  Ghostly stellar haloes are extended haloes of stars composed solely of debris
of pre-reionization fossil galaxies and should exist in dwarf galaxies with
total masses $<10^{10}$ M$_\odot$. Fossil galaxies are even smaller mass dwarf
galaxies that stopped forming stars after the epoch of reionization and have
been identified in the Local Group as the ultra-faint dwarf satellites. Using
cosmological N-body simulations we present an empirical model for the shapes
and masses of ghostly stellar haloes. We compare the model to available
observations of stellar haloes in six isolated dwarf galaxies in the Local
Group (Leo T, Leo A, IC 10, WLM, IC 1613, NGC 6822) to infer the star formation
efficiency in dwarf galaxies at the epoch of reionization. We find an
efficiency of star formation in dark matter haloes with masses $10^6 - 10^8$
M$_\odot$ at $z\sim7$ in rough agreement with independent methods using data on
the luminosity function of ultra-faint dwarf galaxies but systematically higher
by a factor of 3-5. The systematic uncertainty of our results is still large,
mainly because available observations of stellar halo profiles do not extend
over a sufficiently large distance from the center of the host dwarf galaxy.
Additional observations, easily within reach of current telescopes, can
significantly improve the accuracy of this method and can also be used to
constrain the present day dark matter masses of dwarf galaxies in the Local
Group. Our method is based on a set of observations never used before, hence it
is a new independent test of models of hierarchical galaxy formation.
