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Astron. Astrophys. 364, L89-L92 (2000)

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3. Results and discussions

With this EOS at finite T, the TOV equation is solved to find out the MR relationship of the strange star at finite T. Here we find that the stellar mass and radius decrease with increasing T and the central energy density goes upto 22 times the normal saturation density of nuclear matter. No star can be formed beyond T = 70 MeV since the star surface must have pressure zero for SS. The MR curves for the stars at the three values of T are given in Fig. 3 showing that the radii and the masses decrease slightly with T. The conclusions of D98 and Li et al. (1999a & 1999b) remain unchanged so far as compactness of the stars is concerned.

[FIGURE] Fig. 3. MR curves for T = 0, 20, 50 & 70 MeV. Core densities for [FORMULA] are 16.5, 19.5 and 22 [FORMULA]. We have drawn a vertical line at [FORMULA] for T = 70 MeV to show that the mass of star increases as T increases, for fixed radius.

We thank the anonymous referee for pointing out to us that the decrease in the maximum mass and the corresponding radius [FORMULA] of the star at finite T is somewhat surprising. We offer explanations of this fact as follows:

(1) We show in the Fig. 3 that the mass of the star with a given radius increases with T. This is clear from the vertical line which connects the maximum mass for T = 70 MeV with [FORMULA] km to the star mass for T = 0 for the same radius. This is in accord with the usual expectation that the star mass should increase with T.

(2) With increasing T, the size of any self sustaining system decreases due to the restriction placed on the energy balance by the increased thermal energy. The shrinking of a self-sustained system with increasing T is also seen for the Skyrmion (Dey and Eisenberg 1994). Interestingly the latter is also an example of the success of the large [FORMULA] phenomenon. Note that P in our system (Fig. 2), or the Skyrmion, is calculated self consistently whereas in the earlier literature on strange stars at finite T (Kettner et al. 1995) employing bag model, the variation of the bag pressure with T is neglected. It is pointed out in (Chmaj and Somiski 1989) at low P the bag pressure dominates and as P grows the results are close to the free relativistic gas limit. With an unchanged bag parameter therefore bag model calculations find an almost unchanged mass and radius for the stars at finite T.

(3) As thermal energy increases the binding energy per baryon decreases. This supports the argument given in (1) and (2) above that as T decreases the masses corresponding to the same radius will decrease.

The entropy S increases with T and decreases with density. Comparable to our entropy is that calculated by Das, Tripathi and Cugnon (1986) (DTC) for interacting hadrons. The results of DTC checks with experiment. The minimum T considered by DTC is 10 MeV and [FORMULA] is a little less than 1 at a density 2.5 times [FORMULA].

In Fig. 4 we have plotted [FORMULA] as a function of the star radius for T = 20, 50 and 70 MeV. It is interesting to see here that entropy is maximum at the surface showing that the surface is more disordered than the core. The extrapolated entropies from the plots of DTC at 5 [FORMULA] agree with our [FORMULA] at the stellar surface for all the three cases.

[FIGURE] Fig. 4. The entropy per quark at different T(20, 50 & 70 MeV) as a function of the star radius.

Recently Glendenning (Glendenning 2000) has argued that the SAX could be explained as a neutron star rather than bare SS, not with any of the existing known EOS, but with one based only on well-accepted principles and having a core density about 26 [FORMULA]. Of course, such high density cores imply hybrid strange stars, subject to Glendenning's assumption that such stars can exist with matching EOS for two phases. There is the further constraint that if the most compact hybrid star has a given mass, all lighter stars must be larger. It was found in Li et al. (1999b) that the star 4U 1728-34 may have a mass less than that of SAX and yet have a radius less than [FORMULA]. Another serious difference is that in our model the strange quark matter EOS derived, using the formalism of large [FORMULA] approximation, indeed shows a bound state in the sense of having minimum at about [FORMULA] whereas in Glendenning (2000) one of the assumptions is that strange matter has no bound state.

In summary, we find that beyond T = 70 MeV, the EOS has no zero pressure point. A self-bound star cannot exist in our model at higher T. The entropies at T = 20, 50 and 70 MeV (intermediate values are quite obvious) match onto hadronic entropies at corresponding T, suggesting the possibility of smooth phase transition between the hadronic and the quark states.

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© European Southern Observatory (ESO) 2000

Online publication: January 29, 2001
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