Faint Stars in a Faint Galaxy: I. Ultra Deep Photometry of the Bo\"otes
  I Ultra Faint Dwarf Galaxy
  We present an analysis of new extremely deep images of the resolved stellar
population of the Bo\"otes I ultra faint dwarf spheroidal galaxy. These new
data were taken with the Hubble Space Telescope, using the Advanced Camera for
Surveys (Wide Field Camera) and Wide Field Camera 3 (UVIS), with filters F606W
and F814W (essentially V and I), as part of a program to derive the low-mass
stellar initial mass function in this galaxy. We compare and contrast two
approaches to obtaining the stellar photometry, namely ePSF and DAOPHOT. We
identify likely members of Bo\"otes I based on the location of each star on the
color-magnitude diagram, obtained with the DAOPHOT photometry from the ACS/WFC
data. The probable members lie close to stellar isochrones that were chosen to
encompass the known metallicity distribution derived from spectroscopic data of
brighter radial-velocity member stars and are consistent with the main-sequence
turnoff. The resulting luminosity function of the Bo\"otes I galaxy has a 50%
completeness limit of 27.4 in F814W and 28.2 in F606W (Vega magnitude system),
which corresponds to a limiting stellar mass of $\le 0.3 M_\odot$.
