Bounds on hadronic axions from stellar evolution

We consider in detail the effect of the emission of ``hadronic'' invisible axions (which do not couple to electrons) from the interior of stars on stellar evolution. To this end we calculate plasma emission rates for axions due to the Primakoff process for the full range of conditions encountered in a giant star. Much attention is paid to plasma, degeneracy, and screening effects. We reconsider the solar bound by evolving a 1.0 M_ star to solar age and lowering the presolar helium abundance so as to obtain the correct present-day luminosity of the Sun. The previous bound on the axion-photon coupling of G₉{}2.5 (corresponding to mₐ{}17 eV R where R is a model-dependent factor of order unity) is confirmed, where G₉ is the coupling constant G in units of 10^-9 GeV^-1. We then follow the evolution of a 1.3M_ star from zero age to the top of the giant branch.Helium ignites for all values of G consistent with the solar bound; however, the core mass, surface temperature, and luminosity at the helium flash exceed the standard values. The luminosity at the helium flash is larger than about twice the standard value unless G₉{}0.3 (corresponding to mₐ{}2 eV R), in conflict with observational data, which are statistically weak, however. We find our most stringent limits from the helium-burning lifetime. In the absence of axion cooling we calculate a lifetime of 1.2×{}10⁸ yr which corresponds well with the value 1.5×{}10⁸ yr derived from the number of red giants in the ``clump'' of the open cluster M67 and with the value 1.3×{}10⁸ yr derived from the number of such stars in the old galactic disk population. We obtain a conservative limit of G₉0.3 which, at saturation, results in a helium-burning lifetime an order of magnitude low. We believe that G₉{}0.1 (mₐ{}0.7 eV R) is a reasonably safe limit which, if saturated, leads to a calculated helium-burning lifetime a factor of 2 below the observed value. Our results exclude the recently suggested possibility of detecting cosmic axions through their 2{γ} decay and probably the possibility of measuring the solar hadronic axion flux which, according to our bounds, must be less than 2×{}10^-3 of the solar luminosity. There remains a narrow range of parameters (0.01{}G₉{}0.1, mₐ{}10^-4 eV) in which a recently proposed laboratory experiment might still measure axionlike particles.