MAXIMUM QUARK CORE IN A NEUTRON-STAR FOR REALISTIC EQUATIONS OF STATE

For recently developed realistic equations of state (Wiringa, Fiks, & Fabrocini 1988), we establish conditions which the quark matter equati on of state should satisfy in order to produce as big a quark core as possible inside neutron stars. We impose constraints that (1) the phas e transition to quark matter occurs above nuclear saturation density a nd (2) the maximum neutron star mass exceeds 1.55 M.. The quark phase is described phenomenologically by a two-parameter bag model equation of state. The maximum quark core is found for such values of the param eters which admit a continuous phase transition to quark matter. Its s ize is determined by the transition density which is as yet unknown. T he maximum neutron star mass depends only weakly on the transition den sity but is sensitive to the parameter determining the density depende nce of the bag model equation of state. The observational lower limit of 1.55 M. for the maximum neutron star mass severely limits allowed v alues of this parameter. We find the parameters of the quark equation of state which correspond to the largest quark core inside a neutron s tar to be compatible with predictions of quark matter models consisten t with empirical hadronic data.