Universality in oscillation modes of superfluid neutron stars?

It has been well established that the f -mode of relativistic ordinary-fluid neutron stars displays a universal scaling behavior. Here we study whether the “ordinary” foand “superfluid” fs-modes of superfluid neutron stars also show similar universal behavior. We first consider a simple case where the neutron superfluid and normal fluid are decoupled, and with each fluid modeled by a polytropic equation of state. We find that the fo-mode obeys the same scaling laws as established for the f -mode of orindary-fluid stars. However, the oscillation frequency of the fs-mode obeys a different scaling law, which can be derived analytically from a homogenous two-fluid stellar model in Newtonian gravity. Next the coupling effect between the two fluids is studied via a parameterized model of entrainment. We find that the coupling in general breaks the universal behavior seen in the case of decoupled fluids. Based on a relativistic variational principle, an approximated expression is derived for the first-order shift of the fs-mode squared frequency due to the entrainment. Subject headings: dense matter—equation of state—gravitational waves—stars: neutron—stars: oscillations