  The emission measure distribution in the upper transition region and corona
of Epsilon Eri is derived from observed emission line fluxes. Theoretical
emission measure distributions are calculated assuming that the radiation
losses are balanced by the net conductive flux. We discuss how the area factor
of the emitting regions as a function of temperature can be derived from a
comparison between these emission measure distributions. It is found that the
filling factor varies from ~0.2 in the mid transition region to ~1.0 in the
inner corona. The sensitivity of these results to the adopted ion fractions,
the iron abundance and other parameters is discussed. The area factors found
are qualitatively similar to the observed structure of the solar atmosphere,
and can be used to constrain two-component models of the chromosphere. Given
further observations, the method could be applied to investigate the trends in
filling factors with indicators of stellar activity.
