The Pristine Dwarf-Galaxy survey -- IV. Probing the outskirts of the dwarf galaxy Boötes 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, 27 are found to be Boo I's stars, resulting in an excellent success rate of 75% 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 16 members are derived, including 3 extremely metal-poor stars ([Fe/H] < -3.0), which translates into a 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 find a systemic velocity gradient of 0.40 +/- 0.10 km/s/arcmin and a small but resolved metallicity gradient of -0.008 +/- 0.003 dex/arcmin. 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.