We develop a new perturbative framework for studying the r-modes of rotating superfluid neutron stars. Our analysis accounts for the centrifugal deformation of the star, and considers the two-fluid dynamics at linear order in the perturbed velocities. Our main focus is on a simple model system where the total density profile is that of an n = 1 polytrope. We derive a partially analytic solution for the superfluid analogue of the classical r-mode. This solution is used to analyse the relevance of the vortex mediated mutual friction damping, confirming that this dissipation mechanism is unlikely to suppress the gravitational-wave driven instability in rapidly spinning superfluid neutron stars. Our calculation of the superfluid r-modes is significantly simpler than previous approaches, because it decouples the r-mode from all other inertial modes of the system. This leads to the results being clearer, but it also means that we cannot comment on the relevance of potential avoided crossings (and associated "resonances") that may occur for particular parameter values. Our analysis of the mutual friction damping differs from previous studies in two important ways. Firstly, we incorporate realistic pairing gaps which means that the regions of superfluidity in the star's core vary with temperature. Secondly, we allow the mutual friction parameters to take the whole range of permissible values rather than focussing on a particular mechanism. Thus, we consider not only the weak drag regime, but also the strong drag regime where the fluid dynamics is significantly different.

Gravitational waves from core-collapse supernovae are produced by the excitation of different oscillation modes in the proto-neutron star (PNS) and its surroundings, including the shock. In this work we study the relationship between the post-bounce oscillation spectrum of the PNS-shock system and the characteristic frequencies observed in gravitational-wave signals from core-collapse simulations. This is a fundamental first step in order to develop a procedure to infer astrophysical parameters of the PNS formed in core-collapse supernovae. Our method combines information from the oscillation spectrum of the PNS, obtained through linear-perturbation analysis in general relativity of a background physical system, with information from the gravitational-wave spectrum of the corresponding non-linear, core-collapse simulation. Using results from the simulation of the collapse of a 35 M presupernova progenitor we show that both types of spectra are indeed related and we are able to identify the modes of oscillation of the PNS, namely g-modes, p-modes, hybrid modes, and standing-accretion-shock-instability (SASI) modes, obtaining a remarkably close correspondence with the time-frequency distribution of the gravitational-wave modes. The analysis presented in this paper provides a proof-of-concept that asteroseismology is indeed possible in the core-collapse scenario, and it may serve as a basis for future work on PNS parameter inference based on gravitational-wave observations.

We study ambipolar diffusion in strongly magnetised neutron stars, with special focus on the effects of neutrino reaction rates and the impact of a superfluid/superconducting transition in the neutron star core. For axisymmetric magnetic field configurations, we determine the deviation from β−equilibrium induced by the magnetic force and calculate the velocity of the slow, quasi-stationary, ambipolar drift. We study the temperature dependence of the velocity pattern and clearly identify the transition to a predominantly solenoidal flow. For stars without superconducting/superfluid constituents and with a mixed poloidal-toroidal magnetic field of typical magnetar strength, we find that ambipolar diffusion proceeds fast enough to have a significant impact on the magnetic field evolution only at low core temperatures, T 1 − 2 × 10 8 K. The ambipolar diffusion timescale becomes appreciably shorter when fast neutrino reactions are present, because the possibility to balance part of the magnetic force with pressure gradients is reduced. We also find short ambipolar diffusion timescales in the case of superconducting cores for T 10 9 K, due to the reduced interaction between protons and neutrons. In the most favourable scenario, with fast neutrino reactions and superconducting cores, ambipolar diffusion results in advection velocities of several km/kyr. This velocity can substantially reorganize magnetic fields in magnetar cores, in a way that can only be confirmed by dynamical simulations.

Improvements in ground-based, advanced gravitational wave (GW) detectors may allow in the near future to observe the GW signal of a nearby core-collapse supernova. For the most common type of progenitors, likely with slowly rotating cores, the dominant GW emission mechanisms are the post-bounce oscillations of the proto-neutron star (PNS) before the explosion. We present a new procedure to compute the eigenmodes of the system formed by the PNS and the stalled accretion shock in general relativity including spacetime perturbations. The new method improves on previous results by accounting for perturbations of both the lapse function and the conformal factor. We apply our analysis to two numerical core-collapse simulations and show that our improved method is able to obtain eigenfrequencies that accurately match the features observed in the GW signal and to predict the qualitative behaviour of quasi-radial oscillations. Our analysis is possible thanks to a newly developed algorithm to classify the computed eigenmodes in different classes (f-, p-, and g-modes), improving previous results which suffered from misclassification issues. We find that most of the GW energy is stored in the lowest order eigenmodes, in particular in the 2 g 1 mode and in the 2 f mode. Our results also suggest that a low-frequency component of the GW signal attributed in previous works to the characteristic frequency of the Standing Accretion Shock Instability, should be identified as the fundamental quadrupolar f-mode. We also develop a formalism to estimate the contribution of quasi-radial (l = 0) modes to the quadrupolar component of the GW emission in the case of a deformed background, with application to rapidly rotating cores. This work provides further support for asteroseismology of core-collapse supernovae and the inference of PNS properties based on GW observations.

Using time evolutions of the relevant linearized equations, we study non‐axisymmetric oscillations of rapidly rotating and superfluid neutron stars. We consider perturbations of Newtonian axisymmetric background configurations and account for the presence of superfluid components via the standard two‐fluid model. Within the Cowling approximation, we are able to carry out evolutions for uniformly rotating stars up to the mass‐shedding limit. This leads to the first detailed analysis of superfluid neutron star oscillations in the fast rotation regime, where the star is significantly deformed by the centrifugal force. For simplicity, we focus on background models where the two fluids (superfluid neutrons and protons) corotate, are in β‐equilibrium and co‐exist throughout the volume of the star. We construct sequences of rotating stars for two analytical model equations of state. These models represent relatively simple generalizations of single fluid, polytropic stars. We study the effects of entrainment, rotation and symmetry energy on non‐radial oscillations of these models. Our results show that entrainment and symmetry energy can have a significant effect on the rotational splitting of non‐axisymmetric modes. In particular, the symmetry energy modifies the inertial mode frequencies considerably in the regime of fast rotation.