Axion cooling of neutron stars

Cooling simulations of neutron stars and their comparison with the data from thermally emitting x-ray sources put constraints on the properties of axions, and by extension, of any light pseudoscalar dark matter particles, whose existence has been postulated to solve the strong-$CP$ problem of QCD. We incorporate the axion emission by pair-breaking and formation processes by $S$- and $P$-wave nucleonic condensates in a benchmark code for cooling simulations, as well as provide fit formulas for the rates of these processes. Axion cooling of neutron stars has been simulated for 24 models covering the mass range 1 to 1.8 solar masses, featuring nonaccreted iron and accreted light-element envelopes, and a range of nucleon-axion couplings. The models are based on an equation state predicting conservative physics of superdense nuclear matter that does not allow for the onset of fast cooling processes induced by phase transitions to non-nucleonic forms of matter or high proton concentration. The cooling tracks in the temperature vs age plane were confronted with the (time-averaged) measured surface temperature of the central compact object in the Cas A supernova remnant as well as surface temperatures of three nearby middle-aged thermally emitting pulsars. We find that the axion coupling is limited to ${f}_{a}/{10}^{7}\text{ }\text{ }\mathrm{GeV}\ensuremath{\ge}(5--10)$, which translates into an upper bound on axion mass ${m}_{a}\ensuremath{\le}(0.06--0.12)\text{ }\text{ }\mathrm{eV}$ for Peccei-Quinn charges of the neutron $|{C}_{n}|\ensuremath{\sim}0.04$ and proton $|{C}_{p}|\ensuremath{\sim}0.4$ characteristic for hadronic models of axions.