The crust of a neutron star is thought to be comprised of a lattice of nuclei immersed in a sea of free electrons and neutrons. As the neutrons are superfluid their angular momentum is carried by an array of quantized vortices. These vortices can pin to the nuclear lattice and prevent the neutron superfluid from spinning down, allowing it to store angular momentum which can then be released catastrophically, giving rise to a pulsar glitch. A crucial ingredient for this model is the maximum pinning force that the lattice can exert on the vortices, as this allows us to estimate the angular momentum that can be exchanged during a glitch. In this paper we perform, for the first time, a detailed and quantitative calculation of the pinning force per unit length acting on a vortex immersed in the crust and resulting from the mesoscopic vortexlattice interaction. We consider realistic vortex tensions, allow for displacement of the nuclei and average over all possible orientation of the crystal with respect to the vortex. We find that, as expected, the mesoscopic pinning force becomes weaker for longer vortices and is generally much smaller than previous estimates, based on vortices aligned with the crystal. Nevertheless the forces we obtain still have maximum values of order f pin ≈ 10 15 dyn/cm, which would still allow for enough angular momentum to be stored in the crust to explain large Vela glitches, if part of the star is decoupled during the event.

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Many pulsars are observed to ‘glitch’, i.e. show sudden jumps in their rotational frequency ν, some of which can be as large as Δν/ν ≈ 10−6–10−5 in a subset of pulsars known as giant glitchers. Recently, Pizzochero has shown that an analytic model based on realistic values for the pinning forces in the crust and for the angular momentum transfer in the star can describe the average properties of giant glitches, such as the inter‐glitch waiting time, the step in frequency and that in frequency derivative. In this paper, we extend the model (originally developed in Newtonian gravity and for a polytropic equation of state) to realistic backgrounds obtained by integrating the relativistic equations of stellar structure and using physically motivated equations of state to describe matter in the neutron star. We find that this more detailed treatment still reproduces the main features of giant glitches in the Vela pulsar and allows us to set constraints on the equation of state. In particular, we find that stiffer equations of state are favoured and that it is unlikely that the Vela pulsar has a high mass (larger than M ≈ 1.5 M⊙).

The high density interior of a neutron star is expected to contain superconducting protons and superfluid neutrons. Theoretical estimates suggest that the protons will form a type II superconductor in which the stellar magnetic field is carried by flux tubes. The strong interaction between the flux tubes and the neutron rotational vortices could lead to strong 'pinning', i.e. vortex motion could be impeded. This has important implications especially for pulsar glitch models as it would lead to a large part of the vorticity of the star being decoupled from the 'normal' component, to which the electromagnetic emission is locked. In this paper we explore the consequences of strong pinning in the core on the 'snowplow' model for pulsar glitches (Pizzochero 2011), making use of realistic equations of state and relativistic background models for the neutron star. We find that in general a large fraction of pinned vorticity in the core is not compatible with observations of giant glitches in the Vela pulsar. The conclusion is thus that either most of the core is in a type I superconducting state or that the interaction between vortices and flux tubes is weaker than previously assumed.