  We introduce a new method to determine the relative contributions of
different types of stars to the integrated light of nearby early-type galaxies.
As is well known, the surface brightness of these galaxies shows pixel-to-pixel
fluctuations due to Poisson variations in the number of giant stars.
Differential spectroscopy of pixels as a function of fluctuation strength
("fluctuation spectroscopy") effectively measures the spectral variation of
stars as a function of their luminosity, information that is otherwise
difficult to obtain for individual stars outside of the Local Group. We apply
this technique to the elliptical galaxy NGC 4472, using HST/ACS imaging in six
narrow-band ramp filters tuned to spectral features in the range 0.8-1.0
micron. Pixels with +- 5% broad-band variations show differential color
variations of 0.1% - 1.0% in the narrow-band filters. These variations are
primarily due to the systematic increase in TiO absorption strength with
increasing luminosity on the upper giant branch. The data are very well
reproduced by the same Conroy & van Dokkum (2012) stellar population synthesis
model that is the best fit to the integrated light, with residuals in the range
0.03% - 0.09%. Models with ages or metallicities that are significantly
different from the integrated-light values do not yield good fits. We can also
rule out several modifications to the underlying model, including the presence
of a significant (>3% of the light) population of late M giants. The current
observations constitute a powerful test of the expected luminosities and
temperatures of metal-rich giants in massive early-type galaxies. Studies of
pixels with much larger (negative) fluctuations will provide unique information
on main sequence stars and the stellar initial mass function.

Astrophysics of Galaxies;Instrumentation and Methods for Astrophysics;Solar and Stellar Astrophysics