VLT Spectroscopy of Ultra-Faint Dwarf Galaxies. 1. Bo\"otes I, Leo IV,
  Leo V
  We perform consistent reductions and measurements for three ultra-faint dwarf
galaxies (UFDs): Bo\"otes I, Leo IV and Leo V. Using the public archival data
from the GIRAFFE spectrograph on the Very Large Telescope (VLT), we locate new
members and provide refined measurements of physical parameters for these dwarf
galaxies. We identify nine new Leo IV members and four new Leo V members, and
perform a comparative analysis of previously discovered members. Additionally,
we identify one new binary star in both Leo IV and Leo V. After removing binary
stars, we recalculate the velocity dispersions of Bo\"otes I and Leo IV to be
5.1$^{+0.7}_{-0.8}$ and 3.4$^{+1.3}_{-0.9}$ km s$^{-1}$, respectively; We do
not resolve the Leo V velocity dispersion. We identify a weak velocity gradient
in Leo V that is $\sim$4$\times$ smaller than the previously calculated
gradient and that has a corresponding position angle which differs from the
literature value by $\sim$120 deg. Combining the VLT data with previous
literature, we re-analyze the Bo\"otes I metallicity distribution function and
find that a model including infall of pristine gas while Bo\"otes I was forming
stars best fits the data. Our analysis of Leo IV, Leo V and other UFDs will
enhance our understanding of these enigmatic stellar populations and contribute
to future dark matter studies. This is the first in a series of papers
examining thirteen UDFs observed with VLT/GIRAFFE between 2009 and 2017.
Similar analyses of the remaining ten UFDs will be presented in forthcoming
papers.
