Compact stellar objects like supernovae and neutron stars cool by the emission of light particles
like neutrinos and axions from their very dense interiors. In this article, we study in detail the
photo-production of axions and neutrinos. We point out that this channel is an unavoidable
consequence of the existence of the anomaly-induced Wess-Zumino-Witten term and compute
the relevant cooling rates. We then perform a complementary data-driven study where the rate
of photo-production can be estimated from low-energy pion photo-production data. We however
conclude that the cooling rates induced by the photo-production of axions and neutrinos are typically
sub-dominant with respect to the main channels usually included.