The sulfur plume in the Horsehead nebula: New detections of S$_2$H, SH$^+$, and CO$^+$

Sulfur is essential for life, but its abundance and distribution in the interstellar medium remain uncertain, with over 90% of sulfur undetected in cold molecular clouds. Sulfur allotropes (S$_{\rm n}$) have been proposed as possible reservoirs, but the only detected interstellar molecule with a disulfide bond is S$_2$H in the Horsehead Nebula, making the estimation of sulfur chains abundances difficult. Here we present total-power ALMA images of H$_2$S, S$_2$H, SO$_2$, CO$^+$, and SH$^+$ towards the Horsehead nebula. These observations, with unprecedented sensitivity (rms $\sim$ 1.5 mK), provide the first detections of SH$^+$ and CO$^+$ in this region, together with the identification of a new S$_2$H line. The comparison of the spectroscopic images of H$_2$S, S$_2$H, SO$_2$, CO$^+$ and SH$^+$ shows that the S$_2$H emission originates from a warm gas layer adjacent to the photodissociation front. The emission peak of S$_2$H is offset from those of reactive ions such as SH$^+$, CO$^+$, and SO$^+$, suggesting that gas-phase reactions involving SH$^+$ and H$_2$S are not the dominant formation pathway of S$_2$H. Instead, we propose that S$_2$H is desorbed from irradiated grain surfaces by non-thermal processes. The SH$^+$ detection indicates that sulfur is not significantly depleted at the UV-irradiated edge of the molecular cloud, arguing against a major refractory sulfur reservoir in the interior of molecular clouds.