We aim to improve our knowledge on the structure and dynamics of the circumstellar disk of the LMC B[e] supergiant LHA 120-S 73. High-resolution optical and near-IR spectroscopic data were obtained over a period of 16 and 7 years, respectively. The spectra cover the diagnostic emission lines from [CaII] and [OI], as well as the CO bands. These features trace the disk at different distances from the star. We analyzed the kinematics of the individual emission regions by modeling their emission profiles. A low-resolution mid-infrared spectrum was obtained as well, which provides information on the composition of the dusty disk. All diagnostic emission features display double-peaked line profiles, which we interpret as due to Keplerian rotation. We find that LHA 120-S 73 is surrounded by at least four individual rings of material with alternating densities (or by a disk with strongly non-monotonic radial density distribution). Moreover, we find that the molecular ring must have gaps or at least strong density inhomogeneities, or in other words, a clumpy structure. The mid-infrared spectrum displays features of oxygen- and carbon-rich grain species, which indicates a long-lived, stable dusty disk. We cannot confirm the previously reported high value for the stellar rotation velocity. The line profile of HeI 5876 A is strongly variable in both width and shape and resembles of those seen in non-radially pulsating stars. A proper determination of the real underlying stellar rotation velocity is hence not possible. The existence of multiple stable and clumpy rings of alternating density recalls ring structures around planets. Although there is currently insufficient observational evidence, it is tempting to propose a scenario with one (or more) minor bodies or planets revolving around LHA 120-S 73 and stabilizing the ring system, in analogy to the shepherd moons in planetary systems.
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