Supernova cooling in a dark matter smog

A light hidden gauge boson with kinetic mixing with the usual photon is a popular setup in theories of dark matter. The supernova cooling via radiating the hidden boson is known to put an important constraint on the mixing. I consider the possible role dark matter, which under reasonable assumptions naturally exists inside supernova, can play in the cooling picture. Because the interaction between the hidden gauge boson and DM is likely unsuppressed, even a small number of dark matter compared to protons inside the supernova could dramatically shorten the free streaming length of the hidden boson. A picture of a dark matter smog inside the supernova, which substantially relaxes the cooling constraint, is discussed in detail.