Simple stellar population modelling of low S/N galaxy spectra and quasar host galaxy applications

To study the effect of supermassive black holes (SMBHs) on their host galaxies it is important to study the hosts when the SMBH is near its peak activity. A method to investigate the host galaxies of high luminosity quasars is to obtain optical spectra at positions offset from the nucleus where the relative contribution of the quasar and host is comparable. However, at these extended radii the galaxy surface brightness is often low (20–22 mag arcsec−2) and the resulting spectrum might have such low signal-to-noise ratio (S/N) that it hinders analysis with standard stellar population modelling techniques. To address this problem, we have developed a method that can recover galaxy star formation histories (SFHs) from rest-frame optical spectra with S/N ∼ 5 Å−1. This method uses the statistical technique diffusion k-means to tailor the stellar population modelling basis set. Our diffusion k-means minimal basis set, composed of four broad age bins, is successful in recovering a range of galaxy SFHs. Additionally, using an analytic prescription for seeing conditions, we are able to simultaneously model scattered quasar light and the SFH of quasar host galaxies (QHGs). We use synthetic data to compare results of our novel method with previous techniques. We also present the modelling results on a previously published QHG and show that galaxy properties recovered from a diffusion k-means basis set are less sensitive to noise added to this QHG spectrum. Our new method has a clear advantage in recovering information from QHGs and could also be applied to the analysis of other low S/N galaxy spectra such as those typically obtained for high redshift objects or integral field spectroscopic surveys.