At late stages, massive stars experience strong mass-loss rates, losing their external layers and thus producing a dense H-rich circumstellar medium (CSM). After the explosion of a massive star, the collision and continued interaction of the supernova (SN) ejecta with the CSM power the SN light curve through the conversion of kinetic energy into radiation. When the interaction is strong, the light curve shows a broad peak and high luminosity that lasts for several months. For these SNe, the spectral evolution is also slower compared to non-interacting SNe. Notably, energetic shocks between the ejecta and the CSM create the ideal conditions for particle acceleration and the production of high-energy (HE) neutrinos above 1 TeV. We study four strongly interacting Type IIn SNe, 2021acya, 2021adxl, 2022qml, and 2022wed, in order to highlight their peculiar characteristics, derive the kinetic energy of their explosion and the characteristics of the CSM, infer clues on the possible progenitors and their environment, and relate them to the production of HE neutrinos. We analysed spectro-photometric data of a sample of interacting SNe to determine their common characteristics and derive the physical properties (radii and masses) of the CSM and the ejecta kinetic energies and compare them to HE neutrino production models. The SNe analysed in this sample exploded in dwarf star-forming galaxies, and they are consistent with energetic explosions and strong interaction with the surrounding CSM. For SNe 2021acya and 2022wed, we find high CSM masses and mass-loss rates, linking them to very massive progenitors. For SN 2021adxl, the spectral analysis and less extreme CSM mass suggest a stripped-envelope massive star as a possible progenitor. SN 2022qml is marginally consistent with being a Type Ia thermonuclear explosion embedded in a dense CSM. The mass-loss rates for all the SNe are consistent with the expulsion of several solar masses of material during eruptive episodes in the last few decades before the explosion. Finally, we find that the SNe in our sample are marginally consistent with HE neutrino production.
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