This paper presents the gravitationalwave measurement of the Hubble constant HSUB0SUB using the detections from the first and second observing runs of the Advanced LIGO and Virgo detector network. The presence of the transient electromagnetic counterpart of the binary neutron star GW170817 led to the first standardsiren measurement of HSUB0SUB. Here we additionally use binary black hole detections in conjunction with galaxy catalogs and report a joint measurement. Our updated measurement is HSUB0SUB  69816 km sSUP1SUP MpcSUP1SUP 68.3 of the highest density posterior interval with a flatinlog prior which is an improvement by a factor of 1.04 about 4 over the GW170817only value of 69817 km sSUP1SUP MpcSUP1SUP. A significant additional contribution currently comes from GW170814 a loud and welllocalized detection from a part of the sky thoroughly covered by the Dark Energy Survey. With numerous detections anticipated over the upcoming years an exhaustive understanding of other systematic effects are also going to become increasingly important. These results establish the path to cosmology using gravitationalwave observations with and without transient electromagnetic counterparts.
['Gravitational wave astronomy', 'Hubble constant', 'Astrophysics - Cosmology and Nongalactic Astrophysics', 'General Relativity and Quantum Cosmology']
A Gravitationalwave Measurement of the Hubble Constant Following the Second Observing Run of Advanced LIGO and Virgo
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O ganesyan , 16, 17 G. H. O gin , 175 J. J. O h , 153 S. H. O h , 153 F. O hme , 9, 10 H. O hta , 83 M. A. O kada , 15 M. O liver , 101 P. O ppermann , 9, 10 R ichard J. O ram , 7 B. O'R eilly , 7 R. G. O rmiston , 43 L. F. O rtega , 30 R. O'S haughnessy , 62 S. O ssokine , 76 D. J. O ttaway , 57 H. O vermier , 7 B. J. O wen , 85 A. E. P ace , 90 G. P agano , 20, 21 M. A. P age , 66 G. P agliaroli , 16, 17 A. P ai , 130 S. A. P ai , 60 J. R. P alamos , 72 O. P alashov , 150 C. P alomba , 33 H. P an , 91 P. K. P anda , 144 P. T. H. P ang , 94, 37 C. P ankow , 58 F. P annarale , 119, 33 B. C. P ant , 60 F. P aoletti , 21 A. P aoli , 29 A. P arida , 3 W. P arker , 7, 169 D. P ascucci , 46, 37 A. P asqualetti , 29 R. P assaquieti , 20, 21 D. P assuello , 21 M. P atil , 158 B. P atricelli , 20, 21 E. P ayne , 6 B. L. P earlstone , 46 T. C. P echsiri , 30 A. J. P edersen , 42 M. P edraza , 1 R. P edurand , 23, 176 A. P ele , 7 S. P enn , 177 A. P erego , 117, 118 C. J. P erez , 47 C. P' erigois , 34 A. P erreca , 117, 118 J. P etermann , 134 H. P. P feiffer , 76 M. P helps , 9, 10 K. S. P hukon , 3 O. J. P iccinni , 119, 33 M. P ichot , 65 F. P iergiovanni , 63, 64 V. P ierro , 116, 69 G. P illant , 29 L. P inard , 23 I. M. P into , 116, 69, 89 M. P irello , 47 M. P itkin , 46 W. P lastino , 165, 166 R. P oggiani , 20, 21 D. Y. T. P ong , 94 S. P onrathnam , 3 P. P opolizio , 29 E. K. P orter , 26 J. P owell , 168 A. K. P rajapati , 111 J. P rasad , 3 K. P rasai , 51 R. P rasanna , 144 G. P ratten , 101 T. P restegard , 24 M. P rincipe , 116, 89, 69 G. A. P rodi , 117, 118 L. P rokhorov , 13 M. P unturo , 41 P. P uppo , 33 M. Purrer , 76 H. Q i , 106 V. Q uetschke , 108 P. J. Q uinonez , 35 F. J. R aab , 47 G. R aaijmakers , 142, 37 H. R adkins , 47 N. R adulesco , 65 P. R affai , 110 S. R aja , 60 C. R ajan , 60 B. R ajbhandari , 85 M. R akhmanov , 108 K. E. R amirez , 108 A. R amos -B uades , 101 J aved R ana , 3 K. R ao , 58 P. R apagnani , 119, 33 V. R aymond , 106 M. R azzano , 20, 21 J. R ead , 27 T. R egimbau , 34 L. R ei , 59 S. R eid , 25 D. H. R eitze , 1, 30 P. R ettegno , 127, 178 F. R icci , 119, 33 C. J. R ichardson , 35 J. W. R ichardson , 1 P. M. R icker , 19 G. R iemenschneider , 178, 127 K. R iles , 137 M. R izzo , 58 N. A. R obertson , 1, 46 F. R obinet , 28 A. R occhi , 32 L. R olland , 34 J. G. R ollins , 1 V. J. R oma , 72 M. R omanelli , 71 J. R omano , 85 R. R omano , 4, 5 C. L. R omel , 47 J. H. R omie , 7 C. A. R ose , 24 D. R ose , 27 K. R ose , 121 D. R osi ' nska , 74 S. G. R osofsky , 19 M. P. R oss , 179 S. R owan , 46 A. Rudiger , 9, 10, GLYPH<3> P. R uggi , 29 G. R utins , 132 K. R yan , 47 S. S achdev , 90 T. S adecki , 47 M. S akellariadou , 146 O. S. S alafia , 180, 44, 45 L. S alconi , 29 M. S aleem , 31 A. S amajdar , 37 L. S ammut , 6 E. J. S anchez , 1 L. E. S anchez , 1 N. S anchis -G ual , 181 J. R. S anders , 182 K. A. S antiago , 36 E. S antos , 65 N. S arin , 6 B. S assolas , 23 B. S. S athyaprakash , 90, 106 O. S auter , 137, 34 R. L. S avage , 47 P. S chale , 72 M. S cheel , 48 J. S cheuer , 58 P. S chmidt , 13, 67 R. S chnabel , 134 R. M. S. S chofield , 72 A. S ch onbeck , 134 E. S chreiber , 9, 10 B. W. S chulte , 9, 10 B. F. S chutz , 106 J. S cott , 46 S. M. S cott , 8 E. S eidel , 19 D. S ellers , 7 A. S. S engupta , 183 N. S ennett , 76 D. S entenac , 29 V. S equino , 59 A. S ergeev , 150 Y. S etyawati , 9, 10 D. A. S haddock , 8 T. S haffer , 47 M. S. S hahriar , 58 M. B. S haner , 133 A. S harma , 16, 17 P. S harma , 60 P. S hawhan , 77 H. S hen , 19 R. S hink , 184 D. H. S hoemaker , 14 D. M. S hoemaker , 78 K. S hukla , 141 S. S hyam S undar , 60 K. S iellez , 78 M. S ieniawska , 56 D. S igg , 47 L. P. S inger , 81 D. S ingh , 90 N. S ingh , 74 A. S inghal , 16, 33 A. M. S intes , 101 S. S itmukhambetov , 108 V. S kliris , 106 B. J. J. S lagmolen , 8 T. J. S laven -B lair , 66 J. R. S mith , 27 R. J. E. S mith , 6 S. S omala , 185 E. J. S on , 153 S. S oni , 2 B. S orazu , 46 F. S orrentino , 59 T. S ouradeep , 3 E. S owell , 85 A. P. S pencer , 46 M. S pera , 53, 54 A. K. S rivastava , 111 V. S rivastava , 42 K. S taats , 58 C. S tachie , 65 M. S tandke , 9, 10 D. A. S teer , 26 M. S teinke , 9, 10 J. S teinlechner , 134, 46 S. S teinlechner , 134 D. S teinmeyer , 9, 10 S. P. S tevenson , 168 D. S tocks , 51 R. S tone , 108 D. J. S tops , 13 K. A. S train , 46 G. S tratta , 186, 64 S. E. S trigin , 61 A. S trunk , 47 R. S turani , 187 A. L. S tuver , 188 V. S udhir , 14 T. Z. S ummerscales , 189 L. S un , 1 S. S unil , 111 A. S ur , 56 J. S uresh , 83 P. J. S utton , 106 B. L. S winkels , 37 M. J. S zczepa ' nczyk , 35 M. T acca , 37 S. C. T ait , 46 C. T albot , 6 D. B. T anner , 30 D. T ao , 1 M. T' apai , 131 A. T apia , 27 J. D. T asson , 98 R. T aylor , 1 R. T enorio , 101 L. T erkowski , 134 M. T homas , 7 P. T homas , 47 S. R. T hondapu , 60 K. A. T horne , 7 E. T hrane , 6 S hubhanshu T iwari , 117, 118 S rishti T iwari , 135 V. T iwari , 106 K. T oland , 46 M. T onelli , 20, 21 Z. T ornasi , 46 A. T orres -F orn ' e , 190 C. I. T orrie , 1 D. Toyr a , 13 F. T ravasso , 29, 41 G. T raylor , 7 M. C. T ringali , 74 A. T ripathee , 137 A. T rovato , 26 L. T rozzo , 191, 21 K. W. T sang , 37 M. T se , 14 R. T so , 48 L. T sukada , 83 D. T suna , 83 T. T sutsui , 83 D. T uyenbayev , 108 K. U eno , 83 D. U golini , 192 C. S. U nnikrishnan , 135 A. L. U rban , 2 S. A. U sman , 93 H. V ahlbruch , 10 G. V ajente , 1 G. V aldes , 2 M. V alentini , 117, 118 N. van B akel , 37 M. van B euzekom , 37 J. F. J. van den B rand , 75, 37 C. V an D en B roeck , 37, 193 D. C. V ander -H yde , 42 L. van der S chaaf , 37 J. V. V an H eijningen , 66 A. A. van V eggel , 46 M. V ardaro , 53, 54 V. V arma , 48 S. V ass , 1 M. V as ' uth , 50 A. V ecchio , 13 G. V edovato , 54 J. V eitch , 46 P. J. V eitch , 57 K. V enkateswara , 179 G. V enugopalan , 1 D. V erkindt , 34 F. V etrano , 63, 64 A. V icer ' e , 63, 64 A. D. V iets , 24 S. V inciguerra , 13 D. J. V ine , 132 J.-Y. V inet , 65 S. V itale , 14 T. V o , 42 H. V occa , 40, 41 C. V orvick , 47 S. P. V yatchanin , 61 A. R. W ade , 1 L. E. W ade , 121 M. W ade , 121 R. W alet , 37 M. W alker , 27 L. W allace , 1 S. W alsh , 24 H. W ang , 13 J. Z. W ang , 137 S. W ang , 19 W. H. W ang , 108 Y. F. W ang , 94 R. L. W ard , 8 Z. A. W arden , 35 J. W arner , 47 M. W as , 34 J. W atchi , 102 B. W eaver , 47 L.-W. W ei , 9, 10  \n6  \nM. W einert , 9, 10 A. J. W einstein , 1 R. W eiss , 14 F. W ellmann , 9, 10 L. W en , 66 E. K. W essel , 19 P. W eGLYPH<25>els , 9, 10 J. W. W esthouse , 35 K. W ette , 8 J. T. W helan , 62 B. F. W hiting , 30 C. W hittle , 14 D. M. W ilken , 9, 10 D. W illiams , 46 A. R. W illiamson , 142, 37 J. L. W illis , 1 B. W illke , 10, 9 W. W inkler , 9, 10 C. C. W ipf , 1 H. W ittel , 9, 10 G. W oan , 46 J. W oehler , 9, 10 J. K. W offord , 62 J. L. W right , 46 D. S. W u , 9, 10 D. M. W ysocki , 62 S. X iao , 1 R. X u , 109 H. Y amamoto , 1 C. C. Y ancey , 77 L. Y ang , 120 Y. Y ang , 30 Z. Y ang , 43 M. J. Y ap , 8 M. Y azback , 30 D. W. Y eeles , 106 H ang Y u , 14 H aocun Y u , 14 S. H. R. Y uen , 94 A. K. Z adro ˙ zny , 108 A. Z adro ˙ zny , 157 M. Z anolin , 35 T. Z elenova , 29 J.-P. Z endri , 54 M. Z evin , 58 J. Z hang , 66 L. Z hang , 1 T. Z hang , 46 C. Z hao , 66 G. Z hao , 102 M. Z hou , 58 Z. Z hou , 58 X. J. Z hu , 6 A. B. Z immerman , 194 M. E. Z ucker , 1, 14 and J. Z weizig 1 T he LIGO S cientific C ollaboration and the V irgo C ollaboration  \n1 LIGO, California Institute of Technology, Pasadena, CA 91125, USA  \n2 Louisiana State University, Baton Rouge, LA 70803, USA  \n3 Inter-University Centre for Astronomy and Astrophysics, Pune 411007, India  \n4 Dipartimento di Farmacia, Universit'a di Salerno, I-84084 Fisciano, Salerno, Italy  \n5 INFN, Sezione di Napoli, Complesso Universitario di Monte S.Angelo, I-80126 Napoli, Italy  \nOzGrav, School of Physics  \n&  \nAstronomy, Monash University, Clayton 3800, Victoria, Australia  \n7 LIGO Livingston Observatory, Livingston, LA 70754, USA  \n8 OzGrav, Australian National University, Canberra, Australian Capital Territory 0200, Australia  \n9 Max Planck Institute for Gravitational Physics (Albert Einstein Institute), D-30167 Hannover, Germany  \n10 Leibniz Universitat Hannover, D-30167 Hannover, Germany  \n11 Theoretisch-Physikalisches Institut, Friedrich-Schiller-Universitat Jena, D-07743 Jena, Germany  \n12 University of Cambridge, Cambridge CB2 1TN, United Kingdom  \n13 University of Birmingham, Birmingham B15 2TT, United Kingdom  \n14 LIGO, Massachusetts Institute of Technology, Cambridge, MA 02139, USA  \n15 Instituto Nacional de Pesquisas Espaciais, 12227-010 S˜ao Jos'e dos Campos, S˜ao Paulo, Brazil  \n16 Gran Sasso Science Institute (GSSI), I-67100 L'Aquila, Italy  \n17 INFN, Laboratori Nazionali del Gran Sasso, I-67100 Assergi, Italy  \n18 International Centre for Theoretical Sciences, Tata Institute of Fundamental Research, Bengaluru 560089, India  \n19 NCSA, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA  \n20 Universit'a di Pisa, I-56127 Pisa, Italy  \n21 INFN, Sezione di Pisa, I-56127 Pisa, Italy  \n22 Departamento de Astronom'ıa y Astrof'ısica, Universitat de Val'encia, E-46100 Burjassot, Val'encia, Spain  \n23 Laboratoire des Mat'eriaux Avanc'es (LMA), CNRS / IN2P3, F-69622 Villeurbanne, France  \n24 University of Wisconsin-Milwaukee, Milwaukee, WI 53201, USA  \n25 SUPA, University of Strathclyde, Glasgow G1 1XQ, United Kingdom  \n26 APC, AstroParticule et Cosmologie, Universit'e Paris Diderot, CNRS / IN2P3, CEA / Irfu, Observatoire de Paris, Sorbonne Paris Cit'e, F-75205 Paris Cedex 13,  \nFrance  \n27 California State University Fullerton, Fullerton, CA 92831, USA  \n28 LAL, Univ. Paris-Sud, CNRS / IN2P3, Universit'e Paris-Saclay, F-91898 Orsay, France  \n29 European Gravitational Observatory (EGO), I-56021 Cascina, Pisa, Italy  \n30 University of Florida, Gainesville, FL 32611, USA  \n31 Chennai Mathematical Institute, Chennai 603103, India  \n32 INFN, Sezione di Roma Tor Vergata, I-00133 Roma, Italy  \n33 INFN, Sezione di Roma, I-00185 Roma, Italy  \n34 Laboratoire d'Annecy de Physique des Particules (LAPP), Univ. Grenoble Alpes, Universit'e Savoie Mont Blanc, CNRS / IN2P3, F-74941 Annecy, France  \n35 Embry-Riddle Aeronautical University, Prescott, AZ 86301, USA  \n36 Montclair State University, Montclair, NJ 07043, USA  \n37 Nikhef, Science Park 105, 1098 XG Amsterdam, The Netherlands  \n38 Korea Institute of Science and Technology Information, Daejeon 34141, South Korea  \n39 West Virginia University, Morgantown, WV 26506, USA  \n40 Universit'a di Perugia, I-06123 Perugia, Italy  \n41 INFN, Sezione di Perugia, I-06123 Perugia, Italy  \n42 Syracuse University, Syracuse, NY 13244, USA  \n43 University of Minnesota, Minneapolis, MN 55455, USA  \n44 Universit'a degli Studi di Milano-Bicocca, I-20126 Milano, Italy  \n45 INFN, Sezione di Milano-Bicocca, I-20126 Milano, Italy  \n46 SUPA, University of Glasgow, Glasgow G12 8QQ, United Kingdom  \n47 LIGO Hanford Observatory, Richland, WA 99352, USA  \n48 Caltech CaRT, Pasadena, CA 91125, USA  \n49 Dipartimento di Medicina, Chirurgia e Odontoiatria 'Scuola Medica Salernitana,' Universit'a di Salerno, I-84081 Baronissi, Salerno, Italy 50 Wigner RCP, RMKI, H-1121 Budapest, Konkoly Thege Mikl'os 'ut 29-33, Hungary 51 Stanford University, Stanford, CA 94305, USA 52 Universit'a di Camerino, Dipartimento di Fisica, I-62032 Camerino, Italy 53 Universit'a di Padova, Dipartimento di Fisica e Astronomia, I-35131 Padova, Italy 54 INFN, Sezione di Padova, I-35131 Padova, Italy 55 Montana State University, Bozeman, MT 59717, USA 56 Nicolaus Copernicus Astronomical Center, Polish Academy of Sciences, 00-716, Warsaw, Poland 57 OzGrav, University of Adelaide, Adelaide, South Australia 5005, Australia 58 Center for Interdisciplinary Exploration & Research in Astrophysics (CIERA), Northwestern University, Evanston, IL 60208, USA 59 INFN, Sezione di Genova, I-16146 Genova, Italy 60 RRCAT, Indore, Madhya Pradesh 452013, India 61 Faculty of Physics, Lomonosov Moscow State University, Moscow 119991, Russia 62 Rochester Institute of Technology, Rochester, NY 14623, USA 63 Universit'a degli Studi di Urbino 'Carlo Bo,' I-61029 Urbino, Italy 64 INFN, Sezione di Firenze, I-50019 Sesto Fiorentino, Firenze, Italy 65 Artemis, Universit'e Cˆote d'Azur, Observatoire Cˆote d'Azur, CNRS, CS 34229, F-06304 Nice Cedex 4, France 66 OzGrav, University of Western Australia, Crawley, Western Australia 6009, Australia 67 Department of Astrophysics / IMAPP, Radboud University Nijmegen, P.O. Box 9010, 6500 GL Nijmegen, The Netherlands 68 Dipartimento di Fisica 'E.R. Caianiello,' Universit'a di Salerno, I-84084 Fisciano, Salerno, Italy 69 INFN, Sezione di Napoli, Gruppo Collegato di Salerno, Complesso Universitario di Monte S. Angelo, I-80126 Napoli, Italy 70 Physik-Institut, University of Zurich, Winterthurerstrasse 190, 8057 Zurich, Switzerland 71 Univ Rennes, CNRS, Institut FOTON - UMR6082, F-3500 Rennes, France 72 University of Oregon, Eugene, OR 97403, USA 73 Laboratoire Kastler Brossel, Sorbonne Universit'e, CNRS, ENS-Universit'e PSL, Coll'ege de France, F-75005 Paris, France 74 Astronomical Observatory Warsaw University, 00-478 Warsaw, Poland 75 VU University Amsterdam, 1081 HV Amsterdam, The Netherlands 76 Max Planck Institute for Gravitational Physics (Albert Einstein Institute), D-14476 Potsdam-Golm, Germany 77 University of Maryland, College Park, MD 20742, USA 78 School of Physics, Georgia Institute of Technology, Atlanta, GA 30332, USA 79 Universit'e de Lyon, Universit'e Claude Bernard Lyon 1, CNRS, Institut Lumi'ere Mati'ere, F-69622 Villeurbanne, France 80 Universit'a di Napoli 'Federico II,' Complesso Universitario di Monte S.Angelo, I-80126 Napoli, Italy 81 NASA Goddard Space Flight Center, Greenbelt, MD 20771, USA 82 Dipartimento di Fisica, Universit'a degli Studi di Genova, I-16146 Genova, Italy 83 RESCEU, University of Tokyo, Tokyo, 113-0033, Japan. 84 Tsinghua University, Beijing 100084, China 85 Texas Tech University, Lubbock, TX 79409, USA 86 Universit'a di Roma Tor Vergata, I-00133 Roma, Italy 87 The University of Mississippi, University, MS 38677, USA 88 Missouri University of Science and Technology, Rolla, MO 65409, USA 89 Museo Storico della Fisica e Centro Studi e Ricerche 'Enrico Fermi,' I-00184 Roma, Italy 90 The Pennsylvania State University, University Park, PA 16802, USA 91 National Tsing Hua University, Hsinchu City, 30013 Taiwan, Republic of China 92 Charles Sturt University, Wagga Wagga, New South Wales 2678, Australia 93 University of Chicago, Chicago, IL 60637, USA 94 The Chinese University of Hong Kong, Shatin, NT, Hong Kong 95 Dipartimento di Ingegneria Industriale (DIIN), Universit'a di Salerno, I-84084 Fisciano, Salerno, Italy 96 Seoul National University, Seoul 08826, South Korea 97 Pusan National University, Busan 46241, South Korea 98 Carleton College, Northfield, MN 55057, USA 99 INAF, Osservatorio Astronomico di Padova, I-35122 Padova, Italy 100 OzGrav, University of Melbourne, Parkville, Victoria 3010, Australia 101 Universitat de les Illes Balears, IAC3-IEEC, E-07122 Palma de Mallorca, Spain 102 Universit'e Libre de Bruxelles, Brussels 1050, Belgium 103 Sonoma State University, Rohnert Park, CA 94928, USA 104 Departamento de Matem'aticas, Universitat de Val'encia, E-46100 Burjassot, Val'encia, Spain 105 Columbia University, New York, NY 10027, USA  \n106 Cardi GLYPH<11> University, Cardi GLYPH<11> CF24 3AA, United Kingdom  \n107 University of Rhode Island, Kingston, RI 02881, USA  \n108 The University of Texas Rio Grande Valley, Brownsville, TX 78520, USA  \n109 Bellevue College, Bellevue, WA 98007, USA  \n110 MTA-ELTE Astrophysics Research Group, Institute of Physics, Eotvos University, Budapest 1117, Hungary  \n111 Institute for Plasma Research, Bhat, Gandhinagar 382428, India  \n112 The University of She GLYPH<14> eld, She GLYPH<14> eld S10 2TN, United Kingdom  \n113 IGFAE, Campus Sur, Universidade de Santiago de Compostela, 15782 Spain  \n114 Dipartimento di Scienze Matematiche, Fisiche e Informatiche, Universit'a di Parma, I-43124 Parma, Italy  \n115 INFN, Sezione di Milano Bicocca, Gruppo Collegato di Parma, I-43124 Parma, Italy  \n116 Dipartimento di Ingegneria, Universit'a del Sannio, I-82100 Benevento, Italy  \n117 Universit'a di Trento, Dipartimento di Fisica, I-38123 Povo, Trento, Italy  \n118 INFN, Trento Institute for Fundamental Physics and Applications, I-38123 Povo, Trento, Italy  \n119 Universit'a di Roma 'La Sapienza,' I-00185 Roma, Italy  \n120 Colorado State University, Fort Collins, CO 80523, USA  \n121 Kenyon College, Gambier, OH 43022, USA  \n122 Christopher Newport University, Newport News, VA 23606, USA  \n123 CNR-SPIN, c / o Universit'a di Salerno, I-84084 Fisciano, Salerno, Italy  \n124 Scuola di Ingegneria, Universit'a della Basilicata, I-85100 Potenza, Italy  \n125 National Astronomical Observatory of Japan, 2-21-1 Osawa, Mitaka, Tokyo 181-8588, Japan  \n126 Observatori Astron'omic, Universitat de Val'encia, E-46980 Paterna, Val'encia, Spain  \n127 INFN Sezione di Torino, I-10125 Torino, Italy  \n128 School of Mathematics, University of Edinburgh, Edinburgh EH9 3FD, United Kingdom  \n129 Institute Of Advanced Research, Gandhinagar 382426, India  \n130 Indian Institute of Technology Bombay, Powai, Mumbai 400 076, India  \n131 University of Szeged, D'om t'er 9, Szeged 6720, Hungary  \n132 SUPA, University of the West of Scotland, Paisley PA1 2BE, United Kingdom  \n133 California State University, Los Angeles, 5151 State University Dr, Los Angeles, CA 90032, USA  \n134 Universitat Hamburg, D-22761 Hamburg, Germany  \n135  \nTata Institute of Fundamental Research, Mumbai 400005, India  \n136 INAF, Osservatorio Astronomico di Capodimonte, I-80131 Napoli, Italy  \n137 University of Michigan, Ann Arbor, MI 48109, USA  \n138  \nWashington State University, Pullman, WA 99164, USA  \n139 American University, Washington, D.C. 20016, USA  \n140 University of Portsmouth, Portsmouth, PO1 3FX, United Kingdom  \n141 University of California, Berkeley, CA 94720, USA  \n142 GRAPPA, Anton Pannekoek Institute for Astronomy and Institute for High-Energy Physics, University of Amsterdam, Science Park 904, 1098 XH Amsterdam, The Netherlands  \n143 Delta Institute for Theoretical Physics, Science Park 904, 1090 GL Amsterdam, The Netherlands  \n144 Directorate of Construction, Services & Estate Management, Mumbai 400094 India  \n145 University of Białystok, 15-424 Białystok, Poland  \n146 King's College London, University of London, London WC2R 2LS, United Kingdom  \n147 University of Southampton, Southampton SO17 1BJ, United Kingdom  \n148 Institut de F'ısica d'Altes Energies (IFAE), Barcelona Institute of Science and Technology, and ICREA, E-08193 Barcelona, Spain  \n149 University of Washington Bothell, Bothell, WA 98011, USA  \n150 Institute of Applied Physics, Nizhny Novgorod, 603950, Russia  \n151 Ewha Womans University, Seoul 03760, South Korea  \n152 Inje University Gimhae, South Gyeongsang 50834, South Korea  \n153 National Institute for Mathematical Sciences, Daejeon 34047, South Korea  \n154 Ulsan National Institute of Science and Technology, Ulsan 44919, South Korea  \n155 Maastricht University, P.O. Box 616, 6200 MD Maastricht, The Netherlands  \n156 Bard College, 30 Campus Rd, Annandale-On-Hudson, NY 12504, USA  \n157 NCBJ, 05-400 ' Swierk-Otwock, Poland  \n158 Institute of Mathematics, Polish Academy of Sciences, 00656 Warsaw, Poland  \n159 Cornell University, Ithaca, NY 14850, USA  \n160 Hillsdale College, Hillsdale, MI 49242, USA  \n161 Hanyang University, Seoul 04763, South Korea  \n193  \n162 Korea Astronomy and Space Science Institute, Daejeon 34055, South Korea  \n163 Institute for High-Energy Physics, University of Amsterdam, Science Park 904, 1098 XH Amsterdam, The Netherlands  \n164 NASA Marshall Space Flight Center, Huntsville, AL 35811, USA  \n165 Dipartimento di Matematica e Fisica, Universit'a degli Studi Roma Tre, I-00146 Roma, Italy  \n166 INFN, Sezione di Roma Tre, I-00146 Roma, Italy  \n167 ESPCI, CNRS, F-75005 Paris, France  \n168 OzGrav, Swinburne University of Technology, Hawthorn VIC 3122, Australia  \n169 Southern University and A & MCollege, Baton Rouge, LA 70813, USA  \n170 Centre Scientifique de Monaco, 8 quai Antoine Ier, MC-98000, Monaco  \n171 Indian Institute of Technology Madras, Chennai 600036, India  \n172 Institut des Hautes Etudes Scientifiques, F-91440 Bures-sur-Yvette, France  \n173 IISER-Kolkata, Mohanpur, West Bengal 741252, India  \n174 Institut fur Kernphysik, Theoriezentrum, 64289 Darmstadt, Germany  \n175  \nWhitman College, 345 Boyer Avenue, Walla Walla, WA 99362 USA  \n176 Universit'e de Lyon, F-69361 Lyon, France  \n177 Hobart and William Smith Colleges, Geneva, NY 14456, USA  \n178 Dipartimento di Fisica, Universit'a degli Studi di Torino, I-10125 Torino, Italy  \n179 University of Washington, Seattle, WA 98195, USA  \n180 INAF, Osservatorio Astronomico di Brera sede di Merate, I-23807 Merate, Lecco, Italy  \n181 Centro de Astrof'ısica e Gravita¸c˜ao (CENTRA), Departamento de F'ısica, Instituto Superior T'ecnico, Universidade de Lisboa, 1049-001 Lisboa, Portugal  \n182 Marquette University, 11420 W. Clybourn St., Milwaukee, WI 53233, USA  \n183 Indian Institute of Technology, Gandhinagar Ahmedabad Gujarat 382424, India  \n184 Universit'e de Montr'eal / Polytechnique, Montreal, Quebec H3T 1J4, Canada  \n185 Indian Institute of Technology Hyderabad, Sangareddy, Khandi, Telangana 502285, India  \n186 INAF, Osservatorio di Astrofisica e Scienza dello Spazio, I-40129 Bologna, Italy  \n187 International Institute of Physics, Universidade Federal do Rio Grande do Norte, Natal RN 59078-970, Brazil  \n188 Villanova University, 800 Lancaster Ave, Villanova, PA 19085, USA  \n189 Andrews University, Berrien Springs, MI 49104, USA  \n190 Max Planck Institute for Gravitationalphysik (Albert Einstein Institute), D-14476 Potsdam-Golm, Germany  \n191 Universit'a di Siena, I-53100 Siena, Italy  \n192 Trinity University, San Antonio, TX 78212, USA  \nVan Swinderen Institute for Particle Physics and Gravity, University of Groningen, Nijenborgh 4, 9747 AG Groningen, The Netherlands 194 Department of Physics, University of Texas, Austin, TX 78712, USA  \n(Dated: November 9, 2021)", 'ABSTRACT': 'This paper presents the gravitational-wave measurement of the Hubble constant H 0 using the detections from the first and second observing runs of the Advanced LIGO and Virgo detector network. The presence of the transient electromagnetic counterpart of the binary neutron star GW170817 led to the first standard-siren measurement of H 0. Here we additionally use binary black hole detections in conjunction with galaxy catalogs and report a joint measurement. Our updated measurement is H 0 = 68 : 7 + 17 : 0 GLYPH<0> 7 : 8 km s GLYPH<0> 1 Mpc GLYPH<0> 1 (68 : 3% highest density posterior interval with a flat-in-log prior) which is an improvement by a factor of 1.04 (about 4%) over the GW170817-only value of 68 : 7 + 17 : 5 GLYPH<0> 8 : 3 km s GLYPH<0> 1 Mpc GLYPH<0> 1 . A significant additional contribution currently comes from GW170814, a loud and well-localized detection from a part of the sky thoroughly covered by the Dark Energy Survey. With numerous detections anticipated over the upcoming years, an exhaustive understanding of other systematic e GLYPH<11> ects are also going to become increasingly important. These results establish the path to cosmology using gravitational-wave observations with and without transient electromagnetic counterparts.', '1. INTRODUCTION': 'Gravitational waves (GWs) from compact binary coalescences allow for a direct measurement of the luminosity  \ndistance to their source. This makes them standard-distance indicators, and in conjunction with an identified host galaxy or a set of possible host galaxies, they can be used as standard sirens to construct a redshift-distance relationship and measure cosmological parameters like the Hubble constant H 0 (Schutz 1986; Holz & Hughes 2005; MacLeod & Hogan  \n2008; Nissanke et al. 2010; Sathyaprakash et al. 2010). The GW signature from the binary neutron star (BNS) merger GW170817, along with its coincident electromagnetic (EM) transient associated with the host galaxy NGC4993, led to a first standard-siren measurement of H 0 (Abbott et al. 2017a). This measurement is independent of other state-ofthe-art measurements of H 0, and in particular, independent of the cosmic distance ladder used to calibrate standardizable sources like Type Ia supernovae. The importance of an independent measurement of H 0 is worth highlighting. With the Planck 2018 data release (Aghanim et al. 2020), and the recalibration of supernovae using Large Magellanic Cloud Cepheids (Riess et al. 2019), the tension between early universe measurements of H 0 from Planck and local measurements from the SH0ES project has risen to the 4 : 4GLYPH<27> level. Independent measurements using cosmological Baryon Acoustic Oscillations to calibrate Type Ia supernovae via the inverse distance ladder (Macaulay et al. 2019) and gravitational lensing of quasars in the nearby universe (H0LiCOW Collaboration, Birrer et al. 2019) favor to some degree the early-universe Planck and the local SH0ES measurements respectively. A complementary measurement of H 0 from the multi-messenger GW astronomy sector would help clarify whether the current tension is a statistical anomaly or evidence for new physics beyond the GLYPH<3> CDMmodel of cosmology. 1  \nThe GW standard-siren measurement in Abbott et al. (2017a) is broadly consistent with other measurements. By combining information from multiple detections, one can improve the accuracy reaching about one percent with O (100) detections in the coming years (Dalal et al. 2006; Nissanke et al. 2013; Chen et al. 2018; Feeney et al. 2019; Vitale & Chen 2018; Mortlock et al. 2019).  \nAn unambiguous identification of the host galaxy is unlikely for all BNS detections; only a crude estimate of the sky position may be available. Moreover there are sources such as binary black hole (BBH) mergers with no expected EMcounterparts. Even in the absence of an EM counterpart, the method outlined in Schutz (1986) can be used: with a set of potential host galaxies identified in a galaxy catalog for each detection, one can build up information by a process of statistical cross-correlation. The method was demonstrated on a set of simulations in Del Pozzo (2012), where a 5% estimate on H 0 was obtained from O (100) detections in  \nan idealized situation of nearby events and complete galaxy catalogs; similar results with projections for third-generation detectors have been obtained in Nair et al. (2018). It has further been shown in Chen et al. (2018) that the main benefit of the galaxy-catalog method would be for the case of multiple well-localized sources.  \nAn understanding of GW selection e GLYPH<11> ects (Abbott et al. 2017a; Chen et al. 2018; Mandel et al. 2019; Vitale et al. 2020) and features of galaxy catalogs, such as their incompleteness and measurement uncertainties, is necessary for an accurate measurement of H 0. Prescriptions to handle incomplete galaxy catalogs have been outlined in Chen et al. (2018), Fishbach et al. (2019), and Gray et al. (2020), and an extensive study of selection e GLYPH<11> ects including galaxy catalog completeness has been performed in Gray et al. (2020). The simulations in Gray et al. (2020) demonstrate that the current method is able to handle galaxy catalog completeness down to GLYPH<24> 25% for O (100) detections in the nearby universe (luminosity distance d L . 115 Mpc) with idealized galaxy catalogs, without introducing additional systematic features. The galaxy-catalog method was used in Fishbach et al. (2019) to infer H 0 from GW170817 without its optical counterpart. An estimate of H 0 from GW170814 and the photometric redshift catalog from the Dark Energy Survey (DES) Year 3 data was also obtained in Soares-Santos et al. (2019).  \nIn this paper we report the first joint GW estimate of H 0 from detections during O1 and O2, the first and second observing runs of the Advanced LIGO and Virgo detector network. For our final result, along with the BNS GW170817, we choose the six O1 and O2 BBH detections which satisfy our selection criterion of a network signal-to-noise ratio SNR > 12 in at least one search pipeline for GW detections. The detections for which we have significant galaxy catalog support are GW150914, GW151226, GW170608, and GW170814. For these events, we expect the inferred H 0 posteriors to be driven by the additional EM information. The two remaining BBHs which satisfy the selection criterion, GW170104 and GW170809, need to be retained in the analysis for consistency with the assumed population model. These events for which a significant fraction of potential host galaxies are missing in the associated galaxy catalog, can also potentially contribute to the H 0 measurement, since there is information about cosmology present in the observed source distribution (Taylor et al. 2012; Taylor & Gair 2012; Farr et al. 2019). The distribution of the observed source parameters, including the observed luminosity distance distribution, is driven by H 0 in addition to the intrinsic astrophysical source distributions. With a known underlying astrophysical distribution of sources, H 0 would be measureable solely from the observed distance distribution of BBH detections (Chen & Holz 2014). This latter contribution is not expected to provide significant information at this stage given  \nhow uncertain the inferred astrophysical distribution parameters such as the power law index of the binary mass distribution, or the index characterizing the evolution of the binary merger rate with redshift are, even when H 0 is held fixed (Abbott et al. 2019a). In an ideal situation, one should jointly estimate these astrophysical population parameters along with H 0. We choose to fix the astrophysical population to a fiducial distribution instead, and perform our analysis with di GLYPH<11> erent choices for the mass distribution and binary merger rate evolution with redshift in order to quantify possible systematic e GLYPH<11> ects resulting from this assumption. We set aside a more thorough treatment involving the marginalization over the unknown astrophysical distribution for future work.  \nThe main result of our analysis-a posterior distribution on H 0-is dominated by the contribution from GW170817 with its optical counterpart, with a modest improvement from the inclusion of the O1 and O2 BBHs. These results, possibly refined and marginalized over the aforementioned assumptions, can be used as a prior for future GW estimates of H 0. The analysis performed in this paper thus serves as a precursor of future analyses for the third and subsequent observing runs of the Advanced detector network.  \nThe rest of this paper is arranged as follows. We describe our method in Section 2. We summarize the GW detections we use in our analysis and the corresponding EM data in Section 3. Our main results are presented in Section 4, with a more detailed discussion and a study of possible systematic e GLYPH<11> ects in Section 5. We conclude in Section 6 and highlight some future directions and prospects.  \nThroughout this paper we assume a GLYPH<3> CDM cosmology and use the best-fit Planck 2015 values of GLYPH<10> m = 0 : 308, GLYPH<10>GLYPH<3> = 0 : 692, respectively for the fractional matter and dark energy densities in the present epoch (Planck Collaboration 2016). Although these parameters enter the redshift-distance relationship central to the method for Bayesian inference of Hubble constant ( H 0), we have verified that our results are robust with regards to a variation of their values within the current measurement uncertainties.', '2. METHOD': 'We follow and apply the Bayesian analysis described in Gray et al. (2020) to compute the posterior probability density on H 0, given the set f D GW g of N det detections and the associated GW data f x GW g :  \np ( H 0 jf x GW g ; f D GW g ) / p ( H 0) p ( N det j H 0) N det Y i p ( x GW i j D GW i ; H 0) : (1)  \nHere, D GW i indicates that the event i was detected as a GW, p ( H 0) is the prior on H 0, and the term p ( N det j H 0) is the likelihood of detecting N det events over the time of observation with the associated detector configuration for the given  \nvalue of H 0. The number of detected events is some fraction of the total number of sources Ns , and this fraction depends on H 0; thus N det = f det( H 0) Ns . If the intrinsic astrophysical merger rate, R , which Ns is proportional to, 2 is marginalized over with a prior p ( R ) / R GLYPH<0> 1 , then p ( N det j H 0) = R p ( N det j H 0 ; R ) p ( R ) dR is independent of f det( H 0), and thus loses its dependence on H 0 (see, e.g., Fishbach et al. 2018). For simplicity, we make this approximation throughout our analysis. The final term factorises into the individual likelihoods for each detection. In the following, we write out the expressions for a single GW event i , omitting the subscript i for brevity of notation,  \np ( x GW j D GW ; H 0) = p ( D GW j x GW ; H 0) p ( x GW j H 0) p ( D GW j H 0) : (2)  \nThe denominator, p ( D GW j H 0), is evaluated as an integral over all possible x GW (Abbott et al. 2017a; Chen et al. 2018; Mandel et al. 2019):  \np ( D GW j H 0) = Z p ( D GW j x GW ; H 0) p ( x GW j H 0) dx GW ; (3)  \nwhere p ( D GW j x GW ; H 0) = 1 in the case where the signal-tonoise ratio (SNR) of x GW passes some detection threshold, and 0 in the case where it does not.', '2.1. The electromagnetic counterpart case': 'In the presence of an EM counterpart, there is additional information in the EM data, x EM, which appears as an EM likelihood term. Together with this, there is an underlying assumption that there has been an EM detection; we denote this assumption as D EM. Thus, for a single event with an EM counterpart,  \np ( x GW ; x EM j D GW ; D EM ; H 0) = p ( x GW j H 0) p ( x EM j H 0) p ( D EM j D GW ; H 0) p ( D GW j H 0) : (4)  \nWe assume that the detectability of an EM counterpart is dependent on luminosity distance (as opposed to redshift) because it is flux-limited. As GW detectability is also a function of luminosity distance, we expect p ( D EM j D GW ; H 0) to be a constant that does not depend on H 0. This leads to  \np ( x GW ; x EM j D GW ; D EM ; H 0) GLYPH<25> p ( x GW j H 0) p ( x EM j H 0) p ( D GW j H 0) : (5)', '2.2. The galaxy-catalog case': 'In the absence of an EM counterpart, the analogous data comes from galaxy catalogs which provide a set of galaxies and their associated sky locations, redshifts, and apparent  \nmagnitudes. As we are in the regime where the detectability of GW sources extends beyond the distance to which current catalogs are complete, the possibility that the GW host galaxy is not contained in the catalog, because it is too faint, has to be taken into account. This is done by marginalizing over the cases where the host is in the catalog (denoted G ), and where it is not (denoted ¯ G ):  \np ( x GW j D GW ; H 0) = p ( x GW j G ; D GW ; H 0) p ( G j D GW ; H 0) + p ( x GW j ¯ G ; D GW ; H 0) p ( ¯ G j D GW ; H 0) : (6)  \nIn the case where the host galaxy is in the catalog, the EM data enters in the form of information available in the galaxy catalog, as also in Fishbach et al. (2019) and Soares-Santos et al. (2019). This assumption is included in our conditioning on G . The EM information is used to modify our priors on galaxy redshift, sky location, and (apparent) magnitude, which are common among all GW events using the same catalog. This di GLYPH<11> ers from the counterpart case where the EM data enters the expression as a likelihood term, x EM, a transient which is informative for only one GW event. In the case where the host galaxy is not in the catalog, the complementary condition ¯ G implies that we include the information about the limitations of the EM survey. Following Gray et al. (2020), we model the galaxy catalog as having an apparent magnitude threshold, m th, since galaxy catalogs are flux-limited. This magnitude threshold, alongside the intrinsic (absolute) brightness of a galaxy and its luminosity distance, determines the probability that the galaxy is inside or outside the galaxy catalog.  \nThe formalism which we adopt from Gray et al. (2020) is closely analogous to the method described in Chen et al. (2018) and Fishbach et al. (2019). The in-catalog and out-ofcatalog terms in Eq. (6) above correspond to the two terms in Eq. (3) of Fishbach et al. (2019). However the methods start formally di GLYPH<11> ering in the way that the (in)completeness of the galaxy catalog is treated. In the current formalism from Gray et al. (2020), the (in)completeness of the galaxy catalog follows naturally from the parameters of the underlying  \nEM survey(s). The assumption that a galaxy catalog can be modelled by a single m th in each direction of the sky is an idealization. However this can in future be extended to include non-trivial selection functions modeling the optical sensitivity of the telescope instead of a sharp cuto GLYPH<11> at m th, and to composite catalogs coming from multiple surveys.  \nThe quantities appearing on the right in Eq. (6) can be written out explicitly as follows.  \np ( x GW j G ; D GW ; H 0) = P N gal j = 1 R p ( x GW j zj ; GLYPH<10> j ; H 0) p ( s j M ( zj ; mj ; H 0)) p ( zj ) dzj P N gal j = 1 R p ( D GW j zj ; GLYPH<10> j ; H 0) p ( s j M ( zj ; mj ; H 0)) p ( zj ) dzj : (7)  \nHere, N gal is the total number of galaxies in the galaxy catalog, GLYPH<10> j and mj are respectively the sky coordinates and apparent magnitude for galaxy j , and p ( zj ) is a distribution representing the redshift of galaxy j . This quantity, p ( zj ), which enters as a prior for our analysis, is the posterior distribution on the galaxy redshift obtained following analysis of EM data; details of the profiles chosen for p ( zj ) are deferred until Section 3.4.1. The quantity M ( zj ; mj ; H 0) is the absolute magnitude (for the given H 0), and p ( s j M ( zj ; mj ; H 0)) is the probability of a galaxy with these parameters to host a GW source during the observation time, relative to other galaxies. Formally, s is the statement that a GW has been sourced or emitted (as opposed to being detected ); the previous expressions are all implicitly conditioned on the assumption of s . In writing p ( s j M ), we make the approximation that the probability of a galaxy hosting a source depends only on the intrinsic luminosity of the galaxy, and not on its other parameters or on the properties of the GW source. In essence, this term allows for weighting galaxies by their luminosities L ( Mj ( H 0)) as  \np ( s j M ( zj ; mj ; H 0)) / 8 > > > < > > > : constant if unweighted L ( Mj ( H 0)) if luminosity-weighted. (8)  \nThe likelihood when the host galaxy is not in the catalog, p ( x GW j ¯ G ; D GW ; H 0), is a ratio of marginalized integrals:  \np ( x GW j ¯ G ; D GW ; H 0) = # 1 z ( m th ; M ; H 0) p ( x GW j z ; GLYPH<10> ; H 0) p ( z ) p ( GLYPH<10> ) p ( M j H 0) p ( s j M ) dzd GLYPH<10> dM # 1 z ( m th ; M ; H 0) p ( D GW j z ; GLYPH<10> ; H 0) p ( z ) p ( GLYPH<10> ) p ( M j H 0) p ( s j M ) dzd GLYPH<10> dM : (9)  \nHere the fact that the terms are conditioned on ¯ G is incorporated into the redshift limits as a function of the apparent magnitude threshold m th of the galaxy catalog. Finally, the prior probabilities that a given GW detection has or does not have support in the galaxy catalog are respectively  \n(10)  \np ( G j D GW ; H 0) = # z ( m th ; M ; H 0) 0 p ( D GW j z ; GLYPH<10> ; H 0) p ( z ) p ( GLYPH<10> ) p ( M j H 0) p ( s j M ) dzd GLYPH<10> dM # 1 0 p ( D GW j z ; GLYPH<10> ; H 0) p ( z ) p ( GLYPH<10> ) p ( M j H 0) p ( s j M ) dzd GLYPH<10> dM ; and p ( ¯ G j D GW ; H 0) = 1 GLYPH<0> p ( G j D GW ; H 0) :  \nIn Eqs. (9) and (10), p ( z ) is the prior on the redshift of host galaxies of GW events, taken to be of the form  \np ( z ) / 1 1 + z dV c( z ) dz R ( z ) : (11)  \nHere V c( z ) is the comoving volume as a function of redshift and the factor (1 + z ) GLYPH<0> 1 converts the merger rate from the source frame to the detector frame. The merger rate density may in general be a function of redshift; however we set R ( z ) = constant throughout (other than in Section 5, where we consider an alternative redshift-dependent rate model). The prior on the GW sky location p ( GLYPH<10> ) is taken to be uniform across the sky. The term p ( M j H 0) is the prior on absolute magnitudes for all the galaxies in the universe (not just those inside the galaxy catalog), which we set to follow the Schechter luminosity function:  \np ( M j H 0) / 10 GLYPH<0> 0 : 4( GLYPH<11> + 1)( M GLYPH<0> M GLYPH<3> ( H 0)) exp h GLYPH<0> 10 GLYPH<0> 0 : 4( M GLYPH<0> M GLYPH<3> ( H 0)) i : (12)  \nFollowing Gehrels et al. (2016), we use B -band luminosity function parameters GLYPH<11> = GLYPH<0> 1 : 07 for the slope of the Schechter function and M GLYPH<3> ( H 0) = GLYPH<0> 19 : 7 + 5 log 10 h for its characteristic absolute magnitude (with h GLYPH<17> H 0 = 100 km s GLYPH<0> 1 Mpc GLYPH<0> 1 ) throughout, unless otherwise specified. 3 For the upper limits of integration over M , we choose the magnitude of the dimmest galaxies to be GLYPH<0> 12 : 2 + 5 log 10 h . The integrals are not sensitive to the choice of their lower limits, i.e. the magnitudes of the brightest galaxies. More complex models for p ( M j H 0) can be used; in fact, we expect the luminosity distribution of galaxies to also evolve with redshift (Caditz & Petrosian 1989), as well as to depend on galaxy type and color (Madgwick et al. 2002). While the consideration of such dependence is beyond the scope of the current work, we refer the reader to Gray et al. (2020) for a brief discussion on the misspecification of the luminosity function parameters.  \nFurther details and complete derivations for the framework described above are discussed in Gray et al. (2020).', '2.3. Posterior samples re-weighting': 'The GW data x GW has undergone parameter estimation, providing a set of posterior samples on source parameters, including the luminosity distance d L, sky-coordinates GLYPH<10> , and the observed component masses in the detector frame m det 1 ; 2 . We need the likelihood of the GW data p ( x GW j H 0), which requires removing the priors used for the parameter estimation. In particular, this means that the d 2 L prior must be removed before the priors on z and H 0 can be applied.  \nAdditionally, a more subtle e GLYPH<11> ect comes into play regarding source- and detector-frame masses. The treatment of GW  \nselection e GLYPH<11> ects requires a marginalisation over the sourceframe mass distribution, while the data x GW contains information about the detector-frame masses. In order to be selfconsistent, the analysis must be performed using the same prior assumptions on both the individual event data, and the normalizing p ( D GW j H 0) term. This requires removing the detector-frame mass prior and re-weighting the posterior samples with the source-frame mass prior.  \nThe source-frame mass distribution is p ( m 1 ; m 2 j GLYPH<22> ) where GLYPH<22> denotes the hyper-parameters describing the astrophysical model (concrete details of the assumed model are discussed later in Section 4). To re-weight the likelihood we use the measured detector-frame masses and luminosity distances to compute the corresponding source-frame masses as a function of H 0,  \nm 1 ; 2 = m det 1 ; 2 1 + z ( d L ; H 0) : (13)  \nWe marginalize out the source-frame mass dependence, using the prior p ( m 1 ; m 2 j GLYPH<22> ). The GW likelihood is a function of d L and GLYPH<10> as before, but now is also a function of H 0. This e GLYPH<11> ect will be most pronounced for high distance (redshift) events, where the conversion between detectorframe and source-frame masses is most noticeable. Additionally, posterior samples from events with particularly high or low detector-frame masses may become inconsistent with the source-frame mass prior for certain values of H 0, leading to additional constraining power (see Section 5.2 for details).', '3.1. Gravitational-wave data': 'The GW searches performed during the first and the second observation runs of Advanced LIGO and Virgo have led to the identification of ten BBH and one BNS mergers (Abbott et al. 2019b). The BNS event GW170817, well-localized and at a nearby distance of 40 + 10 GLYPH<0> 10 Mpc, helped discover the electromagnetic transient from the merger, and was subsequently associated with host galaxy NGC4993. The BBHs span a large range of distances from 320 + 120 GLYPH<0> 110 Mpc to 2840 + 1400 GLYPH<0> 1360 Mpc and are distributed over the sky with 90% credible regions as low as 39 deg 2 to as high as 1666 deg 2 . A summary of the relevant parameters of all the GW detections are given in Table 1.  \nFor the main results presented in Section 4 of this work, we choose the events which meet the selection criterion of network SNR > 12 in at least one of the two pipelines for modeled searches, namely PyCBC and GstLAL. The sensitivity of the results to this choice is explored in Section 5 by reducing the network SNR threshold to 11. In each case, this SNR threshold is also used in the treatment of GW selection e GLYPH<11> ects as described in Eq. (3) above. In practice a detection is claimed not solely on the basis of the SNR, but additionally by applying data quality vetoes in order to re-  \nmove noise transients, and eventually constructing a ranking statistic such as an inverse false alarm rate or a likelihoodratio (Abbott et al. 2019b). A careful treatment should use a threshold on a ranking statistic rather than the SNR as the selection criterion. However a distinction between the two does not cause an appreciable di GLYPH<11> erence if the considered detections are significantly louder than transient noise artifacts (see, e.g. Appendix A.1 of Abbott et al. 2019a). In order to keep the computation of the GW selection e GLYPH<11> ects tractable, one can thus place a more stringent threshold on the SNR and select a subset of loud events from the detected population, which is what we do for our analysis. We note that placing an SNR threshold lower than or close to that set by the detection piplines would again be problematic without modifications to the current method of accounting for GW selection e GLYPH<11> ects.', '3.2. Galaxy Catalogs': "The analysis with BBHs is performed in conjunction with appropriate galaxy catalogs. We use the GLADE catalog (D'alya et al. 2018) as a default, due to its depth and coverage over an extensive region of the sky (see Section 3.2.1). For GWobservations that are particularly well-localized, certain galaxy catalogs show a clear improvement in completeness over GLADE within the relevant localization volume of the event. In particular, we use the DES Year 1 (Y1A1 GOLD or simply Y1) catalog (Drlica-Wagner et al. 2018; Abbott et al. 2018b) for the analysis of GW170814 (see Section 3.2.2). GW170818 lies within the footprint of the Sloan Digital Sky Survey (SDSS). While not used in this work, galaxy catalogs based on Data Release 14 (Abolfathi et al. 2018) or Data Release 16 (Ahumada et al. 2020) of SDSS (including curated versions such as the GWENS catalog, Rahman et al. 2019), could be used to improve the current analysis for events which fall in the SDSS footprint.  \nIn Table 1 we summarize the galaxy catalogs that we use for our analysis for each of the detections, along with the number of galaxies in the 90% error volume calculated from 3D skymaps constructed from posterior samples associated with the data release of Abbott et al. (2019b), 4 and estimates of the probability that the host galaxy is in the catalog, evaluated at the median redshift for each detection assuming a Planck 2015 cosmology.  \nIn the following, we describe in more detail the galaxy catalogs that we use, quantify the probability that the host galaxy for each event is in the galaxy catalog that is used for its analysis and discuss the assessment of the completeness over the relevant localization volume for the best localized events. Finally, we quantify the uncertainties associated with the photometric measurement of redshifts in some of these catalogs.", '3.2.1. GLADE': "We use the Galaxy List for the Advanced Detector Era (GLADE) version 2.4 galaxy catalog (D'alya et al. 2018), 5 to construct the observed redshift distributions for the majority of the detected BBHs. The GLADE catalog has an all sky coverage (Fig. 1 of D'alya et al. 2018) since it is constructed from the GWGC (White et al. 2011), 2MPZ (Bilicki et al. 2014), 2MASS XSC (Skrutskie et al. 2006), HyperLEDA (Makarov et al. 2014) and SDSS-DR12Q (Pˆaris et al. 2017) catalogs. The GLADE catalog is complete (in B -band luminosity) out to 37 Mpc and has an estimated completeness of 50% out to 91 Mpc (Fig. 2 of D'alya et al. 2018). At low redshifts ( . 0 : 05), we expect to be dominated by the peculiar velocity field. GLADE reports peculiar-velocity-corrected redshifts following the reconstruction of Carrick et al. (2015). GLADE provides apparent magnitudes in the B -band, which we can use directly (i.e. without any photometric transformations) for luminosity weighting of the galaxies.", '3.2.2. DES Year 1': "The Dark Energy Survey (DES) is a five year survey mapping GLYPH<25> 300 million galaxies in five filters ( grizY ) over 5000 deg 2 . It is worth noting that the GW170814 sky localization is fully enclosed within the footprint of the DES (Drlica-Wagner et al. 2018; Abbott et al. 2018b) Year 3 (Y3) 'gold' catalog. An estimate of H 0 from the GW170814 distance and the Y3 catalog of the DES has been carried out (Soares-Santos et al. 2019). In this work, we use the publicly available DES-Y1 catalog (Abbott et al. 2018b), 6 to compute the H 0 posterior for GW170814. Approximately 87% of the probability region for the GW170814 sky localization is enclosed within the DES-Y1 catalog. Analysis with a different catalog provides a parallel measurement of H 0 with GW170814, and (given the catalog di GLYPH<11> erences) can potentially be indicative of systematic e GLYPH<11> ects in the catalogs, such as the treatment of redshift uncertainties (provided that a similar set of galaxies are present in both catalogs).  \nWe select the objects in the DES-Y1 catalog that are classified as high-confidence galaxies using the default classification scheme, 'MODEST CLASS' (Drlica-Wagner et al. 2018; Sevilla-Noarbe et al. 2018). We use the photometric redshifts which are derived using the Bayesian Photometric Redshift (BPZ) template fitting method (Hoyle et al. 2018). We use the median redshifts provided in the catalog and discard (around 5%) galaxies with redshift errors larger than twice their corresponding quoted median redshift value. Such a choice is not expected to bias our result since the discarded galaxies are highly uninformative.  \nTable 1. Relevant parameters of the O1 and O2 detections: network signal-to-noise ratio (SNR) for the search pipeline (PyCBC / GstLAL) in which the signal is the loudest, 90% sky localization region GLYPH<1>GLYPH<10> (deg 2 ), luminosity distance d L (Mpc, median with 90% credible intervals), and estimated redshift z event (median with 90% range assuming Planck 2015 cosmology) from Abbott et al. (2019b). In the remaining columns we report the corresponding 90% 3D localization comoving volumes, the number of galaxies within each volume for public catalogs which we find to be the most complete, and the apparent magnitude threshold, m th, of the galaxy catalog associated with the corresponding sky region (as described in Section 3.3). The final column gives the probability that the host galaxy is inside the galaxy catalog for each event, p ( G j z event ; D GW), also evaluated at the median redshift for each event.  \nWe convert from the DES grizY magnitudes to the SDSS ugriz system using the photometric transformations provided in the DES-Y1 paper (Drlica-Wagner et al. 2018), which requires discarding a further GLYPH<24> 5% of galaxies with inadequate color information. This transformation enables us to apply K corrections to obtain source-frame luminosities (see Sec. 3.4.2 for details). We use the SDSS g -band magnitudes, as these are closest to B -band, and update the Schechter parameters of our analysis to have GLYPH<11> = GLYPH<0> 0 : 89 and M GLYPH<3> ( H 0) = GLYPH<0> 19 : 39 + 5 log 10 h based on Blanton et al. (2003).", '3.3. Probability that the host galaxy is in the catalog': "In this work, we assume that we can characterize the completeness of a galaxy catalog using an apparent magnitude threshold (limiting magnitude) m th. We estimate m th by calculating the median value from the apparent magnitude distribution of all the galaxies within the sky localization of each event. For GLADE, this choice allows us to account for some of the larger changes in completeness across the sky, which come from it being a composite catalog, comprised of many surveys of di GLYPH<11> ering depths. Galaxy catalogs are directional, and a more sophisticated analysis would involve calculating the limiting magnitude for a given line of sight. Obtaining the H 0 posterior distribution would thus require a joint estimate of m th along the lines of sights within an event's sky localization. We leave this for future work. That the completeness of  \na galaxy catalog is modelled by a set of limiting magnitude thresholds, can by itself be a non-trivial assumption, especially for photometric catalogs, since galaxies may be missing for various reasons other than them being too faint. This will also need to be revisited in the future in a catalog-specific manner.  \nFor now, we use the m th estimated as described above, and show in Fig.1 the probability of a host galaxy being inside the catalog p ( G j z ; D GW) as a function of redshift z , for each of the galaxy catalogs under consideration. For GLADE this quantity is calculated for each event using the m th calculated for each event's sky localization. For DES-Y1, the curve is for the patch of sky covering GW170814. These probabilities are calculated using the expressions in Eq. (10), but as a function of z , and are therefore independent of the choice of H 0. We additionally show as the vertical lines in Fig. 1 the median redshift for each event z event (calculated assuming a Planck 2015 cosmology). In the final two columns of Table 1, we report the m th of the relevant catalog within the sky localization of each event, and the probability of the host galaxy being in the catalog at the median redshift of each event.", '3.4. Detailed analysis of DES-Y1': "The high completeness fraction of DES-Y1 within the GW170814 sky localization is apparent from Fig. 1. The catalog is expected to be more complete than GLADE since it  \n<!-- image -->  \nz  \nFigure 1. The probability that the host galaxy is inside the galaxy catalog, shown for GLADE (gray curves) and DES-Y1 (orange curve), as a function of redshift. For GLADE this quantity is calculated for each individual event, using the completeness estimated within each event's sky localization. For DES-Y1 the curve is only valid in the patch of sky covering GW170814. Each curve is independent of the value of H 0. The vertical lines show the median redshift (assuming a Planck 2015 cosmology) for each event as in Table 1. These lines are thick and solid up to the intercept with the galaxy catalog they are used with, and thin and dashed above.Figure 2. Probability distribution for the redshifts of potential host galaxies p cat( z ), with redshift uncertainties taken into account, divided out by a uniform in comoving volume distribution p vol( z ) of galaxies. When computing p cat( z ) we include all galaxies brighter than 0 : 05 L GLYPH<3> g within the corresponding event's 99% sky localization region and weight each galaxy by weights proportional to their g -band luminosity (solid lines) as well as with uniform weights (dotted lines). We show these distributions for the DES-Y1 galaxies within the GW170814 sky localization region. We also show the 90% median estimated redshift range for GW170814 (calculated assuming a Planck 2015 cosmology) for reference.  \n<!-- image -->  \nhas a limiting magnitude of approximately 23.8 for DES-Y1. We analyze the EM information coming from this catalog in greater detail. It is helpful to have an assessment of the contribution from potential host galaxies as a function of redshift for these events. In order to quantify this contribution, we perform a treatment analogous to Fishbach et al. (2019) and compute the ratio p cat( z ) = p vol( z ) between the probability distribution for the redshifts of potential host galaxies p cat( z ) and of a uniform in comoving volume distribution of galaxies p vol( z ). When computing p cat( z ) we include all galaxies brighter than 0 : 05 L GLYPH<3> g within the corresponding event's 99% sky localization region defined as,  \np cat( z ) GLYPH<17> Z p ( x GW j GLYPH<10> ) p 0( z ; GLYPH<10> ) d GLYPH<10> ; (14)  \nwhere p ( x GW j GLYPH<10> ) is the GW likelihood as a function of the sky position GLYPH<10> (this e GLYPH<11> ectively weights each galaxy with the 2D skymap probability), and p 0( z ; GLYPH<10> ) represents the galaxy catalog contribution, obtained from the distribution of galaxies in the catalog, marginalized over their redshift uncertainties also obtained from the catalog, and weighted by their probability of hosting a GW source (assuming a Planck 2015 cosmology for the required magnitude conversion). We consider weights for each galaxy proportional to their g -band luminosity as well as uniform weights to explore the e GLYPH<11> ects due to this choice.  \nIn Fig. 2 we show the distributions p cat( z ) = p vol( z ) for the DES-Y1 galaxies within the GW170814 sky localization region, for the redshift range 0 < z < 0 : 5. The unweighted  \ncurve traces the over / under-density of galaxies, and then falls o GLYPH<11> at larger redshift due to incompleteness in the catalog. The luminosity-weighted redshift distribution is driven partially by the over-density of galaxies at z GLYPH<25> 0 : 4, and partially by bright high-redshift galaxies. The host galaxies for GW170814 are more likely to be located near the higher galaxy density regions in the DES-Y1 catalog - these features in the redshift prior are expected to drive the inferred H 0 posteriors for the corresponding events. Features we see in the DES-Y1 catalog are not as pronounced as the overdensity in the DES-Y3 data seen in Soares-Santos et al. (2019). While the DES-Y3 survey is deeper, and may reveal finer features, a part of the above di GLYPH<11> erence is likely also driven by the di GLYPH<11> erence in the photometric redshift estimation algorithms, namely, template fitting methods such as BPZ (Hoyle et al. 2018) and machine learning based methods such as the ANNz2 algorithm (Sadeh et al. 2016), with the latter used for GW170814 in (Soares-Santos et al. 2019). Only the former of the two has been used for the DES-Y1 catalog and a combination of both for the DES-Y3 catalog. The di GLYPH<11> erent selection criteria for choosing galaxies from the two catalogs, such as the stringent redshift cut placed in Soares-Santos et al. (2019) versus a more relaxed redshift prior used in this work, is another potential source of di GLYPH<11> erence between the corresponding redshift distributions.", '3.4.1. Redshift uncertainties': 'An important source of measurement uncertainty with galaxy catalogs is in the galaxy redshifts, which are often photometric estimates due to lack of spectroscopic measurements out to large redshifts. In our formalism, the uncertainty in redshift is reflected in the term p ( zj ) in Eq. (7). We model the individual galaxy redshift probability distributions, p ( zj ), as a Gaussian distribution with mean set to the quoted median photometric redshift z photo, and with standard deviation of GLYPH<27> z photo (both obtained from the galaxy catalog data). Photometric redshift estimates are often not approximated by Gaussian distributions, and we make this assumption only due to limited information present in some of the public galaxy catalogs which we use. A rigorous quantification of the e GLYPH<11> ect of this assumption is beyond the scope of this work. In practice, we implement the redshift uncertainty by the process of a Monte Carlo integration: the integral over zj in Eq. (7) becomes an additional sum over N photo random samples. This number varies between the di GLYPH<11> erent galaxies, and is always high enough to ensure that the final event likelihood is independent of the set of random draws from each galaxy.', '3.4.2. Source-frame luminosities': 'For galaxy catalogs which are complete to high redshifts, it is important to note that the observed apparent magnitudes are redshifted from their source frame. Galaxies do not emit  \nuniformly in all wavelengths, and galaxy surveys are only sensitive in certain bands. In order to compare the properties of galaxies at di GLYPH<11> erent redshifts, e.g. to apply luminosity weighting, or to apply a luminosity cut to the galaxy sample, the K correction, described in Oke & Sandage (1968); Hogg et al. (2002), needs to be applied. In particular, the K correction term is redshift dependent, and so neglecting it could lead to systematic bias in the estimation of H 0.  \nFor DES, we compute the K corrections using the calculator described in Chilingarian et al. (2010); Chilingarian & Zolotukhin (2012). These K corrections are valid out to redshifts of 0.5, and so we apply a hard redshift cut. In order to remain self-consistent, the method is adjusted to include this redshift cut, such that the probability of the host galaxy being in the catalog above z = 0 : 5 is zero, and below the cut it is determined according to the apparent magnitude threshold, as before.  \nIn the case where galaxies have high redshifts and large redshift uncertainties, this uncertainty must be accounted for in the calculation of the K corrections. Using only the mean redshift to calculate the K correction would lead to unrealistically bright or faint luminosities at the tail ends of the redshift distribution. In our implementation, the K corrections are calculated in-situ for each redshift Monte Carlo random draw described in 3.4.1, automatically taking the galaxy redshift uncertainties into account.', '4. RESULTS': "We apply the method described above to obtain a measurement of the Hubble constant using GW standard sirens only. We carry out our analysis with a prior on H 0 uniform in the interval of [20 ; 140] km s GLYPH<0> 1 Mpc GLYPH<0> 1 ; we report our final results also using a flat-in-log prior p ( H 0) / H GLYPH<0> 1 0 in the same interval for ease of comparison with previous studies. We use the marginalized distance likelihood and skymaps constructed from the posterior samples of Abbott et al. (2019b). 7 For the BBHs, we choose all galaxies in the 99 : 9% sky region of the corresponding catalog and we further weight the galaxies in proportion to their B ( g )-band luminosities. In order to calculate the term p ( D GW j H 0) in the denominator, we use a Monte Carlo integration, sampling parameters which a GLYPH<11> ect an event's detectability (masses, sky location, inclination angle, and polarisation) from chosen priors. We choose a power-law mass distribution for BBHs with p ( m 1) / m GLYPH<0> GLYPH<11> 1 and m 2 uniform in its range with 5 M GLYPH<12> < m 2 < m 1 < 100 M GLYPH<12> in the source frame, and a distribution of merger rates that does not evolve with redshift; for the power-law index GLYPH<11> , we choose GLYPH<11> = 1 : 6 (which is supported by Model B of Abbott  \net al. 2019a). For BNSs, we use a Gaussian mass distribution with a mean of 1 : 35 M GLYPH<12> and a standard deviation of 0 : 15 M GLYPH<12> (Kiziltan et al. 2013). 8 The remaining GW parameters are marginalized over their natural distributions: uniform in the sky, uniform on the sphere for orientation, uniform in polarization. We use the time-averaged power-spectraldensity of detector noise for the corresponding observation run from Abbott et al. (2018a), and for the selection criterion, we use a network SNR threshold of 12 in at least one search pipeline. The O1 and O2 BBHs which pass this criterion are GW150914, GW151226, GW170104, GW170608, GW170809, and GW170814 (see Table 1).  \nOur result for these O1 and O2 BBHs is shown in Fig. 3. The detections for which there is considerable support from the galaxies present in the catalog show features of the galaxy catalog in their H 0 posterior distribution. The GW170814 estimate is qualitatively similar to the result in Soares-Santos et al. (2019) with analogous peaks in the posterior distribution. The di GLYPH<11> erences in peak locations can be attributed to a di GLYPH<11> erence in the redshift distribution for the DES-Y3 catalog used in Soares-Santos et al. (2019) versus that for the public DES-Y1 catalog used in this work. For the detections for which the galaxy catalogs are relatively empty, we see the features of the assumptions on mass distribution and redshift evolution of binary merger rate that have entered our analysis. The more distant events such as GW170809 lead to H 0 estimates pushed to the lower end of the prior. This is due to the following reason. In a universe where host galaxies are distributed uniformly in comoving volume, for lower values of H 0, the expected distribution of detected GW events favors relatively higher luminosity distances. Thus events at high luminosity distances have more support for smaller values of H 0, while relatively nearby events, namely GW150914, GW151226, GW170608 and GW170814, correspondingly have lower support at smaller values of H 0. The information present in the observed luminosity distance distribution would thereby potentially contribute to the H 0 measurement, independent of, or even in absence of information in galaxy catalogs, if the underlying distributions of source parameters were known. In the absence of knowledge of the astrophysical distribution of BBH source parameters, a thorough treatment would involve a marginalization over all possible mass distributions and rate models. The following section discusses the systematic di GLYPH<11> erences that the assumptions on the assumed population model could lead to.  \nFor our final result we combine the contribution of the BBHs with the result from GW170817 obtained using the low spin prior samples from Abbott et al. (2019b) and an es-  \ntimated Hubble velocity of v H GLYPH<17> cz = 3017 GLYPH<6> 166 kms GLYPH<0> 1 (where c is the speed of light) for NGC4993 from Abbott et al. (2017a). Our final combined result is shown in Fig. 4, with the posterior distribution plotted assuming a uniform H 0 prior: we obtain H 0 = 69 : 6 + 20 : 4 GLYPH<0> 8 : 6 km s GLYPH<0> 1 Mpc GLYPH<0> 1 (68 : 3% highest density posterior interval). To compare with values in the literature, we also use a flat-in-log prior, p ( H 0) / H GLYPH<0> 1 0 , and calculate H 0 = 68 : 7 + 17 : 0 GLYPH<0> 7 : 8 km s GLYPH<0> 1 Mpc GLYPH<0> 1 , which corresponds to an improvement by a factor of 1.04 (about 4%) over the GW170817-only value of 68 : 7 + 17 : 5 GLYPH<0> 8 : 3 km s GLYPH<0> 1 Mpc GLYPH<0> 1 . We also quote the median and symmetric 90% credible interval for this measurement, which is 74 : 9 + 39 : 2 GLYPH<0> 13 : 9 km s GLYPH<0> 1 Mpc GLYPH<0> 1 .", '5. SYSTEMATIC EFFECTS': 'In this section, we repeat the previous analysis with a few alternative assumptions for the GW selection criterion, the GW population model, and source host properties. Subsequently, we discuss other sources of systematic e GLYPH<11> ects, a detailed study of which is beyond the scope of this work.', '5.1. Selection criterion': 'We first look into the sensitivity of our results to the GW selection criterion. We reduce the threshold on the network SNR from 12 chosen in the previous section to 11 in least one search pipeline. The computation of the GW selection e GLYPH<11> ects is adjusted accordingly. Fig. 5 shows the results with the two sets of assumptions. Reducing the SNR threshold to 11 introduces two additional events in our analysis, namely GW170818 and GW170823, neither of which have a significant in-catalog contribution. Di GLYPH<11> erences are expected due to the fact that additional low-SNR events are introduced, and also because the individual likelihoods change slightly with a di GLYPH<11> erent SNR threshold used in the GW selection term. In the regime of a large number of events, these two e GLYPH<11> ects are expected to cancel, provided that the additional low-SNR events do not have significant in-catalog support. For our result, this di GLYPH<11> erence is not significant; however the small variation is a reminder that we are still in the regime of a low number of events.', '5.2. Population model': "Going back to our default assumption of a network SNR threshold of 12, we test the sensitivity to our assumptions regarding the population model, i.e. the mass distribution and the distribution of binary merger rate with redshift. In addition to the power-law mass distribution with GLYPH<11> = 1 : 6 (median inferred value using Model B of Abbott et al. 2019a), we choose a shallower flat-in-log mass distribution with GLYPH<11> = 1, and a steeper distribution with GLYPH<11> = 2 : 3 (both within the support of the inferred range in Abbott et al. 2019a). Our results are shown in the left panel of Fig. 6, and they demonstrate that the systematic di GLYPH<11> erences due to the choice of powerlaw slope GLYPH<11> are insignificant.  \nFigure 3. Individual estimates of H 0 from the six binary black hole detections which satisfy the selection criterion of network SNR > 12 in at least one search pipeline. These results assume a m GLYPH<0> 1 : 6 power-law distribution on masses and a non-evolving rate model. All results assume a prior on H 0 uniform in the interval [20, 140] km s GLYPH<0> 1 Mpc GLYPH<0> 1 (dotted blue). We also show the estimates of H 0 from CMB (Planck: Aghanim et al. 2020) and supernova observations (SH0ES: Riess et al. 2019).  \n<!-- image -->  \nAs a test case, we vary the upper cut-o GLYPH<11> for the mass distribution, M max. For our default analysis, M max was chosen to be 100 M GLYPH<12> , consistent with all the considered BBHs for all values of H 0 within the prior range. Reducing this cuto GLYPH<11> to a slightly restrictive M max = 50 M GLYPH<12> (e.g., motivated by the pair instability supernova process, Fowler & Hoyle 1964), we see a significant di GLYPH<11> erence (right panel of Fig. 6). Lowering M max corresponds to a closer GW detection horizon. This systematically leads each event to prefer slightly lower values of H 0 than in the main result, for the reasons outlined in Section 4 - namely the relationship between the predicted event distribution (from our GW selection e GLYPH<11> ects) and the real detected event distribution.  \nNext, we relax our assumption on the evolution of rate of binary mergers with redshift. A constant merger rate density, R ( z ) = constant, implicit in the previous treatment, assumed that the merger rate traces the comoving volume. In  \naddition, we repeat our analysis using a merger rate R ( z ) / (1 + z ) 3 , which traces the star formation rate at low redshifts ( z < 2 : 5) (Saunders et al. 1990), as well as a merger rate R ( z ) / (1 + z ) GLYPH<0> 3 which could arise if typical delay times are very long, as may be expected from the chemically homogeneous evolution formation channel (Mandel & de Mink 2016). These relaxed assumptions thus cover a large fraction of physically viable and inferred population models (Abbott et al. 2019a). We show our results for the di GLYPH<11> erent assumed redshift evolution models in Fig. 7. The model in which the merger rate traces star formation shows a significant di GLYPH<11> erence, with a tendency to prefer lower values of H 0, compared to the other two models which are quite similar. This is the only systematic e GLYPH<11> ect that leads to a significant di GLYPH<11> erence in the results at this time.  \n5.3. Luminosity weighting  \nFigure 4. The gravitational-wave measurement of H 0 (dark blue) from the detections in the first two observing runs of Advanced LIGO and Virgo. The GW170817 estimate (orange) comes from the identification of its host galaxy NGC4993 (Abbott et al. 2017a). The additional contribution comes from binary black holes in association with appropriate galaxy catalogs; for GW170814 we use the DES-Y1 galaxy catalog, while for the remaining five BBHs, GW150914, GW151226, GW170104, GW170608, and GW170809, we use the GLADE catalog. The 68% maximum a-posteriori intervals are indicated with the vertical dashed lines. All results assume a prior on H 0 uniform in the interval [20, 140] km s GLYPH<0> 1 Mpc GLYPH<0> 1 (dotted blue). We also show the estimates of H 0 from CMB (Planck: Aghanim et al. 2020) and supernova observations (SH0ES: Riess et al. 2019).  \n<!-- image -->  \nThe results in the previous section assumed a weighting of galaxies by their luminosities in the B-band, which are indicative of galaxies' star formation rates. In order to quantify the di GLYPH<11> erence likely to be caused by alternate ways of weighting the galaxies, we repeat our analysis with no luminosity weighting. These results are shown in Fig. 8.  \nWith uniform luminosity weights, we obtain a result on a joint binary black hole estimate which is close to flat (thin orange line in Fig. 8). This can be understood as follows: 1) The out-of-catalog terms in Eq. (6) take into account the lack of galaxies beyond the apparent magnitude threshold m th of the catalog in a uniform way. When galaxies are unweighted, the probability of the host galaxy being inside the catalog is reduced compared to the luminosity-weighted case. More  \nweight is given to the uniform out-of-catalog contribution, and the events become less informative. 2) The catalogs used in this analysis contain high numbers of low-luminosity galaxies. The contribution from these more evenly distributed dim galaxies, in the unweighted case, again reduces the informativeness of each event and flattens the final result. This is also in agreement with our expectations from Fishbach et al. (2019) and Gray et al. (2020), where weighting by luminosities enhance the features in the posterior distribution coming from the galaxy catalog.", '5.4. Waveform models': 'The posterior samples of Abbott et al. (2019b) used for the results in this paper have been obtained combining the results of gravitational waveform models which incorporate  \nFigure 5. Sensitivity of the results to the selection criterion on the signal-to-noise ratio (SNR). The final joint result as well as the contribution from all the BBHs which satisfy the selection criterion are shown for a threshold network SNR of 12 (thick orange) and 11 (thin orange); the variation is shown as a shaded band. The GW170817 counterpart result (gray) is added to guide the eye. Six BBHs (GW150914, GW151226, GW170104, GW170608, GW170809, and GW170814) pass the selection criterion with SNR > 12. Two additional BBHs (GW170818 and GW170823) are included with SNR > 11. These results assume the default m GLYPH<0> 1 : 6 power-law distribution on masses and a non-evolving rate model.  \n<!-- image -->  \nspin and precession e GLYPH<11> ects to di GLYPH<11> erent extents (Husa et al. 2016; Khan et al. 2016; Hannam et al. 2014; Pan et al. 2014; Taracchini et al. 2014; Babak et al. 2017). These models are restricted to quasi-circular orbits (i.e., they do not include orbital eccentricity) and neglect higher-order harmonics. Systematic di GLYPH<11> erences in GW parameter estimation results with the employed waveform models constitute only a small fraction of the total uncertainty budget (see, e.g., Abbott et al. 2016a, 2017b), and given the large statistical uncertainties, the ignored e GLYPH<11> ects in waveform modeling are not expected to cause a di GLYPH<11> erence to the current measurement of H 0. However cumulative systematic e GLYPH<11> ects arising from limitations of waveform models will become increasingly important as the statistical uncertainties become smaller and, in particular, features that can lead to biases in the GW estimation of distance will need to be incorporated.', '5.5. Detector calibration': 'An independent e GLYPH<11> ect to be considered is the calibration of the GW detectors. Currently, the GW parameter estimation results are marginalized over the detector calibration uncertainties ( . 4% in amplitude in O1 and O2), which accounts for both the statistical uncertainty and the systematic error correlated between detections (Abbott et al. 2019b). Both the statistical uncertainty and the systematic error in GW detector calibration are much smaller than the other measure-  \nment uncertainties, and thus negligible for H 0 estimates from a handful of detections that we have now or expect in the near future (Cahillane et al. 2017). However, the impact of correlated systematic calibration errors between detections will become relatively more important in the long term, with an increasing number of detections driving down the statistical uncertainties, and an improved understanding of other systematic e GLYPH<11> ects that possibly govern our current uncertainty budget. Further quantitative study of the e GLYPH<11> ect of correlated calibration uncertainties is ongoing.', '6. CONCLUSION AND OUTLOOK': 'In this paper we have presented the first measurement of the Hubble constant using multiple GW observations. Our result reanalyzes and combines the posterior probability distribution obtained from the BNS event GW170817 using the redshift of the host galaxy inferred from the observed EM counterpart (Abbott et al. 2017a), along with constraints using galaxy catalogs for the BBH events observed by Advanced LIGO and Virgo in their first and second observing runs. We measure H 0 = 68 : 7 + 17 : 0 GLYPH<0> 7 : 8 km s GLYPH<0> 1 Mpc GLYPH<0> 1 (68 : 3%highest density posterior interval with a flat-in-log prior). This result is mainly dominated by the information from GW170817 with its counterpart, but does show a modest improvement with the inclusion of the BBHs. The BBHs contribute both from associated galaxy catalogs as well as via their observed luminosity distance distribution. Since the latter contribution is sensitive to the assumptions on the mass distribution and rate evolution, a more thorough treatment requires a marginalization over these unknown population parameters.  \nThe contribution from events without counterparts is dominated by GW170814, for which the associated galaxy catalog is highly complete. This highlights the importance of deeper surveys and of dedicated EM follow-up of sky regions following GW triggers for a better H 0 measurement. With numerous anticipated detections in the upcoming observing runs with improved detector sensitivities (Abbott et al. 2018a, 2016b,a, 2017c, 2019b,a), these results pave the road towards an era of precision multimessenger cosmology to be performed with a multitude of sources, including both neutron star and black hole mergers, with or without transient EM counterparts.', 'ACKNOWLEDGMENTS': "Analyses in this paper made use of N um P y (Harris et al. 2020), S ci P y (Virtanen et al. 2020), A stropy (Robitaille et al. 2013; Price-Whelan et al. 2018), gwcosmo (https: // git. ligo.org / lscsoft / gwcosmo), and IP ython (Perez & Granger 2007); plots were produced with M atplotlib (Hunter 2007), and S eaborn (Waskom et al. 2020). This research made use of the K-corrections calculator service available at http: // kcor.sai.msu.ru / .  \n<!-- image -->  \nFigure 6. Sensitivity of the results to the assumed mass distribution model. Left panel: Variation of the results with three di GLYPH<11> erent choices of the power-law index for the mass distribution, GLYPH<11> = 1 : 6 (thick solid), GLYPH<11> = 2 : 3 (thin solid) and GLYPH<11> = 1 (thin dashed) assuming a constant intrinsic astrophysical merger rate, R ( z ) = constant and M max = 100 M GLYPH<12> . Right panel: Variation of the results with two di GLYPH<11> erent choices for the allowed black hole maximum mass, M max = 100 M GLYPH<12> (thick solid), and M max = 50 M GLYPH<12> (thin solid), both assuming R ( z ) = constant and GLYPH<11> = 1 : 6.  \n<!-- image -->  \nFigure 7. Variation of the results with two di GLYPH<11> erent choices for the rate evolution, R ( z ) = constant (thick solid), and R ( z ) / (1 + z ) 3 (thin solid) and R ( z ) / (1 + z ) GLYPH<0> 3 (thin dashed) for GLYPH<11> = 1 : 6 and Mmax = 100 M GLYPH<12> .  \n<!-- image -->  \nThe authors gratefully acknowledge the support of the United States National Science Foundation (NSF) for the construction and operation of the LIGO Laboratory and Advanced LIGO as well as the Science and Technology Facilities Council (STFC) of the United Kingdom, the Max-Planck-Society (MPS), and the State of Niedersachsen / Germany for support of the construction of Advanced LIGO and construction and operation of the GEO600 detector. Additional support for Advanced LIGO was provided by the Australian Research Council. The authors gratefully acknowledge the Italian Istituto Nazionale di Fisica Nucleare (INFN), the French Centre National de la Recherche  \nFigure 8. Sensitivity of the results to luminosity weighting. We show how the results vary when we weight the galaxies in the catalog by their B(g)-band luminosity (thick solid) as well as with constant (uniform) weights (thin solid), both assuming a power-law index for the mass distribution, GLYPH<11> = 1 : 6 and constant intrinsic astrophysical merger rate, R ( z ) = constant.  \n<!-- image -->  \nScientifique (CNRS) and the Foundation for Fundamental Research on Matter supported by the Netherlands Organisation for Scientific Research, for the construction and operation of the Virgo detector and the creation and support of the EGO consortium. The authors also gratefully acknowledge research support from these agencies as well as by the Council of Scientific and Industrial Research of India, the Department of Science and Technology, India, the Science & Engineering Research Board (SERB), India, the Ministry of Human Resource Development, India, the Spanish Agencia Estatal de Investigaci'on, the Vicepresid'encia i  \nConselleria d'Innovaci'o, Recerca i Turisme and the Conselleria d'Educaci'o i Universitat del Govern de les Illes Balears, the Conselleria d'Educaci'o, Investigaci'o, Cultura i Esport de la Generalitat Valenciana, the National Science Centre of Poland, the Swiss National Science Foundation (SNSF), the Russian Foundation for Basic Research, the Russian Science Foundation, the European Commission, the European Regional Development Funds (ERDF), the Royal Society, the Scottish Funding Council, the Scottish Universities Physics Alliance, the Hungarian Scientific Research Fund (OTKA), the Lyon Institute of Origins (LIO), the Paris ˆ Ile-de-France Region, the National Research, Development and Innovation O GLYPH<14> ce Hungary (NKFIH), the National Research Founda-  \nof Korea, Industry Canada and the Province of Ontario through the Ministry of Economic Development and Innovation, the Natural Science and Engineering Research Council Canada, the Canadian Institute for Advanced Research, the Brazilian Ministry of Science, Technology, Innovations, and Communications, the International Center for Theoretical Physics South American Institute for Fundamental Research (ICTP-SAIFR), the Research Grants Council of Hong Kong, the National Natural Science Foundation of China (NSFC), the Leverhulme Trust, the Research Corporation, the Ministry of Science and Technology (MOST), Taiwan and the Kavli Foundation. The authors gratefully acknowledge the support of the NSF, STFC, INFN and CNRS for provision of computational resources."}