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In a recent paper we showed that for eccentric-orbit extreme-mass-ratioinspirals the analytic forms of the leading-logarithm energy and angularmomentum post-Newtonian (PN) flux terms (radiated to infinity) can, toarbitrary PN order, be determined by sums over the Fourier spectrum of theNewtonian quadrupole moment. We further showed that an essential part of theeccentricity dependence of the related subleading-logarithm PN sequences, atlowest order in the symmetric mass ratio $\nu$, stems as well from theNewtonian quadrupole moment. Once that part is factored out, the remainingeccentricity dependence is more easily determined by black hole perturbationtheory. In this paper we show how the sequences that are the 1PN corrections tothe entire leading-logarithm series, namely terms that appear at PN orders$x^{3k+1} \log^k(x)$ and $x^{3k+5/2} \log^k(x)$ (for PN compactness parameter$x$ and integers $k\ge 0$), at lowest order in $\nu$, are determined by theFourier spectra of the Newtonian mass octupole, Newtonian current quadrupole,and 1PN part of the mass quadrupole moments. We also develop a conjectured (butplausible) form for 1PN correction to the leading logs at second order in$\nu$. Further, in analogy to the first paper, we show that these same sourcemultipole moments also yield nontrivial parts of the 1PN correction to thesubleading-logarithm series, and that the remaining eccentricity dependence (atlowest order in $\nu$) can then more easily be determined using black holeperturbation theory. We use this method to determine the entire analyticeccentricity dependence of the perturbative (i.e., lowest order in $\nu$) 4PNnon-log terms, $\mathcal{R}_4(e_t)$ and $\mathcal{Z}_4(e_t)$, for energy andangular momentum respectively.

physical review. d/physical review. d.

Eccentric-orbit extreme-mass-ratio-inspiral radiation II: 1PN correction  to leading-logarithm and subleading-logarithm flux sequences and the entire  perturbative 4PN flux