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The µ$_{0}$ range with a stable quark core changes depend- ing on the parameters used to Λ$_{2}$. In Fig. (9) are shown the different configurations for the different values of µ$_{0}$ in the case of Λ$_{2}$ with a = 0 . 17. The value of maxi- mum mass decreases if µ$_{0}$ increases. We have plotted the mass of the maximum mass configuration as a func- tion µ$_{0}$ in Fig. 10. The limit of stability corresponds to the minimum in this plot. In Fig. 11 the different star configurations for different values of a and the same µ$_{0}$ = 347 MeV, are shown. We conclude that increasing a decreases the mass of the maximum mass configuration and the corresponding radius, because the EOS becomes softer. 

It is seen from Table II that a smaller parameter µ$_{0}$ and a harder cutoff Λ gives rise to a smaller maximum mass. The occurrence of a quark core reduces a lot the maximum mass but we can still get a reasonable value, ∼ 1 . 45 M$_{⊙}$ , which is consistent with the observed maximum neutron star masses, except for the still not confirmed, highly massive compact stars, the millisec- ond pulsars PSR B1516 + 02B [34], and PSR J1748- 2021B [35] with masses well above 2 M$_{⊙}$ . 

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Fig. 12 shows the u and s quark condensates as a func- tion of the chemical potential for both cutoff parametriza- tions. For the cutoff Λ$_{1}$ the module of the condensates starts to increase for µ ≳ 475 MeV. This is not the case Λ$_{2}$: the module of the condensates decreases with den- sity leading the system to chiral symmetry restauration. Therefore, the cutoff proposed in this work is physically favored to cutoff Λ$_{1}$. We believe the behavior of Λ$_{1}$ at high densities is due to the high value of the cutoff Λ$_{1}$ at these densities. 

We have studied the possibility of formation of sta- ble compact stars with a quark core within the su(3) NJL model with a chemical potential dependent ultra- violet cutoff. We use a su(3) NJL model parametriza- tion which describes the vacuum properties of low mass mesons (pions and kaons) and choose the parametriza- tion of the cutoff so that it increases with density. One 

## IV. SUMMARY 

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of the consequences of increasing the cutoff is a faster decrease the constituent s quark mass with density and, therefore, the onset of s quark at lower densities, giving rise to a larger pressure for the same chemical potential. The phase transition to a deconfined quark phase occurs at smaller densities and pressures and the density dis- continuity at the phase transition is smaller. For cutoff Λ$_{2}$ ( a = 0 . 17), stars with a quark core are obtained for a choice of the parameter µ$_{0}$ < 360 MeV. The maximum mass of these stars is between (1.46-1.51) M$_{⊙}$ , and is compatible with most of the compact star observations. However, the highly massive stars PSR B1516 + 02B [34], and PSR J1748-2021B [35], in case they are confirmed, would not reproduced. 

According to Baldo et al the instability of compact stars within the NJL model is probably due to the lack 

