  Satellites in electronic spectra are pure many-body effects, and their study
has been of increasing interest in both experiment and theory. The presence of
satellites due to plasmon excitations can be understood with simple models of
electron-boson coupling. It is far from obvious how to match such a model to
real spectra, where more than one kind of quasi-particle and of satellite
excitation coexist. Our joint experimental and theoretical study shows that
satellites in the angle-resolved photoemission spectra of the prototype simple
metal aluminum consist of a superposition of dispersing and non-dispersing
features. Both are due to electron-electron interaction, but the non-dispersing
satellites also reflect the thermal motion of the atoms. Moreover, besides
their energy dispersion, we also show and explain a strong shape dispersion of
the satellites. By taking into account these effects, our first principles
calculations using the GW+C approach of many-body perturbation theory reproduce
and explain the experimental spectra to an unprecedented extent.
