$s$-process production in rotating massive stars at solar and low metallicities

Rotation was shown to have a strong impact on the structure and light element nucleosynthesis in massive stars. In particular, models including rotation can reproduce the primary nitrogen observed in halo extremely metal-poor (EMP) stars. Additional exploratory models showed that rotation may enhance $s$-process production at low metallicity. Here we present a large grid of massive star models including rotation and a full $s$-process network to study the impact of rotation on the weak $s$-process. We explore the possibility of producing significant amounts of elements beyond the strontium peak, which is where the weak $s$-process usually stops. We used the Geneva stellar evolution code coupled to an enlarged reaction network with 737 nuclear species up to bismuth to calculate $15-40\,\text{M}_\odot$ models at four metallicities ($Z = 0.014,10^{-3}$, $10^{-5}$, and $10^{-7}$) from the main sequence up to the end of oxygen burning. We confirm that rotation-induced mixing between the convective H-shell and He-core enables an important production of primary $^{14}$N and $^{22}$Ne and $s$-process at low metallicity. At low metallicity, even though the production is still limited by the initial number of iron seeds, rotation enhances the $s$-process production, even for isotopes heavier than strontium, by increasing the neutron to seed ratio. The increase in this ratio is a direct consequence of the primary production of $^{22}$Ne. Despite nuclear uncertainties affecting the $s$-process production and stellar uncertainties affecting the rotation-induced mixing, our results show a robust production of $s$ process at low metallicity when rotation is taken into account. Considering models with a distribution of initial rotation rates enables to reproduce the observed large range of the [Sr/Ba] ratios in (carbon-enhanced and normal) EMP stars.