Geometric approach for the modified second generation time delay interferometry

Detalhes bibliográficos
Autor(a) principal: Wang, Pan-Pan
Data de Publicação: 2022
Outros Autores: Qian, Wei-Liang [UNESP], Tan, Yu-Jie, Wu, Han-Zhong, Shao, Cheng-Gang
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Institucional da UNESP
Texto Completo: http://dx.doi.org/10.1103/PhysRevD.106.024003
http://hdl.handle.net/11449/240526
Resumo: Time delay interferometry (TDI) is an algorithm proposed to suppress the laser frequency noise in space-borne gravitational-wave detectors. As a post-processing technique, it is implemented by constructing a virtual equal-arm interferometer through an appropriate combination of the time-shifted data streams. Such an approach is tailored to the intrinsic feature of space-based gravitational-wave detection, namely, the distances between spacecraft are governed by orbital dynamics and thus cannot be held constant. Among different implementations, geometric TDI was introduced as a method of exhaustion to evaluate the second-generation TDI combinations. The applications of the algebraic approach based on computational algebraic geometry, on the other hand, are mostly restricted to first- and modified first-generation TDI. Besides, geometric TDI furnishes an intuitive physical interpretation of the synthesis of the virtual optical paths. In this paper, geometric TDI is utilized to investigate the modified second-generation TDI combinations in conjunction with a ternary search algorithm. The distinction between second-generation and modified second-generation TDI solutions is elaborated regarding the rate of change of the arm lengths with respect to the opposite cyclic directions. For the 16-link combinations, 40 second-generation TDI solutions are recovered, among which nine are identified as the modified second-generation ones. Furthermore, we explore the properties of the modified second-generation TDI solutions, which turn out to be potentially preferable in practice. Regarding the Taylor expansion of arm lengths in time, the expressions for the leading-order optical path residuals for the relevant geometric TDI combinations are derived, which are further specified using the Keplerian orbits of the spacecraft for the LISA detector constellation. The response function, noise power spectral density, and signal-to-noise ratio of the TDI solutions are given analytically and discussed. We obtain three distinct sensitivity curves among nine 16-link modified second-generation TDI combinations, while eight sensitivity curves are encountered out of 31 second-generation ones. It is argued that the modified second-generation TDI solutions present a quantitative advantage over their second-generation counterparts. Even though the noise suppressions of both scenarios are found to be at the same level, owing to the cancellations in the response function caused by the temporal symmetry of the arm lengths, the magnitude of the gravitational-wave signals is less pronounced for the second-generation TDI solutions. Moreover, analytic analysis confirms that the alternative modified second-generation TDI solutions are desirable as they possess fewer zeros in the average response function and the noise power spectral density, in accordance with previous findings.
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spelling Geometric approach for the modified second generation time delay interferometryTime delay interferometry (TDI) is an algorithm proposed to suppress the laser frequency noise in space-borne gravitational-wave detectors. As a post-processing technique, it is implemented by constructing a virtual equal-arm interferometer through an appropriate combination of the time-shifted data streams. Such an approach is tailored to the intrinsic feature of space-based gravitational-wave detection, namely, the distances between spacecraft are governed by orbital dynamics and thus cannot be held constant. Among different implementations, geometric TDI was introduced as a method of exhaustion to evaluate the second-generation TDI combinations. The applications of the algebraic approach based on computational algebraic geometry, on the other hand, are mostly restricted to first- and modified first-generation TDI. Besides, geometric TDI furnishes an intuitive physical interpretation of the synthesis of the virtual optical paths. In this paper, geometric TDI is utilized to investigate the modified second-generation TDI combinations in conjunction with a ternary search algorithm. The distinction between second-generation and modified second-generation TDI solutions is elaborated regarding the rate of change of the arm lengths with respect to the opposite cyclic directions. For the 16-link combinations, 40 second-generation TDI solutions are recovered, among which nine are identified as the modified second-generation ones. Furthermore, we explore the properties of the modified second-generation TDI solutions, which turn out to be potentially preferable in practice. Regarding the Taylor expansion of arm lengths in time, the expressions for the leading-order optical path residuals for the relevant geometric TDI combinations are derived, which are further specified using the Keplerian orbits of the spacecraft for the LISA detector constellation. The response function, noise power spectral density, and signal-to-noise ratio of the TDI solutions are given analytically and discussed. We obtain three distinct sensitivity curves among nine 16-link modified second-generation TDI combinations, while eight sensitivity curves are encountered out of 31 second-generation ones. It is argued that the modified second-generation TDI solutions present a quantitative advantage over their second-generation counterparts. Even though the noise suppressions of both scenarios are found to be at the same level, owing to the cancellations in the response function caused by the temporal symmetry of the arm lengths, the magnitude of the gravitational-wave signals is less pronounced for the second-generation TDI solutions. Moreover, analytic analysis confirms that the alternative modified second-generation TDI solutions are desirable as they possess fewer zeros in the average response function and the noise power spectral density, in accordance with previous findings.MOE Key Laboratory of Fundamental Physical Quantities Measurement Hubei Key Laboratory of Gravitation and Quantum Physics PGMF School of Physics Huazhong University of Science and TechnologyEscola de Engenharia de Lorena Universidade de São Paulo, LorenaFaculdade de Engenharia de Guaratinguetá Universidade Estadual Paulista, GuaratinguetáCenter for Gravitation and Cosmology College of Physical Science and Technology Yangzhou UniversityFaculdade de Engenharia de Guaratinguetá Universidade Estadual Paulista, GuaratinguetáHuazhong University of Science and TechnologyUniversidade de São Paulo (USP)Universidade Estadual Paulista (UNESP)Yangzhou UniversityWang, Pan-PanQian, Wei-Liang [UNESP]Tan, Yu-JieWu, Han-ZhongShao, Cheng-Gang2023-03-01T20:21:02Z2023-03-01T20:21:02Z2022-07-15info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articlehttp://dx.doi.org/10.1103/PhysRevD.106.024003Physical Review D, v. 106, n. 2, 2022.2470-00292470-0010http://hdl.handle.net/11449/24052610.1103/PhysRevD.106.0240032-s2.0-85134707990Scopusreponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengPhysical Review Dinfo:eu-repo/semantics/openAccess2023-03-01T20:21:02Zoai:repositorio.unesp.br:11449/240526Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestopendoar:29462024-08-06T00:02:20.728399Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false
dc.title.none.fl_str_mv Geometric approach for the modified second generation time delay interferometry
title Geometric approach for the modified second generation time delay interferometry
spellingShingle Geometric approach for the modified second generation time delay interferometry
Wang, Pan-Pan
title_short Geometric approach for the modified second generation time delay interferometry
title_full Geometric approach for the modified second generation time delay interferometry
title_fullStr Geometric approach for the modified second generation time delay interferometry
title_full_unstemmed Geometric approach for the modified second generation time delay interferometry
title_sort Geometric approach for the modified second generation time delay interferometry
author Wang, Pan-Pan
author_facet Wang, Pan-Pan
Qian, Wei-Liang [UNESP]
Tan, Yu-Jie
Wu, Han-Zhong
Shao, Cheng-Gang
author_role author
author2 Qian, Wei-Liang [UNESP]
Tan, Yu-Jie
Wu, Han-Zhong
Shao, Cheng-Gang
author2_role author
author
author
author
dc.contributor.none.fl_str_mv Huazhong University of Science and Technology
Universidade de São Paulo (USP)
Universidade Estadual Paulista (UNESP)
Yangzhou University
dc.contributor.author.fl_str_mv Wang, Pan-Pan
Qian, Wei-Liang [UNESP]
Tan, Yu-Jie
Wu, Han-Zhong
Shao, Cheng-Gang
description Time delay interferometry (TDI) is an algorithm proposed to suppress the laser frequency noise in space-borne gravitational-wave detectors. As a post-processing technique, it is implemented by constructing a virtual equal-arm interferometer through an appropriate combination of the time-shifted data streams. Such an approach is tailored to the intrinsic feature of space-based gravitational-wave detection, namely, the distances between spacecraft are governed by orbital dynamics and thus cannot be held constant. Among different implementations, geometric TDI was introduced as a method of exhaustion to evaluate the second-generation TDI combinations. The applications of the algebraic approach based on computational algebraic geometry, on the other hand, are mostly restricted to first- and modified first-generation TDI. Besides, geometric TDI furnishes an intuitive physical interpretation of the synthesis of the virtual optical paths. In this paper, geometric TDI is utilized to investigate the modified second-generation TDI combinations in conjunction with a ternary search algorithm. The distinction between second-generation and modified second-generation TDI solutions is elaborated regarding the rate of change of the arm lengths with respect to the opposite cyclic directions. For the 16-link combinations, 40 second-generation TDI solutions are recovered, among which nine are identified as the modified second-generation ones. Furthermore, we explore the properties of the modified second-generation TDI solutions, which turn out to be potentially preferable in practice. Regarding the Taylor expansion of arm lengths in time, the expressions for the leading-order optical path residuals for the relevant geometric TDI combinations are derived, which are further specified using the Keplerian orbits of the spacecraft for the LISA detector constellation. The response function, noise power spectral density, and signal-to-noise ratio of the TDI solutions are given analytically and discussed. We obtain three distinct sensitivity curves among nine 16-link modified second-generation TDI combinations, while eight sensitivity curves are encountered out of 31 second-generation ones. It is argued that the modified second-generation TDI solutions present a quantitative advantage over their second-generation counterparts. Even though the noise suppressions of both scenarios are found to be at the same level, owing to the cancellations in the response function caused by the temporal symmetry of the arm lengths, the magnitude of the gravitational-wave signals is less pronounced for the second-generation TDI solutions. Moreover, analytic analysis confirms that the alternative modified second-generation TDI solutions are desirable as they possess fewer zeros in the average response function and the noise power spectral density, in accordance with previous findings.
publishDate 2022
dc.date.none.fl_str_mv 2022-07-15
2023-03-01T20:21:02Z
2023-03-01T20:21:02Z
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
format article
status_str publishedVersion
dc.identifier.uri.fl_str_mv http://dx.doi.org/10.1103/PhysRevD.106.024003
Physical Review D, v. 106, n. 2, 2022.
2470-0029
2470-0010
http://hdl.handle.net/11449/240526
10.1103/PhysRevD.106.024003
2-s2.0-85134707990
url http://dx.doi.org/10.1103/PhysRevD.106.024003
http://hdl.handle.net/11449/240526
identifier_str_mv Physical Review D, v. 106, n. 2, 2022.
2470-0029
2470-0010
10.1103/PhysRevD.106.024003
2-s2.0-85134707990
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv Physical Review D
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.source.none.fl_str_mv Scopus
reponame:Repositório Institucional da UNESP
instname:Universidade Estadual Paulista (UNESP)
instacron:UNESP
instname_str Universidade Estadual Paulista (UNESP)
instacron_str UNESP
institution UNESP
reponame_str Repositório Institucional da UNESP
collection Repositório Institucional da UNESP
repository.name.fl_str_mv Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)
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