  In the denser and colder regions of the interstellar medium (ISM), gas-phase
sulfur is depleted by 2 or 3 orders of magnitude with respect to its cosmic
abundance. Thus, which species are the main carriers of sulfur is an open
question. Recent studies have proposed S$_n$ species as potential sulfur
reservoirs. Among the various sulfur allotropes, the most stable one is the
S$_8$ ring, detected in the asteroid Ryugu and Orgueil meteorite. Shorter
species, namely S$_3$ and S$_4$, have been found in the comet 67P/C-G, but
their presence in the ISM remains elusive. In this study, we compute the
binding energies (BEs) of S$_n$ (n = 1-8) species on an amorphous water-ice
surface model and analyze their infrared (IR) and Raman spectral features to
provide data for their identification in the ISM. Our computations reveal that
these species exhibit lower BEs than previously assumed and that their spectral
features experience minimal shifts when adsorbed on water ice, because of the
weak and nonspecific S$_n$-ice interactions. Furthermore, these species display
very low IR band intensities and, therefore, very accurate instruments
operating in the mid-IR range are required for detecting the presence of these
species in dense interstellar environments.
