Ultra-Deep Hubble Space Telescope Imaging of the Small Magellanic Cloud:
  The Initial Mass Function of Stars with M <~ 1 Msun
  We present a new measurement of the stellar initial mass function (IMF) based
on ultra-deep, high-resolution photometry of >5,000 stars in the outskirts of
the Small Magellanic Cloud (SMC) galaxy. The Hubble Space Telescope (HST)
Advanced Camera for Surveys (ACS) observations reveal this rich, co-spatial
population behind the foreground globular cluster 47 Tuc, which we targeted for
121 HST orbits. The stellar main sequence of the SMC is measured in the F606W,
F814W color-magnitude diagram (CMD) down to ~30th magnitude, and is cleanly
separated from the foreground star cluster population using proper motions. We
simulate the SMC population by extracting stellar masses (single and unresolved
binaries) from specific IMFs, and converting those masses to luminosities in
our bandpasses. The corresponding photometry for these simulated stars is drawn
directly from a rich cloud of 4 million artificial stars, thereby accounting
for the real photometric scatter and completeness of the data. Over a
continuous and well populated mass range of M = 0.37 - 0.93 Msun (i.e., down to
a ~75% completeness limit at F606W = 28.7), we demonstrate that the IMF is well
represented by a single power-law form with slope \alpha = -1.90
(^{+0.15}_{-0.10}) (3 sigma error) (i.e., dN/dM \propto M^{\alpha}). This is
shallower than the Salpeter slope of \alpha = -2.35, which agrees with the
observed stellar luminosity function at higher masses. Our results indicate
that the IMF does {\it not} turn over to a more shallow power-law form within
this mass range. We discuss implications of this result for the theory of star
formation, the inferred masses of galaxies, and the (lack of a) variation of
the IMF with metallicity.
