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Most works in the literature build their data analysis pipelines relying on a particular set of TDI channels, the so-called AET variables, which are orthogonal under idealized conditions. By relaxing the assumption of a perfectly equilateral LISA configuration, we investigate to which degree these channels remain orthogonal and compare them to other TDI channels. We show that different sets of TDI variables are more robust under perturbations of the perfect equilateral configuration, better preserving their orthogonality and, thus, leading to a more accurate estimate of the instrumental noise. Moreover, we investigate the impact of considering the noise levels associated with each instrumental noise source to be independent of one another, generalizing the analysis from two to twelve noise parameters. We find that, in this scenario, the assumption of orthogonality is broken for all the TDI variables, leading to a misestimation of measurement error for some of the noise parameters. Remarkably, we find that for a flat power-law signal, the reconstruction of the signal parameters is nearly unaffected in these various configurations. We explore the impact of choosing different sets of Time-Delay Interferometry (TDI) variables for detecting and reconstructing Stochastic Gravitational Wave Background (SGWB) signals and estimating the instrumental noise in LISA. Most works in the literature build their data analysis pipelines relying on a particular set of TDI channels, the so-called AET variables, which are orthogonal under idealized conditions. By relaxing the assumption of a perfectly equilateral LISA configuration, we investigate to which degree these channels remain orthogonal and compare them to other TDI channels. We show that different sets of TDI variables are more robust under perturbations of the perfect equilateral configuration, better preserving their orthogonality and, thus, leading to a more accurate estimate of the instrumental noise. Moreover, we investigate the impact of considering the noise levels associated with each instrumental noise source to be independent of one another, generalizing the analysis from two to twelve noise parameters. We find that, in this scenario, the assumption of orthogonality is broken for all the TDI variables, leading to a misestimation of measurement error for some of the noise parameters. Remarkably, we find that for a flat power-law signal, the reconstruction of the signal parameters is nearly unaffected in these various configurations. Hartwig, Olaf; Lilley, Marc; Muratore, Martina; Pieroni, Mauro" /> <meta name="keywords" content="CERN Document Server, WebSearch, CERN Document Server" /> <script type="text/javascript" src="https://cds.cern.ch/js/jquery.min.js"></script>  <link rel="stylesheet" href="https://cds.cern.ch/img/webnews.css" type="text/css" />  <script type="text/javascript" src="https://cds.cern.ch/js/webnews.js?v=20131009"></script> <meta property="fb:app_id" content="137353533001720"/> <script type="text/x-mathjax-config"> MathJax.Hub.Config({ tex2jax: {inlineMath: [['$','$']], processEscapes: true}, showProcessingMessages: false, messageStyle: "none" }); </script> <script src="/MathJax/MathJax.js?config=TeX-AMS_CHTML" type="text/javascript"> </script>  <meta content="APS : Stochastic gravitational wave background reconstruction for a nonequilateral and unequal-noise LISA constellation" name="citation_title" /> <meta content="Hartwig, Olaf" name="citation_author" /> <meta content="Lilley, Marc" name="citation_author" /> <meta content="Pieroni, Mauro" name="citation_author" /> <meta content="Muratore, Martina" name="citation_author" /> <meta content="10.1103/PhysRevD.107.123531" name="citation_doi" /> <meta content="Phys. 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Most works in the literature build their data analysis pipelines relying on a particular set of TDI channels, the so-called AET variables, which are orthogonal under idealized conditions. By relaxing the assumption of a perfectly equilateral LISA configuration, we investigate to which degree these channels remain orthogonal and compare them to other TDI channels. We show that different sets of TDI variables are more robust under perturbations of the perfect equilateral configuration, better preserving their orthogonality and, thus, leading to a more accurate estimate of the instrumental noise. Moreover, we investigate the impact of considering the noise levels associated with each instrumental noise source to be independent of one another, generalizing the analysis from two to twelve noise parameters. We find that, in this scenario, the assumption of orthogonality is broken for all the TDI variables, leading to a misestimation of measurement error for some of the noise parameters. 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We show that different sets of TDI variables are more robust under perturbations of the perfect equilateral configuration, better preserving their orthogonality and, thus, leading to a more accurate estimate of the instrumental noise. Moreover, we investigate the impact of considering the noise levels associated with each instrumental noise source to be independent of one another, generalizing the analysis from two to twelve noise parameters. We find that, in this scenario, the assumption of orthogonality is broken for all the TDI variables, leading to a misestimation of measurement error for some of the noise parameters. Remarkably, we find that for a flat power-law signal, the reconstruction of the signal parameters is nearly unaffected in these various configurations." property="og:description" />  <meta content="summary" name="twitter:card" /> <style></style> </head> <body class="CERN32Document32Server search" lang="zh">  <div id="cern-toolbar"> <h1><a href="http://cern.ch" title="CERN">CERN <span>Accelerating science</span></a></h1> <ul> <li class="cern-accountlinks"><a class="cern-account" href="https://cds.cern.ch/youraccount/login?ln=zh_TW&referer=https%3A//cds.cern.ch/record/2855977%3Fln%3Dzh_TW" title="Sign in to your CERN account">Sign in</a></li> <li><a class="cern-directory" href="http://cern.ch/directory" title="Search CERN resources and browse the directory">Directory</a></li> </ul> </div>   <div role="banner" class="clearfix" id="header"> <div class="header-inner inner"> <hgroup class="clearfix"> <h2 id="site-name"> <a rel="home" title="Home" href="/"><span>CERN Document Server</span></a> </h2> <h3 id="site-slogan">Access articles, reports and multimedia content in HEP</h3> </hgroup> <div role="navigation" id="main-navigation" class="cdsmenu"> <h2 class="element-invisible">Main menu</h2><ul class="links inline clearfix"> <li class="menu-386 first active-trail"><a class="active-trail" href="https://cds.cern.ch/?ln=zh_TW">搜尋</a></li> <li class="menu-444 "><a class="" title="" href="https://cds.cern.ch/submit?ln=zh_TW">提交</a></li> <li class="menu-426 "><a class="" href="https://cds.cern.ch/help/?ln=zh_TW">幫助</a></li> <li class="leaf hassubcdsmenu"> <a hreflang="en" class="header" href="https://cds.cern.ch/youraccount/display?ln=zh_TW">個人化</a> <ul class="subsubcdsmenu"><li><a href="https://cds.cern.ch/youralerts/list?ln=zh_TW">Your alerts</a></li><li><a href="https://cds.cern.ch/yourbaskets/display?ln=zh_TW">Your baskets</a></li><li><a href="https://cds.cern.ch/yourcomments?ln=zh_TW">Your comments</a></li><li><a href="https://cds.cern.ch/youralerts/display?ln=zh_TW">Your searches</a></li></ul></li> </ul> </div> </div> </div>  <table class="navtrailbox"> <tr> <td class="navtrailboxbody"> <a href="/?ln=zh_TW" class="navtrail">主頁</a> > Stochastic gravitational wave background reconstruction for a nonequilateral and unequal-noise LISA constellation </td> </tr> </table> </div> <div class="pagebody"><div class="pagebodystripemiddle"> <div class="detailedrecordbox"> <div class="detailedrecordtabs"> <div> <ul class="detailedrecordtabs"><li class="on first"><a href="/record/2855977/?ln=zh_TW">Information </a></li><li class=""><a href="/record/2855977/files?ln=zh_TW">Files </a></li></ul> <div id="tabsSpacer" style="clear:both;height:0px"> </div></div> </div> <div class="detailedrecordboxcontent"> <div class="top-left-folded"></div> <div class="top-right-folded"></div> <div class="inside">  <abbr class="unapi-id" title="2855977"></abbr> <style type="text/css">  </style> <table class="formatRecordTableFullWidth" > <tr> <td class="formatRecordHeader" style="background-image: url('https://cds.cern.ch/img/journals.jpg');" colspan="2">  Article </td> </tr> <script type="text/javascript"> $( document ).ready(function() { $('.showAuthor').on('click', function() { var author = '<p>' + $(this).data('name') + '</p>'; var affiliation = $(this).data('affiliation') + '</br>'; var contribution = $(this).data('contribution') + '</br>'; $.magnificPopup.open({ items: { src: '<div id="ovelary-mathjax" class="overlay-white oc-content overlay-white-500">' + author + affiliation + contribution + '</div>', type: 'inline' }, callbacks: { open: function() { var div = document.getElementById("overlay-mathjax") MathJax.Hub.Queue(["Typeset", MathJax.Hub, div]); }, } }) }) }); </script> <tr><td class="formatRecordLabel"> Report number </td><td style="padding-left:5px;"><a href="http://arxiv.org/abs/arXiv:2303.15929">arXiv:2303.15929</a></td></tr> <tr><td class="formatRecordLabel"> Title </td><td style="padding-left:5px;"><b>Stochastic gravitational wave background reconstruction for a nonequilateral and unequal-noise LISA constellation</b></td></tr> <tr><td class="formatRecordLabel" style="vertical-align:top;">Related title</td><td style="padding-left:5px; ">Stochastic gravitational wave background reconstruction for a non-equilateral and unequal-noise LISA constellation<br/></td></tr> <tr><td class="formatRecordLabel"><span style="white-space:nowrap;"> Author(s) </span> </td><td style="padding-left:5px;"><a href="https://cds.cern.ch/search?f=author&p=Hartwig%2C%20Olaf&ln=zh_TW">Hartwig, Olaf</a> (SYRTE, Paris) ; <a href="https://cds.cern.ch/search?f=author&p=Lilley%2C%20Marc&ln=zh_TW">Lilley, Marc</a> (SYRTE, Paris) ; <a href="https://cds.cern.ch/search?f=author&p=Muratore%2C%20Martina&ln=zh_TW">Muratore, Martina</a> (Potsdam, Max Planck Inst. ; Trento U. ; TIFPA-INFN, Trento) ; <a href="https://cds.cern.ch/search?f=author&p=Pieroni%2C%20Mauro&ln=zh_TW">Pieroni, Mauro</a> (CERN)</td></tr> <tr><td class="formatRecordLabel"> Publication </td><td style="padding-left:5px;">2023-06-15</td></tr> <tr><td class="formatRecordLabel"> Imprint </td><td style="padding-left:5px;">2023-03-28</td></tr> <tr><td class="formatRecordLabel"> Number of pages </td><td style="padding-left:5px;">31</td></tr> <tr><td class="formatRecordLabel"> Note </td><td style="padding-left:5px;">31 pages, 13 figures, and supplementary material</td></tr> <tr><td class="formatRecordLabel"> In: </td><td style="padding-left:5px;"><a href="http://dx.doi.org/10.1103/PhysRevD.107.123531"><i>Phys. Rev. D</i> 107 (2023) 123531</a> </a></td></tr> <tr><td class="formatRecordLabel"> DOI </td><td style="padding-left:5px;"><a href="http://dx.doi.org/10.1103/PhysRevD.107.123531" title="DOI" target="_blank">10.1103/PhysRevD.107.123531</a> (publication) <tr><td class="formatRecordLabel"> Subject category </td><td style="padding-left:5px;">astro-ph.CO ; Astrophysics and Astronomy ; gr-qc ; General Relativity and Cosmology</td></tr> <tr><td class="formatRecordLabel"> Abstract </td><td style="padding-left:5px;">We explore the impact of choosing different sets of Time-Delay Interferometry (TDI) variables for detecting and reconstructing Stochastic Gravitational Wave Background (SGWB) signals and estimating the instrumental noise in LISA. Most works in the literature build their data analysis pipelines relying on a particular set of TDI channels, the so-called AET variables, which are orthogonal under idealized conditions. By relaxing the assumption of a perfectly equilateral LISA configuration, we investigate to which degree these channels remain orthogonal and compare them to other TDI channels. We show that different sets of TDI variables are more robust under perturbations of the perfect equilateral configuration, better preserving their orthogonality and, thus, leading to a more accurate estimate of the instrumental noise. Moreover, we investigate the impact of considering the noise levels associated with each instrumental noise source to be independent of one another, generalizing the analysis from two to twelve noise parameters. We find that, in this scenario, the assumption of orthogonality is broken for all the TDI variables, leading to a misestimation of measurement error for some of the noise parameters. Remarkably, we find that for a flat power-law signal, the reconstruction of the signal parameters is nearly unaffected in these various configurations.</td></tr> <tr><td class="formatRecordLabel"> Copyright/License </td><td style="padding-left:5px;">publication: © 2023 American Physical Society<br/>preprint: (License: <a href="http://creativecommons.org/licenses/by/4.0/">CC BY 4.0</a>)</td></tr> </table> <br /><div style="max-width:1024px;margin:auto"><div style="overflow-x:auto;display:inline;width:100%;"><a href="/record/2855977/plots#0"><img style="vertical-align:middle;" src="https://cds.cern.ch/record/2855977/files/noise_spectra.png" title=" TM and OMS PSDs as a function of frequency in units of $1/$Hz." width="200px"/></a> <a href="/record/2855977/plots#1"><img style="vertical-align:middle;" src="https://cds.cern.ch/record/2855977/files/Signal_noise_responses_Michelson.png" title=" Signal response (first row), noise spectra (second row), and strain sensitivities (last row) defined as in~\cref{eq:signal_and_noise_projections}, for the XYZ Michelson variables (first column) and for their orthogonal AET combinations as well as for the $\zeta$ variable (second column) considering equal (solid lines) and un-equal (dashed-line) arm-lengths." width="200px"/></a> <a href="/record/2855977/plots#2"><img style="vertical-align:middle;" src="https://cds.cern.ch/record/2855977/files/Signal_noise_responses_Sagnac.png" title=" Signal response (first row), noise spectra (second row) and strain sensitivities (last row) defined as in~\cref{eq:signal_and_noise_projections}, for the Sagnac $\alpha, \beta, \gamma$ variables (first column) and for their orthogonal combinations $\mathcal{A}$, $\mathcal{E}$, and $\mathcal{T}$ as well as for the $\zeta$ variable (second column)." width="200px"/></a> <a href='/record/2855977/plots'>Show more plots</a></div></div><br /> <br/>Corresponding record in: <a href="http://inspirehep.net/record/2646534">Inspire</a> <small> </small> <br/> <br/><br/><div align="right"><div style="padding-bottom:2px;padding-top:30px;"><span class="moreinfo" style="margin-right:10px;"> <a href="" class="moreinfo">Back to search</a> </span></div></div> <div class="bottom-left-folded"><div class="recordlastmodifiedbox" style="position:relative;margin-left:1px"> 記錄創建於2023-04-13，最後更新在2023-07-08</div></div> <div class="bottom-right-folded" style="text-align:right;padding-bottom:2px;"> <span class="moreinfo" style="margin-right:10px;"><a href="/search?ln=zh_TW&p=recid%3A2855977&rm=wrd" class="moreinfo">相似記錄</a></span></div> </div> </div> </div> <br/> <br /> <div class="detailedrecordminipanel"> <div class="top-left"></div><div class="top-right"></div> <div class="inside"> <div id="detailedrecordminipanelfile" style="width:33%;float:left;text-align:center;margin-top:0"> <div><small class="detailedRecordActions">全文:</small> <br /><a href="/record/2855977/files/2303.15929.pdf"><img style="border:none" src="/img/file-icon-text-34x48.gif" alt="Download fulltext" /><br />PDF</a><br /></div> </div> <div id="detailedrecordminipanelreview" style="width:30%;float:left;text-align:center"> </div> <div id="detailedrecordminipanelactions" style="width:36%;float:right;text-align:right;"> <ul class="detailedrecordactions"> <li><a href="/yourbaskets/add?ln=zh_TW&recid=2855977">Add to personal basket</a></li> <li>Export as <a style="text-decoration:underline;font-weight:normal" href="/record/2855977/export/hx?ln=zh_TW">BibTeX</a>, <a style="text-decoration:underline;font-weight:normal" href="/record/2855977/export/hm?ln=zh_TW">MARC</a>, <a style="text-decoration:underline;font-weight:normal" href="/record/2855977/export/xm?ln=zh_TW">MARCXML</a>, <a style="text-decoration:underline;font-weight:normal" href="/record/2855977/export/xd?ln=zh_TW">DC</a>, <a style="text-decoration:underline;font-weight:normal" href="/record/2855977/export/xe?ln=zh_TW">EndNote</a>,  <a style="text-decoration:underline;font-weight:normal" href="/record/2855977/export/xn?ln=zh_TW">NLM</a>, <a style="text-decoration:underline;font-weight:normal" href="/record/2855977/export/xw?ln=zh_TW">RefWorks</a> </li> </ul> <div style='padding-left: 13px;'>  <div id="bookmark"></div> <div id="bookmark_sciencewise"></div> <style type="text/css"> #bookmark_sciencewise, #bookmark {float: left;} #bookmark_sciencewise li {padding: 2px; 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