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 .
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 \lesssim 4 and if strong gravity is around a TeV , the compactification topology is to be more complex than that of a torus .