## 2. Strange stars at finite temperaturesThe interesting point made in D98 is that starting from an
empirical form for the density dependent masses of the up (u), down
(d) and strange (s) q-s given below one can constrain the parametric
form of this mass from recent astronomical
data Restoration of chiral quark masses at high density is incorporated
in this model. Using the model parameter
() for this restoration one can
calculate the density dependence of the strong coupling constant (Ray
et al. 2000b). In other words the masses of stars in units of solar
mass, (), found as a function of the
star radius It is interesting to plot the up (u), down (d) and strange (s) q- masses at various radii in a star. This is done with strong coupling constant , chiral symmetry restoration parameter and the QCD scale parameter already discussed in D98 & Li et al. (1999a,b). Fig. 1 shows that the quarks do not have the constituent masses as in zero density hadrons nor do they have the current masses of the bag model. Upto a radius about 2 kms the quarks have their chiral current mass but in the major portion of the star their masses are substantially higher. At the surface the strange q- mass is about 278 MeV and the u, d q- masses MeV.
We use the large (colour) approximation of 't Hooft (1974) for quarks, where quark loops are suppressed by and the calculation can be performed at the tree level with a mean field derived from a qq interaction (Witten 1979). This was done for baryons (Dey et al. 1986; Dey et al. 1991; Ray et al. 2000a) and extended to dense systems like stars (D98). Following is the Hamiltonian, with a two-body potential : The vector potential in Eq. 2 between quarks originate from gluon exchanges, and the -s are the color SU(3) matrices for the two interacting quarks. In the absence of an accurate evaluation of the potential (e.g. from large planar diagrams) we borrow it from meson phenomenology, namely the Richardson potential (Richardson 1979). The potential reproduces heavy as well as light meson spectra (Crater et al. 1984). It has been well tested for baryons in Fock calculations (Dey et al. 1986; Dey et al. 1991). Recently, using the Vlasov approach with the Richardson potential, Bonasera (1999) finds a transition from nuclear to quark matter at densities 5 times . We had to calculate the potential energy (PE) contribution in two
steps: the single particle potential,
, for momentum The is parametrized as sum of
exponentials in
Finite temperature can be incorporated in the system through the Fermi function: with the flavour dependent single particle energy Now we evaluate For we get the number density and for , the energy density. is the spin-colour degeneracy. Even at very high The pressure ( We find
© European Southern Observatory (ESO) 2000 Online publication: January 29, 2001 |