Seeing Red in M32: Constraints on the Stellar Content from Near- and
  Mid-Infrared Observations and Applications for Studies of More Distant
  Galaxies
  The properties of asymptotic giant branch (AGB) stars in the Local Group
galaxy M32 are investigated using ground and space-based observations that span
the 1 - 8um wavelength interval, with the goal of demonstrating the utility of
infrared observations as probes of stellar content. Comparisons with isochrones
indicate that the brightest resolved stars in M32 have ages of a few Gyr, and
are younger on average than AGB stars with the same intrinsic brightness in the
outer disk of M31. Accounting for stellar variability is shown to be essential
for modelling AGB luminosity functions (LFs). Model LFs that assume the
star-forming history measured by Monachesi et al. (2012, ApJ, 745, 97) and the
variability properties of Galactic AGB stars match both the K and [5.8] LFs of
M32. Models also suggest that the slope of the [5.8] LF between M_[5.8] = -8.5
and --10.0 is sensitive to the mix of stellar ages, and a sizeable fraction of
the stars in M32 must have an age older than 7 Gyr in order to match the [5.8]
LF. The structural properties of M32 in the infrared are also investigated. The
effective radii that are computed from near-infrared and mid-infrared isophotes
are similar to those measured at visible wavelengths, suggesting that the
stellar content of M32 is well-mixed. However, isophotes at radii > 16 arcsec
(> 60 parsecs) in the near and mid-infrared are flatter than those at visible
wavelengths. The coefficient of the fourth-order cosine term in the fourier
expansion of isophotes changes from `boxy' values at r < 16 arcsec to `disky'
values at r > 48 arcsec in [3.6] and [4.5]. The mid-infrared colors near the
center of M32 do not vary systematically with radius, providing evidence of a
well-mixed stellar content in this part of the galaxy.
