– 1 –1. Galaxy Integrated Light Models1.1. Models of Integrated Light of GalaxiesModels of galactic evolution including chemical evolution can be used to predict thecontinuous spectrum and absorption lines fr om the stellar population, and emission linesfrom the gaseous ISM a s a function of a ssumed star formation history, IMF, age, and,with less importance (at least for massive galaxies), the time dependence of mass loss viagalactic winds. Inputs also include evolutionary tracks (function of stellar mass, age, andmetallicity, as well as mass loss history), nucleosynthesis yields (ranging from just studyingsome total metallicity to following each element individually). See the earlier discussion ofchemical evolution models, both analytical and numerical, as well as the semi-analyticalmodels which combine these factors with a cosmological hierarchical formation scenario.The earliest models assumed a single age, single metallicity population. Broad bandcolors were the first things attempted as they were easiest to calculate. Only isochronesand a transformation fr om Teff, log(g), and metallicity to colors was needed. Thetransformations were usually validated using globular cluster stars, as these clusters usuallyhave constant [Fe/H] and age. These models were applied to GCs and t o elliptical g alaxies.A key early paper was Aaronson, Cohen, Mould & Malkan (1978, apj, 223, 824).The major arguements with early models were how to include the post-He flash stagesof stellar evolution which are generally not included in most isochrones. They were added byhand, matched to observations of Gala ctic AGB and HBs. Another problem was the limitedrange of [Fe/H] for the Galactic GCs. Calibration at solar and super-solar metallicity isvery difficult as the well studied GCs have [Fe/H] < −0.6 dex; only those buried in theGalactic bulge, with severe reddening and membership problems, have higher metallicity.These issues a re still of concern if one is interested in relatively new spectral regions which– 2 –have not yet been fully explored.The desire to examine galaxies in more detail, but still without the necessity forhigh S/N high quality spectra, led to the definition of systems o f relatively narrow-bandindice (FWHM ∼ 30 to 100˚A), the most popular of which a re known as the Lick indices.There are about 20 defined indices arising from features between 4000 and 6000˚A of(predominantly) Fe, Mg, CN, CH, and Balmer lines. The key metallicity index is Mgb,measuring the strength of the Mg triplet at 5170˚A. This is among the strongest features inthe optical spectrum longer tha n 4000˚A for late type stars, the others being the G band ofCH at 4300˚A a nd a few Fe I lines.The first attempts were in papers by Faber and Trager, with early good calibrationefforts by Guy Worthey (1994, AJ, 1 28, 2826), and see earlier references from that paper.The Lick indices were a series o f bandpasses centered on the obvious strong absorptionfeatures with adjacent “continuum” bandpasses, and so in effect represent an equivalentwidth f or strong absorption features. This system has a relatively good and reproduciblecalibration, and was used extensively by Faber and her grad students, and hence becamepopular. The indices are calibrated to a set of standard stars defined in the early papers.The metallicity dependence was originally calibrated using “response functions” in lieu offull spectral syntheses. Problems arise because the original calibration was with respect toobservations made with a particular spectrograph in use a t the Lick 3-m telescope, andbecause the calibration stars do not span the full ra ng e of stellar parameters that one mightneed to construct the integrated light.When used for galaxies, corrections as a function of velocity dispersion are required,because a higher σvsmoothes out the spectrum, reducing the apparent strength of aspectral feature. These are calculated empirically from observations of stars.The basic concept is to try to find single indices or combinations of a small number– 3 –of indices that are sensitive to one of the desired parameters (the age or metallicitychara cteristic of a stellar population) with minimal sensitivity to the ot her parameters. Ofcourse in real life there are a lot of degeneracies, and determining a unique solution givenless than perfect data...The next improvement was to add the α/Fe ratio, again a mean for the population.Since there are Lick indices which are primarily dominated by features of Fe and tho seresponding primarily to Mg, which is an α element, some combination of indices should dothis. These were initially calibrated using GC stars and some old calculations by Thomas,Maraston & Bender (2003, MNRAS, 343, 379 ) and independently by Lee & Worthy (2 005,ApJS, 160, 176). But a problem was that the calibration stars do no t uniformly cover therange of α/Fe over the full range o f stellar parameters. A better calibration using modelatmospheres and spectral synthesis by Korn, Thomas & Maraston (2005, A&A, 438, 685)followed. These models were applied to refine the ages of elliptical ga la xies deduced fromthe Lick indices by Thomas & Maraston (2003, A&A, 401, 429 ). The metallicities are notaffected much by considering α/Fe as well, but t he ages for galaxies and globular clustersusing some α-enhanced models reached as high as 15 Gyr. The problem appears to lie inthe isochrones adopted for the calculations.The Balmer lines, which have the strongest age sensitivity, are tricky. It was at thattime quite hard to get them right (i.e. the atomic physics that went int o calculating the lineprofile was not fully developed) as discussed by Thomas, Maraston & Korn (2004, MNRAS,351, L19). Even today they still give problems; Poo le, Worthey, Lee & Serven (2010,AJ2010, arXiv:0905.24 07) discuss the Hβ anonomaly (Hβ is predicted too weak comparedto the observations, which leads to deduced ages come higher than 15 Gyr for many GCs.They suggest it is not the horizontal branch nor blue strag lers (both of which are oftensuggested as culprits, as they might contribute extra hot flux in the blue which may not be– 4 –included appropriately in the models), but rather flar ing M giants which fill in Hβ.Lee, Wo rt hey, Dotter et al (2009, ApJ, 694, 902 ) carried this type o f exercise to an(unnecessary) extreme, evaluating the sensitivity of the standard Lick indices to variationsin the abundance of many elements, adjusting one