Radial Modes of Neutron Stars with a Quark Core

We make a first calculation of eigenfrequencies of radial pulsations of neutron stars with quark cores in a general relativistic formalism given by Chandrasekhar. The equations of state (EOS) used to estimate such eigenfrequencies have been derived by taking proper care of the hadron-quark phase transition. The hadronic EOS’s have been obtained in the framework of the Brueckner-Hartree-Fock and relativistic mean field theories, whereas the quark EOS has been derived within the MIT bag model. We find that the periods of oscillations of neutron stars with a quark core show a kink, which is associated with the presence of a mixed phase region. Also, oscillation periods show significant differences between ordinary neutron stars and neutron stars with dynamical quark phases. Subject headings: dense matter — equation of state — stars: neutron — stars: oscillations Nuclear matter at sufficiently high density and temperature is expected to undergo a phase transition to a quark-gluon plasma. The indirect evidences from heavy-ion experiments at CERN (Heinz 2000; Heinz & Jacobs 2000) and more recently at RHIC (Blaizot 2001) assume to confirm the formation of a quark-gluon plasma. Such a phase transition might occur inside neutron stars, because these are cold and very compact astrophysical objects. It is therefore very interesting to study the effects of possible phase transitions in neutron stars observable like maximum gravitational masses, radii, oscillation frequencies, etc. In the present letter, we analyze the consequences of a hadron-quark phase transition on the periods of radial oscillations in neutron stars. In fact, more than three decades ago, Cameron (1965) made a suggestion that vibration of neutron stars could excite motions that can have interesting astrophysical implications. There are several investigations of vibrating neutron stars and the simple dimensional analysis suggest that the period of fundamental mode would be the order of milliseconds. More than two decades later, Cutler et al. (1990) concluded that neutron stars of about one solar mass and radius about 10 km give periods (3– 5) ms, and these turned out to be relatively insensitive to the exact value of central density.