  Toy Stars are gas masses where the compressibility is treated without
approximations but gravity is replaced by a force which, for any pair of
masses, is along their line of centres and proportional to their separation.
They provide an invaluable resource for testing the suitability of numerical
codes for astrophysical gas dynamics. In this paper we derive the equations for
both small amplitude oscillations and non linear solutions for rotating and
pulsating Toy Stars in two dimensions, and show that the solutions can be
reduced to a small number of ordinary differential equations. We compare the
accurate solutions of these equations with Smoothed Particle Hydrodynamics
(SPH) simulations. The two dimensional Toy Star solutions are found to provide
an excellent benchmark for SPH algorithms, highlighting many of the strengths
and also some weaknesses of the method.
