The Pristine Inner Galaxy Survey (PIGS) X. Probing the early chemical evolution of the Sagittarius dwarf galaxy with carbon abundances

We aim to constrain the chemo-dynamical properties of the Sagittarius (Sgr) dwarf galaxy using carbon abundances. Our sample from the $\mathit{\text{Pristine}}$ Inner Galaxy Survey (PIGS) includes $\sim 350$ metal-poor ([Fe/H]~$<-1.5$) stars in the main body of Sgr with good quality spectroscopic observations. Our metal-poor Sgr population has a larger velocity dispersion than metal-rich Sgr from the literature, which could be explained by outside-in star formation, extreme Galactic tidal perturbations and/or the presence of a metal-rich disc/bar $+$ a metal-poor halo. The average carbon abundance [C/Fe] in Sgr is similar to that of other classical dwarf galaxies (DGs) and consistently lower than in the Milky Way by $\sim 0.2-0.3$~dex at low metallicity. The interstellar medium in DGs, including Sgr, may have retained yields from more energetic Population~III~and~II supernovae (SNe), thereby reducing the average [C/Fe]. Additionally, SNe~Ia, producing more Fe than C, would start to contribute at lower metallicity in DGs/Sgr than in the Galaxy. The presence of a [C/Fe] gradient for Sgr stars with [Fe/H]~$\gtrsim -2.0$ ($\sim 6.8\times {10}^{-4}\mathrm{d}\mathrm{e}\mathrm{x}\mathrm{a}\mathrm{r}\mathrm{c}\mathrm{m}\mathrm{i}{\mathrm{n}}^{-1}$) suggests that SNe~Ia contributed in the system at those metallicities, especially in its inner regions. There is a low frequency of carbon-enhanced metal-poor (CEMP) stars in our Sgr sample. At higher metallicity/carbon abundance (mostly CEMP-s) this may be due to photometric selection effects, but those are less likely to affect CEMP-no stars. We propose that, given the lower average [C/Fe] in DGs, using the same CEMP definition ([C/Fe]~$>+0.7$) as in the Galaxy under-predicts the number of CEMP stars in DGs, and for Sgr a cut at [C/Fe]$\sim +0.35$ may be more appropriate, which brings the frequency of CEMP stars in agreement with that in the Galaxy.