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

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. 1 Following Gusakov et al. (2014a), by the normal r-modes of a superfluid NS we mean the modes which, at a given temperature, have properties similar to ordinary r-modes in the non-superfluid NSs. They correspond to co-motion of superfluid and normal liquid components, and their eigenfrequencies do not depend on temperature. Normal r-modes are most unstable. By superfluid inertial modes we understand inertial modes which show superfluid-like behaviour at a given temperature. The oscillations of such modes are mostly counter-moving, baryon current is almost zero, their eigenfrequencies depend on temperature. These modes have no analogue in nonsuperfluid NSs. Note that, with temperature variation, a given mode can switch from a 'superfluid' regime to 'normal' regime and vice versa, experiencing avoided-crossings with neighbouring modes.

Temperature-dependent oscillation modes in rotating superfluid neutron stars

“…One may expect to find avoided crossings of r o -mode with another inertial modes under more realistic assumptions about the NS composition, and/or for modes with larger l0. In the future work we are going to calculate the spectrum using realistic critical temperature profiles and accounting for muons, which play very important role in defining oscillation spectrum (Kantor & Gusakov 2017).…”

“…For the uniform density stars all coefficients with l > l0 are strictly zero (Lockitch & Friedman 1999). For a given m, there are two nodeless modes with l0 −|m| = 1: the purely toroidal normal r-mode with σ0 = 2/(m+1), and the superfluid r-mode, which, in the limit Ynp = 0, is also purely toroidal and has the same frequency (Andersson & Comer 2001;Lee & Yoshida 2003;Andersson et al 2009;Kantor & Gusakov 2017). For a given m and l0 > |m| + 1 there are l0 − |m| normal inertial modes (i o -modes) and l0 − |m| superfluid inertial modes (i s -modes).…”

“…Lindblom & Mendell 2000;Prix et al 2002;Lee & Yoshida 2003;Andersson et al 2009) the inertial modes are studied only in zero-temperature limit, when all neutrons and protons are assumed to be in a superfluid state. Kantor & Gusakov (2017) considered normal and superfluid r-modes, incorporating finite-temperature effects and stratification by muons (µ), and subsequently found avoided crossings between normal and superfluid r-modes in the next-to-leading order in stellar rotation frequency. This work ignored the entrainment between superfluid neutrons and protons, which significantly affects the spectrum of superfluid inertial modes (see, e.g.…”

“…Lee & Yoshida 2003). Also Kantor & Gusakov (2017) focused only on r-modes and have not studied other inertial modes, which also can interact with the normal r-mode. To fill this gap, we calculate the spectrum of inertial modes in superfluid NSs whose cores consist of neutrons (n), protons (p) and electrons (e), accounting for both entrainment and finite-temperature effects.…”

How to search for gravitational waves from r -modes of known pulsars

“…support this idea. A similar issue arises with the coupling between the r-modes and the buoyant force responsible for g-modes [30]. In either case, in the vicinity of the other mode's frequency the avoided crossing introduces large errors into the simple r-mode frequency dependence posited in Eq.…”