Pixel Color Magnitude Diagrams for Semi-Resolved Stellar Populations:
  The Star Formation History of Regions within the Disk and Bulge of M31
  The analysis of stellar populations has, by and large, been developed for two
limiting cases: spatially-resolved stellar populations in the color-magnitude
diagram, and integrated light observations of distant systems. In between these
two extremes lies the semi-resolved regime, which encompasses a rich and
relatively unexplored realm of observational phenomena. Here we develop the
concept of pixel color magnitude diagrams (pCMDs) as a powerful technique for
analyzing stellar populations in the semi-resolved regime. pCMDs show the
distribution of imaging data in the plane of pixel luminosity vs. pixel color.
A key feature of pCMDs is that they are sensitive to all stars, including both
the evolved giants and the unevolved main sequence stars. An important variable
in this regime is the mean number of stars per pixel, $N_{\rm pix}$. Simulated
pCMDs demonstrate a strong sensitivity to the star formation history (SFH) and
allow one to break degeneracies between age, metallicity and dust based on two
filter data for values of $N_{\rm pix}$ up to at least $10^4$. We extract pCMDs
from Hubble Space Telescope (HST) optical imaging of M31 and derive
non-parametric SFHs from $10^6$ yr to $10^{10}$ yr for both the crowded disk
and bulge regions (where $N_{\rm pix}\approx30-10^3$). From analyzing a small
region of the disk we find a non-parametric SFH that is smooth and consistent
with an exponential decay timescale of 4 Gyr. The bulge SFH is also smooth and
consistent with a 2 Gyr decay timescale. pCMDs will likely play an important
role in maximizing the science returns from next generation ground and
space-based facilities.
