  We model the spin pulse intensity and hardness ratio profiles of the isolated
neutron star RXJ0720.4--3125 using XMM-Newton data. The observed variation is
approximately sinusoidal with a peak-to-peak amplitude of 15%, and the hardness
ratio is softest slightly before flux maximum. By using polar cap models we are
able to derive maximum polar cap sizes and acceptable viewing geometries. The
inferred sizes of the caps turn out to be more compatible with a scenario in
which the neutron star is heated by accretion, and place limits on the magnetic
field strength. The hardness ratio modulation can then be explained in terms of
energy-dependent beaming effects, and this constrains the acceptable models of
the emerging radiation to cases in which softer photons are more strongly
beamed than harder photons. An alternative explanation in terms of spatially
variable absorption co-rotating in the magnetosphere is also discussed.
