The secular effect of gravitational radiation damping on the periastron advance of binary stars in second order perturbation theory

The second order perturbation effect of gravitational radiation damping on the periastron advance of binary stars is studied. The second order analytic solution is obtained based on the first order theory in the 2014 article by Li. Theoretical results show that secular variation exists in the periastron advance of binary stars in the second order theory, but secular variation does not exist in the first order perturbation theory. Numerical results for two compact binary stars (PSR J0737-3039 and M33 X-7) are given, demonstrating the theoretical significance even though the effect is very small. (paper)