Abstract Observations of pulsar glitches have the potential to provide constraints on the dynamics of the high density interior of neutron stars. However, to do so, realistic glitch models must be constructed and compared to the data. We take a step towards this goal by testing non-linear models for the mutual friction force, which is responsible for the exchange of angular momentum between the neutron superfluid and the observable normal component in a glitch. In particular, we consider a non-linear dependence of the drag force on the relative velocity between superfluid vortices and the normal component, in which the contributions of both kelvin and phonon excitations are included. This non-linear model produces qualitatively new features, and is able to reproduce the observed bimodal distribution of glitch sizes in the pulsar population. The model also suggests that the differences in size distributions in individual pulsars may be due to the glitches being triggered in regions with different pinning strengths, as stronger pinning leads to higher vortex velocities and a qualitatively different mutual friction coupling with respect to the weak pinning case. Glitches in pulsars that appear to glitch quasi-periodically with similar sizes may thus be due to the same mechanisms as smaller events in pulsars that have no preferred glitch size, but simply originate in stronger pinning regions, possibly in the core of the star.

Models of turbulent flows require the resolution of a vast range of scales, from large eddies to small-scale features directly associated with dissipation. As the required resolution is not within reach of large scale numerical simulations, standard strategies involve a smoothing of the fluid dynamics, either through time averaging or spatial filtering. These strategies raise formal issues in general relativity, where the split between space and time is observer dependent. To make progress, we develop a new covariant framework for filtering/averaging based on the fibration of spacetime associated with fluid elements and the use of Fermi coordinates to facilitate a meaningful local analysis. We derive the resolved equations of motion, demonstrating how "effective" dissipative terms arise because of the coarse-graining, and paying particular attention to the thermodynamical interpretation of the resolved quantities. Finally, as the smoothing of the fluid-dynamics inevitably leads to a closure problem, we propose a new closure scheme inspired by recent progress in the modelling of dissipative relativistic fluids, and crucially, demonstrate the linear stability of the proposed model. I. MOTIVATIONFluid models inevitably involve aspects of averaging-we have to average over a large number of particles in order to describe a fluid system in terms of a small number of macroscopic quantities (in the thermodynamic sense). However, in the simplest settings we do not have to worry (too much) about the actual process of averaging. For example, the transition from particle kinetic theory to fluid model follows intuitively when the momentum distribution develops a well-defined peak. Similarly, the notion of a fluid element enters naturally on scales much larger than the individual particle mean-free paths. However, the story changes when we turn to numerical simulations and problems involving, for example, turbulence. When we consider the problem from a simulation point of view, we have to consider the scale associated with the numerical resolution. This numerical scale tends to be vast compared to (say) the size of a fluid element. For example, in the high-density core of a neutron star we would typically deal with mean-free paths of a fraction of a millimeter while the best current large-scale numerical simulations of neutron-star mergers involve a resolution of order 10 meters [1]. This scale discrepancy has "uncomfortable" implications. In a highly dynamical situation we may not be able to resolve the full range of scales involved. Quite a lot of action can be hidden inside each computational cell. This problem is, of course, not new. It is a well-known fact that motivates the (considerable) effort going into developing large-eddy schemes in computational fluid dynamics (the subject of numerous textbooks, see for example [2][3][4]).The astrophysical significance of the problem is obvious given that many relevant situations involve/require the modelling of hydro(-magnetic) turbulence. Again, the dynamics of neutron stars com...

In order to extract the precise physical information encoded in the gravitational and electromagnetic signals from powerful neutron-star merger events, we need to include as much of the relevant physics as possible in our numerical simulations. This presents a severe challenge, given that many of the involved parameters are poorly constrained. In this paper we focus on the role of nuclear reactions. Combining a theoretical discussion with an analysis connecting to state-ofthe-art simulations, we outline multiple arguments that lead to a reactive system being described in terms of a bulk viscosity. The results demonstrate that in order to properly account for nuclear reactions, future simulations must be able to handle different regimes where rather different assumptions/approximations are appropriate. We also touch upon the link to models based on the large-eddy-strategy required to capture turbulence.

Fully non-linear equations of motion for dissipative general relativistic fluids can be obtained from an action principle involving the explicit use of lower dimensional matter spaces. More traditional strategies for incorporating dissipation-like the famous Müller-Israel-Stewart model-are based on expansions away from equilibrium defined, in part, by the laws of thermodynamics. The goal here is to build a formalism to facilitate comparison of the action-based results with those based on the traditional approach. The first step of the process is to use the action-based approach itself to build self-consistent notions of equilibrium. Next, first-order deviations are developed directly on the matter spaces, which motivates the latter as the natural arena for the underlying thermodynamics. Finally, we identify the dissipation terms of the action-based model with firstorder "thermodynamic" fluxes, on which the traditional models are built. A simple application of a single viscous fluid is considered. The description is developed in a general setting so that the formalism can be used to describe more complicated systems, for which causal and stable modelsare not yet available. Finally, even though our expansions are halted at first order, we sketch out how a causal response can be implemented with telegraph-type equations.

We consider a framework for non-ideal magnetohydrodynamics in general relativity, paying particular attention to the physics involved. The discussion highlights the connection between the microphysics (associated with a given equation of state) and the global dynamics (from the point of view of numerical simulations), and includes a careful consideration of the assumptions that lead to ideal and resistive magnetohydrodynamics. We pay particular attention to the issue of local charge neutrality, which tends to be assumed but appears to be more involved than is generally appreciated. While we do not resolve all the involved issues, we highlight how some of the assumptions and simplifications may be tested by simulations. The final formulation prepares the ground for a new generation of models of relevant astrophysical scenarios.