利用简单数学原理分析引力波数据  

Gravitational wave data processing based on fundamental mathematics

作　　者：陈雪玲 孙浩然 张蕴熙 胡一鸣 CHEN Xue-ling;SUN Hao-ran;ZHANG Yun-xi;HU Yi-ming(School of Physics and Astronomy,Sun Yat-sen University,Zhuhai,Guangdong 519802,China)

机构地区：[1]中山大学物理与天文学院,广东珠海519082

出　　处：《大学物理》2025年第3期106-111,118,共7页College Physics

基　　金：国家自然科学基金(12173104);国家重点研发计划(2020YFC2201400);广东省基础与应用基础研究基金委员会重大项目(2019B0303020)资助。

摘　　要：自从2015年激光干涉引力波天文台探测到引力波事件GW150914以来,人类打开了用引力波手段探知宇宙的新窗口,引力波研究也成为了物理学与天文学的科研热点,也促使3位引力波专家获得了2017年的诺贝尔奖.虽然引力波研究的前沿会应用到数值相对论、大规模高性能数值计算等技术,但是引力波数据分析的核心原理其实极为简单.在本文中,我们尝试展示利用简单数学原理分析引力波数据:通过短时傅里叶变换,将时域的引力波数据转化成时间-频率域;将双黑洞旋近信号的时间-频率关系与数据进行匹配,获取双致密星质量、并合时刻的最可几值.与LIGO官方结果的对比表明,相关方法虽然精度有限,但在噪声表现较为理想时,上述简单数学原理可以有效实现对引力波源物理参数的提取.Since the Laser Interferometric Gravitational Wave Observatory detected the gravitational wave event GW150914 in 2015,the gravitatinoal wave window has been opened to explore the Universe.Gravitational wave research has become a hotspot in physics and astronomy,and it helped three gravitational wave experts to win the Nobel Prize in 2017.Although the frontier of gravitational wave research requires advanced methods such as numerical relativity and large-scale high-performance numerical computation,the core principle of gravitational wave data analysis is actually very simple.In this paper,we try to demonstrate the use of simple mathematical principles to analyze gravitational wave data:through the short-time Fourier transform,the time domain gravitational wave data can be transformed into the time-frequency domain;the time-frequency relation of the binary black hole inspiral signal is matched with the data to obtain the most probable value of the mass of the binary dense star,the moment of merger.Comparison with the official results of LIGO shows that the relevant method,although with limited accuracy,the above simple mathematical principle can efficiently extract the physical parameters of the gravitational wave source when the noise behaviour is close to ideal.

关 键 词：引力波 数据处理 时频分析 恒Q变换 

分 类 号：P141[天文地球—天体物理]