标题： 圆轨道双星系统产生的引力波：带电多极截断的收敛性 显示英文标题

标题： Gravitational waves from binary systems in circular orbits: Convergence of a dressed multipole truncation

摘要： 引力辐射起源于圆形轨道上的致密双星系统，通常表示为辐射多极矩的无限求和。 在慢速运动近似下，每个多极矩则表示为关于v/c的后牛顿展开式，其中v/c是轨道速度与光速的比值。 辐射的裸多极截断是指仅保留每个矩的后牛顿展开式的主导项，但对所有多极矩进行求和。 在质量比很小的双星系统情况下，先前的一篇论文表明，裸多极级数对于所有v/c < 2/e的值都收敛，其中e是自然对数的底数。 在本文中，我们将分析扩展到辐射的修饰多极截断，在这种截断中，主导项被相对阶为(v/c)^2和(v/c)^3的项进行修正。 我们发现，修饰多极级数也对所有v/c < 2/e的值收敛，并且在v/c < 0.2时，与数值“精确”结果（在1%以内）一致。 显示英文摘要

摘要： The gravitational radiation originating from a compact binary system in circular orbit is usually expressed as an infinite sum over radiative multipole moments. In a slow-motion approximation, each multipole moment is then expressed as a post-Newtonian expansion in powers of v/c, the ratio of the orbital velocity to the speed of light. The bare multipole truncation of the radiation consists in keeping only the leading-order term in the post-Newtonian expansion of each moment, but summing over all the multipole moments. In the case of binary systems with small mass ratios, the bare multipole series was shown in a previous paper to converge for all values v/c < 2/e, where e is the base of natural logarithms. In this paper, we extend the analysis to a dressed multipole truncation of the radiation, in which the leading-order moments are corrected with terms of relative order (v/c)^2 and (v/c)^3. We find that the dressed multipole series converges also for all values v/c < 2/e, and that it coincides (within 1%) with the numerically ``exact'' results for v/c < 0.2.