Quantitative analysis of the thermal damping of coherent axion oscillations

Unruh and Wald have recently discussed a new mechanism for damping coherent axion oscillations, ``thermal damping,'' which occurs due to the temperature dependence of the axion mass and neutrino viscosity. We investigate the effect quantitatively and find that the present energy density in axions can be written as ρₐ=ρₐ₀/(1+JUW), where ρₐ₀ is what the axion energy density would be in the absence of the thermal-damping effect and JUW is an integral whose integrand depends upon (dmₐ/dT)². As a function of f_PQ(≡Peccei-Quinn symmetry-breaking scale) JUW achieves its maximum value for f_PQ3×10¹² GeV; unless the axion mass turn-on is very sudden, {}(T/mₐ)(dmₐ/dT){}{}1, JUW is {}1, implying that this damping mechanism is not significant.