  A growing number of solar-like oscillations has been detected in red giant
stars thanks to CoRoT and Kepler space-crafts. The seismic data gathered by
CoRoT on red giant stars allow us to test mode driving theory in physical
conditions different from main-sequence stars. Using a set of 3D hydrodynamical
models representative of the upper layers of sub- and red giant stars, we
computed the acoustic mode energy supply rate (Pmax). Assuming adiabatic
pulsations and using global stellar models that assume that the surface
stratification comes from the 3D hydrodynamical models, we computed the mode
amplitude in terms of surface velocity. This was converted into intensity
fluctuations using either a simplified adiabatic scaling relation or a
non-adiabatic one. From L and M (the luminosity and mass), the energy supply
rate Pmax is found to scale as (L/M)^2.6 for both main-sequence and red giant
stars, extending previous results. The theoretical amplitudes in velocity
under-estimate the Doppler velocity measurements obtained so far from the
ground for red giant stars by about 30%. In terms of intensity, the theoretical
scaling law based on the adiabatic intensity-velocity scaling relation results
in an under-estimation by a factor of about 2.5 with respect to the CoRoT
seismic measurements. On the other hand, using the non-adiabatic
intensity-velocity relation significantly reduces the discrepancy with the
CoRoT data. The theoretical amplitudes remain 40% below, however, the CoRoT
measurements. Our results show that scaling relations of mode amplitudes cannot
be simply extended from main-sequence to red giant stars in terms of intensity
on the basis of adiabatic relations because non-adiabatic effects for red giant
stars are important and cannot be neglected. We discuss possible reasons for
the remaining differences.
