  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.
