Astron. Astrophys. 330, 569-577 (1998)

3. Results

3.1. Properties of nuclear matter

In Fig. 1 we show the energy per nucleon of symmetric nuclear matter calculated in the RMF theory. As a comparison, we also display the result based on the relativistic Dirac-Brueckner (RDB) theory calculated by Li et al. (1992). It is obvious that the RMF result resembles the RDB one. In the RMF theory, the bulk incompressibility (K), saturation density () and binding energy per nucleon () of symmetric nuclear matter are 227.6 MeV, 0.1589 fm^-3 and MeV, respectively. These values are very close to those derived from the nuclear experiments. In addition, the bulk symmetry energy coefficient () at the saturation density is 29.35 MeV.

Fig. 1. The energy per nucleon versus baryon density for symmetric nuclear matter based on the ZM model, and the relativistic Dirac-Brueckner theory (RDB) of Li et al. (1992).

Next we apply the RMF theory to asymmetric nuclear matter. In Figs. 2 and 3 we show the dependence of the saturation density and the bulk incompressibility on the proton concentration , respectively. The saturation density decreases as the proton concentration decreases from to as shown in Fig. 2. The incompressibility at the saturation density rapidly decreases with decreasing the proton concentration from . At , the saturation density is and the incompressibility is MeV. These results are rather different from those of Sumiyoshi & Toki (1994), who used the BB model in the RMF theory and found that the saturation point of asymmetric matter disappears around where the incompressibility becomes almost zero.

Fig. 2. The saturation density of asymmetric nuclear matter as a function of proton concentration.

Fig. 3. The bulk incompressibility of asymmetric nuclear matter as a function of proton concentration.

3.2. Properties of neutron stars

We now apply the RMF theory to a study of neutron-star matter, which is composed of neutrons, protons, electrons and muons under the conditions of beta equilibrium and charge neutrality. Cheng et al. (1996) has already taken this application into account but did not consider the contribution of muons. Here we do not consider the contributions of hyperons or other exotic states such as meson condensations or quark matter.

In Fig. 4 we show the proton and electron concentrations as functions of baryon number density. As a comparison, we also give the results of Cheng et al. (1996). The proton concentration slightly increases with increasing at high densities. At , the proton concentration is 0.085. This value is larger than 0.07 in the case without muons. In Sect. 4 we will discuss an astrophysical implication of this result.

Fig. 4. The proton and electron concentrations as functions of baryon number density.

Giving the EOS, we can calculate the hydrostatic structure of neutron stars by solving the Tolman-Oppenheimer-Volkoff equtaion. In our calculations, we use the EOS obtained by Haensel, et al. (1989) for the outer crusts of the stars, and the EOS derived by Baym, et al. (1971) for the inner crusts from the neutron-drip density to 0.14 fm^-3. These EOSs have been rather accurately expressed as some polynomials by Bao et al. (1994). The structure of neutron stars is displayed in Fig. 5, which shows the mass as a function of the central density, and which shows that the maximum mass of neutron stars is at a central density of with a radius of km.

Fig. 5. Total mass versus central density of neutron stars.

3.3. Properties of supernova matter

We use the RMF theory to study the properties of supernova matter, which consists of protons, neutrons, electrons, muons and neutrinos. Here we want to point out that our calculations are done at zero temperature and zero entropy (i.e. neglecting thermal effects) and in the density range of . This is because below (i) the Fermi energies of particles may not be much larger than kT (where T is the matter temperature), (ii) matter is expected to contain nuclei, and (iii) the ZM model gives negative pressure.

For the ZM model, we find that the muon concentration is negligibly small. This conclusion is similar to that of Chiapparini et al. (1996) based on the BB model. Fig. 6 shows the effective nucleon mass as a function of baryon number density for different lepton concentrations. Clearly, the effective nucleon mass decreases as the baryon density increases, but is almost insensitive to the lepton concentration.

Fig. 6. The effective nucleon mass as a function of baryon number density for different lepton concentrations. "free" denotes the case of neutron-star matter.

Now we define the sound velocity and the adiabatic index as

and

In supernova studies, in order to determine the sonic point of the hydrodynamical evolution of the matter, it is necessary to know the sound velocity as a function of density. In Fig. 7 we show the influence of the neutrino trapping on the sound velocity. This influence is not significant. Fig. 8 gives the dependence of the adiabatic index on baryon number density. It can be seen from this figure that the adiabatic index strongly increases at a density near in the case of neutron-star matter. The reason for this is that the pressure near this density in neutrino-free matter greatly decreases as compared with in neutrino-trapped matter (cf. Fig. 9) and then becomes negative at lower densities. We will simply discuss an implication of this behavior of the adiabatic index next section.

Fig. 7. The sound velocity as a function of baryon number density for different lepton concentrations. "free" denotes the case of neutron-star matter.

Fig. 8. The adiabatic index as a function of baryon number density for different lepton concentrations. "free" denotes the case of neutron-star matter.

Fig. 9. The pressure as a function of mass density for different lepton concentrations. "free" denotes the case of neutron-star matter.

In Fig. 9 we show the effect of neutrino trapping on the equation of state. When neutrinos are taken into account their contribution to the pressure stiffens the EOS at low densities more significantly than that in Chiapparini et al. (1996). The numerical values for the pressure and energy density as functions of baryon number density are listed in Tables 2-5.

Table 2. The energy density and pressure of neutron-star matter based on the ZM model

Table 3. The energy density and pressure of supernova matter based on the ZM model ()

Table 4. The energy density and pressure of supernova matter based on the ZM model ()

Table 5. The energy density and pressure of supernova matter based on the ZM model ()

© European Southern Observatory (ESO) 1998

Online publication: January 16, 1998
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