Axions from cooling compact stars: Pair-breaking processes

Once formed in a supernova explosion, a neutron star cools rapidly via neutrino emission during the first 104-105 yr of its life-time. Here we compute the axion emission rate from baryonic components of a star at temperatures below their respective critical temperatures Tc for normal-superfluid phase transition. The axion production is driven by a charge neutral weak process, associated with Cooper pair breaking and recombination. The requirement that the axion cooling does not overshadow the neutrino cooling puts a lower bound on the axion decay constant fa>6×109Tc9-1 GeV, with Tc9=Tc/109 K. This translates into an upper bound on the axion mass ma<10-3Tc9 eV.