Probing cool giants in unresolved galaxies using fluctuation
  eigenspectra: a demonstration using high-resolution MUSE observations of NGC
  5128
  I describe and demonstrate a new approach to using spectroscopic data to
exploit Poisson sampling fluctuations in unresolved stellar populations. The
method is introduced using spectra predicted for independent samples of stars
from a 10 Gyr population a using a simple stochastic spectral synthesis model.
A principal components analysis shows that >99 per cent of the spectral
variation in the red-optical can be attributed to just three "fluctuation
eigenspectra", which can be related to the number of giant stars present in
each sample, and their distribution along the isochrone. The first
eigenspectrum effectively encodes the spectrum of the coolest giant branch
stars, and is equivalent to the ratio between high- and low-flux pixels
discussed in previous literature. The second and third eigenspectra carry
higher-order information from which the giant-star spectral sequence can in
principle be reconstructed. I demonstrate the method in practice using
observations of part of NGC 5128, obtained with the MUSE narrow-field adaptive
optics mode. The expected first eigenspectrum is easily recovered from the
data, and closely matches the model results except for small differences around
the Ca II triplet. The second eigenspectrum is below the noise level of the
present observations. A future application of the method would be to the cores
of giant ellipticals to probe the spectra of cool giant stars at high
metallicity and with element abundance patterns not accessible in the Milky
Way.
