Supernovae ( SNe ) are copious sources for Kaluza-Klein gravitons which are generic for theories with large extra dimensions .
These massive particles are produced with average velocities \simeq 0.5 c so that many of them are gravitationally retained by the SN core .
Every neutron star thus has a halo of KK gravitons which decay into \nu \bar { \nu } , e ^ { + } e ^ { - } and \gamma \gamma on time scales \simeq 10 ^ { 9 } years .
The EGRET \gamma -flux limits ( E _ { \gamma } \simeq 100 ~ { } { MeV } ) for nearby neutron stars constrain the compactification scale for n = 2 extra dimensions to M \gtrsim 500 ~ { } { TeV } , and M \gtrsim 30 ~ { } { TeV } for n = 3 .
The requirement that neutron stars are not excessively heated by KK decays implies M \gtrsim 1700 ~ { } { TeV } for n = 2 , and M \gtrsim 60 ~ { } { TeV } for n = 3 .