Eccentric-orbit EMRI radiation: Analytic forms of leading-logarithm and subleading-logarithm flux terms at high PN orders

Understand

We present new results on the analytic eccentricity dependence of several sequences of gravitational wave flux terms at high post-Newtonian (PN) order for extreme-mass-ratio inspirals.

• These sequences are the leading logarithms, which appear at PN orders $x^{3k} \log^k(x)$ and $x^{3k+3/2} \log^k(x)$ for integers $k\ge 0$ ($x$ a PN compactness parameter), and the subleading logarithms, which appear at orders $x^{3k} \log^{k-1}(x)$ and $x^{3k+3/2} \log^{k-1}(x)$ ($k\ge 1$), in both the energy and angular momentum radiated to infinity.
• For the energy flux leading logarithms, we show that to arbitrarily high PN order their eccentricity dependence is determined by particular sums over the function $g(n,e_t)$, derived from the Newtonian mass quadrupole moment, that normally gives the spectral content of the Peters-Mathews flux as a function of radial harmonic $n$.
• An analogous power spectrum $\tilde{g}(n,e_t)$ determines the leading logarithms of the angular momentum flux.