[论文解读] Gravitational waves from pulsars: emission by the magnetic field induced distortion

S. Bonazzola, Éric Gourgoulhon|arXiv (Cornell University)|Feb 21, 1996

Pulsars and Gravitational Waves Research参考文献 6被引用 61

一句话总结

本文计算了由自身磁场扭曲的旋转中子星产生的引力波辐射，表明辐射发生在旋转频率Ω及其两倍频率（2Ω）处。关键结果是，对于某些磁场构型（如随机磁场或超导内部结构），即使观测到的磁偶极矩较小，引力波振幅仍足以被LIGO/VIRGO探测到。

ABSTRACT

The gravitational wave emission by a distorted rotating fluid star is computed. The distortion is supposed to be symmetric around some axis inclined with respect to the rotation axis. In the general case, the gravitational radiation is emitted at two frequencies: $Ω$ and $2Ω$, where $Ω$ is the rotation frequency. The obtained formulæ are applied to the specific case of a neutron star distorted by its own magnetic field. Assuming that the period derivative $\dot P$ of pulsars is a measure of their magnetic dipole moment, the gravitational wave amplitude can be related to the observable parameters $P$ and $\dot P$ and to a factor $β$ which measures the efficiency of a given magnetic dipole moment in distorting the star. $β$ depends on the nuclear matter equation of state and on the magnetic field distribution. The amplitude at the frequency $2Ω$, expressed in terms of $P$, $\dot P$ and $β$, is independent of the angle $α$ between the magnetic axis and the rotation axis, whereas at the frequency $Ω$, the amplitude increases as $α$ decreases. The value of $β$ for specific models of magnetic field distributions has been computed by means of a numerical code giving self-consistent models of magnetized neutron stars within general relativity. It is found that the distortion at fixed magnetic dipole moment is very dependent of the magnetic field distribution; a stochastic magnetic field or a superconductor stellar interior greatly increases $β$ with respect to the uniformly magnetized perfect conductor case and might lead to gravitational waves detectable by the VIRGO or LIGO interferometers. The amplitude modulation of the signal induced by the daily rotation of the Earth has been computed and specified to the case of the Crab pulsar and VIRGO

研究动机与目标

• 建立旋转流体中子星在内部磁场作用下产生引力波辐射的模型。
• 将引力波振幅与可观测的脉冲星参数P和Ṗ以及畸变效率因子β相关联。
• 研究β如何依赖于中子星的状态方程和磁场分布。
• 评估此类引力波被LIGO和VIRGO激光干涉仪探测的可能性。
• 探索引力波观测在约束脉冲星内部磁场结构方面的潜力。

提出的方法

• 采用广义相对论框架，计算旋转对称流体星在非轴对称畸变下引力辐射的正式方法。
• 利用广义相对论形式，通过准各向同性坐标系中的度规展开系数计算质量四极矩Izz。
• 将坐标系从准各向同性（QI）转换至渐近笛卡尔多极坐标（ACMC）系统，以提取四极矩。
• 使用广义相对论中自洽磁化中子星模型（Bocquet et al. 1995代码）进行β的数值计算。
• 推导出在频率Ω和2Ω处的引力波振幅h₊和h×，其依赖于β和脉冲星参数。
• 分析地球自转对信号的每日调制效应，以评估在地面激光干涉仪中探测的可行性。

实验结果

研究问题

• RQ1 中子星内部磁场是否能引起足够不对称性，从而产生可探测的引力波？
• RQ2 引力波振幅如何随磁场轴与自转轴之间夹角的变化而变化？
• RQ3 磁场分布（如均匀、随机、超导）在增强引力波信号方面起什么作用？
• RQ4 观测到的周期导数Ṗ在多大程度上可用于通过畸变因子β推断引力波振幅？
• RQ5 由于地球自转引起的信号调制是否有助于将引力波信号与仪器噪声区分开来？

主要发现

• 引力辐射在Ω和2Ω频率处均有发射，且2Ω分量与磁场轴和自转轴之间的夹角α无关。
• Ω频率的振幅随α减小而增大，表明当磁场轴与自转轴更接近对齐时，辐射更强。
• 对于随机磁场或II型超导体内部结构，β值显著高于均匀磁化理想导体的情况。
• 在有利构型下，引力波振幅可达到LIGO和VIRGO探测器的灵敏度水平，即使基于观测到的磁偶极矩。
• 由于地球自转引起的信号调制可用于区分引力波波形，尤其对蟹状星云脉冲星和VIRGO探测器而言。
• 若实现正向探测，将有助于约束内部磁场结构，为理解脉冲星磁层和中子星内部提供新见解。