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Seeds of Life in Space SOLIS. IX. Chemical segregation of $\rm SO_2$ and SO toward the low-mass protostellar shocked region of L1157

We present observations of SO and $\rm SO_2$ lines toward the shocked regions along the L1157 chemically rich outflow, taken in the context of the Seeds Of Life In Space IRAM-NOrthern Extended Millimeter Array Large Program, and supported by data from Submillimeter Array and IRAM-30 m telescope at 1.1--3.6 mm wavelengths. We simultaneously analyze, for the first time, all of the brightest shocks in the blueshifted lobe, namely, B0, B1, and B2. We found the following. (1) SO and $\rm SO_2$ may trace different gas, given that the large(-scale) velocity gradient analysis indicates for $\rm SO_2$ a volume density ($\rm 10^5\text{--}10^6\,cm^{-3}$) denser than that of the gas emitting in SO by a factor up to an order of magnitude. (2) Investigating the 0.1 pc scale field of view, we note a tentative gradient along the path of the precessing jet. More specifically, $\rm χ({SO/SO_2})$ decreases from the B0-B1 shocks to the older B2. (3) At a linear resolution of 500--1400 au, a tentative spatial displacement between the two emitting molecules is detected, with the SO peak closer (with respect to $\rm SO_2$) to the position where the recent jet is impinging on the B1 cavity wall. Our astrochemical modeling shows that the SO and $\rm SO_2$ abundances evolve on timescales less than about 1000 years. Furthermore, the modeling requires high abundances ($2\times10^{-6}$) of both $\rm H_2S/H$ and S/H injected in the gas phase due to the shock occurrence, so pre-frozen OCS only is not enough to reproduce our new observations.