AI 中文总结
本文提出“由内而外”的解析框架建模超大质量黑洞双星旋进，将从天体物理主导转向引力波主导的轨道半长轴作为自由参数，该参数对引力波背景谱形振幅最敏感，可用于脉冲星计时阵列及激光干涉空间天线的相关研究。
AI 中文摘要
两个超大质量黑洞（SMBHs）的旋进与并合会在低频引力波（GWs）中释放巨大能量。近期脉冲星计时阵列（PTA）对随机纳赫兹引力波背景（GWB）的观测结果与SMBH双星起源相符。来自PTA及即将发射的激光干涉空间天线（LISA）的GW数据，可探测电磁约束稀缺的双星演化晚期阶段，但相关天体物理的复杂性要求采用优化的研究方法。本文提出，利用PTA需约束的关键物理量是双星旋进从天体物理主导阶段转向GW主导阶段的轨道半长轴（记为$a_{\rm GW}$），该量应作为GWB分析中的自由参数。基于此，本文提出一种“由内而外”的简单解析框架来建模SMBH双星旋进：在轨道间距略大于$a_{\rm GW}$时，假设天体物理旋进时标服从幂律标度；而最外层阶段（PTA阶段之前）则通过延迟时间简单建模。研究表明，GWB的谱形与振幅对$a_{\rm GW}$（以$10^9 M_{\odot}$为归一化基准、等质量双星且以引力单位表示）最为敏感，对内幂律指数和外延迟时间的依赖较弱；GWB对$a_{\rm GW}$的质量及质量比标度、以及内外天体物理旋进阶段的边界则基本不敏感。本文将该模型与气体驱动和恒星驱动的双星旋进模型进行对比，并讨论其对LISA及GW源参数推断的意义。
英文摘要
The inspiral and merger of two supermassive black holes (SMBHs) releases immense energy in low-frequency gravitational waves (GWs). Recent pulsar timing array (PTA) observations of the stochastic nHz GW background (GWB) are consistent with a SMBH binary origin. GW data from PTAs and from the upcoming Laser Interferometer Space Antenna (LISA) can probe late-stage binary evolution where electromagnetic constraints are scarce. However, the complexity of the relevant astrophysics necessitates a well optimized approach. I argue that a key physical quantity to constrain with PTAs is the orbital semi-major axis at which binary inspiral transitions from the astrophysical to the GW-dominated regime ($a_{\rm GW}$). This quantity should be treated as a free parameter in analysis of the GWB. Using this premise, I present a simple analytic framework for modeling SMBH binary inspiral in an "inside-out" fashion. At orbital separations slightly larger than $a_{\rm GW}$, a power-law scaling for the astrophysical inspiral timescale is assumed, while the outermost phase (prior to the PTA regime) is simply modeled via a delay time. I show that the GWB spectral shape and amplitude are most sensitive to $a_{\rm GW}$ (normalized to $10^9 M_{\odot}$, equal-mass binaries and expressed in gravitational units), with weaker dependence on the inner power-law index and the outer delay time. The GWB is largely insensitive to the mass and mass-ratio scaling of $a_{\rm GW}$ and to the boundary between the inner and outer astrophysical inspiral regimes. I compare with models for gas- and stellar-driven binary inspiral and discuss implications for LISA and for GW source parameter inference.
Comments29 pages, 12 figures, submitted to ApJ. Comments welcome
