Preprint number: CP3-Origins-2016-10 DNRF90 and DIAS-2016-10
We define the theoretical framework and deduce the conditions under which multi-messenger astronomy can constrain neutrino masses and unveil their ordering. The framework uses time differences between the arrival of neutrinos and the other two light messengers, i.e. light and gravitons, emitted in astrophysical catastrophes. We argue that it is possible to decrease the upper bound on the absolute mass of the lightest neutrino to less than about 0.02 eV for astrophysical sources at around 10 Mpc and with neutrino energies of about 5 MeV. We also show that the potential observation of neutrinos from astrophysical sources located at distances of hundreds of mega parsec similar to the one discovered by the LIGO collaboration leads to stronger constraints on neutrino properties.