The Pristine survey XIII: Uncovering the very metal-poor tail of the thin disc

We evaluate the rotational velocity of stars observed by the Pristine survey towards the Galactic anticentre, spanning a wide range of metallicities from the extremely metal-poor regime ($\mathrm{[Fe/H]}<-3$) to nearly solar metallicity. In the Galactic anticentre direction, the rotational velocity ($V_{\phi}$) is similar to the tangential velocity in the galactic longitude direction ($V_{\ell}$). This allows us to estimate $V_{\phi}$ from Gaia early data-release 3 (Gaia EDR3) proper motions for stars without radial velocity measurements. This substantially increases the sample of stars in the outer disc with estimated rotational velocities. Our stellar sample towards the anticentre is dominated by a kinematical thin disc with a mean rotation of $\sim -220$ km $\mathrm{s}^{-1}$. However, our analysis reveals the presence of more stellar substructures. The most intriguing is a well populated extension of the kinematical thin disc down to $\mathrm{[Fe/H]} \sim -2$. A scarser fast rotating population reaching the extremely metal-poor regime, down to $\mathrm{[Fe/H]} \sim -3.5$ is also detected, but without statistical significance to unambiguously state whether this is the extremely metal-poor extension of the thin disc or the high rotating tail of hotter structures (like the thick disc or the halo). In addition, a more slowly rotating kinematical thick disc component is also required to explain the observed $V_{\ell}$ distribution at $\mathrm{[Fe/H]} > -1.5$. Furthermore, we detect signatures of a "heated disc", the so-called Splash, at metallicities higher than $\sim-1.5$. Finally, at $\mathrm{[Fe/H]} < -1.5$ our anticentre sample is dominated by a kinematical halo with a net prograde motion.