  The optical excess in the spectra of dim isolated neutron stars (XDINs) is a
significant fraction of their rotational energy loss-rate. This is strikingly
different from the situation in isolated radio pulsars. We investigate this
problem in the framework of the fallback disc model. The optical spectra can be
powered by magnetic stresses on the innermost disc matter, as the energy
dissipated is emitted as blackbody radiation mainly from the inner rim of the
disc. In the fallback disc model, XDINs are the sources evolving in the
propeller phase with similar torque mechanisms. In this this model, the ratio
of the total magnetic work that heats up the inner disc matter is expected to
be similar for different XDINs. Optical luminosities that are calculated
consistently with the the optical spectra and the theoretical constraints on
the inner disc radii give very similar ratios of the optical luminosity to the
rotational energy loss rate for all these sources. These ratios indicate that a
significant fraction of the magnetic torque heats up the disc matter while the
remaining fraction expels disc matter from the system. For XDINs, the
contribution of heating by X-ray irradiation to the optical luminosity is
negligible in comparison with the magnetic heating. The correlation we expect
between the optical luminosities and the rotational energy loss-rates of XDINs
can be a property of the systems with low X-ray luminosities, in particular
those in the propeller phase.
