{"id":"https://openalex.org/W7214067533","doi":"https://doi.org/10.48550/arxiv.2609.25662","title":"Probing the Mass--Redshift Dependence of Binary Black Holes and its Implications for $H_0$ with GWTC-5.0","display_name":"Probing the Mass--Redshift Dependence of Binary Black Holes and its Implications for $H_0$ with GWTC-5.0","publication_year":2026,"publication_date":"2026-09-22","ids":{"openalex":"https://openalex.org/W7214067533","doi":"https://doi.org/10.48550/arxiv.2609.25662"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.25662","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.25662","pdf_url":"https://arxiv.org/pdf/2609.25662","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2609.25662","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5152553469","display_name":"Yang Liu","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"government","lineage":["https://openalex.org/I19820366"]},{"id":"https://openalex.org/I2802340896","display_name":"Purple Mountain Observatory","ror":"https://ror.org/02eb4t121","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I2802340896"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Liu, Yang","raw_affiliation_strings":["Purple Mountain Observatory , Chinese Academy of Sciences , No. 10 Yuanhua Road , Nanjing 210023 , China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Purple Mountain Observatory , Chinese Academy of Sciences , No. 10 Yuanhua Road , Nanjing 210023 , China","institution_ids":["https://openalex.org/I19820366","https://openalex.org/I2802340896"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5152533060","display_name":"Puxun Wu","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Wu, Puxun","raw_affiliation_strings":["Department of Physics , Key Laboratory of Low Dimensional Quantum Structures and Quantum Control of Ministry of Education , and"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Physics , Key Laboratory of Low Dimensional Quantum Structures and Quantum Control of Ministry of Education , and","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5122284317","display_name":"Jun-Jie Wei","orcid":"https://orcid.org/0000-0003-0162-2488","observed_orcids":["https://orcid.org/0000-0003-0162-2488"]},"institutions":[{"id":"https://openalex.org/I173759888","display_name":"Hunan Normal University","ror":"https://ror.org/053w1zy07","country_code":"CN","type":"education","lineage":["https://openalex.org/I173759888"]},{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"government","lineage":["https://openalex.org/I19820366"]},{"id":"https://openalex.org/I2802340896","display_name":"Purple Mountain Observatory","ror":"https://ror.org/02eb4t121","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I2802340896"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Wei, Jun-Jie","raw_affiliation_strings":["Hunan Research Center of the Basic Discipline for Quantum Effects and Quantum Technologies , Hunan Normal University , Changsha , Hunan 410081 , China","Purple Mountain Observatory , Chinese Academy of Sciences , No. 10 Yuanhua Road , Nanjing 210023 , China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Hunan Research Center of the Basic Discipline for Quantum Effects and Quantum Technologies , Hunan Normal University , Changsha , Hunan 410081 , China","institution_ids":["https://openalex.org/I173759888"]},{"raw_affiliation_string":"Purple Mountain Observatory , Chinese Academy of Sciences , No. 10 Yuanhua Road , Nanjing 210023 , China","institution_ids":["https://openalex.org/I19820366","https://openalex.org/I2802340896"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5152544346","display_name":"Xue-Feng Wu","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"government","lineage":["https://openalex.org/I19820366"]},{"id":"https://openalex.org/I2802340896","display_name":"Purple Mountain Observatory","ror":"https://ror.org/02eb4t121","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I2802340896"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Wu, Xue-Feng","raw_affiliation_strings":["Purple Mountain Observatory , Chinese Academy of Sciences , No. 10 Yuanhua Road , Nanjing 210023 , China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Purple Mountain Observatory , Chinese Academy of Sciences , No. 10 Yuanhua Road , Nanjing 210023 , China","institution_ids":["https://openalex.org/I19820366","https://openalex.org/I2802340896"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10463","display_name":"Pulsars and Gravitational Waves Research","score":0.9883000254631042,"subfield":{"id":"https://openalex.org/subfields/3103","display_name":"Astronomy and Astrophysics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10463","display_name":"Pulsars and Gravitational Waves Research","score":0.9883000254631042,"subfield":{"id":"https://openalex.org/subfields/3103","display_name":"Astronomy and Astrophysics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10095","display_name":"Cosmology and Gravitation Theories","score":0.0027000000700354576,"subfield":{"id":"https://openalex.org/subfields/3103","display_name":"Astronomy and Astrophysics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10026","display_name":"Galaxies: Formation, Evolution, Phenomena","score":0.0017000000225380063,"subfield":{"id":"https://openalex.org/subfields/3103","display_name":"Astronomy and Astrophysics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/binary-black-holes","display_name":"binary black holes","score":0.9480000138282776},{"id":"https://openalex.org/keywords/hubble-constant","display_name":"Hubble constant","score":0.925000011920929},{"id":"https://openalex.org/keywords/copulas","display_name":"copulas","score":0.7070000171661377},{"id":"https://openalex.org/keywords/clayton-copula","display_name":"Clayton copula","score":0.8999999761581421},{"id":"https://openalex.org/keywords/gaussian-copula","display_name":"Gaussian copula","score":0.8309999704360962},{"id":"https://openalex.org/keywords/black-hole-mass-distribution","display_name":"black hole mass distribution","score":0.5920000076293945},{"id":"https://openalex.org/keywords/gwtc-5-0","display_name":"GWTC-5.0","score":0.8539999723434448},{"id":"https://openalex.org/keywords/bayesian-model-selection","display_name":"Bayesian model selection","score":0.8339999914169312},{"id":"https://openalex.org/keywords/black-hole-formation-channels","display_name":"black hole formation channels","score":0.5870000123977661}],"concepts":[{"id":"https://openalex.org/C33024259","wikidata":"https://www.wikidata.org/wiki/Q76250","display_name":"Redshift","level":3,"score":0.769599974155426},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.7569000124931335},{"id":"https://openalex.org/C44870925","wikidata":"https://www.wikidata.org/wiki/Q37547","display_name":"Astrophysics","level":1,"score":0.6270999908447266},{"id":"https://openalex.org/C103874350","wikidata":"https://www.wikidata.org/wiki/Q179916","display_name":"Hubble's law","level":4,"score":0.5077999830245972},{"id":"https://openalex.org/C26405456","wikidata":"https://www.wikidata.org/wiki/Q338","display_name":"Cosmology","level":2,"score":0.4749000072479248},{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"score":0.47209998965263367},{"id":"https://openalex.org/C2908647359","wikidata":"https://www.wikidata.org/wiki/Q2625603","display_name":"Population","level":2,"score":0.45579999685287476},{"id":"https://openalex.org/C134222618","wikidata":"https://www.wikidata.org/wiki/Q2713132","display_name":"Mass distribution","level":3,"score":0.4424999952316284},{"id":"https://openalex.org/C32602459","wikidata":"https://www.wikidata.org/wiki/Q4913879","display_name":"Binary black hole","level":3,"score":0.41429999470710754},{"id":"https://openalex.org/C17618745","wikidata":"https://www.wikidata.org/wiki/Q207509","display_name":"Copula (linguistics)","level":2,"score":0.37880000472068787},{"id":"https://openalex.org/C37061001","wikidata":"https://www.wikidata.org/wiki/Q3531721","display_name":"Binary Independence Model","level":3,"score":0.34929999709129333},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.33219999074935913},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.299699991941452},{"id":"https://openalex.org/C165216359","wikidata":"https://www.wikidata.org/wiki/Q670653","display_name":"Marginal distribution","level":3,"score":0.2847000062465668},{"id":"https://openalex.org/C98444146","wikidata":"https://www.wikidata.org/wiki/Q318","display_name":"Galaxy","level":2,"score":0.2766999900341034},{"id":"https://openalex.org/C149441793","wikidata":"https://www.wikidata.org/wiki/Q200726","display_name":"Probability distribution","level":2,"score":0.2565000057220459},{"id":"https://openalex.org/C18653775","wikidata":"https://www.wikidata.org/wiki/Q1333358","display_name":"Joint probability distribution","level":2,"score":0.25459998846054077},{"id":"https://openalex.org/C186603090","wikidata":"https://www.wikidata.org/wiki/Q55505926","display_name":"Distribution function","level":2,"score":0.25029999017715454}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.25662","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.25662","pdf_url":"https://arxiv.org/pdf/2609.25662","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2609.25662","doi":"https://doi.org/10.48550/arxiv.2609.25662","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.25662","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2609.25662","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.25662","pdf_url":"https://arxiv.org/pdf/2609.25662","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G1001267258","display_name":null,"funder_award_id":"12422307","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G2550178766","display_name":null,"funder_award_id":"12373053","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3240438835","display_name":null,"funder_award_id":"12321003","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3913827429","display_name":null,"funder_award_id":"2025M783235","funder_id":"https://openalex.org/F4320321543","funder_display_name":"China Postdoctoral Science Foundation"},{"id":"https://openalex.org/G4811230103","display_name":null,"funder_award_id":"XDB0550400","funder_id":"https://openalex.org/F4320321133","funder_display_name":"Chinese Academy of Sciences"},{"id":"https://openalex.org/G7486532588","display_name":null,"funder_award_id":"12275080","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320321133","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35"},{"id":"https://openalex.org/F4320321543","display_name":"China Postdoctoral Science Foundation","ror":"https://ror.org/0426zh255"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7214067533.pdf","grobid_xml":"https://content.openalex.org/works/W7214067533.grobid-xml"},"referenced_works_count":89,"referenced_works":["https://openalex.org/W1939611531","https://openalex.org/W2021748112","https://openalex.org/W2061930234","https://openalex.org/W2088668851","https://openalex.org/W2126507078","https://openalex.org/W2168500122","https://openalex.org/W2252795400","https://openalex.org/W2444247080","https://openalex.org/W2471282254","https://openalex.org/W2512413576","https://openalex.org/W2606855799","https://openalex.org/W2669423079","https://openalex.org/W2765081049","https://openalex.org/W2767506920","https://openalex.org/W2783579090","https://openalex.org/W2795322206","https://openalex.org/W2807614683","https://openalex.org/W2808670662","https://openalex.org/W2891084346","https://openalex.org/W2891993472","https://openalex.org/W2898683405","https://openalex.org/W2900135842","https://openalex.org/W2935849916","https://openalex.org/W2958936606","https://openalex.org/W2964797456","https://openalex.org/W2969942922","https://openalex.org/W2980421388","https://openalex.org/W2994776863","https://openalex.org/W2999365684","https://openalex.org/W3002026006","https://openalex.org/W3018876182","https://openalex.org/W3035016752","https://openalex.org/W3041142389","https://openalex.org/W3081939279","https://openalex.org/W3082518999","https://openalex.org/W3122936591","https://openalex.org/W3138392732","https://openalex.org/W3153656148","https://openalex.org/W3160629185","https://openalex.org/W3161193838","https://openalex.org/W3161363993","https://openalex.org/W3170997806","https://openalex.org/W3173762688","https://openalex.org/W3199919347","https://openalex.org/W3201054534","https://openalex.org/W3202225058","https://openalex.org/W4213225762","https://openalex.org/W4221161590","https://openalex.org/W4226083230","https://openalex.org/W4280536472","https://openalex.org/W4289346401","https://openalex.org/W4289594454","https://openalex.org/W4292875581","https://openalex.org/W4306746299","https://openalex.org/W4311533701","https://openalex.org/W4362655360","https://openalex.org/W4378093011","https://openalex.org/W4380589207","https://openalex.org/W4386874560","https://openalex.org/W4387427453","https://openalex.org/W4388447243","https://openalex.org/W4391335311","https://openalex.org/W4392019584","https://openalex.org/W4394604606","https://openalex.org/W4401216590","https://openalex.org/W4404461157","https://openalex.org/W4405766394","https://openalex.org/W4406143476","https://openalex.org/W4408519095","https://openalex.org/W4409908306","https://openalex.org/W4409981637","https://openalex.org/W4410790771","https://openalex.org/W4410927464","https://openalex.org/W4414534509","https://openalex.org/W4414699576","https://openalex.org/W4415329223","https://openalex.org/W4415620163","https://openalex.org/W4415678274","https://openalex.org/W7084068803","https://openalex.org/W7117115319","https://openalex.org/W7155524359","https://openalex.org/W7161834721","https://openalex.org/W7162392274","https://openalex.org/W7162569353","https://openalex.org/W7162575693","https://openalex.org/W7163780866","https://openalex.org/W7168158497","https://openalex.org/W7172494905","https://openalex.org/W7212318354"],"related_works":["https://openalex.org/W4390193229","https://openalex.org/W4390136650","https://openalex.org/W7084068803","https://openalex.org/W4387427453","https://openalex.org/W4409908306","https://openalex.org/W4391923782","https://openalex.org/W4402641027","https://openalex.org/W4392019584","https://openalex.org/W4410770110","https://openalex.org/W7154763380"],"abstract_inverted_index":{"The":[0],"mass":[1,21,57,76,115,253],"and":[2,58,77,92,116],"redshift":[3,60,78,117,248,257],"distributions":[4,73],"of":[5,13,45,61,74,88,250],"merging":[6],"binary":[7],"black":[8],"holes":[9],"(BBHs)":[10],"bear":[11],"imprints":[12],"their":[14,46,95],"astrophysical":[15],"formation":[16],"channels.":[17],"Whether":[18],"the":[19,40,51,55,59,71,80,83,113,122,126,129,155,164,167,179,183,201,205,212,229,232,240,251,256],"BH":[20],"distribution":[22,254],"evolves":[23],"with":[24,79,128,140,149,204,219,246],"redshift,":[25],"however,":[26],"remains":[27,244],"an":[28],"open":[29],"question.":[30],"In":[31],"this":[32],"paper,":[33],"we":[34,93,105],"employ":[35],"copula":[36,151],"functions,":[37],"which":[38,112,134],"describe":[39],"dependence":[41,52,196],"between":[42,54],"variables":[43],"independently":[44],"marginal":[47,72],"distributions,":[48],"to":[49,223,225],"probe":[50],"structure":[53],"primary":[56,75,114,137,252],"BBH":[62,99],"mergers.":[63],"We":[64],"construct":[65],"five":[66],"population":[67],"models":[68,174],"by":[69],"coupling":[70],"Gaussian":[81],"copula,":[82,85,133],"Clayton":[84,132],"or":[86],"one":[87],"its":[89,150],"three":[90],"rotations,":[91],"constrain":[94],"hyperparameters":[96],"using":[97],"235":[98],"events":[100],"from":[101,154,172],"GWTC-5.0.":[102],"For":[103],"comparison,":[104],"also":[106],"adopt":[107],"a":[108,146,194],"baseline":[109,184,213],"model":[110,127,185,209,214],"in":[111],"are":[118,175],"assumed":[119],"independent.":[120],"Among":[121],"copula-based":[123,217],"models,":[124],"only":[125],"$180^\\circ$":[130],"rotated":[131],"couples":[135],"higher":[136],"masses":[138],"preferentially":[139],"high":[141],"redshifts,":[142],"exhibits":[143],"evidence":[144,227],"for":[145,193],"nonzero":[147],"correlation,":[148],"parameter":[152],"deviating":[153],"independence":[156],"limit":[157],"at":[158],"more":[159],"than":[160],"$1\u03c3$":[161],"significance.":[162],"Importantly,":[163],"constraints":[165],"on":[166,231],"Hubble":[168],"constant":[169],"($H_0$)":[170],"derived":[171],"these":[173],"mutually":[176],"consistent":[177,245],"within":[178],"$68\\%$":[180],"confidence":[181],"level;":[182],"yields":[186],"$H_0=74.3^{+13.7}_{-19.6}~\\mathrm{km\\":[187],"s^{-1}\\":[188],"Mpc^{-1}}$,":[189],"indicating":[190],"that":[191,239],"allowing":[192],"mass--redshift":[195],"does":[197],"not":[198],"significantly":[199],"bias":[200],"$H_0$":[202],"inference":[203],"current":[206,241],"dataset.":[207],"Bayesian":[208],"comparison":[210],"favors":[211],"over":[215,255],"all":[216],"alternatives,":[218],"log-Bayes":[220],"factors":[221],"corresponding":[222],"weak":[224],"moderate":[226],"against":[228],"latter":[230],"Jeffreys":[233],"scale.":[234],"Our":[235],"results":[236],"thus":[237],"imply":[238],"GWTC-5.0":[242],"sample":[243],"no":[247],"evolution":[249],"range":[258],"probed.":[259]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-24T00:00:00"}