  We investigate the properties of anisotropic, spherically symmetric compact
stars, especially neutron stars and strange quark stars, made of strongly
magnetized matter. The neutron stars are described by SLy equation of state,
the strange quark stars by an equation of state based on the MIT Bag model. The
stellar models are based on an a priori assumed density dependence of the
magnetic field and thus anisotropy. Our study shows that not only the presence
of a strong magnetic field and anisotropy, but also the orientation of the
magnetic field itself, have an important influence on the physical properties
of stars. Two possible magnetic field orientations are considered, a radial
orientation, where the local magnetic fields point in the radial direction, and
a transverse orientation, where the local magnetic fields are perpendicular to
the radial direction. Interestingly, we find that for a transverse orientation
of the magnetic field, the stars become more massive with increasing anisotropy
and magnetic field strength and increase in size, since the repulsive,
effective anisotropic force increases in this case. In the case of a radially
orientated magnetic field, however, the masses and radii of the stars decrease
with increasing magnetic field strength, because of the decreasing effective
anisotropic force. Importantly, we also show that in order to achieve
hydrostatic equilibrium configurations of magnetized matter, it is essential to
account for both the local anisotropy effects as well as the anisotropy effects
caused by a strong magnetic field. Otherwise, hydrostatic equilibrium is not
achieved for magnetized stellar models.
