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(Abridged) We present new theoretical predictions for surface brightnessfluctuations (SBFs) using models optimized for this purpose. Our predictionsagree well with SBF data for globular clusters and elliptical galaxies. Weprovide refined theoretical calibrations and k-corrections needed to use SBFsas standard candles. We suggest that SBF distance measurements can be improvedby using a filter around 1 micron and calibrating I-band SBFs with theintegrated V-K galaxy color. We also show that current SBF data provide usefulconstraints on population synthesis models, and we suggest SBF-based tests forfuture models. The data favor specific choices of evolutionary tracks andspectra in the models among the several choices allowed by comparisons based ononly integrated light. In addition, the tightness of the empirical I-band SBFcalibration suggests that model uncertainties in post-main sequence lifetimesare less than +/-50% and that the IMF in ellipticals is not much steeper thanthat in the solar neighborhood. Finally, we analyze the potential of SBFs forprobing unresolved stellar populations. We find that optical/near-IR SBFs aremuch more sensitive to metallicity than to age. Therefore, SBF magnitudes andcolors are a valuable tool to break the age/metallicity degeneracy. Our initialresults suggest that the most luminous stellar populations of bright clustergalaxies have roughly solar metallicities and about a factor of three spread inage.Comment: Astrophysical Journal, in press (uses Apr 20, 2000 version of  emulateapj5.sty). Reposted version has a minor cosmetic change to Table

Theoretical Predictions for Surface Brightness Fluctuations and Implications for Stellar Populations of Elliptical Galaxies