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 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.