Surface brightness fluctuation spectrum: a new probe of evolved stars in unresolved stellar populations

The surface brightness fluctuation (SBF) method measures spatial fluctuations due to the most luminous stars in a galaxy. Besides being useful for distance measurements, it also provides diagnostic power to investigate the contribution of the brightest stars to the underlying unresolved stellar population. We apply the SBF technique to every wavelength layer in integral field spectroscopy data obtained with the MUSE instrument. This yields the first SBF spectrum of a galaxy. SBF spectra combine the sensitivity of SBF to luminous stars with the physical information content of spectra. We show that the SBF spectrum of the S0 galaxy NGC 5102 is dominated by spectra of M-type giants (red giant branch, asymptotic giant branch, and red supergiant stars). We build the first stellar population synthesis tool that predicts SBF spectra. Through comparison of integrated spectra from our new tool with published model spectra, we confirm that it is mathematically correct. We use the integrated spectrum and a bootstrap method to derive an ensemble of (degenerate) star formation histories of NGC 5102. We compute a model SBF spectrum for each star formation history. Given that some models do not reproduce the observed SBF spectrum well, we are able to obtain additional constraints on the star formation history, leading to marginally reduced uncertainties on the mean age and metallicity. This result is confirmed by modelling mock spectra with different star formation histories