When the next galactic supernova will occur, present and future detectors -- e.g. Super-Kamiokande, IceCube or JUNO- will hopefully guarantee many neutrino events in many channels of detection. At present, however, huge uncertainties on the emission models make not clear to understand what kind and how much information
about the initial emission parameters we can extract from the data. This situation is worsen by priors usually taken by analysts in order to simplify the problem, which hinder a direct comparison among results and could not be reflected in te real explosion.

In order to better understand the point we performed a Monte Carlo based likelihood analysis on the events as could be seen in water Cherenkov detectors, namely Super-Kamiokande and Hyper-Kamiokande, without any priors. The aim is to reconstruct the emission parameters as well as the total energy emitted in neutrinos, in a perspective of multi-messengers physics and the goal to give better constraint on the neutron star equation of state and radius. In this sense, the results of a new analysis are shown. The reconstruction of the radius is linked to the neutron-star equations of states and could be used to test theories beyond General Relativity, such as the f(R) gravity.