The Pristine survey : XXVII. The extremely metal-poor stream C-19 stretches over more than 100 degrees

The discovery of the most metal-poor stream, C-19, provides us with a fossil record of a stellar structure born very soon after the Big Bang. In this work, we search for new C-19 members over the whole sky by combining two complementary stream-searching algorithms, STREAMFINDER and StarGO,, and utilizing low-metallicity star samples from the Pristine survey as well as Gaia BP/RP spectro-photometric catalogues. We confirm twelve new members, spread over more than 100$^\circ$, using velocity and metallicity information from a set of spectroscopic follow-up programs that targeted a quasi-complete sample of our bright candidates ($G \lesssim 16.0$). From the updated set of stream members, we confirm that the stream is wide, with a stream width of $\sim200$ pc, and dynamically hot, with a derived velocity dispersion of $10.9^{+2.1}_{-1.5}$ km/s. The tension remains between these quantities and a purely baryonic scenario in which the relatively low-mass stream (even updated to a few $10^4M_{\odot}$) stems from a globular cluster progenitor, as suggested by its chemical abundances. Some heating mechanism, such as preheating of the cluster in its own dark matter halo or through interactions with halo sub-structures appears necessary to explain the tension. The impact of binaries on the measured dispersion also remains unknown. Detailed elemental abundances of more stream members as well as multi-epoch radial velocities from spectroscopic observations are therefore crucial to fully understand the nature and past history of the most metal-poor stream of the Milky Way.