Temperature-dependent r-modes in superfluid neutron stars stratified by muons

We calculate the finite-temperature r-mode spectrum of a slowly rotating superfluid Newtonian neutron star neglecting the entrainment between neutron and proton liquid components (i.e., neglecting the off-diagonal element of the entrainment matrix). We show that for `minimal' NS core composition (neutrons, protons, and electrons) only two $m=2$ r-modes exist --- normal mode, which is similar to ordinary r-mode in a nonsuperfluid star, and a superfluid temperature-dependent mode. Accounting for muons in the core dramatically modifies the oscillation spectrum, resulting in an infinite set of superfluid r-modes, whose frequencies vary with temperature. We demonstrate that the normal r-mode can exhibit avoided crossings with superfluid modes at certain `resonance' temperatures, where it dissipates strongly, which leads to substantial suppression of the r-mode instability near these temperatures. The corresponding instability windows are calculated and discussed.