Phase transition effects on the dynamical stability of hybrid neutron stars

We study radial oscillations of hybrid non-rotating neutron stars composed by a quark matter core and hadronic external layers. At first, we physically deduce the junction conditions that should be imposed between two any phases in these systems when perturbations take place. Then we compute the oscillation spectrum focusing on the effects of slow and rapid phase transitions at the quark-hadron interface. We use a generic MIT bag model for quark matter and a relativistic mean field theory for hadronic matter. In the case of rapid transitions at the interface we find a general relativistic version of the reaction mode which has similar properties as its classical counterpart. We also show that the usual static stability condition $\partial M/\partial \rho_c\geq 0$, where $\rho_c$ is the central density of a star whose total mass is $M$, remains always true for rapid transitions but breaks down in general for slow transitions. In fact, for slow transitions we find that the frequency of the fundamental mode can be a real number (indicating stability) even for some branches of stellar models that verify $\partial M/\partial \rho_c \leq 0$. Thus, when secular instabilities are suppressed, as expected below some critical stellar rotation rate, it would be possible the existence of twin or even triplet stars with the same gravitational mass but different radii, with one of the counterparts having $\partial M/\partial \rho_c \leq 0$. We explore some astrophysical consequences of these results.