## 3. Model EOS with deconfinement phase transitionFor the investigation of the deconfinement phase transition expected to occur in neutron star matter at densities above the nuclear saturation density several approaches to quark confinement dynamics have been discussed, see e.g. Blaschke et al. (1990) , Blaschke et al. (1999) , Drago et al. (1996)which lead to interesting conclusions for the properties of quark matter at high densities. Most of the approaches to quark deconfinement in neutron star matter, however, use a thermodynamical bag-model for the quark matter and employ a standard two-phase description of the equation of state (EOS) where the hadronic phase and the quark matter phase are modeled separately and the resulting EOS is obtained by imposing Gibbs' conditions for phase equilibrium with the constraint that baryon number as well as electric charge of the system are conserved (Glendenning 1992, 1997). Since the focus of our work is the elucidation of qualitative features of signals for a possible deconfinement transition in the pulsar timing, we will consider here such a rather standard, phenomenological model for an EOS with deconfinement transition. The total pressure as a thermodynamical potential is given by where is the EOS of the relativistic mean-field model (Walecka model) for nuclear matter (Walecka 1974; Kapusta 1989), where the masses and chemical potentials have to be renormalized by the mean-values of the and fields , . The pressure for two-flavor quark matter within a bag model EOS is given by where In a neutron star, these phases of strongly interacting matter are in equilibrium with electrons and muons which contribute to the pressure balance with In the above expressions is the
partial pressure of the Fermion species where . All the other thermodynamic quantities of interest can be derived from the pressure (32) as, e.g., the partial densities of the species The chemical equilibrium due to the direct and inverse
- decay processes imposes additional
constraints on the values of the chemical potentials of leptonic and
baryonic species (Glendenning 1997; Sahakian 1995). Only two
independent chemical potentials remain according to the corresponding
two conserved charges of the system, the total baryon number
as well as electrical charge
The deconfinement transition is obtained following the construction
which obeys the global conservation laws and allows one to find the
volume fraction of the quark matter phase
in the mixed phase where
, so that at given
and In Fig. 1 we show the model EoS with deconfinement transition
as described above. Note that in the density region of the phase
transition there is a monotonous increase of the pressure which gives
rise to an extended mixed phase region in the compact star after
solution of the equations of hydrodynamic stability (13). For
comparison, the relativistic mean-field EoS of Glendenning
(1989)including mesons, hyperons
and muons (incompressibility MeV,
dotted line) and that of Glendenning (1992)including a deconfinement
transition to three-flavor quark matter in a bag model with
MeV
In Fig. 2 we show the composition of the hybrid star matter as a function of the total baryon density at . Solving the Tolman-Oppenheimer-Volkoff equations (13)- (15) for the hydrodynamical equilibrium of static spherically symmetric relativistic stars with the above defined EOS, we find that a configuration at the stability limit could have a quark matter core with a radius as large as of the stars radius.
What implications this phase transition for rotating star configurations might have will be investigated in the next section by applying the method developed in Sect. 2 for the above EOS. © European Southern Observatory (ESO) 2000 Online publication: June 5, 2000 |