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

## TL;DR

This paper investigates how superfluidity and muons in neutron star cores influence the spectrum and stability of r-modes, revealing temperature-dependent mode interactions and potential suppression of instabilities.

## Contribution

It introduces a detailed calculation of temperature-dependent superfluid r-modes in neutron stars with muons, highlighting the impact of muons on the mode spectrum and stability.

## Key findings

- Existence of two main r-modes in minimal NS cores: normal and superfluid.
- Muons cause an infinite set of superfluid r-modes with temperature-dependent frequencies.
- Normal r-mode can strongly dissipate at resonance temperatures, suppressing instabilities.

## Abstract

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.