  An exoplanet-exomoon system presents a superposition of phase curves to
observers - the dominant component varies according to the planetary period,
and the lesser varies according to both the planetary and the lunar period. If
the spectra of the two bodies differs significantly, then it is likely there
are wavelength regimes where the contrast between the moon and planet is
significantly larger. In principle, this effect could be used to isolate
periodic oscillations in the combined phase curve. Being able to detect the
exomoon component would allow a characterisation of the exomoon radius, and
potentially some crude atmospheric data.
  We run a parameter survey of combined exoplanet-exomoon phase curves, which
show that for most sets of planet-moon parameters, the lunar component of the
phase curve is undetectable to current state-of-the-art transit observations.
Even with future transit survey missions, measuring the exomoon signal will
most likely require photometric precision of 10 parts per million or better.
  The only exception to this is if the moon is strongly tidally heated or in
some way self-luminous. In this case, measurements of the phase curve at
wavelengths greater than a few microns can be dominated by the lunar
contribution. Instruments like the James Webb Space Telescope and its
successors are needed to make this method feasible.
