Counting Low-Mass Stars in Integrated Light

Low-mass stars (M<0.4Msun) are thought to comprise the bulk of the stellar mass of galaxies but they constitute only of order a percent of the bolometric luminosity of an old stellar population. Directly estimating the number of low-mass stars from integrated flux measurements of old stellar systems is therefore possible but very challenging given the numerous variables that can affect the light at the percent level. Here we present a new population synthesis model created specifically for the purpose of measuring the low-mass initial mass function (IMF) down to ~0.1Msun for metal-rich stellar populations with ages in the range 3-13.5 Gyr. Our fiducial model is based on the synthesis of three separate isochrones and a combination of optical and near-IR empirical stellar libraries in order to produce integrated light spectra over the wavelength interval 0.35mu<lambda<2.4mu at a resolving power of R~2000. New synthetic stellar atmospheres and spectra have been computed in order to model the spectral variations due to changes in individual elemental abundances including C, N, Na, Mg, Si, Ca, Ti, Fe, and generic alpha elements. We demonstrate the power of combining blue spectral features with surface gravity-sensitive near-IR features in order to simultaneously constrain the low-mass IMF, stellar population age, metallicity, and abundance pattern from integrated light measurements. Finally, we show that the shape of the low-mass IMF can also be directly constrained by employing a suite of surface gravity-sensitive spectral features, each of which is most sensitive to a particular mass interval.