引力波探测原理札记：LIGO干涉相移的五个起源

Abstract

巨型迈克尔逊激光干涉仪是探测引力波的有效手段。本文研究了激光干涉引力波观察仪(Laser Interferometer Gravitational-Wave Observatory, LIGO)中的干涉臂长、干涉激光波长和频率等物理量在引力波振幅与引力波潮汐力作用下的变化量。本文总结出引力波引起LIGO干涉相位移动的五个物理因素: ①干涉臂标准长度的纯几何改变(非潮汐力贡献); ②激光标准波长的纯几何改变(非潮汐力贡献)；③干涉臂长度受潮汐力影响导致的改变(属引力波潮汐力贡献)；④激光波长受潮汐力影响导致的胀缩效应(属引力波潮汐力贡献)；⑤激光频率的弱相干效应。在引力波作用下，在互相垂直的两条干涉臂中的激光会有不同频移，这一频率弱相干条件也会影响干涉相位差。本文说明引力波潮汐力(引力落差)所导致的干涉激光波长屈伸效应能在LISA (Laser Interferometer Space Antenna)中有测量意义。本文还讨论了GW150914引力波信号频率变化率与描述螺旋合并双黑洞的引力波Blanchet频率方程之间的符合程度,发现GW150914引力波信号观察与理论在±30%差距上相符。 Giant Michelson interferometer is one of the essential means of gravitational wave detection. The influence of gravitational-tidal-force assisted laser wavelength stretch and laser-frequency soft coherence on the interference phase in LIGO (Laser Interferometer Gravitational-Wave Observatory) is investigated. It can be found that there are five physical origins of LIGO interference phase shift in LIGO gravitational wave detection: i) purely geometric change in standard length of interferometer arms (non-tidal contribution), ii) purely geometric change in standard length of laser wavelength (non-tidal contribution), iii) gravitational-wave tidal-force assisted change in interferometer arms (tidal contribution), iv) gravitational-wave tidal-force assisted change in laser wavelength (tidal contribution), and v) feeble coherence of laser frequency caused by gravitational wave in LIGO interferometer. The laser frequency shift in two vertical interference arms can occur due to gravitational wave, and hence such a faint coherence condition would also lead to interference pattern change when the gravitational wave propagates through the LIGO. The effect of flexion and extension in laser wavelength resulting from gravitational tidal force caused by a passing gravitational wave would have significance of measurement in LISA (Laser Interferometer Space Antenna). The frequency change rate of GW150914 gravitational wave signal resulting from in spiral, merger and ring-down of black-hole binaries has been addressed, and it can be found that the logarithm of the detected gravitational-wave frequency change rate agrees with the first-order Blanchet frequency equation within accuracy of ±30%.