This paper reports a new phenomenological analysis of the neutrino burst detected from SN 1987 A , and it reveals the presence of two mass eigenstates . The heavier mass eigenstate has m _ { H } = 21.4 \pm 1.2 eV / c ^ { 2 } , while the lighter one has m _ { L } = 4.0 \pm 0.5 eV / c ^ { 2 } . It is not the first paper to make such a claim , but it expands on a 1988 conditional analysis by Cowsik , and it attempts to make the evidence more robust through an improved statistical analysis , and through providing reasons why alternative explanations are unlikely . It also shows how the result can be made consistent with existing smaller electron neutrino mass limits from tritium beta decay and cosmology through the existence of a third tachyonic ( superluminal ) mass eigenstate .