FAUST-XXII. Deuteration in the VLA1623-2417 protostellar hot-corinos, cavities, and streamers

The study of deuterium fractionation is a valuable tool for reconstructing our chemical history from the early prestellar stages to the formation of planets. In the context of the ALMA Large Programme FAUST, we observed formaldehyde, H$_2$CO, and its singly and doubly deuterated forms, HDCO and D$_2$CO, towards the protostellar cluster VLA1623-2417, on scales of ~ 2000 - 50 au. Formaldehyde probes the inner envelopes of the protostars VLA1623A, B, and W, the rotating cavities opened by the VLA1623A outflow, and several streamers. The HDCO and D$_2$CO emissions are observed towards VLA1623A, in its outflow cavities, and in one of the streamers. We estimate the gas temperature from the HDCO lines: T~ 125 K towards VLA1623A, indicating hot-corino emission, lower temperatures in the outflow cavities (20 - 40 K), and in the streamers ($\le15$ K). The D$_2$CO lines also trace the flattened envelope of VLA1623A, where H$_2$CO and HDCO are fainter. This may be due to D$_2$CO formation on dust grains in the cold prestellar phase, and subsequent photodesorption caused by the enhanced UV flux from two nearby B stars. We inferred the molecular deuteration: [HDCO]/[H$_2$CO] ~ 0.16, ~ 0.07 - 0.13, and ~ 0.3; [D$_2$CO]/[H$_2$CO] ~ 0.003, ~ 0.05 - 0.13, and ~ 0.03 in the hot corino, in the outflow cavities, and in the streamer, respectively. The spatial distribution of D$_2$CO, which points to formation on dust grains, and the similar values of [HDCO]/[H$_2$CO] and [D$_2$CO]/[H$_2$CO] in the components of the system, suggest that deuterium fractionation occurs at the prestellar stage and is then inherited, mostly unaltered, in the protostellar phase.