Supernova and neutron-star limits on large extra dimensions reexamined

In theories with large extra dimensions, supernova (SN) cores are powerful sources of Kaluza-Klein (KK) gravitons. A large fraction of these massive particles are gravitationally retained by the newly born neutron star (NS). The subsequent slow KK decays produce potentially observable $\gamma$ rays and heat the NS. We here show that the back-absorption of the gravitationally trapped KK gravitons does not significantly change our previous limits. We calculate the graviton emission rate in a nuclear medium by combining the low-energy classical bremsstrahlung rate with detailed-balancing arguments. This approach reproduces the previous thermal emission rate, but it is much simpler and allows for a calculation of the absorption rate by a trivial phase-space transformation. We derive systematically the dependence of the SN and NS limits on the number of extra dimensions.