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Neutron stars generally cools off by the emission of gamma rays andneutrinos. But axions can also be produced inside a neutron star by the processof nucleon-nucleon axion bremsstrahlung. The escape of these axions adds to thecooling process of neutron star. We explore the nature of cooling of neutronstars including the axion emission and compare our result with the scenariowhen the neutron star is cooled by only the emission of gamma rays andneutrinos. In our calculations we consider both the degenerate andnon-degenerate limits for such axion energy loss rate and the resultingvariation of luminosity with time and variation of surface temperature withtime of the neutron star. In short the thermal evolution of a neutron star isstudied with three neutron star masses (1.0, 1.4, 1.8 solar masses) and byincluding the effect of axion emission for different axion masses($m_{a}=10^{-5}\rm{eV}, 10^{-3}\rm{eV}, 10^{-2}\rm{eV}$) and compared with thesame when the axion emission is not considered. We compared theoretical coolingcurve with the observational data of three pulsars PSR B056+14, Geminga and PSRB1055-52 and finally give an upper bound on axion mass limits$m_{a}\leq10^{-3}$ eV which implies that the axion decay constant$f_{a}\geq0.6\times10^{10}\hspace{1mm}\rm{GeV}$.

Neutron Star Cooling via Axion Emission by Nucleon-Nucleon Axion Bremsstrahlung