陈-西蒙斯修正引力中来自脉冲星周期跃变的引力波宇称破缺应变

中文摘要 AI 辅助

我们研究了动力学陈-西蒙斯引力中脉冲星周期跃变产生的引力波双折射效应，动力学陈-西蒙斯引力是受弦论与量子引力启发的广义相对论宇称破缺扩展理论。我们采用Hartle-Thorne慢转形式体系构建中子星背景模型，并对陈-西蒙斯耦合参数$\alpha$进行微扰处理，推导了描述轴向引力扰动的修正Regge-Wheeler方程，计算了由此产生的与偏振相关的相移。宇称破缺相互作用会在右旋与左旋圆偏振之间产生分数不对称性，该不对称性与$\alpha^2$成正比，随频率和自转速率线性增长，且随恒星半径的四次方衰减。对于常密度内部模型，我们得到了背景标量场的解析匹配解，并证明内部曲率因子恒为零——内部解是共形平坦的——因此标量偶极子完全由真空外部区域提供；中心致密的物态方程只会增大预测的信号强度。我们进一步将分析扩展到包含中子超流体与带电成分之间较差自转的双流体模型；由此产生的修正受周期跃变的分数振幅本身限制，与物态方程无关，对于典型脉冲星参数而言可以忽略不计。通过无量纲量$\zeta\propto \alpha M/R_\star^{3}$表示时，毫秒脉冲星的偏振分数不对称性在微扰有效性边界的千赫兹频率下可达约$10^{-3}$，比当前地面探测器对应变不对称性的灵敏度高出四个数量级。不过，实际的约束上限受分辨引力波应变比值所需的信噪比限制。

英文摘要

We investigate gravitational-wave birefringence from pulsar glitches in dynamical Chern-Simons gravity, a parity-violating extension of general relativity motivated by string theory and quantum gravity. Using the Hartle-Thorne slow-rotation formalism to model the neutron star background and a perturbative treatment of the Chern-Simons coupling $α$, we derive the modified Regge-Wheeler equation governing axial gravitational perturbations and compute the resulting polarization-dependent phase shift. The parity-violating interaction produces a fractional asymmetry between the right- and left-handed circular polarizations that scales as $α^2$, grows linearly with frequency and rotation rate, and falls as the fourth power of the stellar radius. For a constant-density interior model we obtain an analytic matching solution for the background scalar field, and show that the interior curvature factor vanishes identically--the interior solution being conformally flat--so that the scalar dipole is sourced entirely in the vacuum exterior; a centrally condensed equation of state can only increase the predicted signal. We further extend the analysis to a two-fluid model incorporating differential rotation between the neutron superfluid and the charged component; the resulting correction is bounded by the fractional glitch amplitude itself, independently of the equation of state, and is negligible for typical pulsar parameters. Expressed through the dimensionless quantity $ζ\propto αM/R_\star^{3}$, the fractional polarization asymmetry for millisecond pulsars reaches $\sim 10^{-3}$ at kilohertz frequencies at the boundary of perturbative validity--four orders of magnitude above the sensitivity of current ground-based detectors to strain asymmetries. However, realistic bounds are limited by the signal-to-noise ratio required to resolve a ratio of gravitational wave strains.

补充信息

备注

41 pages