  The muonic and electromagnetic components of air showers are sensitive to the
mass of the primary cosmic particle. The sizes of the components can be
measured with particle detectors on ground, and the electromagnetic component
in addition indirectly via its radio emission in the atmosphere. The
electromagnetic particles do not reach the ground for very inclined showers. On
the contrary, the atmosphere is transparent for the radio emission and its
footprint on ground increases with the zenith angle. Therefore, the radio
technique offers a reliable detection over the full range of zenith angles, and
in particular for inclined showers. In this work, the mass sensitivity of a
combination of the radio emission with the muons is investigated in a case
study for the site of the Pierre Auger Observatory using CORSIKA Monte Carlo
simulations of showers in the EeV energy range. It is shown, that the
radio-muon combination features superior mass separation power in particular
for inclined showers, when compared to established mass observables such as a
combination of muons and electrons or the shower maximum Xmax. Accurate
measurements of the energy-dependent mass composition of ultra-high energy
cosmic rays are essential to understand their still unknown origin. Thus, the
combination of muon and radio detectors can enhance the scientific performance
of future air-shower arrays and offers a promising upgrade option for existing
arrays.
