  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 ~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
\~10^9 years. The EGRET gamma-flux limits (E_gamma ~ 100 MeV) for nearby
neutron stars constrain the fundamental scale for n=2 extra dimensions to M
>500 TeV, and M>30 TeV for n=3. The upcoming GLAST satellite is a factor ~30
more sensitive and thus may detect KK decays, for example at the nearby neutron
star RX J185635--3754. The requirement that neutron stars are not excessively
heated by KK decays implies M>1700 TeV for n=2, and M>60 TeV for n=3.
