Stringent Neutron-Star Limits on Large Extra Dimensions

Supernovae (SNe) are copious sources for Kaluza-Klein (KK) gravitons which are generic for theories with large extra dimensions. These massive particles are produced with average velocities $\simeq 0.5c$ 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 $\nu \overline{\nu }$, $e^{+}{e}^{-}$, and $\gamma \gamma$ on time scales $\simeq {10}^9$ years. The EGRET $\gamma$-flux limits ( $E_{\gamma }\simeq 100\mathrm{MeV}$) for nearby neutron stars constrain the compactification scale for $n=2\mathrm{}$ extra dimensions to $M\gtrsim 500\mathrm{TeV}$, and $M\gtrsim 30\mathrm{TeV}$ for $n=3\mathrm{}$. The requirement that neutron stars are not excessively heated by KK decays implies $M\gtrsim 1700\mathrm{TeV}$ for $n=2\mathrm{}$, and $M\gtrsim 60\mathrm{TeV}$ for $n=3\mathrm{}$.