  Force-free neutron star magnetospheres are nowadays well known and found
through numerical simulations. Even extension to general relativity has
recently been achieved. However, those solutions are by definition
dissipationless, meaning that the star is unable to accelerate particles and
let them radiate any photon. Interestingly, the force-free model has no free
parameter however it must be superseded by a dissipative mechanism within the
plasma. In this paper, we investigate the magnetosphere electrodynamics for
particles moving in the radiation reaction regime, using the limit where
acceleration is fully balanced by radiation, also called Aristotelian dynamics.
An Ohm's law is derived, from which the dissipation rate is controlled by a one
parameter family of solutions depending on the pair multiplicity~$\kappa$. The
spatial extension of the dissipation zone is found self-consistently from the
simulations. We show that the radiative magnetosphere of an aligned rotator
tends to the force-free regime whenever the pair multiplicity becomes
moderately large, $\kappa \gg 1$. However, for low multiplicity, a substantial
fraction of the spindown energy goes into particle acceleration and radiation
in addition to the Poynting flux, the latter remaining only dominant for large
multiplicities. We show that the work done on the plasma occurs predominantly
in the equatorial current sheet right outside the light-cylinder.
