  We present a new set of Surface Brightness Fluctuation spectra computed with
the E-MILES stellar population synthesis models. The model SBF spectra cover
the range 1680-50000 Angstrom at moderately high resolution, all based on
extensive empirical stellar libraries. The models span the metallicity range
-2.3<[M/H<+0.26 for a suite of IMF types with varying slopes. These predictions
can complement and aid fluctuation magnitudes studies, permitting a first order
approximation by applying filter responses to the SBF spectra to obtain
spectroscopic SBF magnitudes. We provide a recipe for obtaining the latter and
discuss their uncertainties and limitations. We compare our spectroscopic SBF
magnitudes to photometric data of a sample of early-type galaxies. We also show
that the SBF spectra can be very useful for constraining relevant stellar
population parameters. We find small (<5%) mass-fractions of extremely
metal-poor components ([M/H]<-1) on the top of the dominant, old and metal-rich
stellar population. These results put stringent constraints on the early stages
of galaxy formation in massive elliptical galaxies. This is remarkable given
the high degree of degeneracy of the standard spectral analysis to such
metal-poor stellar populations in the visible and in the near-IR. The new SBF
models show great potential for exploiting ongoing surveys, particularly those
based on narrow-band filters.
