One-cycle radiation-reaction Magnusian for eccentric binaries through relative 1PN order
Abstract
We derive the one-cycle first Magnusian for nonspinning compact binaries on planar, bound eccentric orbits through relative first post-Newtonian (1PN) order and linear order in radiation reaction, and construct the associated first-order periastron return map. Combining the conservative 1PN dynamics and its Jacobi transport with the 2.5PN and 3.5PN radiation-reaction forces, we obtain all four components in closed form for 0<e<1, without expanding in eccentricity. The dependence on all eight Iyer--Will radiation-reaction gauge parameters reduces to periodic coboundaries and therefore cancels over a radial cycle. The result reproduces the averaged energy and angular-momentum losses, their circular limit, and the secular evolution of the 1PN radial orbital elements. The two remaining components encode the dissipative angle-sector information. Projecting the resulting phase-space update onto the perturbed periastron return section yields the corrections to the return time and apsidal phase. We then compare the strict first-order map with a partially exponentiated map built from the same Magnusian. The comparison is observable dependent: at fixed periastron index, the strict map gives smaller residuals for a representative evolution over 40 radial cycles, whereas partial exponentiation reduces the accumulated periastron-timing residual by about an order of magnitude. Across a representative one-cycle grid at equal masses, partial exponentiation improves the radial-action and energy updates at every sampled point.
Related
- The Magnusian generator for dissipative systems and application to leading 2.5PN radiation-reaction dynamics
- Computing gravitational radiation from highly eccentric bound binaries in the small-mass-ratio limit
- Parameter Estimation for Eccentric Supermassive Black Hole Binaries with Pulsar Timing Arrays
- A parametrized test of general relativity for inspiralling eccentric binaries in LISA
- Implications of the LISA stochastic signal from eccentric stellar mass black hole binaries in vacuum
BibTeX
@misc{placidi2026onecycle,
title = {{One-cycle radiation-reaction Magnusian for eccentric binaries through relative 1PN order}},
author = {Andrea Placidi},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.01713},
eprint = {2609.01713},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.01713},
}
RIS
TY - UNPB
TI - One-cycle radiation-reaction Magnusian for eccentric binaries through relative 1PN order
AU - Andrea Placidi
PY - 2026
DA - 2026/09/01
PB - arXiv
DO - 10.48550/arxiv.2609.01713
UR - https://arxiv.org/abs/2609.01713
AB - We derive the one-cycle first Magnusian for nonspinning compact binaries on planar, bound eccentric orbits through relative first post-Newtonian (1PN) order and linear order in radiation reaction, and construct the associated first-order periastron return map. Combining the conservative 1PN dynamics and its Jacobi transport with the 2.5PN and 3.5PN radiation-reaction forces, we obtain all four components in closed form for 0<e<1, without expanding in eccentricity. The dependence on all eight Iyer--Will radiation-reaction gauge parameters reduces to periodic coboundaries and therefore cancels over a radial cycle. The result reproduces the averaged energy and angular-momentum losses, their circular limit, and the secular evolution of the 1PN radial orbital elements. The two remaining components encode the dissipative angle-sector information. Projecting the resulting phase-space update onto the perturbed periastron return section yields the corrections to the return time and apsidal phase. We then compare the strict first-order map with a partially exponentiated map built from the same Magnusian. The comparison is observable dependent: at fixed periastron index, the strict map gives smaller residuals for a representative evolution over 40 radial cycles, whereas partial exponentiation reduces the accumulated periastron-timing residual by about an order of magnitude. Across a representative one-cycle grid at equal masses, partial exponentiation improves the radial-action and energy updates at every sampled point.
ER -