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An intriguing feature of extra dimensions is the possible production of Kaluza--Klein gravitons by nucleon-nucleon bremsstrahlung in the course of core collapse of massive stars, as pointed out by Hannestad and Raffelt. In this event Kaluza--Klein gravitons are copiously produced and a significant fraction of them remains trapped around the newly born neutron stars. They slowly decay into 2 gamma rays, making neutron stars gamma-ray sources. In this letter, we strengthen considerably the limits on the radius of compactification of extra-dimensions for small number $n$ of them, or alternatively the fundamental scale of quantum gravity, considering the gamma-ray emission of the whole population of neutron stars sitting in the Galactic bulge, instead of the closest member of this category. For $n=1$ the constraint on the compactification radius is $R<400\mu$m, overlapping with the distance ($180\mu$m) at which Newtons law is directly measured. In addition, for n=1 and n=2, the fundamental energy scale of quantum gravity is far beyond the collider technology. These results imply that if $n\lesssim4$ and if strong gravity is around a TeV, the compactification topology is to be more complex than that of a torus

Gamma Rays from the Galactic Bulge and Large Extra Dimensions