The Pristine Dwarf-Galaxy survey -- IV. Probing the outskirts of the
  dwarf galaxy Bo\"otes I
  We present a new spectroscopic study of the dwarf galaxy Bootes I (Boo I)
with data from the Anglo-Australian Telescope and its AAOmega spectrograph
together with the Two Degree Field multi-object system. We observed 36
high-probability Boo I stars selected using Gaia Early Data Release 3 proper
motions and photometric metallicities from the Pristine survey. Out of those,
29 are found to be Boo I's stars, resulting in an excellent success rate of 80%
at finding new members. Our analysis uses a new pipeline developed to estimate
radial velocities and equivalent widths of the calcium triplet lines from
Gaussian and Voigt line profile fits. The metallicities of 18 members are
derived, including 3 extremely metal-poor stars ([Fe/H] < -3.0), which
translates into an exceptional success rate of 25% at finding them with the
combination of Pristine and Gaia. Using the large spatial extent of our new
members that spans up to 4.1 half-light radii and spectroscopy from the
literature, we are able to detect a systemic velocity gradient of 0.15+/-0.10
km s-1 arcmin-1 and a small but resolved metallicity gradient of -0.007+/-0.003
dex arcmin-1. Finally, we show that Boo I is more elongated than previously
thought with an ellipticity of {\epsilon} = 0.68+/-0.15. Its velocity and
metallicity gradients as well as its elongation suggest that Boo I may have
been affected by tides, a result supported by direct dynamical modelling.
