  We discuss the appearance of quark matter in neutron star cores', focussing
on the possibility that the recent observation of a very heavy neutron star
could constrain free parameters of quark matter models. For that, we use the
equation of state derived with the Field Correlator Method, extended to the
zero temperature limit, whereas for the hadronic phase we use the equation of
state obtained within both the non-relativistic and the relativistic
Brueckner-Hartree-Fock many-body theory. We find a strong dependence of the
maximum mass both on the value of the q\bar q interaction V_1, and on the gluon
condensate G_2, for which we introduce a dependence on the baryon chemical
potential mu_B. We find that the maximum masses are consistent with the
observational limit for not too small values of V_1.
