5 while it has been shown in [26] that the Maxwell descrip- tion of the mixed phase gives a good description if the surface tension is very large. EOS of the quark phase constructed with standard NJL model does not cross the EOS of the hadronic phase on the chemical potential range shown. The inclusion of a cutoff dependent on the chemical potential in the NJL model influences the deconfinement phase transition and, consequently, the stability of the star, as we will show in the next section. For the hadronic sector we use a EOS proposed by Glendenning and Moszkowsky (GM1) [27] with the in- clusion of the baryonic octet. In order to fix the hyperon coupling constants we have used one of choices discussed in literature [1, 27], namely we took for all the hyper- ons the same coupling constants which are a fraction x$_{i}$ of the meson-nucleon coupling constants, x$_{σ}$ = 0 . 7, x$_{ω}$ = 0 . 783 = x$_{ρ}$ . For low densities (near zero density) we use the Baym, Pethick and Sutherland (BPS) model [28]. The standard and the modified su(3) NJL models are used to describe quark matter phase. In Fig. 6 we plot the pressure as a function of the baryonic density for the complete EOS discussed above. The plateaus, identified with an M, represent the deconfinement phase transition as a consequence of the first order Maxwell construction. In the case of cutoff Λ$_{1}$ and lower values of µ$_{0}$ the transition from hadron to quark phase occurs at lower values of the pressure and the plateau decreases. The same situation occurs with cutoff the Λ$_{2}$. The presence of strangeness in the core and crust of the star can have an important influence in the stability of the star [29, 30]. We have calculated the strangeness content of the EOS for the different parametrizations of the cutoff. In Fig. 7 we plot the strangeness fraction given by for the quark phase and In this section we investigate the properties of stars constructed using the modified su(3) NJL model. The Maxwell construction [24] is considered for the phase transition from the hadronic phase to the quark phase. In this case the phase transition is identified by the crossing point between the hadronic and the quark EOS in the pressure versus baryonic chemical potential plane. At lower densities (below the transition point) an hadronic phase is favored and at higher densities (above the tran- sition chemical potential) quark matter is favored. However, we should point out that the Maxwell con- struction is an approximation for which only baryon num- ber conservation is considered and does not take correctly into account the existence of two charge conserving con- ditions, nor surface effects and the Coulomb field [25, 26]. Instead, we could have considered a Gibbs construction [1], which takes into account the existence of two charge conserving conditions. However, a complete treatment of the mixed phase requires the knowledge of the surface tension between the two phases which is not well estab- lished and may have a value between 10-100 MeV/fm 2 [26]. The Gibbs construction gives results close to the ones obtained with the lower value of the above surface tension range, and is recovered for a zero surface tension, FIG. 6: EOS of hybrid stellar matter: Maxwell construction for a first order phase transition. Pressure as a function of the baryon density for different parametrizations of the cutoff. The hadronic, mixed and quark phases are identified respec- tively with a H, M and Q label. FIG. 5: Pressure as a function of the chemical potential for quark stellar matter in β -equilibrium with different choices of the cutoff and standard NJL model. The hadronic EOS, GM1 with hyperons [27], is also included (dotted curve). III. THE NEUTRON STAR STABILITY r Q$_{S}$ s = ρ$_{s}$ 3 ρ , r Q$_{S}$ s = ∑ B | q B s | ρ$_{B}$ 3 ρ , 0 2 4 6 8 10 50 100 150 200 250 300 350 / 0 P (MeV.fm −3 ) GM1 with hyp. + BPS $_{1}$( $_{0}$ = 400 MeV) $_{1}$( $_{0}$ = 350 MeV) $_{2}$( $_{0}$ = 400 MeV) $_{2}$( $_{0}$ = 350 MeV) M H Q 350 400 450 500 0 100 200 300 400 500  (MeV) P (MeV.fm −3 ) NJL $_{1}$( $_{0}$ = 400 MeV) $_{1}$( $_{0}$ = 350 MeV) $_{2}$( $_{0}$ = 400 MeV) $_{2}$( $_{0}$ = 350 MeV) GM1 with hyperons