Pulsar glitches and superfluid dynamics in neutron stars
AuthorHowitt, George Alec William
AffiliationSchool of Physics
Document TypePhD thesis
Access StatusOpen Access
© 2020 George Alec William Howitt
Glitches are sudden jumps in the spin frequency of pulsars that occur at random times and over several orders of magnitude in size. One popular theory holds that glitches are caused by differential rotation between the neutron star crust and a superfluid component in the interior. This implies that glitches can be used to study the dense nuclear matter inside neutron stars, testing a regime of physics inaccessible to present-day laboratory experiments or other electromagnetic observations. In the vortex avalanche model of pulsar glitches, the angular momentum of the superfluid is determined by the configuration of an array of quantized vortices which pin to impurities in the interior. As the star spins down, individual vortices unpin and move outwards, triggering unpinning in other nearby vortices leading to an avalanche. The angular momentum lost by the vortices as they move outward is transferred to the crust, which causes it to spin up. This thesis tests the superfluid model of pulsar glitches using hydrodynamic simulations of glitch recovery, statistical analysis of astronomical glitch data and N-body point vortex simulations of avalanches in an idealised neutron star model. Following a glitch, pulsars often have a lengthy recovery period of weeks to months, which is a key piece of evidence for the presence of a superfluid phase inside neutron stars. We perform simulations of glitch recovery using a pseudo-spectral Navier-Stokes-like solver. We model a neutron star as a two component superfluid consisting of a viscous proton-electron plasma and an inviscid superfluid neutron condensate in a spherical Couette geometry. The two fluid components are coupled through mutual friction. We prepare the system in a state of differential rotation between the core and the outer crust and examine the response of the outer boundary to glitches induced by instantaneously changing the angular velocity of the boundaries and by recoupling the fluid interior. We find that with strong mutual friction the characteristic glitch recovery time scale decreases by as much as a factor of three. For glitches originating in the fluid, strong mutual friction decreases the maximum spin up by a factor of up to five. These effects may be partially responsible for the diversity of glitch recoveries observed in the pulsar population, which vary from rapid, complete recoveries to slow partial recoveries or step changes in the spin frequency with no observed change in the spin down rate. The strength of mutual friction depends on where in the star a superfluid phase exists, so these results may allow future observations to constrain the star's internal structure. The vortex avalanche model of glitches is similar to other non-equilibrium systems in nature such as sandpiles, earthquakes and solar flares. Such systems are often studied in the paradigm of self-organized criticality (SOC), a hallmark of which is scale invariant size probability density functions (PDFs) and exponential waiting time PDFs. We perform a statistical study of the size and waiting time PDFs for the five most prolific glitching pulsars using the non-parametric kernel density estimator. This work complements previous parametric studies of glitches, which typically fit the PDFs to known distributions such as power laws, Gaussian or log-normal distributions. Two objects, PSR J1740-3015 and the Crab pulsar PSR J0534+2200, appear to have exponential waiting time PDFs and scale-invariant size PDFs over several decades. Two other objects, PSR J0537-6910 and the Vela pulsar PSR J0835-4510 have quasiperiodic size and waiting time PDFs, typical of fast-driven SOC systems. One object, PSR J1341-6220, appears to exhibit hybrid behaviour. We test the ability of the kernel density estimator to resolve multimodality in synthetic data drawn from a composite Gaussian distribution (which is qualitatively similar to the waiting time PDF in J1341-6220), and find that the small number of glitches observed in this object (N = 23) makes confirmation of multimodality in the PDFs difficult. In order to study the non-equilibrium dynamics of the vortex avalanche theory of glitches, it is useful to have an idealised model which can make falsifiable predictions about the properties of glitches, such as PDFs of sizes and waiting times, correlations between these observables, and the dependence of the PDFs on the internal parameters of the model. Previous work with Gross-Pitaevskii simulations has been unable to study systems larger than ~100 vortices, far from the ~10^18 vortices in neutron stars. With such small numbers of vortices, it is impossible to resolve the dynamics over multiple orders of magnitude. We develop a mathematical model for simulating the motion of point vortices in two dimensions under the influence of deceleration, dissipation, and pinning. We describe a numerical solver for this model, which uses an N-body method to compute the vortex velocities and an adaptive time step scheme for time evolution. We present the results of numerical experiments validating the method, including stability of a vortex ring and dissipative formation of an Abrikosov array. We then perform simulations of 1000-5000 vortices with a wide range of values for the strengths of dissipation and pinning, pinning site density and deceleration of the container. Vortex avalanches occur routinely in the N-body simulations, when chains of unpinning events are triggered collectively by vortex-vortex repulsion, consistent with previous, smaller scale studies using the Gross-Pitaevskii equation. The PDFs of the avalanche sizes and waiting times are consistent with both exponential and lognormal distributions. We find weak cross-correlations between glitch sizes and waiting times. These correlations are consistent with astronomical data and meta-models of pulsar glitch activity as a state-dependent Poisson process or a Brownian stress-accumulation process, and inconsistent with another popular alternative, a threshold-triggered stress-release model with a single, global stress reservoir. The spatial distribution of the effective stress within the simulation volume is analysed before and after a glitch.We find that stress is distributed homogeneously throughout the system and remains near the critical threshold both before and after glitches. This implies that there is no 'memory' in the system; glitches do not significantly reduce the global or local stress. This is consistent with the lack of strong cross-and-auto correlations between glitch sizes and waiting times in the simulations and pulsar data.
KeywordsNeutron stars; Pulsars; Pulsar glitches; Statistical mechanics; Hydrodynamics; Numerical methods
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