  The magnetic vortex structure, that is present in several nanoscopic systems,
is stable and can be manipulated through the application of a magnetic field or
a spin polarized current. The size and shape of the core are strongly affected
by the anisotropy, however its role on the core behavior has not yet been
clarified. In the present work we investigate the influence of a perpendicular
anisotropy on the annihilation and shape of magnetic vortex cores in permalloy
disks. We have used both micromagnetic simulations with the OOMMF code, and an
analytical model that assumes that the shape of the core does not change during
the hysteresis cycle, known as the rigid core model, to calculate the
annihilation fields. In both cases we found that the annihilation fields
decrease with increasing perpendicular anisotropy for almost all the structures
investigated. The simulations show that for increasing anisotropy or dot
thickness, or both, the vortex core profile changes its shape, becoming
elongated. For every dot thickness, this change does not depend on the dot
radius, but on the relative distance of the core from the center of the dot.
