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To study the effect of supermassive black holes (SMBHs) on their hostgalaxies it is important to study the hosts when the SMBH is near its peakactivity. A method to investigate the host galaxies of high luminosity quasarsis to obtain optical spectra at positions offset from the nucleus where therelative contribution of the quasar and host are comparable. However, at theseextended radii the galaxy surface brightness is often low (20-22 mag perarcsec$^{2}$) and the resulting spectrum might have such low S/N that ithinders analysis with standard stellar population modeling techniques. Toaddress this problem we have developed a method that can recover galaxy starformation histories (SFHs) from rest frame optical spectra with S/N $\sim$5~\AA$^{-1}$. This method uses the statistical technique diffusion k-means totailor the stellar population modeling basis set. Our diffusion k-means minimalbasis set, composed of 4 broad age bins, is successful in recovering a range ofgalaxy SFHs. Additionally, using an analytic prescription for seeingconditions, we are able to simultaneously model scattered quasar light and theSFH of quasar host galaxies (QHGs). We use synthetic data to compare results ofour novel method with previous techniques. We also present the modeling resultson a previously published QHG and show that galaxy properties recovered from adiffusion k-means basis set are less sensitive to noise added to this quasarhost galaxy spectrum. Our new method has a clear advantage in recoveringinformation from QHGs and could also be applied to the analysis of other lowS/N galaxy spectra such as those typically obtained for high redshift objectsor integral field spectroscopic surveys.

Simple Stellar Population Modeling of Low S/N Galaxy Spectra and Quasar Host Galaxy Applications