Wave effect of gravitational waves intersected with a microlens field II:An adaptive hierarchical tree algorithm and population study  

作　　者：Xikai Shan Guoliang Li Xuechun Chen Wen Zhao Bin Hu Shude Mao 

机构地区：[1]Purple Mountain Observatory,Chinese Academy of Sciences,Nanjing 210023,China [2]Department of Astronomy,Tsinghua University,Beijing 100084,China [3]Institute for Frontier in Astronomy and Astrophysics,Beijing Normal University,Beijing 102206,China [4]School of Physics and Astronomy,Beijing Normal University,Beijing 100875,China [5]School of Astronomy and Space Science,University of Science and Technology of China,Hefei 230026,China [6]CAS Key Laboratory for Researches in Galaxies and Cosmology,Department of Astronomy,University of Science and Technology of China,Chinese Academy of Sciences,Hefei 230026,China

出　　处：《Science China(Physics,Mechanics & Astronomy)》2025年第1期237-250,共14页中国科学:物理学、力学、天文学(英文版)

基　　金：supported by the National Natural Science Foundation of China(Grant Nos.U1931210,11673065,and 11273061);the science research grants from the China Manned Space Project(Grant No.CMS-CSST-2021-A11);support by the National Natural Science Foundation of China(Grant No.12333001);support by the National Natural Science Foundation of China(Grant No.12133005)。

摘　　要：The gravitational lensing wave effect generated by a microlensing field embedded in a lens galaxy is an inevitable phenomenon in strong lensed gravitational waves(SLGWs).This effect presents both challenges and opportunities for the detection and appli-cation of SLGWs.However,investigating this wave effect requires computing a complete diffraction integral over each microlens in the field.This is extremely time-consuming due to the large number of microlenses(10^(3)-10^(6)).Therefore,simply adding all the microlenses is impractical.Additionally,the complexity of the time delay surface makes the lens plane resolution a crucial factor in controlling numerical errors.In this paper,we propose a trapezoid approximation-based adaptive hierarchical tree algo-rithm to meet the challenges of calculation speed and precision.We find that this algorithm accelerates the calculation by four orders of magnitude compared to the simple adding method and is one order of magnitude faster than the fixed hierarchical tree algorithm proposed for electromagnetic microlensing.More importantly,our algorithm ensures controllable numerical errors,increasing confidence in the results.Together with our previous work(Sci.China-Phys.Mech.Astron.66,239511,2023),this paper addresses all numerical issues,including integral convergence,precision,and computational time1).Finally,we conducted a population study on the microlensing wave effect of SLGWs using this algorithm and found that the microlensing wave effect cannot be ignored,especially for Type II SLGWs(from saddle position of the time delay surface)due to their intrinsic geometric structures and their typical intersection with a denser microlensing field.Statistically,more than 33%(11%)of SLGWs have a mismatch larger than 1%(3%)compared to the unlensed waveform.Additionally,we found that the mismatch between signal pairs in a doubly imaged GW is generally larger than 10^(−3),and 61%(25%)of signal pairs have a mismatch larger than 1%(3%).Therefore,the microlensing-induced mismatch can redu

关 键 词：gravitational lensing diffractional integral algorithm gravitational wave 

分 类 号：P142.84[天文地球—天体物理] P111[天文地球—天文学]