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Prog:. Purl Nucl Phy.r.. Vol. 36, pp. 407-408, 1996

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SO146-641O(Y6)00045-2

Neutron Stars and Massive Quark Matter

A. DRAGO’, M. HJORTH-JENSEN” and U. TAMBINI’ I Diparrirncnro di Fisico. Umversird dl Frrrur(~ and INFN. Scz~onc di Ferrorn. I-44100

Ferrora. Italy

ABSTRACT

Using the Color-Dielectric model to describe quark confinement, including strange quarks and

accounting for beta-equilibrium, we get masses for a static neutron star in the range 1.3 5 M/A43 <

1.54 for a radius R z 9 km.

In this contribution we study properties of neutron stars like total mass and radius employing a massive

quark model, the so-called Color-Dielectric model (CDM) (P irner, 1992; Birse, 1990 ). The CDM is

a confinement model which has been used with success to study properties of single nucleons, such as

structure functions (Barone et al., 1993, 1994) and form factors (Fiolhais et al., 1994), or to describe

the interaction potential between two nucleons (Brguer et al., 1990), or to investigate quark matter. In

particular it is possible, using the same set of parameters, both to describe the single nucleon properties

and to obtain meaningful results for the deconfinement phase transition (Drago et al., 1995a). The aim

here is therefore to see whether this model gives reasonable predictions for neutron star observables.

The Lagrangian of the SU(3)f version of the model is given by (McGovern 1991):

where V(a,r?) is the “mexican-hat” potential, as in Neuber et al. (1993). The lagrangian L: describes a

system of interacting u, d and s quarks, pions, sigmas and a scalar-isoscalar chiral singlet field x whose

potential U(x) is given by V(x) = iM2x2. Th e coupling constants are given by gu,d = g(fr ZIZ {a) and

g. = g(2fK - fx), where fir = 93 MeV and f~ = 113 MeV are the pion and the kaon decay constants,

respectively, and (3 = fK* - fKo = -0.75 MeV. These coupling constants depend only on a single

parameter g. We will use the parameters g = 0.023 GeV and M = 1.7 GeV, giving a nucleon isoscalar

radius of 0.80 fm (exp. 0.79 fm) and an average delta-nucleon mass of 1.129 GeV (exp. 1.085 GeV).

The quark matter (QM) phase is characterized by a constant value of the scalar fields and by using

plane waves to describe the quarks. The total energy of QM in the mean field approximation reads

EQA, = 0’ c j& jv ( ml 0 Ic: - k) + VU(~) + VW(i+,i? = O), f=u.d.a

where k{ is the Fermi momentum of quarks with flavour f.

The high-density matter in the interior of neutron stars is described by requiring the system to be

globally neutral by setting (2/3)n, - (1/3)nd - (1/3)n,, - n, = 0, where n,,&~ are the densities of the

u, d and s quarks and of the electrons, respectively. Morover, the system must be in P-equilibrium,

i.e. the chemical potentials have to satisfy the following equations &j = p,, + pL, and eL, = p,, + Pi.

These equations have to be solved self-consistently together with field equations, at a fixed baryon

407

408 A. Drago et al

0) 0 2 4 6 8 10 12

Fig. 1. Total mass M/M, as function of central density n where n,, is the nuclear matter saturation density.

Solid line are the results with the CDM EOS. Dotted lines are the results obtained with the Wale&a model for

pure neutron matter.

density n = n, + nd + n,. In our model, strange quarks appear at a density of 2 1/3nc, where no is the

saturation density of nuclear matter.

The energy of P-stable QM, as described by the CDM, is larger than the energy of P-stable nuclear

matter for densities smaller than _ n,,. To describe the system at smaller densities we link our CDM EOS

with the baryonic EOS of Friedman and Pandharipande (1981). F rom the general theory of relativity,

the structure of a static neutron star is determined through the Tolman-Oppenheimer-Volkov equation.

The total mass as function of the central density n is displayed in Fig. 1. We obtain a maximum mass

M “,.3X x 1.54Ma and a radius of 9 km at a central density corresponding to approximately 9 no, in

good agreement with the experimental values for the mass (Finn, 1994) and the estimate for the radius.

Concerning the minimum mass, we obtain a value equal to 1.3M,. We also see from Fig.1, that the

so-called Walecka model for pure neutron matter (Serot and Walecka, 1986), which yields a much stiffer

EOS than the CDM, results in too large masses for the neutron star.

In Drago et al. (1995b) it is also shown that neutrino emissivities from direct quark URCA processes

yield cooling histories for neutron stars in good agreement with present data.

This work has been supported by the Istituto Nazionale di Fisica Nucleare (INFN) , Italy, the Istituto

Trentino di Cultura, Italy, and the Research Council of Norway.

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