Although pulsars are some of the most stable clocks in the Universe, many of them are observed to ‘glitch’, i.e. to suddenly increase their spin frequency  with fractional increases that range from  to . In this paper, we focus on the ‘giant’ glitches, i.e. glitches with fractional increases in the spin rate of the order of , that are observed in a subclass of pulsars including the Vela. We show that giant glitches can be modelled with a two‐fluid hydrodynamical approach. The model is based on the formalism for superfluid neutron stars of Andersson & Comer and on the realistic pinning forces of Grill & Pizzochero. We show that all stages of Vela glitches, from the rise to the post‐glitch relaxation, can be reproduced with a set of physically reasonable parameters and that the sizes and waiting times between giant glitches in other pulsars are also consistent with our model.

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The angular momentum transfer associated with Vela-like glitches has never been calculated directly within a realistic scenario for the storage and release of superfluid vorticity; therefore, the explanation of giant glitches in terms of vortices has not yet been tested against observations. We present the first physically reasonable model, both at the microscopic and macroscopic level (spherical geometry, n = 1 polytropic density profile, densitydependent pinning forces compatible with vortex rigidity), to determine where in the star the vorticity is pinned, how much of it is pinned, and for how long. For standard neutron star parameters (M = 1.4 M , R s = 10 km, Ω =Ω Vela = −10 −10 Hz s −1 ), we find that maximum pinning forces of order f m ≈ 10 15 dyn cm −1 can accumulate ΔL gl ≈ 10 40 erg s of superfluid angular momentum, and release it to the crust at intervals Δt gl ≈ 3 years. This estimate of ΔL gl is one order of magnitude smaller than that implied indirectly by current models for post-glitch recovery, where the core and inner-crust vortices are taken as physically disconnected; yet, it successfully yields the magnitudes observed in recent Vela glitches for both jump parameters, ΔΩ gl and ΔΩ gl , provided one assumes that only a small fraction (<10%) of the total star vorticity is coupled to the crust on the short timescale of a glitch. This is reasonable in our approach, where no layer of normal matter exists between the core and the inner-crust, as indicated by existing microscopic calculation. The new scenario presented here is nonetheless compatible with current post-glitch models.

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