A mathematical description of glitches in neutron stars

Abstract

In a pulsar, there are gaps and difficulties in our knowledge of glitches, mainly because of the absence of information about the physics of the matter of the star. This has motivated several authors to suggest dynamical models that interpret most of the astronomical data. Many predictions are based on the assumption that the inner part is analogous to the structure of matter of superfluids. Here, we illustrate a new mathematical model, partially inspired by the dynamics of superfluid helium. We obtain two evolution equations for the angular velocities (of the crust and of superfluid), which are supported by another evolution equation for the average vortex line length per unit volume. This third equation is more delicate from an analytical perspective and is probably at the origin of glitches. We identify two stationary solutions, corresponding to the straight vortex regime and the turbulent regime.

Turbulent, pinned superfluids in neutron stars and pulsar glitch recoveries

“…We assume that the two parts of LT can be ideally considered as a straight array of pinned vortices, with length per unit volume Ls, and a homogeneous and isotropic tangle with length per unit volume Lr which we will approximate as formed by vortex rings, ignoring in the current analysis higher order contributions to the shape of the turbulent tangle, which is likely to exhibit a high degree of topological complexity (Mesgarnezhad et al 2018). Note also that different forms may be possible for the evolution equations in ( 17) or ( 18), which may lead to a difference dependence on relative velocity in the mutual friction (Andersson et al 2007;Mongiovì et al 2017;Celora et al 2020), and may thus be constrained observationally, as we shall see in the following.…”

“…whether it is rectilinear or a turbulent tangle (Gorter & Mellink 1949;Hall & Vinen 1956;Bekarevich & Khalatnikov 1961). To date very few experiments have dealt with turbulence polarized by rotation (Yarmchuk & Glaberson 1978;Swanson et al 1983;Finne et al 2003), and only a limited number of studies investigate mutual friction for such systems (Andersson et al 2007;Sciacca et al 2008;Jou et al 2011;Mongiovì et al 2017). Neutron star interiors are, however, thought to be exactly in such a polarized turbulent regime (Andersson et al 2007), where differences in velocity between the normal and superfluid components can lead to instabilities (Sidery et al 2008;Glampedakis et al 2009;Andersson et al 2013;Khomenko et al 2019), and are possibly linked to the glitch trigger (Peralta et al 2006;Melatos & Peralta 2007;Mongiovì et al 2017).…”

“…To date very few experiments have dealt with turbulence polarized by rotation (Yarmchuk & Glaberson 1978;Swanson et al 1983;Finne et al 2003), and only a limited number of studies investigate mutual friction for such systems (Andersson et al 2007;Sciacca et al 2008;Jou et al 2011;Mongiovì et al 2017). Neutron star interiors are, however, thought to be exactly in such a polarized turbulent regime (Andersson et al 2007), where differences in velocity between the normal and superfluid components can lead to instabilities (Sidery et al 2008;Glampedakis et al 2009;Andersson et al 2013;Khomenko et al 2019), and are possibly linked to the glitch trigger (Peralta et al 2006;Melatos & Peralta 2007;Mongiovì et al 2017). Furthermore, the neutron star case involves pinning in the bulk of the superfluid, with pinning sites acting as a grid that is continuously passed through the superfluid as the rotational lag develops, and it is well established from the study of terrestrial superfluids that the presence of such irregularities and pinning sites can aid the formation of vortex rings and lower the threshold for the onset of turbulence (Stagg et al 2017).…”

Modelling Pulsar Glitches: The Hydrodynamics of Superfluid Vortex Avalanches in Neutron Stars

“…This is a complex problem, given that the microphysics that governs vortex pinning acts on scales much smaller than the hydrodynamical scale. Attempts have been made in this direction in the context of superfluid turbulence, in which case an additional equation is included to model the evolution of the vortex length (Mongiovì, Russo, & Sciacca 2017). Here, however, we will not derive a full mean-field description of vortex unpinning, but rather focus on how different prescriptions for short-timescale movement of vortices during an avalanche can affect astrophysical observables.…”

“…This is a complex problem, given that the micro-physics that governs vortex pinning acts on scales much smaller than the hydrodynamical scale. Attempts have been made in this direction in the context of superfluid turbulence, in which case an additional equation is included to model the evolution of the vortex length (Mongiovì et al, 2017).…”