It should be however noted that in the case of strange stars we calculate the total baryon mass of the star using the nucleon mass and thus we include the binding energy of strange matter with respect to nuclear matter.

Table 1. Properties of the strange stars within the Dey model with maximal masses. The symbols are as follows: M and are gravitational and baryon masses respectively, is circumferential radius; is the central baryon density; is the central proper energy density divided by , P is the rotation period; , , are the redshift for an emission at the equator and in the direction of rotation, the redshift for an emission at the equator and in the direction opposite to rotation and the redshift at the stellar pole respectively.

© European Southern Observatory (ESO) 2000

Online publication: December 5, 2000
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