发表机构
Dipartimento di Fisica e Geologia, Università di Perugia, I.N.F.N. Sezione di Perugia（佩鲁贾大学物理与地质学系，意大利国家核物理研究所佩鲁贾分部）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究推导了偏心双星经1PN阶的单周期一阶Magnusian，构造了近星点返回映射，对比了严格一阶与部分指数化映射的残差，为致密双星轨道演化研究提供了关键的理论结果。
AI 中文摘要
我们推导了平面束缚偏心轨道上无自旋致密双星经相对一阶后牛顿（1PN）阶且辐射反应为线性阶的单周期一阶 Magnusian，并构造了相关的一阶近星点返回映射。结合保守1PN动力学及其雅可比输运，以及2.5PN和3.5PN辐射反应力，我们在0<e<1的范围内得到了所有四个分量的闭式解，未对偏心率进行展开。对所有8个Iyer-Will辐射反应规范参数的依赖简化为周期上同调，因此在径向周期内抵消。该结果重现了平均能量和角动量损失、其圆极限以及1PN径向轨道要素的长期演化。剩余的两个分量编码了耗散角 sector 信息。将得到的相空间更新投影到受扰近星点返回截面上，得到了返回时间和 apsidal 相位的修正。随后，我们将严格一阶映射与由同一 Magnusian 构造的部分指数化映射进行比较。该比较与可观测量相关：在固定近星点指数下，经过40个径向周期的代表性演化，严格映射给出更小的残差；而部分指数化使累积近星点计时残差减少了约一个数量级。在等质量的代表性单周期网格上，部分指数化在每个采样点都改善了径向作用量和能量更新。
英文摘要
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.
Comments24 pages, 2 figures
