We examine a phenomenon recently predicted by numerical simulations of supernova neutrino flavor evolution : the swapping of supernova \nu _ { e } and \nu _ { \mu, \tau } energy spectra below ( above ) energy E _ { \mathrm { C } } for the normal ( inverted ) neutrino mass hierarchy .
We present the results of large-scale numerical calculations which show that in the normal neutrino mass hierarchy case , E _ { \mathrm { C } } decreases as the assumed effective 2 \times 2 vacuum \nu _ { e } \rightleftharpoons \nu _ { \mu, \tau } mixing angle ( \simeq \theta _ { 13 } ) is decreased .
In contrast , these calculations indicate that E _ { \mathrm { C } } is essentially independent of the vacuum mixing angle in the inverted neutrino mass hierarchy case .
With a good neutrino signal from a future Galactic supernova , the above results could be used to determine the neutrino mass hierarchy even if \theta _ { 13 } is too small to be measured by terrestrial neutrino oscillation experiments .