PRODIGE -- envelope to disk with NOEMA. VI. The missing sulfur problem

Determining the amount of sulfur in volatiles and refractories in the interstellar medium remains one of the main problems in astrochemistry. The detection of H₂S ices, which are thought to be one of the main sulfur reservoirs, is still a great challenge and has not been achieved yet, and the only sulfur-bearing species detected in the ices to date is OCS. The PROtostars and DIsks: Global Evolution (PRODIGE) large survey observations with the NOrthern Extended Millimeter Array (NOEMA) of several Class 0/I protostars in the Perseus Molecular Cloud provide a perfect opportunity to study the H₂S and OCS composition of the ices through the volatiles sublimated in the warm inner core (T>100K, n∼10⁶cm^-3) of these protostars. Our aim is to determine the H₂S/OCS ratio in the warm inner core of the protostars of our sample in order to study how it is affected by different factors during its evolution. We used the NOEMA millimeter observations from the PRODIGE program of H₂S, H₂³3S, OCS, OC³3S, and OC³4S to estimate the H₂S and OCS column densities in the warm inner core of 24 protostars of Perseus. In addition, we used SO and SO₂ data from the Atacama Large Millimeter/submillimeter Array (ALMA) archive to complete the sulfur budget and give a rough estimate of the total sulfur abundance in each of the sources. We explored the chemistry of H₂S and OCS in the warm cores using chemical and dynamical simulations of the collapse of a dense core to form a protostar. The compound H₂S is detected in 21 protostars and OCS in 17 protostars of our sample. The estimated H₂S/OCS ratio reveals a segregation of the sources into "OCS-poor" and "OCS-rich" protostars, where the OCS-poor protostars present higher H₂S/OCS ratios than the OCS-rich ones. The total sulfur abundance, which is always dominated by either H₂S or OCS, grows with evolution during the Class 0 phase, reaching a minimum depletion of a factor less than eight in the Class 0/I objects and decreasing again in the Class I. Chemo-MHD simulations show that temperature changes in the pre-stellar phase and during the collapse can produce substantial differences in the H₂S and OCS (ice and gas-phase) abundances and in the H₂S/OCS ratio. Our analysis shows that the H₂S/OCS ratio is strongly influenced by the environment and the initial conditions of the cloud.