  Shock waves are common in astrophysical environments. On many occasions, they
are collisionless, which means they occur in settings where the mean free path
is much larger than the dimensions of the system. For this very reason,
magnetohydrodynamic (MHD) is not equipped to deal with such shocks, be it
because it assumes binary collisions, hence temperature isotropy, when such
isotropy is not guaranteed in the absence of collisions. Here we solve a model
capable of dealing with perpendicular shocks with anisotropic upstream
pressure. The system of MHD conservation equations is closed assuming the
temperature normal to the flow is conserved at the crossing of the shock front.
In the strong shock sonic limit, the behavior of a perpendicular shock with
isotropic upstream is retrieved, regardless of the upstream anisotropy.
Generally speaking, a rich variety of behaviors is found, inaccessible to MHD,
depending on the upstream parameters. The present work can be viewed as the
companion paper of MNRAS 520, 6083-6090 (2023), where the case of a parallel
shock was treated. Differences and similarities with the present case are
discussed.
