  Of a total of 177 cool G, K, and M giants and supergiants, we measured the Mg
II h+k line emission of extended chromospheres in high-resolution (LWR) IUE
spectra by using the IUE final data archive at STScI, and derived the
respective stellar surface fluxes. They represent the chromospheric radiative
energy losses presumably related to basal heating by the dissipation of
acoustic waves, plus a highly variable contribution due to magnetic activity.
Thanks to the large sample size, we find a very well defined lower limit, the
basal chromospheric Mg II h+k line flux of cool giant chromospheres, as a
function of T_eff. A total of 16 giants were observed several times, over a
period of up to 20 years. Their respective minimal Mg II h+k line fluxes
confirm the basal flux limit very well because none of their emissions dip
beneath the empirically deduced basal flux line representative for the overall
sample. Based on a total of 15 to 22 objects with very low Mg II h+k emission,
we find as limit: log F_Mg_h+k = 7.33 log T_eff - 21.75 (cgs units; based on
B-V). Within its uncertainties, this is almost the same relation as has been
found in the past for the geometrically much thinner chromospheres of main
sequence stars. Concerning any residual dependence of the basal flux on the
surface gravity it can be stated that over a gravity range of more than four
orders of magnitude (main-sequence stars to supergiants), the basal flux does
not appear to vary by more than a factor of 2. These findings are in good
agreement with the predictions by previous hydrodynamic models of acoustic wave
propagation and energy dissipation, as well as with earlier empirical
determinations. Finally, we discuss the idea that the ample energy flux of the
chromospheric acoustic waves in a cool giant may yield, as a by-product, the
energy flux required by its cool wind (i.e., non-dust-driven, "Reimers-type"
mass-loss).
