Measuring Sizes of Ultra-Faint Dwarf Galaxies
  The discovery of Ultra-Faint Dwarf (UFD) galaxies in the halo of the Milky
Way extends the faint end of the galaxy luminosity function to a few hundred
solar luminosities. This extremely low luminosity regime poses a significant
challenge for the photometric characterization of these systems. We present a
suite of simulations aimed at understanding how different observational choices
related to the properties of a low luminosity system impact our ability to
determine its true structural parameters such as half-light radius and central
surface brightness. We focus on estimating half-light radii (on which mass
estimates depend linearly) and find that these numbers can have up to 100%
uncertainties when relatively shallow photometric surveys, such as SDSS, are
used. Our simulations suggest that to recover structural parameters within 10%
or better of their true values: (a) the ratio of the field-of-view to the
half-light radius of the satellite must be greater than three, (b) the total
number of stars, including background objects should be larger than 1000, and
(c) the central to background stellar density ratio must be higher than 20. If
one or more of these criteria are not met, the accuracy of the resulting
structural parameters can be significantly compromised. In the context of
future surveys such as LSST, the latter condition will be closely tied to our
ability to remove unresolved background galaxies. Assessing the reliability of
measured structural parameters will become increasingly critical as the next
generation of deep wide-field surveys detects UFDs beyond the reach of current
spectroscopic limits.
