# The population of merging compact binaries inferred using gravitational waves through GWTC-3

R. Abbott, T. D. Abbott, F. Acernese, K. Ackley, C. Adams, N. Adhikari, R.

X. Adhikari, V. B. Adya, C. Affeldt, D. Agarwal, et al.

► To cite this version:

R. Abbott, T. D. Abbott, F. Acernese, K. Ackley, C. Adams, et al. The population of merging compact binaries inferred using gravitational waves through GWTC-3. Physical Review X, 2023, 13 (1), pp.011048. 10.1103/PhysRevX.13.011048. hal-03862873

HAL Id: hal-03862873

https://hal.in2p3.fr/hal-03862873

Submitted on 23 Nov 2022

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# The population of merging compact binaries inferred using gravitational waves through GWTC-3

R. Abbott,¹ T. D. Abbott,² F. Acernese,³,⁴ K. Ackley,⁵ C. Adams,⁶ N. Adhikari,⁷ R. X. Adhikari,¹ V. B. Adya,⁸

C. Affeldt,⁹,¹⁰ D. Agarwal,¹¹ M. Agathos,¹²,¹³ K. Agatsuma,¹⁴ N. Aggarwal,¹⁵ O. D. Aguiar,¹⁶ L. Aiello,¹⁷

A. Ain,¹⁸ P. Ajith,¹⁹ T. Akutsu,²⁰,²¹ P. F. de Alarc'on,²² S. Akcay,¹³,²³ S. Albanesi,²⁴ A. Allocca,²⁵,⁴ P. A. Altin,⁸

A. Amato,²⁶ C. Anand,⁵ S. Anand,¹ A. Ananyeva,¹ S. B. Anderson,¹ W. G. Anderson,⁷ M. Ando,²⁷,²⁸

T. Andrade,²⁹ N. Andres,³⁰ T. Andrić,³¹ S. V. Angelova,³² S. Ansoldi,³³,³⁴ J. M. Antelis,³⁵ S. Antier,³⁶

F. Antonini,¹⁷ S. Appert,¹ Koji Arai,¹ Koya Arai,³⁷ Y. Arai,³⁷ S. Araki,³⁸ A. Araya,³⁹ M. C. Araya,¹

J. S. Areeda,⁴⁰ M. Arène,³⁶ N. Aritomi,²⁷ N. Arnaud,⁴¹,⁴² M. Arogeti,⁴³ S. M. Aronson,² K. G. Arun,⁴⁴ H. Asada,⁴⁵

Y. Asali,⁴⁶ G. Ashton,⁵ Y. Aso,⁴⁷,⁴⁸ M. Assiduo,⁴⁹,⁵⁰ S. M. Aston,⁶ P. Astone,⁵¹ F. Aubin,³⁰ C. Austin,²

S. Babak,³⁶ F. Badaracco,⁵² M. K. M. Bader,⁵³ C. Badger,⁵⁴ S. Bae,⁵⁵ Y. Bae,⁵⁶ A. M. Baer,⁵⁷ S. Bagnasco,²⁴

Y. Bai,¹ L. Baiotti,⁵⁸ J. Baird,³⁶ R. Bajpai,⁵⁹ M. Ball,⁶⁰ G. Ballardin,⁴² S. W. Ballmer,⁶¹ A. Balsamo,⁵⁷

G. Baltus,⁶² S. Banagiri,⁶³ D. Bankar,¹¹ J. C. Barayoga,¹ C. Barbieri,⁶⁴,⁶⁵,⁶⁶ B. C. Barish,¹ D. Barker,⁶⁷

P. Barneo,²⁹ F. Barone,⁶⁸,⁴ B. Barr,⁶⁹ L. Barsotti,⁷⁰ M. Barsuglia,³⁶ D. Barta,⁷¹ J. Bartlett,⁶⁷ M. A. Barton,⁶⁹,²⁰

I. Bartos,⁷² R. Bassiri,⁷³ A. Basti,⁷⁴,¹⁸ M. Bawaj,⁷⁵,⁷⁶ J. C. Bayley,⁶⁹ A. C. Baylor,⁷ M. Bazzan,⁷⁷,⁷⁸ B. Bécsy,⁷⁹

V. M. Bedakihale,⁸⁰ M. Bejger,⁸¹ I. Belahcene,⁴¹ V. Benedetto,⁸² D. Beniwal,⁸³ T. F. Bennett,⁸⁴ J. D. Bentley,¹⁴

M. BenYaala,³² F. Bergamin,⁹,¹⁰ B. K. Berger,⁷³ S. Bernuzzi,¹³ C. P. L. Berry,¹⁵,⁶⁹ D. Bersanetti,⁸⁵ A. Bertolini,⁵³

J. Betzwieser,⁶ D. Beveridge,⁸⁶ R. Bhandare,⁸⁷ U. Bhardwaj,⁸⁸,⁵³ D. Bhattacharjee,⁸⁹ S. Bhaumik,⁷²

I. A. Bilenko,⁹⁰ G. Billingsley,¹ S. Bini,⁹¹,⁹² R. Birney,⁹³ O. Birnholtz,⁹⁴ S. Biscans,¹,⁷⁰ M. Bischi,⁴⁹,⁵⁰

S. Biscoveanu,⁷⁰ A. Bisht,⁹,¹⁰ B. Biswas,¹¹ M. Bitossi,⁴²,¹⁸ M.-A. Bizouard,⁹⁵ J. K. Blackburn,¹ C. D. Blair,⁸⁶,⁶

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L. D. Bonavena,⁷⁷ F. Bondu,⁹⁹ E. Bonilla,⁷³ R. Bonnand,³⁰ P. Booker,⁹,¹⁰ B. A. Boom,⁵³ R. Bork,¹ V. Boschi,¹⁸

N. Bose,¹⁰⁰ S. Bose,¹¹ V. Bossilkov,⁸⁶ V. Boudart,⁶² Y. Bouffanais,⁷⁷,⁷⁸ A. Bozzi,⁴² C. Bradaschia,¹⁸ P. R. Brady,⁷

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A. Brillet,⁹⁵ M. Brinkmann,⁹,¹⁰ P. Brockill,⁷ A. F. Brooks,¹ J. Brooks,⁴² D. D. Brown,⁸³ S. Brunett,¹ G. Bruno,⁵²

R. Bruntz,⁵⁷ J. Bryant,¹⁴ T. Bulik,¹⁰³ H. J. Bulten,⁵³ A. Buonanno,¹⁰⁴,¹⁰⁵ R. Buscicchio,¹⁴ D. Buskulic,³⁰

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H. S. Cho,¹³⁸ R. K. Choudhary,⁸⁶ S. Choudhary,¹¹ N. Christensen,⁹⁵ H. Chu,¹³¹ Q. Chu,⁸⁶ Y-K. Chu,¹³⁵ S. Chua,⁸

K. W. Chung,⁵⁴ G. Ciani,⁷⁷,⁷⁸ P. Ciecielag,⁸¹ M. Cieślar,⁸¹ M. Cifaldi,¹¹⁹,¹²⁰ A. A. Ciobanu,⁸³ R. Ciolfi,¹³⁹,⁷⁸

F. Cipriano,⁹⁵ A. Cirone,¹¹²,⁸⁵ F. Clara,⁶⁷ E. N. Clark,¹⁴⁰ J. A. Clark,¹,⁴³ L. Clarke,¹⁴¹ P. Clearwater,¹⁴²

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T. D. Creighton,¹⁵⁰ A. W. Criswell,⁶³ M. Croquette,¹⁰² S. G. Crowder,¹⁵¹ J. R. Cudell,⁶² T. J. Cullen,²

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S. Di Pace,⁹⁸,⁵¹ I. Di Palma,⁹⁸,⁵¹ F. Di Renzo,⁷⁴,¹⁸ A. K. Divakarla,⁷² A. Dmitriev,¹⁴ Z. Doctor,⁶⁰ L. D'Onofrio,²⁵,⁴
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J.-G. Ducoin,⁴¹ P. Dupej,⁶⁹ O. Durante,⁹⁶,⁹⁷ D. D'Urso,¹¹⁷,¹¹⁸ P.-A. Duverne,⁴¹ S. E. Dwyer,⁶⁷ C. Eassa,⁶⁷

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S. Eguchi,¹²⁷ J. Eichholz,⁸ S. S. Eikenberry,⁷² M. Eisenmann,³⁰ R. A. Eisenstein,⁷⁰ A. Ejlli,¹⁷ E. Engelby,⁴⁰

Y. Enomoto,²⁷ L. Errico,²⁵,⁴ R. C. Essick,¹⁶² H. Estellés,¹⁴⁴ D. Estevez,¹⁶³ Z. Etienne,¹⁶⁴ T. Etzel,¹ M. Evans,⁷⁰

T. M. Evans,⁶ B. E. Ewing,¹⁴⁸ V. Fafone,¹¹⁹,¹²⁰,³¹ H. Fair,⁶¹ S. Fairhurst,¹⁷ A. M. Farah,¹⁶² S. Farinon,⁸⁵ B. Farr,⁶⁰
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J. Feicht,¹ M. M. Fejer,⁷³ E. Fenyvesi,⁷¹,¹⁶⁷ D. L. Ferguson,¹⁶⁸ A. Fernandez-Galiana,⁷⁰ I. Ferrante,⁷⁴,¹⁸

T. A. Ferreira,¹⁶ F. Fidecaro,⁷⁴,¹⁸ P. Figura,¹⁰³ I. Fiori,⁴² M. Fishbach,¹⁵ R. P. Fisher,⁵⁷ R. Fittipaldi,¹⁶⁹,⁹⁷

V. Fiumara,¹⁷⁰,⁹⁷ R. Flaminio,³⁰,²⁰ E. Floden,⁶³ H. Fong,¹¹⁴ J. A. Font,¹²³,¹⁷¹ B. Fornal,¹⁷² P. W. F. Forsyth,⁸

A. Franke,¹²⁴ S. Frasca,⁹⁸,⁵¹ F. Frasconi,¹⁸ C. Frederick,¹⁷³ J. P. Freed,³⁵ Z. Frei,¹⁵³ A. Freise,¹⁷⁴ R. Frey,⁶⁰

P. Fritschel,⁷⁰ V. V. Frolov,⁶ G. G. Fronzé,²⁴ Y. Fujii,¹⁷⁵ Y. Fujikawa,¹⁷⁶ M. Fukunaga,³⁷ M. Fukushima,²¹

P. Fulda,⁷² M. Fyffe,⁶ H. A. Gabbard,⁶⁹ B. U. Gadre,¹⁰⁵ J. R. Gair,¹⁰⁵ J. Gais,¹⁰⁸ S. Galaudage,⁵ R. Gamba,¹³

D. Ganapathy,⁷⁰ A. Ganguly,¹⁹ D. Gao,¹⁷⁷ S. G. Gaonkar,¹¹ B. Garaventa,⁸⁵,¹¹² F. García,³⁶ C. García-Núñez,⁹³

C. García-Quirós,¹⁴⁴ F. Garufi,²⁵,⁴ B. Gateley,⁶⁷ S. Gaudio,³⁵ V. Gayathri,⁷² G.-G. Ge,¹⁷⁷ G. Gemme,⁸⁵

A. Gennai,¹⁸ J. George,⁸⁷ R. N. George,¹⁶⁸ O. Gerberding,¹²⁴ L. Gergely,¹⁵⁴ P. Gewecke,¹²⁴ S. Ghonge,⁴³

Abhirup Ghosh,¹⁰⁵ Archisman Ghosh,¹⁷⁸ Shaon Ghosh,⁷,¹⁶⁵ Shrobana Ghosh,¹⁷ B. Giacomazzo,⁶⁴,⁶⁵,⁶⁶

L. Giacoppo,⁹⁸,⁵¹ J. A. Giaime,²,⁶ K. D. Giardina,⁶ D. R. Gibson,⁹³ C. Gier,³² M. Giesler,¹⁷⁹ P. Giri,¹⁸,⁷⁴ F. Gissi,⁸²

J. Glanzer,² A. E. Gleckl,⁴⁰ P. Godwin,¹⁴⁸ J. Golomb,¹ E. Goetz,¹⁸⁰ R. Goetz,⁷² N. Gohlke,⁹,¹⁰ B. Goncharov,⁵,³¹

G. González,² A. Gopakumar,¹⁸¹ M. Gosselin,⁴² R. Gouaty,³⁰ D. W. Gould,⁸ B. Grace,⁸ A. Grado,¹⁸²,⁴

M. Granata,¹⁵⁸ V. Granata,⁹⁶ A. Grant,⁶⁹ S. Gras,⁷⁰ P. Grassia,¹ C. Gray,⁶⁷ R. Gray,⁶⁹ G. Greco,⁷⁵ A. C. Green,⁷²

R. Green,¹⁷ A. M. Gretarsson,³⁵ E. M. Gretarsson,³⁵ D. Griffith,¹ W. Griffiths,¹⁷ H. L. Griggs,⁴³ G. Grignani,⁷⁶,⁷⁵

A. Grimaldi,⁹¹,⁹² S. J. Grimm,³¹,¹⁰¹ H. Grote,¹⁷ S. Grunewald,¹⁰⁵ P. Gruning,⁴¹ D. Guerra,¹²³ G. M. Guidi,⁴⁹,⁵⁰

A. R. Guimaraes,² G. Guixé,²⁹ H. K. Gulati,⁸⁰ H.-K. Guo,¹⁷² Y. Guo,⁵³ Anchal Gupta,¹ Anuradha Gupta,¹⁸³

P. Gupta,⁵³,¹¹³ E. K. Gustafson,¹ R. Gustafson,¹⁸⁴ F. Guzman,¹⁸⁵ S. Ha,¹⁸⁶ L. Haegel,³⁶ A. Hagiwara,³⁷,¹⁸⁷

S. Haino,¹³⁵ O. Halim,³⁴,¹⁸⁸ E. D. Hall,⁷⁰ E. Z. Hamilton,¹⁶¹ G. Hammond,⁶⁹ W.-B. Han,¹⁸⁹ M. Haney,¹⁶¹

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K. Hayama,¹²⁷ F. J. Hayes,⁶⁹ J. Healy,¹²⁵ A. Heidmann,¹⁰² A. Heidt,⁹,¹⁰ M. C. Heintze,⁶ J. Heinze,⁹,¹⁰

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N. Kawai,²¹⁸ T. Kawasaki,²⁷ F. Kéfélian,⁹⁵ D. Keitel,¹⁴⁴ J. S. Key,²¹⁹ S. Khadka,⁷³ F. Y. Khalili,⁹⁰ S. Khan,¹⁷

E. A. Khazanov,²²⁰ N. Khetan,³¹,¹⁰¹ M. Khursheed,⁸⁷ N. Kijbunchoo,⁸ C. Kim,²²¹ J. C. Kim,²²² J. Kim,²²³

K. Kim,²²⁴ W. S. Kim,²²⁵ Y.-M. Kim,²²⁶ C. Kimball,¹⁵ N. Kimura,¹⁸⁷ M. Kinley-Hanlon,⁶⁹ R. Kirchhoff,⁹,¹⁰

J. S. Kissel,⁶⁷ N. Kita,²⁷ H. Kitazawa,²⁰³ L. Kleybolte,¹²⁴ S. Klimenko,⁷² A. M. Knee,¹⁸⁰ T. D. Knowles,¹⁶⁴

E. Knyazev,⁷⁰ P. Koch,⁹,¹⁰ G. Koekoek,⁵³,¹⁵⁵ Y. Kojima,²²⁷ K. Kokeyama,²²⁸ S. Koley,³¹ P. Kolitsidou,¹⁷

M. Kolstein,²¹⁷ K. Komori,⁷⁰,²⁷ V. Kondrashov,¹ A. K. H. Kong,²²⁹ A. Kontos,²³⁰ N. Koper,⁹,¹⁰ M. Korobko,¹²⁴

K. Kotake,¹²⁷ M. Kovalam,⁸⁶ D. B. Kozak,¹ C. Kozakai,⁴⁷ R. Kozu,¹⁹² V. Kringel,⁹,¹⁰ N. V. Krishnendu,⁹,¹⁰

A. Królak,²³¹,²³² G. Kuehn,⁹,¹⁰ F. Kuei,¹²⁶ P. Kuijer,⁵³ S. Kulkarni,¹⁸³ A. Kumar,²⁰⁷ P. Kumar,¹⁷⁹ Rahul Kumar,⁶⁷

Rakesh Kumar,⁸⁰ J. Kume,²⁸ K. Kuns,⁷⁰ C. Kuo,¹³¹ H-S. Kuo,¹⁹⁸ Y. Kuromiya,²⁰³ S. Kuroyanagi,²³³,²³⁴

K. Kusayanagi,²¹⁸ S. Kuwahara,¹¹⁴ K. Kwak,¹⁸⁶ P. Lagabbe,³⁰ D. Laghi,⁷⁴,¹⁸ E. Lalande,²³⁵ T. L. Lam,¹⁰⁸

A. Lamberts,⁹⁵,²³⁶ M. Landry,⁶⁷ P. Landry,²³⁷ B. B. Lane,⁷⁰ R. N. Lang,⁷⁰ J. Lange,¹⁶⁸ B. Lantz,⁷³ I. La Rosa,³⁰

A. Lartaux-Vollard,⁴¹ P. D. Lasky,⁵ M. Laxen,⁶ A. Lazzarini,¹ C. Lazzaro,⁷⁷,⁷⁸ P. Leaci,⁹⁸,⁵¹ S. Leavey,⁹,¹⁰

Y. K. Lecoeuche,¹⁸⁰ H. K. Lee,²³⁸ H. M. Lee,¹³⁷ H. W. Lee,²²² J. Lee,¹³⁷ K. Lee,²³⁹ R. Lee,¹³³ J. Lehmann,⁹,¹⁰

A. Lemaître,²⁴⁰ M. Leonardi,²⁰ N. Leroy,⁴¹ N. Letendre,³⁰ C. Levesque,²³⁵ Y. Levin,⁵ J. N. Leviton,¹⁸⁴ K. Leyde,³⁶

A. K. Y. Li,¹ B. Li,¹²⁶ J. Li,¹⁵ K. L. Li,²⁴¹ T. G. F. Li,¹⁰⁸ X. Li,¹³² C-Y. Lin,²⁴² F-K. Lin,¹³⁵ F-L. Lin,¹⁹⁸

H. L. Lin,¹³¹ L. C.-C. Lin,¹⁸⁶ F. Linde,²⁴³,⁵³ S. D. Linker,⁸⁴ J. N. Linley,⁶⁹ T. B. Littenberg,²⁴⁴ G. C. Liu,¹²⁹

J. Liu,⁹,¹⁰ K. Liu,¹²⁶ X. Liu,⁷ F. Llamas,¹⁵⁰ M. Llorens-Monteagudo,¹²³ R. K. L. Lo,¹ A. Lockwood,²⁴⁵ M. Loh,⁴⁰

L. T. London,⁷⁰ A. Longo,²⁴⁶,²⁴⁷ D. Lopez,¹⁶¹ M. Lopez Portilla,¹¹³ M. Lorenzini,¹¹⁹,¹²⁰ V. Loriette,²⁴⁸

M. Lormand,⁶ G. Losurdo,¹⁸ T. P. Lott,⁴³ J. D. Lough,⁹,¹⁰ C. O. Lousto,¹²⁵ G. Lovelace,⁴⁰ J. F. Lucaccioni,¹⁷³

H. Lück,⁹,¹⁰ D. Lumaca,¹¹⁹,¹²⁰ A. P. Lundgren,¹⁵⁶ L.-W. Luo,¹³⁵ J. E. Lynam,⁵⁷ R. Macas,¹⁵⁶ M. MacInnis,⁷⁰

D. M. Macleod,¹⁷ I. A. O. MacMillan,¹ A. Macquet,⁹⁵ I. Magaña Hernandez,⁷ C. Magazzù,¹⁸ R. M. Magee,¹

R. Maggiore,¹⁴ M. Magnozzi,⁸⁵,¹¹² S. Mahesh,¹⁶⁴ E. Majorana,⁹⁸,⁵¹ C. Makarem,¹ I. Maksimovic,²⁴⁸ S. Maliakal,¹

A. Malik,⁸⁷ N. Man,⁹⁵ V. Mandic,⁶³ V. Mangano,⁹⁸,⁵¹ J. L. Mango,²⁴⁹ G. L. Mansell,⁶⁷,⁷⁰ M. Manske,⁷

M. Mantovani,⁴² M. Mapelli,⁷⁷,⁷⁸ F. Marchesoni,²⁵⁰,⁷⁵,²⁵¹ M. Marchio,²⁰ F. Marion,³⁰ Z. Mark,¹³² S. Márka,⁴⁶

Z. Márka,⁴⁶ C. Markakis,¹² A. S. Markosyan,⁷³ A. Markowitz,¹ E. Maros,¹ A. Marquina,¹⁴⁶ S. Marsat,³⁶

F. Martelli,⁴⁹,⁵⁰ I. W. Martin,⁶⁹ R. M. Martin,¹⁶⁵ M. Martinez,²¹⁷ V. A. Martinez,⁷² V. Martinez,²⁶

K. Martinovic,⁵⁴ D. V. Martynov,¹⁴ E. J. Marx,⁷⁰ H. Masalehdan,¹²⁴ K. Mason,⁷⁰ E. Massera,¹⁵⁷ A. Masserot,³⁰

T. J. Massinger,⁷⁰ M. Masso-Reid,⁶⁹ S. Mastrogiovanni,³⁶ A. Matas,¹⁰⁵ M. Mateu-Lucena,¹⁴⁴ F. Matichard,¹,⁷⁰

M. Matiushechkina,⁹,¹⁰ N. Mavalvala,⁷⁰ J. J. McCann,⁸⁶ R. McCarthy,⁶⁷ D. E. McClelland,⁸ P. K. McClincy,¹⁴⁸

S. McCormick,⁶ L. McCuller,⁷⁰ G. I. McGhee,⁶⁹ S. C. McGuire,²⁵² C. McIsaac,¹⁵⁶ J. McIver,¹⁸⁰ T. McRae,⁸

S. T. McWilliams,¹⁶⁴ D. Meacher,⁷ M. Mehmet,⁹,¹⁰ A. K. Mehta,¹⁰⁵ Q. Meijer,¹¹³ A. Melatos,¹¹⁶ D. A. Melchor,⁴⁰

G. Mendell,⁶⁷ A. Menendez-Vazquez,²¹⁷ C. S. Menoni,¹⁶⁶ R. A. Mercer,⁷ L. Mereni,¹⁵⁸ K. Merfeld,⁶⁰ E. L. Merilh,⁶

J. D. Merritt,⁶⁰ M. Merzougui,⁹⁵ S. Meshkov,¹, * C. Messenger,⁶⁹ C. Messick,¹⁶⁸ P. M. Meyers,¹¹⁶ F. Meylahn,⁹,¹⁰

A. Hhaske,¹¹ A. Miani,⁹¹,⁹² H. Miao,¹⁴ I. Michaloliakos,⁷² C. Michel,¹⁵⁸ Y. Michimura,²⁷ H. Middleton,¹¹⁶

L. Milano,²⁵ A. L. Miller,⁵² A. Miller,⁸⁴ B. Miller,⁸⁸,⁵³ S. Miller,¹ M. Millhouse,¹¹⁶ J. C. Mills,¹⁷ E. Milotti,¹⁸⁸,³⁴

O. Minazzoli,⁹⁵,²⁵³ Y. Minenkov,¹²⁰ N. Mio,²⁵⁴ Ll. M. Mir,²¹⁷ M. Miravet-Tenés,¹²³ C. Mishra,²⁵⁵ T. Mishra,⁷²

T. Mistry,¹⁵⁷ S. Mitra,¹¹ V. P. Mitrofanov,⁹⁰ G. Mitselmakher,⁷² R. Mittleman,⁷⁰ O. Miyakawa,¹⁹² A. Miyamoto,²⁰⁴

Y. Miyazaki,²⁷ K. Miyo,¹⁹² S. Miyoki,¹⁹² Geoffrey Mo,⁷⁰ L. M. Modafferi,²² E. Moguel,¹⁷³ K. Mogushi,⁸⁹

S. R. P. Mohapatra,⁷⁰ S. R. Mohite,⁷ I. Molina,⁴⁰ M. Molina-Ruiz,¹⁹⁴ M. Mondin,⁸⁴ M. Montani,⁴⁹,⁵⁰

C. J. Moore,¹⁴ D. Moraru,⁶⁷ F. Morawski,⁸¹ A. More,¹¹ C. Moreno,³⁵ G. Moreno,⁶⁷ Y. Mori,²⁰³ S. Morisaki,⁷

Y. Moriwaki,¹⁹¹ G. Morrás,²⁵⁶ B. Mours,¹⁶³ C. M. Mow-Lowry,¹⁴,¹⁷⁴ S. Mozzon,¹⁵⁶ F. Muciaccia,⁹⁸,⁵¹

Arunava Mukherjee,²⁵⁷ D. Mukherjee,¹⁴⁸ Soma Mukherjee,¹⁵⁰ Subroto Mukherjee,⁸⁰ Suvodip Mukherjee,⁸⁸

N. Mukund,⁹,¹⁰ A. Mullavey,⁶ J. Munch,⁸³ E. A. Muñiz,⁶¹ P. G. Murray,⁶⁹ R. Musenich,⁸⁵,¹¹² S. Muusse,⁸³

S. L. Nadji,⁹,¹⁰ K. Nagano,²⁰⁶ S. Nagano,²⁵⁸ A. Nagar,²⁴,²⁵⁹ K. Nakamura,²⁰ H. Nakano,²⁶⁰ M. Nakano,³⁷

R. Nakashima,²¹⁸ Y. Nakayama,²⁰³ V. Napolano,⁴² I. Nardecchia,¹¹⁹,¹²⁰ T. Narikawa,³⁷ L. Naticchioni,⁵¹

B. Nayak,⁸⁴ R. K. Nayak,²⁶¹ R. Negishi,¹⁹⁷ B. F. Neil,⁸⁶ J. Neilson,⁸²,⁹⁷ G. Nelemans,²⁶² T. J. N. Nelson,⁶

M. Nery,⁹,¹⁰ P. Neubauer,¹⁷³ A. Neunzert,²¹⁹ K. Y. Ng,⁷⁰ S. W. S. Ng,⁸³ C. Nguyen,³⁶ P. Nguyen,⁶⁰

T. Nguyen,⁷⁰ L. Nguyen Quynh,²⁶³ W.-T. Ni,²¹²,¹⁷⁷,¹³³ S. A. Nichols,² A. Nishizawa,²⁸ S. Nissanke,⁸⁸,⁵³

E. Nitoglia,¹³⁶ F. Nocera,⁴² M. Norman,¹⁷ C. North,¹⁷ S. Nozaki,¹⁹¹ J. F. Nuño Siles,²⁵⁶ L. K. Nuttall,¹⁵⁶

J. Oberling,⁶⁷ B. D. O'Brien,⁷² Y. Obuchi,²¹ J. O'Dell,¹⁴¹ E. Oelker,⁶⁹ W. Ogaki,³⁷ G. Oganesyan,³¹,¹⁰¹

J. J. Oh,²²⁵ K. Oh,¹⁹⁹ S. H. Oh,²²⁵ M. Ohashi,¹⁹² N. Ohishi,⁴⁷ M. Ohkawa,¹⁷⁶ F. Ohme,⁹,¹⁰ H. Ohta,¹¹⁴

M. A. Okada,¹⁶ Y. Okutani,²⁰⁰ K. Okutomi,¹⁹² C. Olivetto,⁴² K. Oohara,¹⁹⁷ C. Ooi,²⁷ R. Oram,⁶ B. O'Reilly,⁶

R. G. Ormiston,⁶³ N. D. Ormsby,⁵⁷ L. F. Ortega,⁷² R. O'Shaughnessy,¹²⁵ E. O'Shea,¹⁷⁹ S. Oshino,¹⁹²
S. Ossokine,¹⁰⁵ C. Osthelder,¹ S. Otabe,²¹⁸ D. J. Ottaway,⁸³ H. Overmier,⁶ A. E. Pace,¹⁴⁸ G. Pagano,⁷⁴, ¹⁸

M. A. Page,⁸⁶ G. Pagliaroli,³¹, ¹⁰¹ A. Pai,¹⁰⁰ S. A. Pai,⁸⁷ J. R. Palamos,⁶⁰ O. Palashov,²²⁰ C. Palomba,⁵¹ H. Pan,¹²⁶

K. Pan,¹³³, ²²⁹ P. K. Panda,²⁰⁷ H. Pang,¹³¹ P. T. H. Pang,⁵³, ¹¹³ C. Pankow,¹⁵ F. Pannarale,⁹⁸, ⁵¹ B. C. Pant,⁸⁷

F. H. Panther,⁸⁶ F. Paoletti,¹⁸ A. Paoli,⁴² A. Paolone,⁵¹, ²⁶⁴ A. Parisi,¹²⁹ H. Park,⁷ J. Park,²⁶⁵ W. Parker,⁶, ²⁵²

D. Pascucci,⁵³ A. Pasqualetti,⁴² R. Passaquieti,⁷⁴, ¹⁸ D. Passuello,¹⁸ M. Patel,⁵⁷ M. Pathak,⁸³ B. Patricelli,⁴², ¹⁸

A. S. Patron,² S. Paul,⁶⁰ E. Payne,⁵ M. Pedraza,¹ M. Pegoraro,⁷⁸ A. Pele,⁶ F. E. Peña Arellano,¹⁹² S. Penn,²⁶⁶

A. Perego,⁹¹, ⁹² A. Pereira,²⁶⁰ T. Pereira,²⁶⁷ C. J. Perez,⁶⁷ C. Périgois,³⁰ C. C. Perkins,⁷² A. Perreca,⁹¹, ⁹²

S. Perriès,¹³⁶ J. Petermann,¹²⁴ D. Petterson,¹ H. P. Pfeiffer,¹⁰⁵ K. A. Pham,⁶³ K. S. Phukon,⁵³, ²⁴³ O. J. Piccinni,⁵¹

M. Pichot,⁹⁵ M. Piendibene,⁷⁴, ¹⁸ F. Piergiovanni,⁴⁹, ⁵⁰ L. Pierini,⁹⁸, ⁵¹ V. Pierro,⁸², ⁹⁷ G. Pillant,⁴² M. Pillas,⁴¹

F. Pilo,¹⁸ L. Pinard,¹⁵⁸ I. M. Pinto,⁸², ⁹⁷, ²⁶⁸ M. Pinto,⁴² B. Piotrzkowski,⁷ K. Piotrzkowski,⁵² M. Pirello,⁶⁷

M. D. Pitkin,²⁶⁹ E. Placidi,⁹⁸, ⁵¹ L. Planas,¹⁴⁴ W. Plastino,²⁴⁶, ²⁷⁴ C. Pluchar,¹⁴⁰ R. Poggiani,⁷⁴, ¹⁸ E. Polini,³⁰

D. Y. T. Pong,¹⁰⁸ S. Ponnathnam,¹¹ P. Popolizio,⁴² E. K. Porter,³⁶ R. Poulton,⁴² J. Powell,¹⁴² M. Pracchia,³⁰

T. Pradier,¹⁶³ A. K. Prajapati,⁸⁰ K. Prasai,⁷³ R. Prasanna,²⁰⁷ G. Pratten,¹⁴ M. Principe,⁸², ²⁶⁸, ⁹⁷ G. A. Prodi,²⁷⁰, ⁹²

L. Prokhorov,¹⁴ P. Prosposito,¹¹⁹, ¹²⁰ L. Prudenzi,¹⁰⁵ A. Puecher,⁵³, ¹¹³ M. Punturo,⁷⁵ F. Puosi,¹⁸, ⁷⁴ P. Puppo,⁵¹

M. Pürrer,¹⁰⁵ H. Qi,¹⁷ V. Quetschke,¹⁵⁰ R. Quitzow-James,⁸⁹ F. J. Raab,⁶⁷ G. Raaijmakers,⁸⁸, ⁵³ H. Radkins,⁶⁷

N. Radulesco,⁹⁵ P. Raffai,¹⁵³ S. X. Rail,²³⁵ S. Raja,⁸⁷ C. Rajan,⁸⁷ K. E. Ramirez,⁶ T. D. Ramirez,⁴⁰

A. Ramos-Buades,¹⁰⁵ J. Rana,¹⁴⁸ P. Rapagnani,⁹⁸, ⁵¹ U. D. Rapol,²⁷¹ A. Ray,⁷ V. Raymond,¹⁷ N. Raza,¹⁸⁰

M. Razzano,⁷⁴, ¹⁸ J. Read,⁴⁰ L. A. Rees,¹⁹⁰ T. Regimbau,³⁰ L. Rei,⁸⁵ S. Reid,³² S. W. Reid,⁵⁷ D. H. Reitze,¹, ⁷²

P. Relton,¹⁷ A. Renzini,¹ P. Rettegno,²⁷², ²⁴ A. Reza,⁵³ M. Rezac,⁴⁰ F. Ricci,⁹⁸, ⁵¹ D. Richards,¹⁴¹

J. W. Richardson,¹ L. Richardson,¹⁸⁵ G. Riemenschneider,²⁷², ²⁴ K. Riles,¹⁸⁴ S. Rinaldi,¹⁸, ⁷⁴ K. Rink,¹⁸⁰ M. Rizzo,¹⁵

N. A. Robertson,¹, ⁶⁹ R. Robie,¹ F. Robinet,⁴¹ A. Rocchi,¹²⁰ S. Rodriguez,⁴⁰ L. Rolland,³⁰ J. G. Rollins,¹

M. Romanelli,⁹⁹ R. Romano,³, ⁴ C. L. Romel,⁶⁷ A. Romero-Rodríguez,²¹⁷ I. M. Romero-Shaw,⁵ J. H. Romie,⁶

S. Ronchini,³¹, ¹⁰¹ L. Rosa,⁴, ²⁵ C. A. Rose,⁷ D. Rosińska,¹⁰³ M. P. Ross,²⁴⁵ S. Rowan,⁶⁹ S. J. Rowlinson,¹⁴

S. Roy,¹¹³ Santosh Roy,¹¹ Soumen Roy,²⁷³ D. Rozza,¹¹⁷, ¹¹⁸ P. Ruggi,⁴² K. Ryan,⁶⁷ S. Sachdev,¹⁴⁸ T. Sadecki,⁶⁷

J. Sadiq,¹⁰⁷ N. Sago,²⁷⁴ S. Saito,²¹ Y. Saito,¹⁹² K. Sakai,²⁷⁵ Y. Sakai,¹⁹⁷ M. Sakellariadou,⁵⁴ Y. Sakuno,¹²⁷

O. S. Salafia,⁶⁶, ⁶⁵, ⁶⁴ L. Salconi,⁴² M. Saleem,⁶³ F. Salemi,⁹¹, ⁹² A. Samajdar,⁵³, ¹¹³ E. J. Sanchez,¹ J. H. Sanchez,⁴⁰

L. E. Sanchez,¹ N. Sanchis-Gual,²⁷⁶ J. R. Sanders,²⁷⁷ A. Sanuy,²⁹ T. R. Saravanan,¹¹ N. Sarin,⁵ B. Sassolas,¹⁵⁸

H. Satari,⁸⁶ B. S. Sathyaprakash,¹⁴⁸, ¹⁷ S. Sato,²⁷⁸ T. Sato,¹⁷⁶ O. Sauter,⁷² R. L. Savage,⁶⁷ T. Sawada,²⁰⁴

D. Sawant,¹⁰⁰ H. L. Sawant,¹¹ S. Sayah,¹⁵⁸ D. Schaetzl,¹ M. Scheel,¹³² J. Scheuer,¹⁵ M. Schiworski,⁸³ P. Schmidt,¹⁴

S. Schmidt,¹¹³ R. Schnabel,¹²⁴ M. Schneewind,⁹, ¹⁰ R. M. S. Schofield,⁶⁰ A. Schönbeck,¹²⁴ B. W. Schulte,⁹, ¹⁰

B. F. Schutz,¹⁷, ⁹, ¹⁰ E. Schwartz,¹⁷ J. Scott,⁶⁹ S. M. Scott,⁸ M. Seglar-Arroyo,³⁰ T. Sekiguchi,²⁸ Y. Sekiguchi,²⁷⁹

D. Sellers,⁶ A. S. Sengupta,²⁷³ D. Sentenac,⁴² E. G. Seo,¹⁰⁸ V. Sequino,²⁵, ⁴ A. Sergeev,²²⁰ Y. Setyawati,¹¹³

T. Shaffer,⁶⁷ M. S. Shahriar,¹⁵ B. Shams,¹⁷² L. Shao,²⁰¹ A. Sharma,³¹, ¹⁰¹ P. Sharma,⁸⁷ P. Shawhan,¹⁰⁴

N. S. Shcheblanov,²⁴⁰ S. Shibagaki,¹²⁷ M. Shikauchi,¹¹⁴ R. Shimizu,²¹ T. Shimoda,²⁷ K. Shimode,¹⁹² H. Shinkai,²⁸⁰

T. Shishido,⁴⁸ A. Shoda,²⁰ D. H. Shoemaker,⁷⁰ D. M. Shoemaker,¹⁶⁸ S. ShyamSundar,⁸⁷ M. Sieniawska,¹⁰³

D. Sigg,⁶⁷ L. P. Singer,¹¹¹ D. Singh,¹⁴⁸ N. Singh,¹⁰³ A. Singha,¹⁵⁵, ⁵³ A. M. Sintes,¹⁴⁴ V. Sipala,¹¹⁷, ¹¹⁸ V. Skliris,¹⁷

B. J. J. Slagmolen,⁸ T. J. Slaven-Blair,⁸⁶ J. Smetana,¹⁴ J. R. Smith,⁴⁰ R. J. E. Smith,⁵ J. Soldateschi,²⁸¹, ²⁸², ⁵⁰

S. N. Somala,²⁸³ K. Somiya,²¹⁸ E. J. Son,²²⁵ K. Soni,¹¹ S. Soni,² V. Sordini,¹³⁶ F. Sorrentino,⁸⁵ N. Sorrentino,⁷⁴, ¹⁸

H. Sotani,²⁸⁴ R. Soulard,⁹⁵ T. Souradeep,²⁷¹, ¹¹ E. Sowell,¹⁴⁷ V. Spagnuolo,¹⁵⁵, ⁵³ A. P. Spencer,⁶⁹ M. Spera,⁷⁷, ⁷⁸

R. Srinivasan,⁹⁵ A. K. Srivastava,⁸⁰ V. Srivastava,⁶¹ K. Staats,¹⁵ C. Stachie,⁹⁵ D. A. Steer,³⁶ J. Steinhoff,¹⁰⁵

J. Steinlechner,¹⁵⁵, ⁵³ S. Steinlechner,¹⁵⁵, ⁵³ S. P. Stevenson,¹⁴² D. J. Stops,¹⁴ M. Stover,¹⁷³ K. A. Strain,⁶⁹

L. C. Strang,¹¹⁶ G. Stratta,²⁸⁵, ⁵⁰ A. Strunk,⁶⁷ R. Sturani,²⁶⁷ A. L. Stuver,¹²² S. Sudhagar,¹¹ V. Sudhir,⁷⁰

R. Sugimoto,²⁸⁶, ²⁰⁶ H. G. Suh,⁷ A. G. Sullivan,⁴⁶ T. Z. Summerscales,²⁸⁷ H. Sun,⁸⁶ L. Sun,⁸ S. Sunil,⁸⁰ A. Sur,⁸¹

J. Suresh,¹¹⁴, ³⁷ P. J. Sutton,¹⁷ Takamasa Suzuki,¹⁷⁶ Toshikazu Suzuki,³⁷ B. L. Swinkels,⁵³ M. J. Szczepańczyk,⁷²

P. Szewczyk,¹⁰³ M. Tacca,⁵³ H. Tagoshi,³⁷ S. C. Tait,⁶⁹ H. Takahashi,²⁸⁸ R. Takahashi,²⁰ A. Takamori,³⁹

S. Takano,²⁷ H. Takeda,²⁷ M. Takeda,²⁰⁴ C. J. Talbot,³² C. Talbot,¹ H. Tanaka,²⁸⁹ Kazuyuki Tanaka,²⁰⁴

Kenta Tanaka,²⁸⁹ Taiki Tanaka,³⁷ Takahiro Tanaka,²⁷⁴ A. J. Tanasijczuk,⁵² S. Tanioka,²⁰, ⁴⁸ D. B. Tanner,⁷²

D. Tao,¹ L. Tao,⁷² E. N. Tapia San Martín,⁵³, ²⁰ C. Taranto,¹¹⁹ J. D. Tasson,¹⁹³ S. Telada,²⁹⁰ R. Tenorio,¹⁴⁴

J. E. Terhune,¹²² L. Terkowski,¹²⁴ M. P. Thirugnanasambandam,¹¹ L. Thomas,¹⁴ M. Thomas,⁶ P. Thomas,⁶⁷

J. E. Thompson,¹⁷ S. R. Thondapu,⁸⁷ K. A. Thorne,⁶ E. Thrane,⁵ Shubhanshu Tiwari,¹⁶¹ Srishti Tiwari,¹¹

V. Tiwari,¹⁷ A. M. Toivonen,⁶³ K. Toland,⁶⁹ A. E. Tolley,¹⁵⁶ T. Tomaru,²⁰ Y. Tomigami,²⁰⁴ T. Tomura,¹⁹²

M. Tonelli,⁷⁴, ¹⁸ A. Torres-Forné,¹²³ C. I. Torrie,¹ I. Tosta e Melo,¹¹⁷, ¹¹⁸ D. Töyrä,⁸ A. Trapananti,²⁵⁰, ⁷⁵

F. Travasso,⁷⁵, ²⁵⁰ G. Traylor,⁶ M. Trevor,¹⁰⁴ M. C. Tringali,⁴² A. Tripathee,¹⁸⁴ L. Troiano,²⁹¹, ⁹⁷ A. Trovato,³⁶
L. Trozzo,<fnref n="4" />,¹⁹² R. J. Trudeau,<fnref n="1" /> D. S. Tsai,¹²⁶ D. Tsai,¹²⁶ K. W. Tsang,⁵³,²⁹²,¹¹³ T. Tsang,²⁹³ J.-S. Tsao,¹⁹⁸

M. Tse,⁷⁰ R. Tso,¹³² K. Tsubono,<fnref n="27" /> S. Tsuchida,²⁰⁴ L. Tsukada,¹¹⁴ D. Tsuna,¹¹⁴ T. Tsutsui,¹¹⁴ T. Tsuzuki,<fnref n="21" />

K. Turbang,²⁹⁴,²⁹⁰ M. Turconi,⁹⁵ D. Tuyenbayev,²⁰⁴ A. S. Ubhi,<fnref n="14" /> N. Uchikata,³⁷ T. Uchiyama,¹⁹² R. P. Udall,<fnref n="1" />

A. Ueda,¹⁸⁷ T. Uehara,²⁹⁵,²⁹⁶ K. Ueno,¹¹⁴ G. Ueshima,²⁹⁷ C. S. Unnikrishnan,¹⁸¹ F. Uraguchi,<fnref n="21" /> A. L. Urban,<fnref n="2" />

T. Ushiba,¹⁹² A. Utina,¹⁵⁵,⁵³ H. Vahlbruch,<fnref n="9" />,<fnref n="10" /> G. Vajente,<fnref n="1" /> A. Vajpeyi,<fnref n="5" /> G. Valdes,¹⁸⁵ M. Valentini,⁹¹,⁹²

V. Valsan,<fnref n="7" /> N. van Bakel,⁵³ M. van Beuzekom,⁵³ J. F. J. van den Brand,¹⁵⁵,²⁹⁸,⁵³ C. Van Den Broeck,¹¹³,⁵³

D. C. Vander-Hyde,⁶¹ L. van der Schaaf,⁵³ J. V. van Heijningen,⁵² J. Vanosky,<fnref n="1" /> M. H. P. M. van Putten,²⁹⁹

N. van Remortel,²⁰⁹ M. Vardaro,²⁴³,⁵³ A. F. Vargas,¹¹⁶ V. Varma,¹⁷⁹ M. Vasúth,⁷¹ A. Vecchio,<fnref n="14" /> G. Vedovato,⁷⁸

J. Veitch,⁶⁹ P. J. Veitch,⁸³ J. Venneberg,<fnref n="9" />,<fnref n="10" /> G. Venugopalan,<fnref n="1" /> D. Verkindt,³⁰ P. Verma,²³² Y. Verma,⁸⁷ D. Veske,⁴⁶

F. Vetrano,⁴⁹ A. Viceré,⁴⁹,⁵⁰ S. Vidyant,⁶¹ A. D. Viets,²⁴⁹ A. Vijaykumar,<fnref n="19" /> V. Villa-Ortega,¹⁰⁷ J.-Y. Vinet,⁹⁵

A. Virtuoso,¹⁸⁸,³⁴ S. Vitale,⁷⁰ T. Vo,⁶¹ H. Vocca,⁷⁶,⁷⁵ E. R. G. von Reis,⁶⁷ J. S. A. von Wrangel,<fnref n="9" />,<fnref n="10" /> C. Vorvick,⁶⁷

S. P. Vyatchanin,⁹⁰ L. E. Wade,¹⁷³ M. Wade,¹⁷³ K. J. Wagner,¹²⁵ R. C. Walet,⁵³ M. Walker,⁵⁷ G. S. Wallace,³²

L. Wallace,<fnref n="1" /> S. Walsh,<fnref n="7" /> J. Wang,¹⁷⁷ J. Z. Wang,¹⁸⁴ W. H. Wang,¹⁵⁰ R. L. Ward,<fnref n="8" /> J. Warner,⁶⁷ M. Was,³⁰

T. Washimi,<fnref n="20" /> N. Y. Washington,<fnref n="1" /> J. Watchi,¹⁴⁵ B. Weaver,⁶⁷ S. A. Webster,⁶⁹ M. Weinert,<fnref n="9" />,<fnref n="10" /> A. J. Weinstein,<fnref n="1" />

R. Weiss,⁷⁰ C. M. Weller,²⁴⁵ F. Wellmann,<fnref n="9" />,<fnref n="10" /> L. Wen,⁸⁶ P. Weßels,<fnref n="9" />,<fnref n="10" /> K. Wette,<fnref n="8" /> J. T. Whelan,¹²⁵ D. D. White,⁴⁰

B. F. Whiting,⁷² C. Whittle,⁷⁰ D. Wilken,<fnref n="9" />,<fnref n="10" /> D. Williams,⁶⁹ M. J. Williams,⁶⁹ A. R. Williamson,¹⁵⁶ J. L. Willis,<fnref n="1" />

B. Willke,<fnref n="9" />,<fnref n="10" /> D. J. Wilson,¹⁴⁰ W. Winkler,<fnref n="9" />,<fnref n="10" /> C. C. Wipf,<fnref n="1" /> T. Wlodarczyk,¹⁰⁵ G. Woan,⁶⁹ J. Woehler,<fnref n="9" />,<fnref n="10" />

J. K. Wofford,¹²⁵ I. C. F. Wong,¹⁰⁸ C. Wu,¹³³ D. S. Wu,<fnref n="9" />,<fnref n="10" /> H. Wu,¹³³ S. Wu,¹³³ D. M. Wysocki,<fnref n="7" /> L. Xiao,<fnref n="1" />

W-R. Xu,¹⁹⁸ T. Yamada,²⁸⁹ H. Yamamoto,<fnref n="1" /> Kazuhiro Yamamoto,¹⁹¹ Kohei Yamamoto,²⁸⁹ T. Yamamoto,¹⁹²

K. Yamashita,²⁰³ R. Yamazaki,²⁰⁰ F. W. Yang,¹⁷² L. Yang,¹⁶⁶ Y. Yang,³⁰⁰ Yang Yang,⁷² Z. Yang,⁶³ M. J. Yap,<fnref n="8" />

D. W. Yeeles,<fnref n="17" /> A. B. Yelikar,¹²⁵ M. Ying,¹²⁶ K. Yokogawa,²⁰³ J. Yokoyama,<fnref n="28" />,<fnref n="27" /> T. Yokozawa,¹⁹² J. Yoo,¹⁷⁹

T. Yoshioka,²⁰³ Hang Yu,¹³² Haocun Yu,⁷⁰ H. Yuzurihara,³⁷ A. Zadrożny,²³² M. Zanolin,³⁵ S. Zeidler,³⁰¹

T. Zelenova,⁴² J.-P. Zendri,⁷⁸ M. Zevin,¹⁶² M. Zhan,¹⁷⁷ H. Zhang,¹⁹⁸ J. Zhang,⁸⁶ L. Zhang,<fnref n="1" /> T. Zhang,<fnref n="14" />

Y. Zhang,¹⁸⁵ C. Zhao,⁸⁶ G. Zhao,¹⁴⁵ Y. Zhao,<fnref n="20" /> Yue Zhao,¹⁷² Y. Zheng,⁸⁹ R. Zhou,¹⁹⁴ Z. Zhou,<fnref n="15" />

X. J. Zhu,<fnref n="5" /> Z.-H. Zhu,¹¹⁵ A. B. Zimmerman,¹⁶⁸ Y. Zlochower,¹²⁵ M. E. Zucker,<fnref n="1" />,⁷⁰ and J. Zweizig<fnref n="1" />

<footnote n="1">¹LIGO Laboratory, California Institute of Technology, Pasadena, CA 91125, USA</footnote>

<footnote n="2">²Louisiana State University, Baton Rouge, LA 70803, USA</footnote>

<footnote n="3">³Dipartimento di Farmacia, Università di Salerno, I-84084 Fisciano, Salerno, Italy</footnote>

<footnote n="4">⁴INFN, Sezione di Napoli, Complesso Universitario di Monte S. Angelo, I-80126 Napoli, Italy</footnote>

<footnote n="5">⁵OzGrav, School of Physics & Astronomy, Monash University, Clayton 3800, Victoria, Australia</footnote>

<footnote n="6">⁶LIGO Livingston Observatory, Livingston, LA 70754, USA</footnote>

<footnote n="7">⁷University of Wisconsin-Milwaukee, Milwaukee, WI 53201, USA</footnote>

<footnote n="8">⁸OzGrav, Australian National University, Canberra, Australian Capital Territory 0200, Australia</footnote>

<footnote n="9">⁹Max Planck Institute for Gravitational Physics (Albert Einstein Institute), D-30167 Hannover, Germany</footnote>

<footnote n="10">¹⁰Leibniz Universität Hannover, D-30167 Hannover, Germany</footnote>

<footnote n="11">¹¹Inter-University Centre for Astronomy and Astrophysics, Pune 411007, India</footnote>

<footnote n="12">¹²University of Cambridge, Cambridge CB2 1TN, United Kingdom</footnote>

<footnote n="13">¹³Theoretisch-Physikalisches Institut, Friedrich-Schiller-Universität Jena, D-07743 Jena, Germany</footnote>

<footnote n="14">¹⁴University of Birmingham, Birmingham B15 2TT, United Kingdom</footnote>

<footnote n="15">¹⁵Center for Interdisciplinary Exploration & Research in Astrophysics (CIERA), Northwestern University, Evanston, IL 60208, USA</footnote>

<footnote n="16">¹⁶Instituto Nacional de Pesquisas Espaciais, 12227-010 São José dos Campos, São Paulo, Brazil</footnote>

<footnote n="17">¹⁷Gravity Exploration Institute, Cardiff University, Cardiff CF24 3AA, United Kingdom</footnote>

<footnote n="18">¹⁸INFN, Sezione di Pisa, I-56127 Pisa, Italy</footnote>

<footnote n="19">¹⁹International Centre for Theoretical Sciences, Tata Institute of Fundamental Research, Bengaluru 560089, India</footnote>

<footnote n="20">²⁰Gravitational Wave Science Project, National Astronomical Observatory of Japan (NAOJ), Mitaka City, Tokyo 181-8588, Japan</footnote>

<footnote n="21">²¹Advanced Technology Center, National Astronomical Observatory of Japan (NAOJ), Mitaka City, Tokyo 181-8588, Japan</footnote>

<footnote n="22">²²Universitat de les Illes Balears, IAC3-IEEC, E-07122 Palma de Mallorca, Spain</footnote>

<footnote n="23">²³University College Dublin, Dublin 4, Ireland</footnote>

<footnote n="24">²⁴INFN Sezione di Torino, I-10125 Torino, Italy</footnote>

<footnote n="25">²⁵Università di Napoli “Federico II”, Complesso Universitario di Monte S. Angelo, I-80126 Napoli, Italy</footnote>

<footnote n="26">²⁶Université de Lyon, Université Claude Bernard Lyon 1, CNRS, Institut Lumière Matière, F-69622 Villeurbanne, France</footnote>

<footnote n="27">²⁷Department of Physics, The University of Tokyo, Bunkyo-ku, Tokyo 113-0033, Japan</footnote>

<footnote n="28">²⁸Research Center for the Early Universe (RESCEU), The University of Tokyo, Bunkyo-ku, Tokyo 113-0033, Japan</footnote>

<footnote n="29">²⁹Institut de Ciències del Cosmos (ICCUB), Universitat de Barcelona, C/ Martí i Franquès 1, Barcelona, 08028, Spain</footnote>
<footnote n="30">³⁰Laboratoire d'Annecy de Physique des Particules (LAPP), Univ. Grenoble Alpes,
Université Savoie Mont Blanc, CNRS/IN2P3, F-74941 Annecy, France</footnote>

<footnote n="31">³¹Gran Sasso Science Institute (GSSI), I-67100 L'Aquila, Italy</footnote>

<footnote n="32">³²SUPA, University of Strathclyde, Glasgow G1 1XQ, United Kingdom</footnote>

<footnote n="33">³³Dipartimento di Scienze Matematiche, Informatiche e Fisiche, Università di Udine, I-33100 Udine, Italy</footnote>

<footnote n="34">³⁴INFN, Sezione di Trieste, I-34127 Trieste, Italy</footnote>

<footnote n="35">³⁵Embry-Riddle Aeronautical University, Prescott, AZ 86301, USA</footnote>

<footnote n="36">³⁶Université de Paris, CNRS, Astroparticule et Cosmologie, F-75006 Paris, France</footnote>

<footnote n="37">³⁷Institute for Cosmic Ray Research (ICRR), KAGRA Observatory,
The University of Tokyo, Kashiwa City, Chiba 277-8582, Japan</footnote>

<footnote n="38">³⁸Accelerator Laboratory, High Energy Accelerator Research Organization (KEK), Tsukuba City, Ibaraki 305-0801, Japan</footnote>

<footnote n="39">³⁹Earthquake Research Institute, The University of Tokyo, Bunkyo-ku, Tokyo 113-0032, Japan</footnote>

<footnote n="40">⁴⁰California State University Fullerton, Fullerton, CA 92831, USA</footnote>

<footnote n="41">⁴¹Université Paris-Saclay, CNRS/IN2P3, IJCLab, 91405 Orsay, France</footnote>

<footnote n="42">⁴²European Gravitational Observatory (EGO), I-56021 Cascina, Pisa, Italy</footnote>

<footnote n="43">⁴³School of Physics, Georgia Institute of Technology, Atlanta, GA 30332, USA</footnote>

<footnote n="44">⁴⁴Chennai Mathematical Institute, Chennai 603103, India</footnote>

<footnote n="45">⁴⁵Department of Mathematics and Physics, Gravitational Wave Science Project,
Hirosaki University, Hirosaki City, Aomori 036-8561, Japan</footnote>

<footnote n="46">⁴⁶Columbia University, New York, NY 10027, USA</footnote>

<footnote n="47">⁴⁷Kamioka Branch, National Astronomical Observatory of Japan (NAOJ), Kamioka-cho, Hida City, Gifu 506-1205, Japan</footnote>

<footnote n="48">⁴⁸The Graduate University for Advanced Studies (SOKENDAI), Mitaka City, Tokyo 181-8588, Japan</footnote>

<footnote n="49">⁴⁹Università degli Studi di Urbino “Carlo Bo”, I-61029 Urbino, Italy</footnote>

<footnote n="50">⁵⁰INFN, Sezione di Firenze, I-50019 Sesto Fiorentino, Firenze, Italy</footnote>

<footnote n="51">⁵¹INFN, Sezione di Roma, I-00185 Roma, Italy</footnote>

<footnote n="52">⁵²Université catholique de Louvain, B-1348 Louvain-la-Neuve, Belgium</footnote>

<footnote n="53">⁵³Nikhef, Science Park 105, 1098 XG Amsterdam, Netherlands</footnote>

<footnote n="54">⁵⁴King's College London, University of London, London WC2R 2LS, United Kingdom</footnote>

<footnote n="55">⁵⁵Korea Institute of Science and Technology Information (KISTI), Yuseong-gu, Daejeon 34141, Republic of Korea</footnote>

<footnote n="56">⁵⁶National Institute for Mathematical Sciences, Yuseong-gu, Daejeon 34047, Republic of Korea</footnote>

<footnote n="57">⁵⁷Christopher Newport University, Newport News, VA 23606, USA</footnote>

<footnote n="58">⁵⁸International College, Osaka University, Toyonaka City, Osaka 560-0043, Japan</footnote>

<footnote n="59">⁵⁹School of High Energy Accelerator Science, The Graduate University for
Advanced Studies (SOKENDAI), Tsukuba City, Ibaraki 305-0801, Japan</footnote>

<footnote n="60">⁶⁰University of Oregon, Eugene, OR 97403, USA</footnote>

<footnote n="61">⁶¹Syracuse University, Syracuse, NY 13244, USA</footnote>

<footnote n="62">⁶²Université de Liège, B-4000 Liège, Belgium</footnote>

<footnote n="63">⁶³University of Minnesota, Minneapolis, MN 55455, USA</footnote>

<footnote n="64">⁶⁴Università degli Studi di Milano-Bicocca, I-20126 Milano, Italy</footnote>

<footnote n="65">⁶⁵INFN, Sezione di Milano-Bicocca, I-20126 Milano, Italy</footnote>

<footnote n="66">⁶⁶INAF, Osservatorio Astronomico di Brera sede di Merate, I-23807 Merate, Lecco, Italy</footnote>

<footnote n="67">⁶⁷LIGO Hanford Observatory, Richland, WA 99352, USA</footnote>

<footnote n="68">⁶⁸Dipartimento di Medicina, Chirurgia e Odontoiatria “Scuola Medica Salernitana”,
Università di Salerno, I-84081 Baronissi, Salerno, Italy</footnote>

<footnote n="69">⁶⁹SUPA, University of Glasgow, Glasgow G12 8QQ, United Kingdom</footnote>

<footnote n="70">⁷⁰LIGO Laboratory, Massachusetts Institute of Technology, Cambridge, MA 02139, USA</footnote>

<footnote n="71">⁷¹Wigner RCP, RMKI, H-1121 Budapest, Konkoly Thege Miklós út 29-33, Hungary</footnote>

<footnote n="72">⁷²University of Florida, Gainesville, FL 32611, USA</footnote>

<footnote n="73">⁷³Stanford University, Stanford, CA 94305, USA</footnote>

<footnote n="74">⁷⁴Università di Pisa, I-56127 Pisa, Italy</footnote>

<footnote n="75">⁷⁵INFN, Sezione di Perugia, I-06123 Perugia, Italy</footnote>

<footnote n="76">⁷⁶Università di Perugia, I-06123 Perugia, Italy</footnote>

<footnote n="77">⁷⁷Università di Padova, Dipartimento di Fisica e Astronomia, I-35131 Padova, Italy</footnote>

<footnote n="78">⁷⁸INFN, Sezione di Padova, I-35131 Padova, Italy</footnote>

<footnote n="79">⁷⁹Montana State University, Bozeman, MT 59717, USA</footnote>

<footnote n="80">⁸⁰Institute for Plasma Research, Bhat, Gandhinagar 382428, India</footnote>

<footnote n="81">⁸¹Nicolaus Copernicus Astronomical Center, Polish Academy of Sciences, 00-716, Warsaw, Poland</footnote>

<footnote n="82">⁸²Dipartimento di Ingegneria, Università del Sannio, I-82100 Benevento, Italy</footnote>

<footnote n="83">⁸³OzGrav, University of Adelaide, Adelaide, South Australia 5005, Australia</footnote>

<footnote n="84">⁸⁴California State University, Los Angeles, 5151 State University Dr, Los Angeles, CA 90032, USA</footnote>

<footnote n="85">⁸⁵INFN, Sezione di Genova, I-16146 Genova, Italy</footnote>

<footnote n="86">⁸⁶OzGrav, University of Western Australia, Crawley, Western Australia 6009, Australia</footnote>

<footnote n="87">⁸⁷RRCAT, Indore, Madhya Pradesh 452013, India</footnote>
⁸⁸ GRAPPA, Anton Pannekoek Institute for Astronomy and Institute for High-Energy Physics, University of Amsterdam, Science Park 904, 1098 XH Amsterdam, Netherlands

⁸⁹ Missouri University of Science and Technology, Rolla, MO 65409, USA

⁹⁰ Faculty of Physics, Lomonosov Moscow State University, Moscow 119991, Russia

⁹¹ Università di Trento, Dipartimento di Fisica, I-38123 Povo, Trento, Italy

⁹² INFN, Trento Institute for Fundamental Physics and Applications, I-38123 Povo, Trento, Italy

⁹³ SUPA, University of the West of Scotland, Paisley PA1 2BE, United Kingdom

⁹⁴ Bar-Ilan University, Ramat Gan, 5290002, Israel

⁹⁵ Artemis, Université Côte d'Azur, Observatoire de la Côte d'Azur, CNRS, F-06304 Nice, France

⁹⁶ Dipartimento di Fisica “E.R. Caianiello”, Università di Salerno, I-84084 Fisciano, Salerno, Italy

⁹⁷ INFN, Sezione di Napoli, Gruppo Collegato di Salerno, Complesso Universitario di Monte S. Angelo, I-80126 Napoli, Italy

⁹⁸ Università di Roma “La Sapienza”, I-00185 Roma, Italy

⁹⁹ Univ Rennes, CNRS, Institut FOTON - UMR6082, F-3500 Rennes, France

¹⁰⁰ Indian Institute of Technology Bombay, Powai, Mumbai 400 076, India

¹⁰¹ INFN, Laboratori Nazionali del Gran Sasso, I-67100 Assergi, Italy

¹⁰² Laboratoire Kastler Brossel, Sorbonne Université, CNRS, ENS-Université PSL, Collège de France, F-75005 Paris, France

¹⁰³ Astronomical Observatory Warsaw University, 00-478 Warsaw, Poland

¹⁰⁴ University of Maryland, College Park, MD 20742, USA

¹⁰⁵ Max Planck Institute for Gravitational Physics (Albert Einstein Institute), D-14476 Potsdam, Germany

¹⁰⁶ L2IT, Laboratoire des 2 Infinis - Toulouse, Université de Toulouse, CNRS/IN2P3, UPS, F-31062 Toulouse Cedex 9, France

¹⁰⁷ IGFAE, Campus Sur, Universidade de Santiago de Compostela, 15782 Spain

¹⁰⁸ The Chinese University of Hong Kong, Shatin, NT, Hong Kong

¹⁰⁹ Stony Brook University, Stony Brook, NY 11794, USA

¹¹⁰ Center for Computational Astrophysics, Flatiron Institute, New York, NY 10010, USA

¹¹¹ NASA Goddard Space Flight Center, Greenbelt, MD 20771, USA

¹¹² Dipartimento di Fisica, Università degli Studi di Genova, I-16146 Genova, Italy

¹¹³ Institute for Gravitational and Subatomic Physics (GRASP), Utrecht University, Princetonplein 1, 3584 CC Utrecht, Netherlands

¹¹⁴ RESCEU, University of Tokyo, Tokyo, 113-0033, Japan.

¹¹⁵ Department of Astronomy, Beijing Normal University, Beijing 100875, China

¹¹⁶ OzGrav, University of Melbourne, Parkville, Victoria 3010, Australia

¹¹⁷ Università degli Studi di Sassari, I-07100 Sassari, Italy

¹¹⁸ INFN, Laboratori Nazionali del Sud, I-95125 Catania, Italy

¹¹⁹ Università di Roma Tor Vergata, I-00133 Roma, Italy

¹²⁰ INFN, Sezione di Roma Tor Vergata, I-00133 Roma, Italy

¹²¹ University of Sannio at Benevento, I-82100 Benevento, Italy and INFN, Sezione di Napoli, I-80100 Napoli, Italy

¹²² Villanova University, 800 Lancaster Ave, Villanova, PA 19085, USA

¹²³ Departamento de Astronomía y Astrofísica, Universitat de València, E-46100 Burjassot, València, Spain

¹²⁴ Universität Hamburg, D-22761 Hamburg, Germany

¹²⁵ Rochester Institute of Technology, Rochester, NY 14623, USA

¹²⁶ National Tsing Hua University, Hsinchu City, 30013 Taiwan, Republic of China

¹²⁷ Department of Applied Physics, Fukuoka University, Jonan, Fukuoka City, Fukuoka 814-0180, Japan

¹²⁸ OzGrav, Charles Sturt University, Wagga Wagga, New South Wales 2678, Australia

¹²⁹ Department of Physics, Tamkang University, Danshui Dist., New Taipei City 25137, Taiwan

¹³⁰ Department of Physics and Institute of Astronomy, National Tsing Hua University, Hsinchu 30013, Taiwan

¹³¹ Department of Physics, Center for High Energy and High Field Physics, National Central University, Zhongli District, Taoyuan City 32001, Taiwan

¹³² CaRT, California Institute of Technology, Pasadena, CA 91125, USA

¹³³ Department of Physics, National Tsing Hua University, Hsinchu 30013, Taiwan

¹³⁴ Dipartimento di Ingegneria Industriale (DIIN), Università di Salerno, I-84084 Fisciano, Salerno, Italy

¹³⁵ Institute of Physics, Academia Sinica, Nankang, Taipei 11529, Taiwan

¹³⁶ Université Lyon, Université Claude Bernard Lyon 1, CNRS, IP2I Lyon / IN2P3, UMR 5822, F-69622 Villeurbanne, France

¹³⁷ Seoul National University, Seoul 08826, Republic of Korea

¹³⁸ Pusan National University, Busan 46241, Republic of Korea

¹³⁹ INAF, Osservatorio Astronomico di Padova, I-35122 Padova, Italy

¹⁴⁰ University of Arizona, Tucson, AZ 85721, USA

¹⁴¹ Rutherford Appleton Laboratory, Didcot OX11 0DE, United Kingdom
¹⁴² OzGrav, Swinburne University of Technology, Hawthorn VIC 3122, Australia

¹⁴³ Université libre de Bruxelles, Avenue Franklin Roosevelt 50 - 1050 Bruxelles, Belgium

¹⁴⁴ Universitat de les Illes Balears, IAC3—IEEC, E-07122 Palma de Mallorca, Spain

¹⁴⁵ Université Libre de Bruxelles, Brussels 1050, Belgium

¹⁴⁶ Departamento de Matemáticas, Universitat de València, E-46100 Burjassot, València, Spain

¹⁴⁷ Texas Tech University, Lubbock, TX 79409, USA

¹⁴⁸ The Pennsylvania State University, University Park, PA 16802, USA

¹⁴⁹ University of Rhode Island, Kingston, RI 02881, USA

¹⁵⁰ The University of Texas Rio Grande Valley, Brownsville, TX 78520, USA

¹⁵¹ Bellevue College, Bellevue, WA 98007, USA

¹⁵² Scuola Normale Superiore, Piazza dei Cavalieri, 7 - 56126 Pisa, Italy

¹⁵³ MTA-ELTE Astrophysics Research Group, Institute of Physics, Eötvös University, Budapest 1117, Hungary

¹⁵⁴ University of Szeged, Dóm tér 9, Szeged 6720, Hungary

¹⁵⁵ Maastricht University, P.O. Box 616, 6200 MD Maastricht, Netherlands

¹⁵⁶ University of Portsmouth, Portsmouth, PO1 3FX, United Kingdom

¹⁵⁷ The University of Sheffield, Sheffield S10 2TN, United Kingdom

¹⁵⁸ Université Lyon, Université Claude Bernard Lyon 1,
CNRS, Laboratoire des Matériaux Avancés (LMA),
IP2I Lyon / IN2P3, UMR 5822, F-69622 Villeurbanne, France

¹⁵⁹ Dipartimento di Scienze Matematiche, Fisiche e Informatiche, Università di Parma, I-43124 Parma, Italy

¹⁶⁰ INFN, Sezione di Milano Bicocca, Gruppo Collegato di Parma, I-43124 Parma, Italy

¹⁶¹ Physik-Institut, University of Zurich, Winterthurerstrasse 190, 8057 Zurich, Switzerland

¹⁶² University of Chicago, Chicago, IL 60637, USA

¹⁶³ Université de Strasbourg, CNRS, IPHC UMR 7178, F-67000 Strasbourg, France

¹⁶⁴ West Virginia University, Morgantown, WV 26506, USA

¹⁶⁵ Montclair State University, Montclair, NJ 07043, USA

¹⁶⁶ Colorado State University, Fort Collins, CO 80523, USA

¹⁶⁷ Institute for Nuclear Research, Hungarian Academy of Sciences, Bem t'er 18/c, H-4026 Debrecen, Hungary

¹⁶⁸ Department of Physics, University of Texas, Austin, TX 78712, USA

¹⁶⁹ CNR-SPIN, c/o Università di Salerno, I-84084 Fisciano, Salerno, Italy

¹⁷⁰ Scuola di Ingegneria, Università della Basilicata, I-85100 Potenza, Italy

¹⁷¹ Observatori Astronòmic, Universitat de València, E-46980 Paterna, València, Spain

¹⁷² The University of Utah, Salt Lake City, UT 84112, USA

¹⁷³ Kenyon College, Gambier, OH 43022, USA

¹⁷⁴ Vrije Universiteit Amsterdam, 1081 HV, Amsterdam, Netherlands

¹⁷⁵ Department of Astronomy, The University of Tokyo, Mitaka City, Tokyo 181-8588, Japan

¹⁷⁶ Faculty of Engineering, Niigata University, Nishi-ku, Niigata City, Niigata 950-2181, Japan

¹⁷⁷ State Key Laboratory of Magnetic Resonance and Atomic and Molecular Physics,
Innovation Academy for Precision Measurement Science and Technology (APM),
Chinese Academy of Sciences, Xiao Hong Shan, Wuhan 430071, China

¹⁷⁸ Universiteit Gent, B-9000 Gent, Belgium

¹⁷⁹ Cornell University, Ithaca, NY 14850, USA

¹⁸⁰ University of British Columbia, Vancouver, BC V6T 1Z4, Canada

¹⁸¹ Tata Institute of Fundamental Research, Mumbai 400005, India

¹⁸² INAF, Osservatorio Astronomico di Capodimonte, I-80131 Napoli, Italy

¹⁸³ The University of Mississippi, University, MS 38677, USA

¹⁸⁴ University of Michigan, Ann Arbor, MI 48109, USA

¹⁸⁵ Texas A&M University, College Station, TX 77843, USA

¹⁸⁶ Department of Physics, Ulsan National Institute of Science and Technology (UNIST), Ulju-gun, Ulsan 44919, Republic of Korea

¹⁸⁷ Applied Research Laboratory, High Energy Accelerator Research Organization (KEK), Tsukuba City, Ibaraki 305-0801, Japan

¹⁸⁸ Dipartimento di Fisica, Università di Trieste, I-34127 Trieste, Italy

¹⁸⁹ Shanghai Astronomical Observatory, Chinese Academy of Sciences, Shanghai 200030, China

¹⁹⁰ American University, Washington, D.C. 20016, USA

¹⁹¹ Faculty of Science, University of Toyama, Toyama City, Toyama 930-8555, Japan

¹⁹² Institute for Cosmic Ray Research (ICRR), KAGRA Observatory,
The University of Tokyo, Kamioka-cho, Hida City, Gifu 506-1205, Japan

¹⁹³ Carleton College, Northfield, MN 55057, USA

¹⁹⁴ University of California, Berkeley, CA 94720, USA

¹⁹⁵ Maastricht University, 6200 MD, Maastricht, Netherlands

¹⁹⁶ College of Industrial Technology, Nihon University, Narashino City, Chiba 275-8575, Japan

¹⁹⁷ Graduate School of Science and Technology, Niigata University, Nishi-ku, Niigata City, Niigata 950-2181, Japan

¹⁹⁸ Department of Physics, National Taiwan Normal University, sec. 4, Taipei 116, Taiwan
¹⁹⁹ Astronomy & Space Science, Chungnam National University,
Yuseong-gu, Daejeon 34134, Republic of Korea, Republic of Korea

²⁰⁰ Department of Physics and Mathematics, Aoyama Gakuin University, Sagamihara City, Kanagawa 252-5258, Japan

²⁰¹ Kavli Institute for Astronomy and Astrophysics,
Peking University, Haidian District, Beijing 100871, China

²⁰² Yukawa Institute for Theoretical Physics (YITP),
Kyoto University, Sakyou-ku, Kyoto City, Kyoto 606-8502, Japan

²⁰³ Graduate School of Science and Engineering, University of Toyama, Toyama City, Toyama 930-8555, Japan

²⁰⁴ Department of Physics, Graduate School of Science,
Osaka City University, Sumiyoshi-ku, Osaka City, Osaka 558-8585, Japan

²⁰⁵ Nambu Yoichiro Institute of Theoretical and Experimental Physics (NITEP),
Osaka City University, Sumiyoshi-ku, Osaka City, Osaka 558-8585, Japan

²⁰⁶ Institute of Space and Astronautical Science (JAXA),
Chuo-ku, Sagamihara City, Kanagawa 252-0222, Japan

²⁰⁷ Directorate of Construction, Services & Estate Management, Mumbai 400094, India

²⁰⁸ Vanderbilt University, Nashville, TN 37235, USA

²⁰⁹ Universiteit Antwerpen, Prinsstraat 13, 2000 Antwerpen, Belgium

²¹⁰ University of Bialystok, 15-424 Bialystok, Poland

²¹¹ Department of Physics, Ewha Womans University, Seodaemun-gu, Seoul 03760, Republic of Korea

²¹² National Astronomical Observatories, Chinese Academic of Sciences, Chaoyang District, Beijing, China

²¹³ School of Astronomy and Space Science, University of Chinese Academy of Sciences, Chaoyang District, Beijing, China

²¹⁴ University of Southampton, Southampton SO17 1BJ, United Kingdom

²¹⁵ Institute for Cosmic Ray Research (ICRR), The University of Tokyo, Kashiwa City, Chiba 277-8582, Japan

²¹⁶ Chung-Ang University, Seoul 06974, Republic of Korea

²¹⁷ Institut de Física d'Altes Energies (IFAE), Barcelona Institute
of Science and Technology, and ICREA, E-08193 Barcelona, Spain

²¹⁸ Graduate School of Science, Tokyo Institute of Technology, Meguro-ku, Tokyo 152-8551, Japan

²¹⁹ University of Washington Bothell, Bothell, WA 98011, USA

²²⁰ Institute of Applied Physics, Nizhny Novgorod, 603950, Russia

²²¹ Ewha Womans University, Seoul 03760, Republic of Korea

²²² Inje University Gimhae, South Gyeongsang 50834, Republic of Korea

²²³ Department of Physics, Myongji University, Yongin 17058, Republic of Korea

²²⁴ Korea Astronomy and Space Science Institute, Daejeon 34055, Republic of Korea

²²⁵ National Institute for Mathematical Sciences, Daejeon 34047, Republic of Korea

²²⁶ Ulsan National Institute of Science and Technology, Ulsan 44919, Republic of Korea

²²⁷ Department of Physical Science, Hiroshima University,
Higashihiroshima City, Hiroshima 903-0213, Japan

²²⁸ School of Physics and Astronomy, Cardiff University, Cardiff, CF24 3AA, UK

²²⁹ Institute of Astronomy, National Tsing Hua University, Hsinchu 30013, Taiwan

²³⁰ Bard College, 30 Campus Rd, Annandale-On-Hudson, NY 12504, USA

²³¹ Institute of Mathematics, Polish Academy of Sciences, 00656 Warsaw, Poland

²³² National Center for Nuclear Research, 05-400 Świerk-Otwock, Poland

²³³ Instituto de Física Teórica, 28049 Madrid, Spain

²³⁴ Department of Physics, Nagoya University, Chikusa-ku, Nagoya, Aichi 464-8602, Japan

²³⁵ Université de Montréal/Polytechnique, Montreal, Quebec H3T 1J4, Canada

²³⁶ Laboratoire Lagrange, Université Côte d'Azur,
Observatoire Côte d'Azur, CNRS, F-06304 Nice, France

²³⁷ Canadian Institute for Theoretical Astrophysics,
University of Toronto, Toronto, Ontario M5S 3H8, Canada

²³⁸ Department of Physics, Hanyang University, Seoul 04763, Republic of Korea

²³⁹ Sungkyunkwan University, Seoul 03063, Republic of Korea

²⁴⁰ NAVIER, École des Ponts, Univ Gustave Eiffel, CNRS, Marne-la-Vallée, France

²⁴¹ Department of Physics, National Cheng Kung University, Tainan City 701, Taiwan

²⁴² National Center for High-performance computing, National Applied Research Laboratories,
Hsinchu Science Park, Hsinchu City 30076, Taiwan

²⁴³ Institute for High-Energy Physics, University of Amsterdam,
Science Park 904, 1098 XH Amsterdam, Netherlands

²⁴⁴ NASA Marshall Space Flight Center, Huntsville, AL 35811, USA

²⁴⁵ University of Washington, Seattle, WA 98195, USA

²⁴⁶ Dipartimento di Matematica e Fisica, Università degli Studi Roma Tre, I-00146 Roma, Italy

²⁴⁷ INFN, Sezione di Roma Tre, I-00146 Roma, Italy

²⁴⁸ ESPCI, CNRS, F-75005 Paris, France

²⁴⁹ Concordia University Wisconsin, Mequon, WI 53097, USA

²⁵⁰ Università di Camerino, Dipartimento di Fisica, I-62032 Camerino, Italy
²⁵¹ School of Physics Science and Engineering, Tongji University, Shanghai 200092, China

²⁵² Southern University and A&M College, Baton Rouge, LA 70813, USA

²⁵³ Centre Scientifique de Monaco, 8 quai Antoine Ier, MC-98000, Monaco

²⁵⁴ Institute for Photon Science and Technology, The University of Tokyo, Bunkyo-ku, Tokyo 113-8656, Japan

²⁵⁵ Indian Institute of Technology Madras, Chennai 600036, India

²⁵⁶ Instituto de Fisica Teorica, Universidad Autónoma de Madrid, 28049 Madrid, Spain

²⁵⁷ Saha Institute of Nuclear Physics, Bidhannagar, West Bengal 700064, India

²⁵⁸ The Applied Electromagnetic Research Institute,
National Institute of Information and Communications Technology (NICT), Koganei City, Tokyo 184-8795, Japan

²⁵⁹ Institut des Hautes Etudes Scientifiques, F-91440 Bures-sur-Yvette, France

²⁶⁰ Faculty of Law, Ryukoku University, Fushimi-ku, Kyoto City, Kyoto 612-8577, Japan

²⁶¹ Indian Institute of Science Education and Research, Kolkata, Mohanpur, West Bengal 741252, India

²⁶² Department of Astrophysics/IMAPP, Radboud University Nijmegen,
P.O. Box 9010, 6500 GL Nijmegen, Netherlands

²⁶³ Department of Physics, University of Notre Dame, Notre Dame, IN 46556, USA

²⁶⁴ Consiglio Nazionale delle Ricerche - Istituto dei Sistemi Complessi, Piazzale Aldo Moro 5, I-00185 Roma, Italy

²⁶⁵ Korea Astronomy and Space Science Institute (KASI), Yuseong-gu, Daejeon 34055, Republic of Korea

²⁶⁶ Hobart and William Smith Colleges, Geneva, NY 14456, USA

²⁶⁷ International Institute of Physics, Universidade Federal do Rio Grande do Norte, Natal RN 59078-970, Brazil

²⁶⁸ Museo Storico della Fisica e Centro Studi e Ricerche “Enrico Fermi”, I-00184 Roma, Italy

²⁶⁹ Lancaster University, Lancaster LA1 4YW, United Kingdom

²⁷⁰ Università di Trento, Dipartimento di Matematica, I-38123 Povo, Trento, Italy

²⁷¹ Indian Institute of Science Education and Research, Pune, Maharashtra 411008, India

²⁷² Dipartimento di Fisica, Università degli Studi di Torino, I-10125 Torino, Italy

²⁷³ Indian Institute of Technology, Palaj, Gandhinagar, Gujarat 382355, India

²⁷⁴ Department of Physics, Kyoto University, Sakyou-ku, Kyoto City, Kyoto 606-8502, Japan

²⁷⁵ Department of Electronic Control Engineering, National Institute of Technology,
Nagaoka College, Nagaoka City, Niigata 940-8532, Japan

²⁷⁶ Departamento de Matemática da Universidade de Aveiro and Centre for Research and
Development in Mathematics and Applications, Campus de Santiago, 3810-183 Aveiro, Portugal

²⁷⁷ Marquette University, 11420 W. Clybourn St., Milwaukee, WI 53233, USA

²⁷⁸ Graduate School of Science and Engineering, Hosei University, Koganei City, Tokyo 184-8584, Japan

²⁷⁹ Faculty of Science, Toho University, Funabashi City, Chiba 274-8510, Japan

²⁸⁰ Faculty of Information Science and Technology,
Osaka Institute of Technology, Hirakata City, Osaka 573-0196, Japan

²⁸¹ Università di Firenze, Sesto Fiorentino I-50019, Italy

²⁸² INAF, Osservatorio Astrofisico di Arcetri, Largo E. Fermi 5, I-50125 Firenze, Italy

²⁸³ Indian Institute of Technology Hyderabad, Sangareddy, Khandi, Telangana 502285, India

²⁸⁴ᵢTHEMS (Interdisciplinary Theoretical and Mathematical Sciences Program),
The Institute of Physical and Chemical Research (RIKEN), Wako, Saitama 351-0198, Japan

²⁸⁵ INAF, Osservatorio di Astrofisica e Scienza dello Spazio, I-40129 Bologna, Italy

²⁸⁶ Department of Space and Astronautical Science,
The Graduate University for Advanced Studies (SOKENDAI), Sagamihara City, Kanagawa 252-5210, Japan

²⁸⁷ Andrews University, Berrien Springs, MI 49104, USA

²⁸⁸ Research Center for Space Science, Advanced Research Laboratories,
Tokyo City University, Setagaya, Tokyo 158-0082, Japan

²⁸⁹ Institute for Cosmic Ray Research (ICRR), Research Center for Cosmic Neutrinos (RCCN),
The University of Tokyo, Kashiwa City, Chiba 277-8582, Japan

²⁹⁰ National Metrology Institute of Japan, National Institute of Advanced
Industrial Science and Technology, Tsukuba City, Ibaraki 305-8568, Japan

²⁹¹ Dipartimento di Scienze Aziendali - Management and Innovation Systems (DISA-MIS),
Università di Salerno, I-84084 Fisciano, Salerno, Italy

²⁹² Van Swinderen Institute for Particle Physics and Gravity,
University of Groningen, Nijenborgh 4, 9747 AG Groningen, Netherlands

²⁹³ Faculty of Science, Department of Physics, The Chinese University of Hong Kong, Shatin, N.T., Hong Kong

²⁹⁴ Vrije Universiteit Brussel, Boulevard de la Plaine 2, 1050 Ixelles, Belgium

²⁹⁵ Department of Communications Engineering, National Defense
Academy of Japan, Yokosuka City, Kanagawa 239-8686, Japan

²⁹⁶ Department of Physics, University of Florida, Gainesville, FL 32611, USA

²⁹⁷ Department of Information and Management Systems Engineering,
Nagaoka University of Technology, Nagaoka City, Niigata 940-2188, Japan

²⁹⁸ Vrije Universiteit Amsterdam, 1081 HV Amsterdam, Netherlands

²⁹⁹ Department of Physics and Astronomy, Sejong University, Gwangjin-gu, Seoul 143-747, Republic of Korea

³⁰⁰ Department of Electrophysics, National Chiao Tung University, Hsinchu, Taiwan
³⁰¹Department of Physics, Rikkyo University, Toshima-ku, Tokyo 171-8501, Japan

(Dated: February 24, 2022)

We report on the population properties of 76 compact binary mergers detected with gravitational waves below a false alarm rate of 1 per year through the cumulative Gravitational Wave Transient Catalog 3 (GWTC-3). The catalog contains three classes of binary mergers: binary black hole (BBH), binary neutron star (BNS), and neutron star–black hole (NSBH) mergers. We infer the BNS merger rate to be between $10 \text{ Gpc}^{-3} \text{yr}^{-1}$ and $1700 \text{ Gpc}^{-3} \text{yr}^{-1}$ and the NSBH merger rate to be between $7.8 \text{ Gpc}^{-3} \text{yr}^{-1}$ and $140 \text{ Gpc}^{-3} \text{yr}^{-1}$, assuming a constant rate density versus comoving volume and taking the union of 90% credible intervals for methods used in this work. Accounting for the BBH merger rate to evolve with redshift, we find the BBH merger rate to be between $17.9 \text{ Gpc}^{-3} \text{yr}^{-1}$ and $44 \text{ Gpc}^{-3} \text{yr}^{-1}$ at a fiducial redshift ($z = 0.2$). Using both binary neutron star and neutron star–black hole binaries, we obtain a broad, relatively flat neutron star mass distribution extending from $1.2_{-0.2}^{+0.1} \text{ M}_\odot$ to $2.0_{-0.3}^{+0.3} \text{ M}_\odot$. We can confidently identify a rapid decrease in merger rate versus component mass between neutron star-like masses and black-hole-like masses, but there is no evidence that the merger rate increases again before $10 \text{ M}_\odot$. We also find the binary black hole mass distribution has localized over- and under-densities relative to a power law distribution, with peaks emerging at chirp masses of $8.3_{-0.5}^{+0.3} \text{ M}_\odot$ and $27.9_{-1.8}^{+1.9} \text{ M}_\odot$. While we continue to find the mass distribution of a binary's more massive component strongly decreases as a function of primary mass, we observe no evidence of a strongly suppressed merger rate above $\approx 60 \text{ M}_\odot$, which would highlight the presence of a upper mass gap. The rate of BBH mergers is observed to increase with redshift at a rate proportional to $(1+z)^\kappa$ with $\kappa = 2.9_{-1.8}^{+1.7}$ for $z \lesssim 1$. Observed black hole spins are small, with half of spin magnitudes below $\chi_i \approx 0.25$. We observe evidence of negative aligned spins in the population, and an increase in spin magnitude for systems with more unequal mass ratio. We also observe evidence of misalignment of spins relative to the orbital angular momentum.

# I. INTRODUCTION

We analyze the population properties of black holes (BHs) and neutron stars (NSs) in compact binary systems using data through the end of the third observing run of LIGO–Virgo (O3). Gravitational Wave Transient Catalog 3 (GWTC-3) [1] combines observations from the first three observing runs (O1, O2 [2] and O3 [1, 3, 4]) of the Advanced LIGO [5] and Advanced Virgo [6] gravitational-wave observatories. Counting only events with false alarm rate (FAR) of $< 0.25 \text{ yr}^{-1}$, we have two binary neutron star (BNS) events, two neutron star–black hole (NSBH) events and 63 confident binary black hole (BBH) events. Considering the BBH population only, as in Section V, we lower the detection threshold to count events with FAR of $< 1 \text{ yr}^{-1}$, resulting in 69 confident BBH events. We distinguish between NSs and BHs using prior information about the maximum NS mass, obtained from constraints on the dense-matter equation of state [7–9]. We use the observed population of events to infer the properties of the astrophysical BNS, NSBH and BBH populations. In particular, we infer the mass and spin distributions of the NS and BH populations, the overall merger rate, and investigate their cosmological evolution.

The population includes a number of exceptional events, notably the discovery in O3 data of two NSBH binaries: GW200105_162426 and GW200115_042309 [10]. In these two systems, the primary mass $m_1$ is larger than the maximum mass allowed by the NS equation of state,

and the secondary mass $m_2$ is consistent with known NS masses. Here and throughout the paper, the primary mass $m_1$ refers to the larger of the two component masses in the binary, while the secondary mass $m_2$ refers to the smaller of the two. The inclusion of NSBH events enables the first joint analysis of the full BNS–NSBH–BBH population, including identification of sub-populations of binaries and any mass gaps between them. We also perform an analysis of the NS population properties using both BNS and NSBH systems.

The increased number of BBH observations allows for a more detailed investigation of the mass and spin distributions of BH. Overall, our new observations and results are consistent with the expectations about the mass and spin distribution of BBHs derived with our previous observations through GWTC-2 [11], which capture broad features on larger parameter scales than those emphasized in this study, and which we henceforth denote *coarse-grained features*. We demonstrate the use of non-parametric or broadly modeled methods to characterize the BBH distribution and use these to identify structure in the mass distribution. Another feature of our sample is the accumulation of more BBHs with preferentially negatively aligned spins relative to their orbital angular momentum (e.g., GW191109_010717, GW200225_060421), albeit at a significance that could occur by chance in our large catalog. Finally, the larger sample size allows for more detailed investigations of correlations between black hole masses and spins.

In this work, we adopt a high-purity set of candidate events whose selection biases we understand. Our chosen FAR threshold both ensures a sufficiently pure sample for the analyses performed in this work, particularly of the four binaries containing NS in our sample. How-

<footnote>* Deceased, August 2020.</footnote>
ever, due to the higher observed rate of BBH mergers, even at a less stringent threshold of < 1 yr⁻¹ the relative proportion of background events remains below 10% for analyses of BBH; we therefore adopt this less stringent threshold for analyses of solely the BBH population. Both sensitivity thresholds omit several candidates of moderate significance identified in recent work, including candidates identified by our own search [1, 3], which have required the probability of an event being of astrophysical origin, p<sub>astro</sub> > 0.5 [12]. For example, our chosen FAR threshold excludes some of the most massive events identified in GWTC-3 [1] (e.g., GW190403.051519 and GW200220.061928). We briefly discuss these events, and those identified by other groups, in the context of our reconstructed populations.

The remainder of this paper is organized as follows. In Section II we summarize observations we reported through O3, then highlight our key conclusions about them obtained in this study. In Section III we describe the hierarchical method used to fit population models to data, and to validate their results. In Section IV we describe analyses for the whole compact binary population, including both BHs and NSs. In Section V we describe our results for binaries containing one or more NSs. In Section VI and VII we describe our results for BBH masses and spins respectively. In Section VIII we discuss results obtained with other searches or selection criteria, comparing to the populations identified in this work. In Section IX we discuss the astrophysical interpretation of our observations and population inferences. In Section X we comment on prospects for future searches for the stochastic background of gravitational radiation from all compact binary mergers on our past light cone during the next observing run. We conclude in Section XI with the significance of our results. In our Appendices, we provide the details of how we estimate sensitivity to compact binary mergers (Appendix A), a comprehensive description of the population models used in this work (Appendix B), methods we used to validate our study

against prominent sources of systematic error (Appendix C), and additional details of the BBH results (Appendix D). In Appendix E, we provide revised posterior distributions for all events used in this work, each reassessed using information obtained from an estimate for the full population.

## II. SUMMARY OF OBSERVATIONS AND RESULTS

A total of 90 compact binary coalescences (CBCs) have been detected in the first three observing runs [1]. The threshold used in GWTC-3 requires a probability of astrophysical origin of at least 50%. For the population analysis presented here, it is preferable to work with a different threshold to ensure lower contamination from signals of non-astrophysical origin, and to reduce the model dependence in assessing probabilities of astrophysical origin. Consequently, for the majority of analyses presented in this paper, we require a FAR of < 0.25 yr⁻¹ in at least one of the search analyses in GWTC-3. This threshold limits the number of events to 67; at this threshold, we expect approximately one event not to be of astrophysical origin. For BBH focused analyses, we loosen the threshold to a FAR < 1 yr⁻¹ due to the higher observed rate of BBH mergers, giving 76 events with available parameter estimates, of which approximately 4.6 are expected to be non-astrophysical. This significantly expands the number of observations since GWTC-2, which included 50 events, of which 47 had FAR of < 1 yr⁻¹ and were used in our previous population analysis [11]. Table I shows selected properties of all events used to infer the astrophysical population of binary mergers in the Universe. The table contains all events with FAR < 1 yr⁻¹, with less significant events having FAR between 1 yr⁻¹ and 0.25 yr⁻¹ which are excluded from all but the BBH analyses clearly identified. Henceforth, we abbreviate candidate names by omitting the last six digits when unambiguous.

<table><thead><tr><th>Name</th><th>FAR<sub>min</sub> (yr<sup>-1</sup>)</th><th>p<sub>astro</sub></th><th>m<sub>1</sub>/M<sub>☉</sub></th><th>m<sub>2</sub>/M<sub>☉</sub></th><th>M/M<sub>☉</sub></th><th>&chi;<sub>eff</sub></th><th>First appears in</th></tr></thead><tbody><tr><td>GW150914</td><td>&lt; 1 &times; 10<sup>-5</sup></td><td>&gt; 0.99</td><td>35.6<sup>+4.7</sup><sub>-3.1</sub></td><td>30.6<sup>+3.0</sup><sub>-4.4</sub></td><td>28.6<sup>+1.7</sup><sub>-1.5</sub></td><td>-0.01<sup>+0.12</sup><sub>-0.13</sub></td><td>[13]</td></tr><tr><td>GW151012</td><td>7.92&times;10<sup>-3</sup></td><td>&gt; 0.99</td><td>23.2<sup>+14.9</sup><sub>-5.5</sub></td><td>13.6<sup>+4.1</sup><sub>-4.8</sub></td><td>15.2<sup>+2.1</sup><sub>-1.2</sub></td><td>0.05<sup>+0.31</sup><sub>-0.20</sub></td><td>[14]</td></tr><tr><td>GW151226</td><td>&lt; 1 &times; 10<sup>-5</sup></td><td>&gt; 0.99</td><td>13.7<sup>+8.8</sup><sub>-3.2</sub></td><td>7.7<sup>+2.2</sup><sub>-2.5</sub></td><td>8.9<sup>+0.3</sup><sub>-0.3</sub></td><td>0.18<sup>+0.20</sup><sub>-0.12</sub></td><td>[15]</td></tr><tr><td>GW170104</td><td>&lt; 1 &times; 10<sup>-5</sup></td><td>&gt; 0.99</td><td>30.8<sup>+7.3</sup><sub>-5.6</sub></td><td>20.0<sup>+4.9</sup><sub>-4.6</sub></td><td>21.4<sup>+2.2</sup><sub>-1.8</sub></td><td>-0.04<sup>+0.17</sup><sub>-0.21</sub></td><td>[16]</td></tr><tr><td>GW170608</td><td>&lt; 1 &times; 10<sup>-5</sup></td><td>&gt; 0.99</td><td>11.0<sup>+5.5</sup><sub>-1.7</sub></td><td>7.6<sup>+1.4</sup><sub>-2.2</sub></td><td>7.9<sup>+0.2</sup><sub>-0.2</sub></td><td>0.03<sup>+0.19</sup><sub>-0.07</sub></td><td>[17]</td></tr><tr><td>GW170729</td><td>1.80&times;10<sup>-1</sup></td><td>0.98</td><td>50.2<sup>+16.2</sup><sub>-10.2</sub></td><td>34.0<sup>+9.1</sup><sub>-10.1</sub></td><td>35.4<sup>+6.5</sup><sub>-4.8</sub></td><td>0.37<sup>+0.21</sup><sub>-0.25</sub></td><td>[2]</td></tr><tr><td>GW170809</td><td>&lt; 1 &times; 10<sup>-5</sup></td><td>&gt; 0.99</td><td>35.0<sup>+8.3</sup><sub>-5.9</sub></td><td>23.8<sup>+5.1</sup><sub>-5.2</sub></td><td>24.9<sup>+2.1</sup><sub>-1.7</sub></td><td>0.08<sup>+0.17</sup><sub>-0.17</sub></td><td>[2]</td></tr><tr><td>GW170814</td><td>&lt; 1 &times; 10<sup>-5</sup></td><td>&gt; 0.99</td><td>30.6<sup>+5.6</sup><sub>-3.0</sub></td><td>25.2<sup>+2.8</sup><sub>-4.0</sub></td><td>24.1<sup>+1.4</sup><sub>-1.1</sub></td><td>0.07<sup>+0.12</sup><sub>-0.12</sub></td><td>[18]</td></tr><tr><td>GW170817</td><td>&lt; 1 &times; 10<sup>-5</sup></td><td>&gt; 0.99</td><td>1.46<sup>+0.12</sup><sub>-0.10</sub></td><td>1.27<sup>+0.09</sup><sub>-0.09</sub></td><td>1.186<sup>+0.001</sup><sub>-0.001</sub></td><td>0.00<sup>+0.02</sup><sub>-0.01</sub></td><td>[19]</td></tr><tr><td>GW170818</td><td>&lt; 1 &times; 10<sup>-5</sup></td><td>&gt; 0.99</td><td>35.4<sup>+7.5</sup><sub>-4.7</sub></td><td>26.7<sup>+4.3</sup><sub>-5.2</sub></td><td>26.5<sup>+2.1</sup><sub>-1.7</sub></td><td>-0.09<sup>+0.18</sup><sub>-0.21</sub></td><td>[2]</td></tr><tr><td>GW170823</td><td>&lt; 1 &times; 10<sup>-5</sup></td><td>&gt; 0.99</td><td>39.5<sup>+11.2</sup><sub>-6.7</sub></td><td>29.0<sup>+6.7</sup><sub>-7.8</sub></td><td>29.2<sup>+4.6</sup><sub>-3.6</sub></td><td>0.09<sup>+0.22</sup><sub>-0.26</sub></td><td>[2]</td></tr><tr><td>GW190408.181802</td><td>&lt; 1 &times; 10<sup>-5</sup></td><td>&gt; 0.99</td><td>24.6<sup>+5.1</sup><sub>-3.4</sub></td><td>18.4<sup>+3.3</sup><sub>-3.6</sub></td><td>18.3<sup>+1.9</sup><sub>-1.2</sub></td><td>-0.03<sup>+0.14</sup><sub>-0.19</sub></td><td>[4]</td></tr><tr><td>GW190412.053044</td><td>&lt; 1 &times; 10<sup>-5</sup></td><td>&gt; 0.99</td><td>30.1<sup>+4.7</sup><sub>-5.1</sub></td><td>8.3<sup>+1.6</sup><sub>-0.9</sub></td><td>13.3<sup>+0.4</sup><sub>-0.3</sub></td><td>0.25<sup>+0.08</sup><sub>-0.11</sub></td><td>[20]</td></tr></tbody></table>
<table>
  <tbody>
    <tr>
      <td>GW190413_134308</td>
      <td>1.81×10<sup>-1</sup></td>
      <td>0.99</td>
      <td>47.5<sup>+13.5</sup><sub>-10.7</sub></td>
      <td>31.8<sup>+11.7</sup><sub>-10.8</sub></td>
      <td>33.0<sup>+8.2</sup><sub>-5.4</sub></td>
      <td>-0.03<sup>+0.25</sup><sub>-0.29</sub></td>
      <td>[4]</td>
    </tr>
    <tr>
      <td>GW190421_213856</td>
      <td>2.83×10<sup>-3</sup></td>
      <td>&gt; 0.99</td>
      <td>41.3<sup>+10.4</sup><sub>-6.9</sub></td>
      <td>31.9<sup>+8.0</sup><sub>-8.8</sub></td>
      <td>31.2<sup>+5.9</sup><sub>-4.2</sub></td>
      <td>-0.06<sup>+0.22</sup><sub>-0.27</sub></td>
      <td>[4]</td>
    </tr>
    <tr>
      <td>GW190425_081805</td>
      <td>3.38×10<sup>-2</sup></td>
      <td>0.78</td>
      <td>2.0<sup>+0.6</sup><sub>-0.3</sub></td>
      <td>1.4<sup>+0.3</sup><sub>-0.3</sub></td>
      <td>1.44<sup>+0.02</sup><sub>-0.02</sub></td>
      <td>0.06<sup>+0.11</sup><sub>-0.05</sub></td>
      <td>[21]</td>
    </tr>
    <tr>
      <td>GW190503_185404</td>
      <td>&lt; 1 × 10<sup>-5</sup></td>
      <td>&gt; 0.99</td>
      <td>43.3<sup>+9.2</sup><sub>-8.1</sub></td>
      <td>28.4<sup>+7.7</sup><sub>-8.0</sub></td>
      <td>30.2<sup>+4.2</sup><sub>-4.2</sub></td>
      <td>-0.03<sup>+0.20</sup><sub>-0.26</sub></td>
      <td>[4]</td>
    </tr>
    <tr>
      <td>GW190512_180714</td>
      <td>&lt; 1 × 10<sup>-5</sup></td>
      <td>&gt; 0.99</td>
      <td>23.3<sup>+5.3</sup><sub>-5.8</sub></td>
      <td>12.6<sup>+3.6</sup><sub>-2.5</sub></td>
      <td>14.6<sup>+1.3</sup><sub>-1.0</sub></td>
      <td>0.03<sup>+0.12</sup><sub>-0.13</sub></td>
      <td>[4]</td>
    </tr>
    <tr>
      <td>GW190513_205428</td>
      <td>&lt; 1 × 10<sup>-5</sup></td>
      <td>&gt; 0.99</td>
      <td>35.7<sup>+9.5</sup><sub>-9.2</sub></td>
      <td>18.0<sup>+7.7</sup><sub>-4.1</sub></td>
      <td>21.6<sup>+3.8</sup><sub>-1.9</sub></td>
      <td>0.11<sup>+0.28</sup><sub>-0.17</sub></td>
      <td>[4]</td>
    </tr>
    <tr>
      <td>GW190517_055101</td>
      <td>3.47×10<sup>-4</sup></td>
      <td>&gt; 0.99</td>
      <td>37.4<sup>+11.7</sup><sub>-7.6</sub></td>
      <td>25.3<sup>+7.0</sup><sub>-7.3</sub></td>
      <td>26.6<sup>+4.0</sup><sub>-4.0</sub></td>
      <td>0.52<sup>+0.19</sup><sub>-0.19</sub></td>
      <td>[4]</td>
    </tr>
    <tr>
      <td>GW190519_153544</td>
      <td>&lt; 1 × 10<sup>-5</sup></td>
      <td>&gt; 0.99</td>
      <td>66.0<sup>+10.7</sup><sub>-12.0</sub></td>
      <td>40.5<sup>+11.0</sup><sub>-11.1</sub></td>
      <td>44.5<sup>+6.4</sup><sub>-7.1</sub></td>
      <td>0.31<sup>+0.20</sup><sub>-0.22</sub></td>
      <td>[4]</td>
    </tr>
    <tr>
      <td>GW190521_030229</td>
      <td>&lt; 1 × 10<sup>-5</sup></td>
      <td>&gt; 0.99</td>
      <td>95.3<sup>+28.7</sup><sub>-18.9</sub></td>
      <td>69.0<sup>+22.7</sup><sub>-23.1</sub></td>
      <td>69.2<sup>+17.0</sup><sub>-10.6</sub></td>
      <td>0.03<sup>+0.32</sup><sub>-0.39</sub></td>
      <td>[22]</td>
    </tr>
    <tr>
      <td>GW190521_074359</td>
      <td>1.00×10<sup>-2</sup></td>
      <td>&gt; 0.99</td>
      <td>42.2<sup>+5.9</sup><sub>-4.8</sub></td>
      <td>32.8<sup>+5.4</sup><sub>-6.4</sub></td>
      <td>32.1<sup>+3.2</sup><sub>-2.5</sub></td>
      <td>0.09<sup>+0.10</sup><sub>-0.13</sub></td>
      <td>[22]</td>
    </tr>
    <tr>
      <td>GW190527_092055</td>
      <td>2.28×10<sup>-1</sup></td>
      <td>0.85</td>
      <td>36.5<sup>+16.4</sup><sub>-9.0</sub></td>
      <td>22.6<sup>+10.5</sup><sub>-8.1</sub></td>
      <td>24.3<sup>+9.1</sup><sub>-4.2</sub></td>
      <td>0.11<sup>+0.28</sup><sub>-0.28</sub></td>
      <td>[4]</td>
    </tr>
    <tr>
      <td>GW190602_175927</td>
      <td>&lt; 1 × 10<sup>-5</sup></td>
      <td>&gt; 0.99</td>
      <td>69.1<sup>+15.7</sup><sub>-13.0</sub></td>
      <td>47.8<sup>+14.3</sup><sub>-17.4</sub></td>
      <td>49.1<sup>+9.1</sup><sub>-8.5</sub></td>
      <td>0.07<sup>+0.25</sup><sub>-0.24</sub></td>
      <td>[4]</td>
    </tr>
    <tr>
      <td>GW190620_030421</td>
      <td>1.12×10<sup>-2</sup></td>
      <td>0.99</td>
      <td>57.1<sup>+16.0</sup><sub>-12.7</sub></td>
      <td>35.5<sup>+12.2</sup><sub>-12.3</sub></td>
      <td>38.3<sup>+8.3</sup><sub>-6.5</sub></td>
      <td>0.33<sup>+0.22</sup><sub>-0.25</sub></td>
      <td>[4]</td>
    </tr>
    <tr>
      <td>GW190630_185205</td>
      <td>&lt; 1 × 10<sup>-5</sup></td>
      <td>&gt; 0.99</td>
      <td>35.1<sup>+6.9</sup><sub>-5.6</sub></td>
      <td>23.7<sup>+5.2</sup><sub>-5.1</sub></td>
      <td>24.9<sup>+2.1</sup><sub>-2.1</sub></td>
      <td>0.10<sup>+0.12</sup><sub>-0.13</sub></td>
      <td>[4]</td>
    </tr>
    <tr>
      <td>GW190701_203306</td>
      <td>5.71×10<sup>-3</sup></td>
      <td>0.99</td>
      <td>53.9<sup>+11.8</sup><sub>-8.0</sub></td>
      <td>40.8<sup>+8.7</sup><sub>-12.0</sub></td>
      <td>40.3<sup>+5.4</sup><sub>-4.9</sub></td>
      <td>-0.07<sup>+0.23</sup><sub>-0.29</sub></td>
      <td>[4]</td>
    </tr>
    <tr>
      <td>GW190706_222641</td>
      <td>&lt; 1 × 10<sup>-5</sup></td>
      <td>&gt; 0.99</td>
      <td>67.0<sup>+14.6</sup><sub>-16.2</sub></td>
      <td>38.2<sup>+14.6</sup><sub>-13.3</sub></td>
      <td>42.7<sup>+10.0</sup><sub>-7.0</sub></td>
      <td>0.28<sup>+0.26</sup><sub>-0.29</sub></td>
      <td>[4]</td>
    </tr>
    <tr>
      <td>GW190707_093326</td>
      <td>&lt; 1 × 10<sup>-5</sup></td>
      <td>&gt; 0.99</td>
      <td>11.6<sup>+3.3</sup><sub>-1.7</sub></td>
      <td>8.4<sup>+1.4</sup><sub>-1.7</sub></td>
      <td>8.5<sup>+0.6</sup><sub>-0.5</sub></td>
      <td>-0.05<sup>+0.10</sup><sub>-0.08</sub></td>
      <td>[4]</td>
    </tr>
    <tr>
      <td>GW190708_232457</td>
      <td>3.09×10<sup>-4</sup></td>
      <td>&gt; 0.99</td>
      <td>17.6<sup>+4.7</sup><sub>-2.3</sub></td>
      <td>13.2<sup>+2.0</sup><sub>-2.7</sub></td>
      <td>13.2<sup>+0.9</sup><sub>-0.6</sub></td>
      <td>0.02<sup>+0.10</sup><sub>-0.08</sub></td>
      <td>[4]</td>
    </tr>
    <tr>
      <td>GW190720_000836</td>
      <td>&lt; 1 × 10<sup>-5</sup></td>
      <td>&gt; 0.99</td>
      <td>13.4<sup>+6.7</sup><sub>-3.0</sub></td>
      <td>7.8<sup>+2.3</sup><sub>-2.2</sub></td>
      <td>8.9<sup>+0.5</sup><sub>-0.8</sub></td>
      <td>0.18<sup>+0.14</sup><sub>-0.12</sub></td>
      <td>[4]</td>
    </tr>
    <tr>
      <td>GW190727_060333</td>
      <td>&lt; 1 × 10<sup>-5</sup></td>
      <td>&gt; 0.99</td>
      <td>38.0<sup>+9.5</sup><sub>-6.2</sub></td>
      <td>29.4<sup>+7.1</sup><sub>-8.4</sub></td>
      <td>28.6<sup>+5.3</sup><sub>-3.7</sub></td>
      <td>0.11<sup>+0.26</sup><sub>-0.25</sub></td>
      <td>[4]</td>
    </tr>
    <tr>
      <td>GW190728_064510</td>
      <td>&lt; 1 × 10<sup>-5</sup></td>
      <td>&gt; 0.99</td>
      <td>12.3<sup>+7.2</sup><sub>-2.2</sub></td>
      <td>8.1<sup>+1.7</sup><sub>-2.6</sub></td>
      <td>8.6<sup>+0.5</sup><sub>-0.3</sub></td>
      <td>0.12<sup>+0.20</sup><sub>-0.07</sub></td>
      <td>[4]</td>
    </tr>
    <tr>
      <td>GW190803_022701</td>
      <td>7.32×10<sup>-2</sup></td>
      <td>0.94</td>
      <td>37.3<sup>+10.6</sup><sub>-7.0</sub></td>
      <td>27.3<sup>+7.8</sup><sub>-8.2</sub></td>
      <td>27.3<sup>+5.7</sup><sub>-4.1</sub></td>
      <td>-0.03<sup>+0.24</sup><sub>-0.27</sub></td>
      <td>[4]</td>
    </tr>
    <tr>
      <td>GW190814_211039</td>
      <td>&lt; 1 × 10<sup>-5</sup></td>
      <td>&gt; 0.99</td>
      <td>23.2<sup>+1.1</sup><sub>-1.0</sub></td>
      <td>2.59<sup>+0.08</sup><sub>-0.09</sub></td>
      <td>6.09<sup>+0.06</sup><sub>-0.06</sub></td>
      <td>0.00<sup>+0.06</sup><sub>-0.06</sub></td>
      <td>[23]</td>
    </tr>
    <tr>
      <td>GW190828_063405</td>
      <td>&lt; 1 × 10<sup>-5</sup></td>
      <td>&gt; 0.99</td>
      <td>32.1<sup>+5.8</sup><sub>-4.0</sub></td>
      <td>26.2<sup>+4.6</sup><sub>-4.8</sub></td>
      <td>25.0<sup>+3.4</sup><sub>-2.1</sub></td>
      <td>0.19<sup>+0.15</sup><sub>-0.16</sub></td>
      <td>[4]</td>
    </tr>
    <tr>
      <td>GW190828_065509</td>
      <td>&lt; 1 × 10<sup>-5</sup></td>
      <td>&gt; 0.99</td>
      <td>24.1<sup>+7.0</sup><sub>-7.2</sub></td>
      <td>10.2<sup>+3.6</sup><sub>-2.1</sub></td>
      <td>13.3<sup>+1.2</sup><sub>-1.0</sub></td>
      <td>0.08<sup>+0.16</sup><sub>-0.16</sub></td>
      <td>[4]</td>
    </tr>
    <tr>
      <td>GW190910_112807</td>
      <td>2.87×10<sup>-3</sup></td>
      <td>&gt; 0.99</td>
      <td>43.9<sup>+7.6</sup><sub>-6.1</sub></td>
      <td>35.6<sup>+6.3</sup><sub>-7.2</sub></td>
      <td>34.3<sup>+4.1</sup><sub>-4.1</sub></td>
      <td>0.02<sup>+0.18</sup><sub>-0.18</sub></td>
      <td>[4]</td>
    </tr>
    <tr>
      <td>GW190915_235702</td>
      <td>&lt; 1 × 10<sup>-5</sup></td>
      <td>&gt; 0.99</td>
      <td>35.3<sup>+9.5</sup><sub>-6.4</sub></td>
      <td>24.4<sup>+5.6</sup><sub>-6.1</sub></td>
      <td>25.3<sup>+3.2</sup><sub>-2.7</sub></td>
      <td>0.02<sup>+0.20</sup><sub>-0.25</sub></td>
      <td>[4]</td>
    </tr>
    <tr>
      <td>GW190924_021846</td>
      <td>&lt; 1 × 10<sup>-5</sup></td>
      <td>&gt; 0.99</td>
      <td>8.9<sup>+7.0</sup><sub>-2.0</sub></td>
      <td>5.0<sup>+1.4</sup><sub>-1.9</sub></td>
      <td>5.8<sup>+0.2</sup><sub>-0.2</sub></td>
      <td>0.03<sup>+0.30</sup><sub>-0.09</sub></td>
      <td>[4]</td>
    </tr>
    <tr>
      <td>GW190925_232845</td>
      <td>7.20×10<sup>-3</sup></td>
      <td>0.99</td>
      <td>21.2<sup>+6.9</sup><sub>-3.1</sub></td>
      <td>15.6<sup>+2.6</sup><sub>-3.6</sub></td>
      <td>15.8<sup>+1.1</sup><sub>-1.0</sub></td>
      <td>0.11<sup>+0.17</sup><sub>-0.14</sub></td>
      <td>[3]</td>
    </tr>
    <tr>
      <td>GW190929_012149</td>
      <td>1.55×10<sup>-1</sup></td>
      <td>0.87</td>
      <td>80.8<sup>+33.0</sup><sub>-33.2</sub></td>
      <td>24.1<sup>+19.3</sup><sub>-10.6</sub></td>
      <td>35.8<sup>+14.9</sup><sub>-8.2</sub></td>
      <td>0.01<sup>+0.34</sup><sub>-0.33</sub></td>
      <td>[4]</td>
    </tr>
    <tr>
      <td>GW190930_133541</td>
      <td>1.23×10<sup>-2</sup></td>
      <td>&gt; 0.99</td>
      <td>12.3<sup>+12.4</sup><sub>-2.3</sub></td>
      <td>7.8<sup>+1.7</sup><sub>-3.3</sub></td>
      <td>8.5<sup>+0.5</sup><sub>-0.5</sub></td>
      <td>0.14<sup>+0.31</sup><sub>-0.15</sub></td>
      <td>[4]</td>
    </tr>
    <tr>
      <td>GW191105_143521</td>
      <td>1.18×10<sup>-2</sup></td>
      <td>&gt; 0.99</td>
      <td>10.7<sup>+3.7</sup><sub>-1.6</sub></td>
      <td>7.7<sup>+1.4</sup><sub>-1.9</sub></td>
      <td>7.82<sup>+0.61</sup><sub>-0.45</sub></td>
      <td>-0.02<sup>+0.13</sup><sub>-0.09</sub></td>
      <td>[1]</td>
    </tr>
    <tr>
      <td>GW191109_010717</td>
      <td>1.80×10<sup>-4</sup></td>
      <td>&gt; 0.99</td>
      <td>65<sup>+11</sup><sub>-11</sub></td>
      <td>47<sup>+15</sup><sub>-13</sub></td>
      <td>47.5<sup>+9.6</sup><sub>-7.5</sub></td>
      <td>-0.29<sup>+0.42</sup><sub>-0.31</sub></td>
      <td>[1]</td>
    </tr>
    <tr>
      <td>GW191127_050227</td>
      <td>2.49×10<sup>-1</sup></td>
      <td>0.49</td>
      <td>53<sup>+47</sup><sub>-20</sub></td>
      <td>24<sup>+17</sup><sub>-14</sub></td>
      <td>29.9<sup>+11.7</sup><sub>-9.1</sub></td>
      <td>0.18<sup>+0.34</sup><sub>-0.36</sub></td>
      <td>[1]</td>
    </tr>
    <tr>
      <td>GW191129_134029</td>
      <td>&lt; 1 × 10<sup>-5</sup></td>
      <td>&gt; 0.99</td>
      <td>10.7<sup>+4.1</sup><sub>-2.1</sub></td>
      <td>6.7<sup>+1.5</sup><sub>-1.7</sub></td>
      <td>7.31<sup>+0.43</sup><sub>-0.28</sub></td>
      <td>0.06<sup>+0.16</sup><sub>-0.08</sub></td>
      <td>[1]</td>
    </tr>
    <tr>
      <td>GW191204_171526</td>
      <td>&lt; 1 × 10<sup>-5</sup></td>
      <td>&gt; 0.99</td>
      <td>11.9<sup>+3.3</sup><sub>-1.8</sub></td>
      <td>8.2<sup>+1.4</sup><sub>-1.6</sub></td>
      <td>8.55<sup>+0.38</sup><sub>-0.27</sub></td>
      <td>0.16<sup>+0.08</sup><sub>-0.05</sub></td>
      <td>[1]</td>
    </tr>
    <tr>
      <td>GW191215_223052</td>
      <td>&lt; 1 × 10<sup>-5</sup></td>
      <td>&gt; 0.99</td>
      <td>24.9<sup>+7.1</sup><sub>-4.1</sub></td>
      <td>18.1<sup>+3.8</sup><sub>-4.1</sub></td>
      <td>18.4<sup>+2.2</sup><sub>-1.7</sub></td>
      <td>-0.04<sup>+0.17</sup><sub>-0.21</sub></td>
      <td>[1]</td>
    </tr>
    <tr>
      <td>GW191216_213338</td>
      <td>&lt; 1 × 10<sup>-5</sup></td>
      <td>&gt; 0.99</td>
      <td>12.1<sup>+4.6</sup><sub>-2.3</sub></td>
      <td>7.7<sup>+1.6</sup><sub>-1.9</sub></td>
      <td>8.33<sup>+0.22</sup><sub>-0.19</sub></td>
      <td>0.11<sup>+0.13</sup><sub>-0.06</sub></td>
      <td>[1]</td>
    </tr>
    <tr>
      <td>GW191222_033537</td>
      <td>&lt; 1 × 10<sup>-5</sup></td>
      <td>&gt; 0.99</td>
      <td>45.1<sup>+10.9</sup><sub>-8.0</sub></td>
      <td>34.7<sup>+9.3</sup><sub>-10.5</sub></td>
      <td>33.8<sup>+7.1</sup><sub>-5.0</sub></td>
      <td>-0.04<sup>+0.20</sup><sub>-0.25</sub></td>
      <td>[1]</td>
    </tr>
    <tr>
      <td>GW191230_180458</td>
      <td>5.02×10<sup>-2</sup></td>
      <td>0.95</td>
      <td>49.4<sup>+14.0</sup><sub>-9.6</sub></td>
      <td>37<sup>+11</sup><sub>-12</sub></td>
      <td>36.5<sup>+8.2</sup><sub>-5.6</sub></td>
      <td>-0.05<sup>+0.26</sup><sub>-0.31</sub></td>
      <td>[1]</td>
    </tr>
    <tr>
      <td>GW200105_162426</td>
      <td>2.04×10<sup>-1</sup></td>
      <td>0.36</td>
      <td>8.9<sup>+1.2</sup><sub>-1.5</sub></td>
      <td>1.9<sup>+0.3</sup><sub>-0.2</sub></td>
      <td>3.41<sup>+0.08</sup><sub>-0.07</sub></td>
      <td>-0.01<sup>+0.11</sup><sub>-0.15</sub></td>
      <td>[10]</td>
    </tr>
    <tr>
      <td>GW200112_155838</td>
      <td>&lt; 1 × 10<sup>-5</sup></td>
      <td>&gt; 0.99</td>
      <td>35.6<sup>+6.7</sup><sub>-4.5</sub></td>
      <td>28.3<sup>+4.4</sup><sub>-5.9</sub></td>
      <td>27.4<sup>+2.6</sup><sub>-2.1</sub></td>
      <td>0.06<sup>+0.15</sup><sub>-0.15</sub></td>
      <td>[1]</td>
    </tr>
    <tr>
      <td>GW200115_042309</td>
      <td>&lt; 1 × 10<sup>-5</sup></td>
      <td>&gt; 0.99</td>
      <td>5.9<sup>+2.0</sup><sub>-2.5</sub></td>
      <td>1.44<sup>+0.85</sup><sub>-0.29</sub></td>
      <td>2.43<sup>+0.05</sup><sub>-0.07</sub></td>
      <td>-0.15<sup>+0.24</sup><sub>-0.42</sub></td>
      <td>[10]</td>
    </tr>
    <tr>
      <td>GW200128_022011</td>
      <td>4.29×10<sup>-3</sup></td>
      <td>&gt; 0.99</td>
      <td>42.2<sup>+11.6</sup><sub>-8.1</sub></td>
      <td>32.6<sup>+9.5</sup><sub>-9.2</sub></td>
      <td>32.0<sup>+7.5</sup><sub>-5.5</sub></td>
      <td>0.12<sup>+0.24</sup><sub>-0.25</sub></td>
      <td>[1]</td>
    </tr>
    <tr>
      <td>GW200129_065458</td>
      <td>&lt; 1 × 10<sup>-5</sup></td>
      <td>&gt; 0.99</td>
      <td>34.5<sup>+9.9</sup><sub>-3.2</sub></td>
      <td>28.9<sup>+3.4</sup><sub>-9.3</sub></td>
      <td>27.2<sup>+2.1</sup><sub>-2.3</sub></td>
      <td>0.11<sup>+0.11</sup><sub>-0.16</sub></td>
      <td>[1]</td>
    </tr>
    <tr>
      <td>GW200202_154313</td>
      <td>&lt; 1 × 10<sup>-5</sup></td>
      <td>&gt; 0.99</td>
      <td>10.1<sup>+3.5</sup><sub>-1.4</sub></td>
      <td>7.3<sup>+1.1</sup><sub>-1.7</sub></td>
      <td>7.49<sup>+0.24</sup><sub>-0.20</sub></td>
      <td>0.04<sup>+0.13</sup><sub>-0.06</sub></td>
      <td>[1]</td>
    </tr>
    <tr>
      <td>GW200208_130117</td>
      <td>3.11×10<sup>-4</sup></td>
      <td>&gt; 0.99</td>
      <td>37.8<sup>+9.2</sup><sub>-6.2</sub></td>
      <td>27.4<sup>+6.1</sup><sub>-7.4</sub></td>
      <td>27.7<sup>+3.6</sup><sub>-3.1</sub></td>
      <td>-0.07<sup>+0.22</sup><sub>-0.27</sub></td>
      <td>[1]</td>
    </tr>
    <tr>
      <td>GW200209_085452</td>
      <td>4.64×10<sup>-2</sup></td>
      <td>0.95</td>
      <td>35.6<sup>+10.5</sup><sub>-6.8</sub></td>
      <td>27.1<sup>+7.8</sup><sub>-7.8</sub></td>
      <td>26.7<sup>+6.0</sup><sub>-4.2</sub></td>
      <td>-0.12<sup>+0.24</sup><sub>-0.30</sub></td>
      <td>[1]</td>
    </tr>
    <tr>
      <td>GW200219_094415</td>
      <td>9.94×10<sup>-4</sup></td>
      <td>&gt; 0.99</td>
      <td>37.5<sup>+10.1</sup><sub>-6.9</sub></td>
      <td>27.9<sup>+7.4</sup><sub>-8.4</sub></td>
      <td>27.6<sup>+5.6</sup><sub>-3.8</sub></td>
      <td>-0.08<sup>+0.23</sup><sub>-0.29</sub></td>
      <td>[1]</td>
    </tr>
    <tr>
      <td>GW200224_222234</td>
      <td>&lt; 1 × 10<sup>-5</sup></td>
      <td>&gt; 0.99</td>
      <td>40.0<sup>+6.9</sup><sub>-4.5</sub></td>
      <td>32.5<sup>+5.0</sup><sub>-7.2</sub></td>
      <td>31.1<sup>+3.2</sup><sub>-2.6</sub></td>
      <td>0.10<sup>+0.15</sup><sub>-0.15</sub></td>
      <td>[1]</td>
    </tr>
    <tr>
      <td>GW200225_060421</td>
      <td>&lt; 1 × 10<sup>-5</sup></td>
      <td>&gt; 0.99</td>
      <td>19.3<sup>+5.0</sup><sub>-3.0</sub></td>
      <td>14.0<sup>+2.8</sup><sub>-3.5</sub></td>
      <td>14.2<sup>+1.5</sup><sub>-1.4</sub></td>
      <td>-0.12<sup>+0.17</sup><sub>-0.28</sub></td>
      <td>[1]</td>
    </tr>
    <tr>
      <td>GW200302_015811</td>
      <td>1.12×10<sup>-1</sup></td>
      <td>0.91</td>
      <td>37.8<sup>+8.7</sup><sub>-8.5</sub></td>
      <td>20.0<sup>+8.1</sup><sub>-5.7</sub></td>
      <td>23.4<sup>+4.7</sup><sub>-3.0</sub></td>
      <td>0.01<sup>+0.25</sup><sub>-0.26</sub></td>
      <td>[1]</td>
    </tr>
    <tr>
      <td>GW200311_115853</td>
      <td>&lt; 1 × 10<sup>-5</sup></td>
      <td>&gt; 0.99</td>
      <td>34.2<sup>+6.4</sup><sub>-3.8</sub></td>
      <td>27.7<sup>+4.1</sup><sub>-5.9</sub></td>
      <td>26.6<sup>+2.4</sup><sub>-2.0</sub></td>
      <td>-0.02<sup>+0.16</sup><sub>-0.20</sub></td>
      <td>[1]</td>
    </tr>
  </tbody>
</table>
<table><caption>TABLE I: A table of GW events that meet the criteria for inclusion in this work. Events are separated by a horizontal line into sections of FAR<sub>min</sub> < 0.25 yr<sup>-1</sup> and 1 yr<sup>-1</sup> ≥ FAR<sub>min</sub> ≥ 0.25 yr<sup>-1</sup> (lower), where FAR<sub>min</sub> is the smallest FAR reported over all pipelines. Within these sections, events are listed by the date they were detected. Columns provide the FAR, $p_{astro}$ (from the pipeline with the smallest FAR), and previously-reported estimates of selected parameters. These previously-reported parameters may adopt different priors than our work and do not precisely correspond to our inputs; see Section III for details. The low-significance event GW190531 is not included, lacking parameter inferences.</caption><thead><tr><th></th><th>&lt; 1 &times; 10<sup>-5</sup></th><th>&gt; 0.99</th><th>13.1<sup>+10.2</sup><sub>-2.9</sub></th><th>7.8<sup>+1.9</sup><sub>-2.9</sub></th><th>8.75<sup>+0.62</sup><sub>-0.55</sub></th><th>0.13<sup>+0.27</sup><sub>-0.10</sub></th><th>[1]</th></tr></thead><tbody><tr><td>GW200316.215756</td><td>8.17&times;10<sup>-1</sup></td><td>0.93</td><td>34.7<sup>+12.6</sup><sub>-8.1</sub></td><td>23.7<sup>+7.3</sup><sub>-6.7</sub></td><td>24.6<sup>+5.5</sup><sub>-4.1</sub></td><td>-0.01<sup>+0.29</sup><sub>-0.34</sub></td><td>[4]</td></tr><tr><td>GW190413.052954</td><td>9.12&times;10<sup>-1</sup></td><td>0.14</td><td>5.7<sup>+3.9</sup><sub>-2.3</sub></td><td>1.5<sup>+0.8</sup><sub>-0.5</sub></td><td>2.41<sup>+0.08</sup><sub>-0.08</sub></td><td>-0.03<sup>+0.32</sup><sub>-0.30</sub></td><td>[4]</td></tr><tr><td>GW190719.215514</td><td>6.31&times;10<sup>-1</sup></td><td>0.92</td><td>36.5<sup>+18.0</sup><sub>-10.3</sub></td><td>20.8<sup>+9.0</sup><sub>-7.2</sub></td><td>23.5<sup>+6.5</sup><sub>-4.0</sub></td><td>0.32<sup>+0.29</sup><sub>-0.31</sub></td><td>[4]</td></tr><tr><td>GW190725.174728</td><td>4.58&times;10<sup>-1</sup></td><td>0.96</td><td>11.5<sup>+6.2</sup><sub>-2.7</sub></td><td>6.4<sup>+2.0</sup><sub>-2.0</sub></td><td>7.4<sup>+0.6</sup><sub>-0.5</sub></td><td>-0.04<sup>+0.26</sup><sub>-0.14</sub></td><td>[24]</td></tr><tr><td>GW190731.140936</td><td>3.35&times;10<sup>-1</sup></td><td>0.78</td><td>41.5<sup>+12.2</sup><sub>-9.0</sub></td><td>28.8<sup>+9.7</sup><sub>-9.5</sub></td><td>29.5<sup>+7.1</sup><sub>-5.2</sub></td><td>0.06<sup>+0.24</sup><sub>-0.24</sub></td><td>[4]</td></tr><tr><td>GW190805.211137</td><td>6.28&times;10<sup>-1</sup></td><td>0.95</td><td>48.2<sup>+17.5</sup><sub>-12.5</sub></td><td>32.0<sup>+13.4</sup><sub>-11.4</sub></td><td>33.5<sup>+10.1</sup><sub>-7.0</sub></td><td>0.35<sup>+0.3</sup><sub>-0.36</sub></td><td>[3]</td></tr><tr><td>GW190917.114630</td><td>6.56&times;10<sup>-1</sup></td><td>0.77</td><td>9.3<sup>+3.4</sup><sub>-4.4</sub></td><td>2.1<sup>+1.5</sup><sub>-0.5</sub></td><td>3.7<sup>+0.2</sup><sub>-0.2</sub></td><td>-0.11<sup>+0.24</sup><sub>-0.49</sub></td><td>[3]</td></tr><tr><td>GW191103.012549</td><td>4.58&times;10<sup>-1</sup></td><td>0.94</td><td>11.8<sup>+6.2</sup><sub>-2.2</sub></td><td>7.9<sup>+1.7</sup><sub>-2.4</sub></td><td>8.34<sup>+0.66</sup><sub>-0.57</sub></td><td>0.21<sup>+0.16</sup><sub>-0.10</sub></td><td>[1]</td></tr><tr><td>GW200216.220804</td><td>3.50&times;10<sup>-1</sup></td><td>0.77</td><td>51<sup>+22</sup><sub>-13</sub></td><td>30<sup>+14</sup><sub>-16</sub></td><td>32.9<sup>+9.3</sup><sub>-8.5</sub></td><td>0.10<sup>+0.34</sup><sub>-0.36</sub></td><td>[1]</td></tr></tbody></table>

Fig. 1 shows the properties of the new observations included in this analysis [1]. The shaded regions show two-dimensional marginal distributions for individual events. For reference, the black contours show expected two-dimensional marginal distribution for observed BBH events deduced in our previous analysis of GWTC-2 (the POWERLAW+PEAK model from [11]). In these plots and henceforth, we define $q = m_2/m_1$ and chirp mass

$$ \mathcal{M} = (m_1 m_2)^{3/5} / (m_1 + m_2)^{1/5}. \quad (1) $$

The dimensionless spin of each black hole is denoted $\chi_i = S_i/m_i^2$ and the effective inspiral spin parameter [26]

$$ \chi_{\text{eff}} = \frac{(m_1 \chi_1 + m_2 \chi_2) \cdot \hat{L}}{m_1 + m_2}, \quad (2) $$

where $\hat{L}$ is the instantaneous orbital angular momentum direction. Finally, $z$ is the redshift of the event, inferred from the measured luminosity distance using $H_0 = 67.9\,\text{km}\,\text{s}^{-1}\,\text{Mpc}^{-1}$ and $\Omega_m = 0.3065$ [27]. From these plots, we make several observations that motivate the investigations and results presented in the remainder of the paper.

**Neutron star-black hole binaries.** The two NSBH binary observations GW200105 and GW200115 [10] are apparent in Fig. 1 as two of the lowest-mass new sources. Prior to O3, gravitational wave and Galactic observations had not identified any NSBH binaries [10]. We now know that these objects exist and merge, occupying a previously unexplored region in the mass and merger rate parameter space. NSBHs form a distinct population from the BNS and most BBHs, motivating the detailed multi-component analyses pursued in Sec. IV. For the first time, we are able to present rates for BNS, NSBH and BBH inferred jointly from an analysis of all observations. The NSBH merger rate is substantially larger than the BBH merger rate. As a result, our joint analyses produce a marginal mass distribution $p(m_1)$ which differs substantially from our previous work, and from

analyses in this work based solely on BBHs: the NSBH merger rate overwhelms the BBH rate at low mass.

**Lower Mass Gap.** We identify a relative dearth of observations of binaries with component masses between $3M_\odot$ and $5M_\odot$. This underabundance is visible in the spectrum of observed primary masses plotted in Fig. 1. Gravitational wave and Galactic observations through O3a were consistent with a mass gap for compact objects between the heaviest NSs and the least massive BHs [28–31]. The gap was thought to extend from roughly $3M_\odot$ to $5M_\odot$, potentially due to the physics of core-collapse supernova explosions [32–36]. Both Galactic and gravitational wave observations made contemporaneously with O3 challenge this assumption [23, 37, 38]. Most notably, the secondary in GW190814 sits just above the maximum mass that the dense-matter equation of state is expected to support [23]. The primary of GW200115 [1, 10] may also lie above the maximum NS mass but below $5M_\odot$. Due to considerable uncertainty in their mass ratio, several binaries’ secondaries may also hail from this gap region between $3M_\odot$ and $5M_\odot$. We investigate the prospect of a mass gap in Sec. IV C, treating all compact objects equivalently.

**NS mass distribution.** The observation of NSBH binaries enables a detailed study of the observed mass distribution of NSs, combining results from both BNSs and NSBHs. We discuss this in detail in Sec. V, comparing source classifications informed by the NS equation of state (EOS) as well as the inferred location of the lower mass gap. The inferred NS mass distribution, albeit based upon a limited sample of observations, does not exhibit a peak at $1.35M_\odot$; in contrast, radio observations of Galactic BNS favor such a peak [39–41]. We investigate the impact of outliers in the mass distribution in Sec. V C, particularly GW190814 whose secondary mass lies above the otherwise inferred NS mass range.

**Additional substructure in the BBH mass distribution.** The observed masses of BBH binaries are clumped. This is most visible on the central panel in
<figure><img src="image_2.png" /><figcaption>FIG. 1. New observations since Gravitational Wave Transient Catalog 2 (GWTC-2). The measured properties of new CBC candidates announced since GWTC-2 with FAR< 1/yr and reported parameters (blue shaded regions), compared to the expected population of detected BBHs (black contours) as inferred from past analysis of GWTC-2 with the same FAR threshold [25]. The left hand plot shows the inferred primary mass $m_1$ and mass ratio $q$; the center plot shows the effective spin $\chi_{\text{eff}}$ and chirp mass $M$ and the right plot shows redshift $z$ and primary mass. The least-massive sources in this sample include NSBH events GW200105 and GW200115.</figcaption></figure>

<figure><img src="image_3.png" /><figcaption>FIG. 2. Illustrating substructure in the chirp mass distribution for BBH (with FAR < 1 yr⁻¹, excluding GW190814, as in Sec. VI). **Top** The individual-event observations versus chirp mass (grey) and an inferred distribution of the *observed* chirp mass distribution (black solid) using an adaptive kernel density estimator [42, 43]. The kernel bandwidth is optimized for the local event density and a 90% confidence interval (black dashed) is obtained by bootstrapping [44]. **Bottom** The solid curve is the predicted chirp mass distribution obtained using the flexible mixture model framework (FM); see Sec. III for details. The distribution shows three clusters at low masses and a lack of mergers in the chirp-mass range 10⁻¹² $M_{\odot}$.</figcaption></figure>
Fig. 1, where overdensities in the chirp mass distribution from 8 to $10M_{\odot}$ and around $30M_{\odot}$ are visible. In Fig. 2, we show the one-dimensional chirp mass distribution for BBH events. The top panel shows the observations for individual events, overlaid with the observed distribution. The observations cluster in chirp mass, with about one-eighth of observed events having chirp masses within $8-10.5M_{\odot}$. Compared to chirp mass accuracy for these events $\lesssim 1M_{\odot}$, this region is well-separated from the next most massive binaries in chirp mass. There is also a significant overdensity at $M \approx 30M_{\odot}$ and a weaker feature at $15M_{\odot}$. These features were previously identified using only GWTC-2 [45–48]. In the bottom panel of Fig. 2, we show the inferred astrophysical distribution of chirp mass, as recovered by the same FLEXIBLE MIXTURES (FM) approach that first identified these modulations [47, 49]. The features in the observed distribution are mirrored in the astrophysical one. In Section VI we show that these features are robustly identified by several independent analyses, and demonstrate that the observed structure in the mass distribution is highly significant. Since strong features correlated with chirp mass, but independent of mass ratio, are a priori astrophysically unlikely, these significant overdensities suggest the two-dimensional marginal distribution of the BBH population should also have significant substructure and localized overdensities. We explore this in detail in Sec. VIB.

**BBH Rate evolution with redshift.** We find that the merger rate density increases with redshift. The right plot in Figure 1 shows the distribution of events as a function of redshift. While there is a clear evolution of the observed mass distribution with redshift, this arises from the detectors' greater sensitivity to higher mass systems. Consequently, from Fig. 1 alone, we are not able to draw inferences about the evolution of the population or merger rate with redshift. We explore these issues in detail in Sec. VID, where we show that there is no evidence for the evolution of the mass distribution with redshift. However, the merger rate density does increase with redshift. Modeling the rate as $\propto (1+z)^{\kappa}$, we find that $\kappa = 2.9_{-1.8}^{+1.7}$. Our analysis strongly disfavors the possibility that the merger rate does not evolve with redshift.

**Low BBH spins.** The BBH detections exhibit effective inspiral spins concentrated about $\chi_{\text{eff}} \approx 0$, with the highest inferred spins below 0.6. The spread is consistent with expectations from GWTC-2. The events include individual candidates that probably have negative effective inspiral spin, consistent with our previous conclusion that the spin distribution contains events with $\chi_{\text{eff}} < 0$.

### III. METHODS

#### A. Data and event selection

We consider candidate events identified by our search analyses for compact binary mergers using archival

data, comprising results from the GSTLAL [50–52], PYCBC [53–58], and MBTA [59] analyses using template-based matched filtering techniques, and the CWB [60, 61] analysis using an excess-energy search that does not assume a physically parameterized signal model. Details of these analyses and the configurations used for O3 data are given in [1, 3, 4]. Out of the thousands of candidates produced, only a small minority correspond to astrophysical merger signals, most being caused by instrumental noise. While methods are emerging for performing a joint population analysis including both signal and noise events [12, 62–64], here we largely follow a simple procedure [11, 25] of imposing a significance threshold to identify events for our population analysis and implicitly treating all events passing the threshold as true signals. The choice of threshold will then limit the expected level of noise contamination.

The analyses calculate a ranking statistic for all candidate events, which is used as the basis for estimating the events' FARs. The ranking statistic allows for sources over a broad parameter space of binary component masses and spins to be detected, without making strong assumptions on the form of the source distribution (except in the case of PYCBC-BBH, specialized for comparable-mass BBH mergers). The analyses additionally calculate an estimate of the probability of astrophysical (signal) origin, $p_{\text{astro}}$, using analysis-specific assumptions on the form of the signal distribution (detailed in [1, 3]). Since, in this work, we explore a range of different assumptions and models for the binary merger population, we define our event set by imposing a threshold on FAR values, rather than on $p_{\text{astro}}$ [11].

Our searches and event validation techniques for gravitational wave transients have so far identified 76 candidates with FAR below $1\ \text{yr}^{-1}$ in LIGO and Virgo data through O3. Table I presents these events. In our analysis here, we remove candidates with probable instrumental origin (e.g., 200219.201407 [1]). Assuming our analyses produce noise triggers independently, we expect $\sum_k R T_k \approx 4.6$ false events in our sample, where $R$ is the false alarm rate and $T_k$ is an estimate of the time examined by the $k$th search. For the population studies presented here, the event list can be further restricted by additional FAR thresholds to identify a high-purity list of candidates and to assess the stability of our results to changes in threshold. The choice of FAR threshold to achieve a given level of noise contamination will depend on the number of significant event candidates (and hence, likely signals) considered for an analysis. The most prominent difference concerns analyses for binaries with one or more NS components, in Sections IV and V, as opposed to analyses which only consider BBH systems, in Sections VI and VII. While our data set contains many tens of confidently detected BBH mergers, there is only a handful of comparably significant BNS or NSBH events. This leads us to impose a more stringent threshold of FAR $< 0.25\ \text{yr}^{-1}$ for all analyses considering NS systems.
Because population reconstruction requires careful understanding of search selection biases, we do not include candidates identified by independent analyses [65–71] of the publicly released LIGO and Virgo data [72, 73]. Previous studies [63, 64] suggest that our results are unlikely to change significantly with the inclusion of these events. We similarly omit any triggers produced from our focused IMBH or eccentric binary searches [74], as we have not assessed their sensitivity to the full mass range investigated here using the consistent framework adopted for our primary results. These searches also did not yield any additional significant detections. Future analyses may be able to include events from multiple independent catalogs with a unified framework for calculating event significance independently of specific search methods [75, 76].

Parameter estimation results for each candidate event [4] were obtained using the LALINFERENCE [77], RIFT [78, 79], or BILBY [80, 81] analyses. The parameter estimation analyses use Bayesian sampling methods to produce fair draws from the posterior distribution function of the source parameters, conditioned on the data and a given model for the signal and noise [82]. Unless otherwise noted, we use previously-published samples for each event through GWTC-2.1 [2–4]. For GW200105 and GW200115 [10], we use the inferences reported in GWTC-3 [1]. For previously-reported events through GWTC-2, we adopt the same parameter and event choices reported in our previous population study [11]. For O1 events, we use published samples which equally weight analyses with SEOBNRv3 [83, 84] and IMRPhenomPv2 [85] waveforms, and for new events reported in the GWTC-2 update [4], we use published samples with higher order modes, selected by equally weighting all available higher-order mode analyses (PrecessingIMRPHM). The higher-mode analyses associated with GWTC-2 do not include calibration uncertainty. Regarding new events presented in GWTC-2.1, we use the fiducial analysis reported in that work (unless otherwise noted) comprised of merged posterior samples equally drawn from SEOBNRv4PHM [86, 87] and IMRPHENOMXPHM [88]. Both models implement precession and include beyond-quadrupole radiation for asymptotically quasicircular orbits. For O3b events newly reported in GWTC-3, we use the publicly released C01:Mixed samples from [1], which equally weigh two analyses with the models SEOBNRv4PHM [87] and IMRPhenomXPHM [88]. These samples lack the impact of calibration error on the SEOBNRv4PHM analyses for GW200316, GW200129, and GW200112. A more complete description of the parameter estimation methods and waveform models used can be found in Section V of [4]. To avoid ambiguity where multiple versions of these samples exist, our input posterior samples adopt the $D_L^2$ prior on luminosity distance $D_L$ and have reference spins specified at 20 Hz. In the case of the BNS events GW170817 and GW190425 and the NSBH events GW200105 and GW200115, two versions of the samples are available: one

that assumes component spins $\chi_{1,2} < 0.05$ for putative NSs, and a less restrictive but event-dependent bound otherwise (e.g., $\chi_{1,2} < 0.99$ for GW200105 and GW200115). We use the latter (high-spin) samples here.

The transfer function between the observed strain and astrophysical strain is subject to a systematic calibration uncertainty. Our parameter inferences incorporate our best estimates of calibration uncertainty, as reported in previous work. Since calibration uncertainty has been incorporated independently for each event, we have implicitly assumed any consistent systematic bias applied to all events is small; we estimate less than 0.54% (1.74%) effect for LIGO (Virgo) respectively [89, 90]. For O3a, the amplitude uncertainty was $\lesssim 3\%$ [91]. Because we assume the secular calibration error is much smaller than the calibration error envelope applied when analyzing individual events, we do not incorporate this calibration uncertainty into our estimates of network sensitivity. In O3, this calibration uncertainty implies $\lesssim 10\%$ systematic uncertainty in the sensitive spacetime volume and the inferred merger rate, which is subdominant to our uncertainties from Poisson counting error for most source classes and mass regions.

Each foreground event in O3 has been rigorously validated [1]. Out of the 108 triggers examined in O3 (including events not included in final search results for this or our companion papers), only 4 were rejected due to the presence of instrumental noise artifacts. The number of vetoed events is comparable to or less than the expected number of false events for our fiducial analysis threshold, and far smaller than the number of events examined in this study.

## B. Population analysis framework

To infer the parameters describing population models, we adopt a hierarchical Bayesian approach, in which we marginalize over the uncertainty in our estimate of individual event parameters; see, e.g., [92–94]. Given a set of data, $\{d_i\}$, from $N_{det}$ gravitational-wave detections, we model the total number of events as an inhomogeneous Poisson process, giving the likelihood of the data given population parameters $\Lambda$ as [92, 93, 95]

$$ \mathcal{L}(\{d\}, N_{\text{det}}|\Lambda, N_{\text{exp}}) \propto N^{N_{\text{det}}} e^{-N_{\text{exp}}} \prod_{i=1}^{N_{\text{det}}} \int \mathcal{L}(d_i|\theta) \pi(\theta|\Lambda) d\theta. \quad (3) $$

Here, $N_{exp}$ is the expected number of detections over the full duration of an observation period for the population model $\Lambda$, $N = N_{exp}/\xi(\Lambda)$ is the expected number of mergers over the observation period, with $\xi(\Lambda)$ the fraction of mergers that are detectable for a population with parameters $\Lambda$. The term $\mathcal{L}(d_i|\theta)$ is the individual event likelihood for the $i$th event in our data set that is described by a set of parameters $\theta$. The conditional prior $\pi(\theta|\Lambda)$ governs the population distribution
on event parameters $\theta$ (e.g., the masses, spins, and redshifts) given a specific population model and set of hyper-parameters $\Lambda$ to describe the model. Constraining the population hyper-parameters describing the distribution of gravitational-wave signals according to different models is one of the primary goals of this paper. A notable simplification results if a log-uniform prior is imposed on $N \equiv N_{\text{exp}}/\xi(\Lambda)$, the total number of events (detectable or not): one can then marginalize Eq. (3) over $N$ to obtain [92, 94, 96]

$$ \mathcal{L}(\{d\}|\Lambda) \propto \prod_{i=1}^{N_{\text{det}}} \frac{\int \mathcal{L}(d_i|\theta)\pi(\theta|\Lambda)d\theta}{\xi(\Lambda)}. \quad (4) $$

To evaluate the single-event likelihood $\mathcal{L}(d_i | \theta)$, we use posterior samples that are obtained using some default prior $\pi_{\emptyset}(\theta)$. In this case, we can calculate the integrals over the likelihood with importance sampling over the discrete samples where we denote weighted averages over posterior samples as $\langle \dots \rangle$. Equation (4), for example, becomes

$$ \mathcal{L}(\{d\}|\Lambda) \propto \prod_{i=1}^{N_{\text{det}}} \frac{1}{\xi(\Lambda)} \left\langle \frac{\pi(\theta|\Lambda)}{\pi_{\emptyset}(\theta)} \right\rangle, \quad (5) $$

where the factor of $\pi_{\emptyset}(\theta)$ serves to divide out the prior used for initial parameter estimation. The likelihoods are implemented in a variety of software including GW-POPULATION [97, 98], POPMODELS [99], SODAPOP [100], and Vamana [49]. Each code evaluates one of the likelihoods described above for population models, building a posterior with one of the EMCEE, DYNESTY, or STAN packages [101–104]. Appendix A describes how we estimate search sensitivity using synthetic sources.

We note that the above likelihood formulation includes uncertainty due to the finite number of samples $\theta$ per event used in the Monte Carlo integration (see, e.g., [105, 106]). For details of how we alter the likelihood to mitigate this source of uncertainty see Appendix B. In this paper, we refer to both the astrophysical distribution of a parameter – the version as it appears in nature – and the observed distribution of a parameter – what appears in our detectors due to selection effects. The posterior population distribution for a given model represents our best guess for the astrophysical distribution of some source parameter $\theta$, averaged over the posterior for population parameters $\Lambda$.

$$ p_{\Lambda}(\theta) = \int \pi(\theta|\Lambda)p(\Lambda|\{d\}) d\Lambda. \quad (6) $$

The subscript $\Lambda$ indicates that we have marginalized over population parameters. Meanwhile, the posterior predictive distribution refers to the population-averaged distribution of source parameters $\theta$ conditioned on detection.

### C. Population models used in this work

In this section, we briefly summarize some of the tools and ingredients we use to generate phenomenological models $\pi(\theta|\Lambda)$ in this work. Appendix B provides a comprehensive description of the population models used in this work, including their functional form and prior assumptions.

#### 1. Parametric mass models

**Neutron star mass models:** In the analyses that focus exclusively on the NS-containing events, we model the NS mass distribution as either a power law or a Gaussian with sharp minimum and maximum mass cutoffs. The latter shape is inspired by the Galactic double NS mass distribution [39–41]. In both models, which we call POWER and PEAK respectively, we assume that the components of BNSs are drawn independently from the common NS mass distribution. For NSBHs, we assume a uniform BH mass distribution and random pairing with NSs.

**Fiducial population mass and redshift analysis:** In the fiducial power law plus peak (POWER LAW + PEAK (PP)) model [96, 107], the mass-redshift distribution (per unit comoving volume and observer time) was assumed to be of the form $p(m_1, q, z) \propto q^{\beta}p(m_1)(1+z)^{\kappa-1}$, with $p(m_1)$ a mixture model containing two components: a power law with some slope and limits; and a Gaussian with some mean and variance. [In practice, this model as applied to GWTC-2 also usually included additional smoothing parameters for the upper and lower limit of the power law.] The merger rate normalization is chosen such that the source-frame merger rate per comoving volume at redshift $z$ is given by

$$ \begin{aligned} \mathcal{R}(z) &= \frac{dN}{dV_c dt}(z) \\ &= \mathcal{R}_0(1+z)^{\kappa}, \end{aligned} \quad (7) $$

where $\mathcal{R}_0$ is the local merger rate density at $z=0$ and $\kappa$ is a free parameter governing the evolution of $R(z)$ with higher redshift. The corresponding redshift distribution of BBHs (per unit redshift interval) is [96]

$$ p(z|\kappa) \propto \frac{1}{1+z} \frac{dV_c}{dz}(1+z)^{\kappa}, \quad (8) $$

where the leading factor of $(1+z)^{-1}$ converts time increments from the source frame to the detector frame. Past analyses generally fixed the redshift distribution of binaries, assuming a source-frame merger rate that is constant and uniform in comoving volume; this choice corresponds to $\kappa=0$. Our previous population studies [11, 25] additionally considered an evolving merger rate with variable $\kappa$.

**POWER LAW + DIP + BREAK model (PDB):** To fit the distribution of BH and NS masses, we use a parameterized model described in [108] and [109], consisting of a
broken power law with a notch filter. The variable depth of this notch filter allows for a dearth of events between two potential subpopulations at low and high mass. It also uses a low-pass filter at high masses to allow for a potential tapering of the mass distribution at high BH masses. The component mass distribution is then

$$p(m|\lambda) = n(m|M_{\text{low}}^{\text{gap}}, M_{\text{high}}^{\text{gap}}, A) \times l(m|m_{\text{max}}, \eta) \times \begin{cases} m^{\alpha_1} & \text{if } m < M_{\text{high}}^{\text{gap}} \\ m^{\alpha_2} & \text{if } m > M_{\text{high}}^{\text{gap}} \\ 0 & \text{if } m > m_{\text{max}} \text{ or } m < m_{\text{min}} \end{cases}. \quad (9)$$

Here, $l(m|m_{\text{max}}, \eta)$ is the low pass filter with powerlaw $\eta$ applied at mass $m_{\text{max}}$, $n(m|M_{\text{low}}^{\text{gap}}, M_{\text{high}}^{\text{gap}}, A)$ is the notch filter with depth $A$ applied between $M_{\text{low}}^{\text{gap}}$ and $M_{\text{high}}^{\text{gap}}$. In this model, the primary and secondary masses are fit by the same parameters and are related by a pairing function [110, 111]. Two pairing functions are considered. The first is random pairing: primary and secondary masses take independent values so long as $m_2 < m_1$. This model takes the form

$$p(m_1, m_2|\Lambda) \propto p(m=m_1|\Lambda) p(m=m_2|\Lambda) \times \Theta(m_2 < m_1), \quad (10)$$

where $\Theta$ is the Heaviside step function that enforces primary masses are greater than secondary masses and $\Lambda$ is the full set of eight hyperparameters. The second is a power-law-in-mass-ratio pairing function, as in [111]. The full mass distribution in the power-law-in-mass-ratio model is thus described by

$$p(m_1, m_2|\Lambda) \propto p(m=m_1|\Lambda) p(m=m_2|\Lambda) \times q^\beta \Theta(m_2 < m_1). \quad (11)$$

Unless otherwise stated, the results from the random pairing model are presented in this work.

## 2. Spin models

**Fiducial population spin analyses:** Compact binary spins may be parameterized in several different ways. In addition to the dimensionless spin magnitudes $\chi_i$ ($i \in \{1, 2\}$) and the polar tilt angles $\theta_i$ between each spin vector and a binary's orbital angular momentum [112], we often appeal to the *effective* spin parameters $\chi_{\text{eff}}$ and $\chi_{\text{p}}$. The effective inspiral spin $\chi_{\text{eff}}$ characterizes a mass-averaged spin angular momentum in the direction parallel to the binaries orbital angular momentum. The effective precessing spin $\chi_{\text{p}}$, meanwhile, corresponds approximately to the degree of *in-plane* spin, and phenomenologically parametrizes the rate of relativistic precession of the orbital plane [113]:

$$\chi_{\text{p}} = \max \left[ \chi_1 \sin \theta_1, \left( \frac{3+4q}{4+3q} \right) q \chi_2 \sin \theta_2 \right]. \quad (12)$$

We leverage these two descriptions to explore the nature of BBH spins in two complementary ways. First, we use the DEFAULT spin model [114] to directly measure the distribution of BBH component spin magnitudes and tilts. We model component spin magnitudes as being independently and identically drawn from a Beta distribution [113], with

$$p(\chi_i|\alpha_\chi, \beta_\chi) \propto \chi_i^{\alpha_1-1} (1-\chi_i)^{\beta_1-1}. \quad (13)$$

Values of the shape parameters $\alpha_\chi$ and $\beta_\chi$ are restricted to $\alpha_\chi > 1$ and $\beta_\chi > 1$ to ensure a non-singular component spin distribution. We describe component spin tilts, in turn, via a mixture between two sub-populations, one with isotropically oriented tilts and another with tilts preferentially concentrated about $\theta_i = 0$ [114]:

$$p(\cos \theta_i | \zeta, \sigma_t) = \frac{1}{2} (1 - \zeta) + \zeta N_{[-1,1]}(\cos \theta_i; 1, \sigma_t). \quad (14)$$

Here, $N_{[-1,1]}(\cos \theta_i; 1, \sigma_t)$ is a normal distribution truncated to the interval $-1 \le \cos \theta_i \le 1$, centered at 1 with a standard deviation $\sigma_t$. The mixing parameter $\zeta$ governs the relative fraction of systems drawn from each sub-population. The form of Eq. (14) is motivated by a desire to capture the behavior of BBHs originating from both dynamical and isolated evolution channels, which are expected to yield preferentially isotropic and aligned spin orientations, respectively. *Perfect* spin-orbit alignment across the BBH population would correspond to $\zeta = 1$ or $\sigma_t = 0$, which our prior analysis on GWTC-2 ruled out at high confidence [11]. This default spin model is characterized by two parameters characterizing the spin magnitude distribution (e.g., $\alpha, \beta$) and two parameters characterizing the spin misalignment mixture model (i.e., $\xi, \sigma_t$). In part because this parameterization approaches isotropy in two independent limits ($\sigma_t = \infty$ or $\zeta = 0$), it assigns high prior weight to nearly-isotropic spin distributions.

**Gaussian spin model:** Our second approach is to instead seek to measure the distribution of effective spin parameters $\chi_{\text{eff}}$ and $\chi_{\text{p}}$. In this case, we phenomenologically model the joint $\chi_{\text{eff}}-\chi_{\text{p}}$ distribution as a bivariate Gaussian [115, 116]:

$$p(\chi_{\text{eff}}, \chi_{\text{p}} | \mu_{\text{eff}}, \sigma_{\text{eff}}, \mu_{\text{p}}, \sigma_{\text{p}}, r) \propto N(\chi_{\text{eff}}, \chi_{\text{p}} | \mu, \Sigma), \quad (15)$$

centered at $\mu = (\mu_{\text{eff}}, \mu_{\text{p}})$ and with a covariance matrix

$$\Sigma = \begin{pmatrix} \sigma_{\text{eff}}^2 & r\sigma_{\text{eff}}\sigma_{\text{p}} \\ r\sigma_{\text{eff}}\sigma_{\text{p}} & \sigma_{\text{p}}^2 \end{pmatrix}. \quad (16)$$

Equation (15) is truncated to the intervals $-1 \le \chi_{\text{eff}} \le 1$ and $0 \le \chi_{\text{p}} \le 1$ over which the effective spin parameters are defined. This second model has five parameters for spin: two mean values and three parameters describing the covariance.
### 3. Multi-source mixture model

MULTI SOURCE model (MS): MS models all source categories in a mixture model, with one subpopulation for BNS, NSBH, and BBH. The BBH subpopulation follows the MULTISPIN model introduced in [11]. This model features a power law continuum $q^\beta m_1^\alpha$, plus a peak modeled as a bivariate Gaussian in $m_1, m_2$. Consequently, the mass distribution is similar to the PP model. However, the spin distribution in the power law and Gaussian subpopulations are independent, as are the primary and secondary spins, with each of the four scenarios following the DEFAULT spin model, with $\zeta = 1$.

New to MS are two additional bivariate Gaussian subpopulations, characterizing BNS and NSBH mergers. The BH component of NSBH follow an independent Gaussian mass distribution. As with BBH, these BH follow an independent DEFAULT spin model with $\zeta = 1$. All three types of NS (two in BNS and one in NSBH) are assumed to follow the same Gaussian mass distribution. Each type of NS follows an independent DEFAULT spin model, except here the spin magnitudes are scaled down to $\chi_{max} = 0.05$, and $\zeta \equiv 0$ since tilts are not well measured.

### 4. Nonparametric models

POWER LAW + SPLINE model (PS): The PS model parameterizes perturbations to a simpler phenomenological primary mass model, that is modeled as a cubic spline function.

$$p_{\text{PS}}(m_1|\Lambda, \{f_i\}) \propto p(m_1|\Lambda) \exp[f(m_1|\{f_i\})]. \quad (17)$$

Here, $f(m_1|\{f_i\})$ is the perturbation function interpolated from a set of $n$ knots, fixed uniformly in $\log m_1$ space, and with heights $\{f_i\}$ [45]. In this work, we choose as a base model a truncated power law [11, 117] with a low mass taper, similar to our fiducial model but lacking a Gaussian peak in $p(m_1)$. This model has all the parameters of the truncated model in mass and spin, as well as an additional parameter that characterizes the low mass tapering and $n$ more describing the heights of the cubic spline knots.

FLEXIBLE MIXTURES model (FM): Vamana, the FM model, characterizes the population as a mixture model, summing over individually separable components describing the distribution of chirp mass, mass ratio, and $\chi_{i,z}$ [49]. Each component is composed of a Gaussian to model the chirp mass, another Gaussian to model the aligned-spin component, and a power law to model the mass ratio distribution. The weights follow a uniform prior and are proposed using a Dirichlet distribution. We choose eleven components. This choice maximizes the marginal likelihood; however, our results are robust against selecting different numbers of components.

BINNED GAUSSIAN PROCESS model (BGP): We also model the two-dimensional mass distribution as a binned

Gaussian Process based on methods outlined in [118, 119]. In this approach, while the redshift and spin distribution are fixed (here, to uniform in comoving volume and isotropic and uniform in magnitude, respectively), we assume the merger rate over distinct mass bins is related via a Gaussian process that correlates the merger rates of neighboring bins. We use conventional techniques provided by PYMC3 [120] to explore the hyperparameters of the Gaussian process, in particular its covariance, to optimally reproduce our data.

## IV. BINARY MERGER POPULATION ACROSS ALL MASSES

In this Section, we jointly analyze the masses of all events in Table I for several reasons. First, it allows for the inclusion of all events regardless of their inferred source type. This eliminates issues of ambiguity in source classification for a number of events in O3. Second, it makes possible the detection and characterization of additional features such as a lower mass gap between the lowest-mass objects (likely though not necessarily NS) and the more massive BH populations [108], or multiple subpopulations [119]. Third, it facilitates a self-consistent calculation of merger rates in different regions of the mass spectrum without explicitly counting the number of events in each category [12, 121]. Last, it naturally produces an overall rate of compact binary coalescences that does not require combining rates produced by disjoint models which may have differing systematics. We choose a detection threshold of FAR < 0.25 yr⁻¹ which ensures even sub-populations and features driven by a few events are not contaminated by our background.

When searching for features in the population of compact binary coalescences, we want to draw robust conclusions, stable to different choices of model and approach. We, therefore, fit three independent population models, described in Sec. III. The PDB model uses a parametrized dip in the mass distribution to characterize modulations of a simple broken power law at low mass. The BGP model is a nonparametric method allowing considerable flexibility in the mass distribution, constrained only weakly by certain smoothness priors. The BGP and PDB models assume an isotropically-oriented, uniform-magnitude spin distribution for simplicity. For most merging binaries and particularly those with component masses below $10M_\odot$, spin effects have a sub-dominant impact on our sensitivity and thus on our inferences about the compact binary merger rate distribution versus mass, as shown in Appendix C 1. The MS model uses a multi-component mixture model, treating the mass, rate, and spin parameters of each component almost entirely independently. However, to be directly comparable to the BBH-only analyses presented in Sec. VI, our MS analysis omits the outlier event GW190814. To ensure consistent estimates of spin selection effects, the MS analysis presented here only employs O3 events; however, in Ap-
pendix C, we have demonstrated that our many analyses
produce comparable results when including or excluding
pre-O3 results.

A. Merger Rates

Models spanning all source classifications allow us to
self-consistently measure the merger rates for all detected
CBCs, both overall and subdivided into astrophysically
interesting mass ranges, assuming they are independent
of redshift. Moreover, because events can be classified
into each category using mass limits with relatively high
confidence, this approach also provides our fiducial BNS,
NSBH, and BBH merger rates. Specifically, taking NS
masses to lie between 1 and $2.5M_{\odot}$ and BH masses to
be between 2.5 and $100M_{\odot}$ and taking the lowest 5%
and highest 95% credible interval out of all three mod-
els, we infer merger rates between $10\ Gpc^{-3}yr^{-1}$ – $1700\ Gpc^{-3}yr^{-1}$ for BNS, $7.8\ Gpc^{-3}yr^{-1}$ – $140\ Gpc^{-3}yr^{-1}$ for NSBH, and $16\ Gpc^{-3}yr^{-1}$ – $61\ Gpc^{-3}yr^{-1}$ for BBH.
Our choice of $2.5M_{\odot}$ as a boundary between BH and
NS, albeit different than the nominal threshold of $3M_{\odot}$
adopted in GWTC-3, is consistent with our subsequent
classification, based both on EOS and merger rate. Ta-
ble II provides the rate estimates obtained for the three
models used in this section and, in addition, shows rates
for events in the mass gap, as discussed in detail in Sec-
tion IV C.

For most categories, our merger rate estimates are con-
sistent with previously published estimates. For exam-
ple, following GWTC-2 we inferred a binary black hole
merger rate to be $23.9_{-8.6}^{+14.9} \ Gpc^{-3}yr^{-1}$. Our knowl-
edge of the coarse-grained mass spectrum has not signif-
icantly evolved since our previous analysis, and we find
the inferred BBH rate is consistent with the previously
reported rate, which also omitted GW190814.

We previously reported a BNS merger rate of
$320_{-240}^{+490} \text{ Gpc}^{-3} \text{yr}^{-1}$ [21]. With data from GWTC-3, in
addition to inferring the BNS merger rate by fitting var-
ious population models, we also make an estimate by
fixing the mass, spin, and redshfit distributions under
simple assumptions. For this rate estimate, we assume
the masses of NSs in merging binaries are uniformly
distributed between $1M_{\odot}$ and $2.5M_{\odot}$ and the merger
rate is constant in comoving volume out to a redshift
of $z = 0.15$. We also model component spin magnitudes
distributed uniformly below 0.4, consistent with assump-
tions made in [3]. Under these assumptions, we infer a
BNS merger rate of $105.5_{-83.9}^{+190.2} \text{ Gpc}^{-3} \text{yr}^{-1}$.

For BNS, the inferred merger rate depends on the pre-
sumed mass distribution. With few observations to pin
down their behavior at low mass, the three approaches
adopted in this Section arrive at different compact bi-
nary mass distributions between $1M_{\odot}$ and $2.5M_{\odot}$. Be-
cause the merger rate in this region scales $\propto \langle VT \rangle^{-1}$ $\simeq$
$\langle M^{15/6} \rangle^{-1}$ (where VT denotes the sensitive 4-volume for
a specific binary and the angled brackets denote averag-

ing over objects less than $2.5M_{\odot}$, the upper boundary
used in this Section for NS masses), the three methods
used in this Section arrive at merger rates within each
others' uncertainty but with medians differing by factors
of up to approximately ten.

For NSBH we previously inferred a merger rate of
$45_{-33}^{+75} \text{Gpc}^{-3} \text{yr}^{-1}$ assuming the observed NSBH are repre-
sentative of the population or $130_{-69}^{+112} \text{Gpc}^{-3} \text{yr}^{-1}$ assum-
ing a broad NSBH population [10]. In this work, each
of our joint analyses recovers and adopts different mass
spectra, producing a broadly consistent rate (between 7.8
$Gpc^{-3}yr^{-1}$ and 140 $Gpc^{-3}yr^{-1}$, including sytematics).
Combined, our results for the NSBH and BNS merger
rates highlight the important role of modeling systemat-
ics when drawing inferences about populations with few
confident members.

To further highlight the impact of model systematics
on inferred merger rates, in Table II, we present our de-
duced merger rates across the mass space using all three
models presented in this section. For simplicity, we label
mass bins with NS and BH based solely on a boundary
at $2.5M_{\odot}$. We also provide a rate for events in the mass
gap between 2.5 and $5M_{\odot}$, in a binary with either NS
or BH. The bin intervals here are chosen for ease of use
to roughly capture features in the mass spectrum but do
not reflect our methods for event classification nor our
inference on features such as the maximum NS mass or
edges of any potential mass gaps.

The models used in this Section do not model the red-
shift evolution of the merger rate, and instead report a
constant in comoving volume merger rate density [i.e.
$\kappa = 0$ in Eq. (7)]. For most of the mass intervals con-
sidered, our surveys to date extend to only modest red-
shift, so rate evolution versus redshift can be safely ne-
glected. However, for high-mass binary black holes, our
network has cosmologically significant reach, over which
the merger rate may evolve. Furthermore, as discussed
in Sec. II, we observe structure in the mass distribution
for black hole binaries. Therefore, in Sec. VI we pro-
vide a more detailed description of BBH merger rates,
incorporating both redshift and mass dependence.

B. Identifying sub-populations of CBCs

As discussed in Sec. II, electromagnetic observations
had previously suggested a mass gap between black holes
and NSs. On the one hand, astrophysical EOS inferences
limit nonrotating NS masses to be below the Tolman–
Oppenheimer–Volkoff (TOV) mass, $M_{\text{max,TOV}} \sim 2.2$
$-2.5M_{\odot}$ [8, 9, 122–124], and studies of GW170817’s rem-
nant limit them to $\lesssim 2.3M_{\odot}$ [125–130]. On the other
hand, until recently [23, 37, 38] black holes had not been
observed below $\sim 5M_{\odot}$. The sparsity of observations be-
tween $\sim 2.5M_{\odot}$ and $\sim 5M_{\odot}$ suggested a potential lower
mass gap [28–31].

Figure 3 shows the two-dimensional merger rate versus
component masses for the three models used in this Sec-
<table><caption>TABLE II. Merger rates in Gpc⁻³ yr⁻¹ for the various mass bins, assuming merger rates per unit comoving volume are redshift-independent. BNS, NSBH and BBH regions are based solely upon component masses, with the split between NS and BH taken to be 2.5M☉. We also provide rates for binaries with one component in the purported mass gap between 2.5M☉ and 5M☉. For all but the last row, merger rates are quoted at the 90% credible interval. For the last row, we provide the union of 90% credible intervals for the preceding three rows, as our most conservative realistic estimate of the merger rate for each class accounting for model systematics. The PDB (pair) model is distinct from the other three models due to its use of a pairing function [111] and is therefore excluded from the union of credible intervals in the final row. In Sec. VI we estimate the merger rate for BBH alone, accounting for variation in merger rate versus redshift.</caption><thead><tr><th></th><th>BNS</th><th>NSBH</th><th>BBH</th><th>NS-Gap</th><th>BBH-gap</th><th>Full</th></tr><tr><th></th><th>m<sub>1</sub> ∈ [1, 2.5]M<sub>☉</sub></th><th>m<sub>1</sub> ∈ [2.5, 50]M<sub>☉</sub></th><th>m<sub>1</sub> ∈ [2.5, 100]M<sub>☉</sub></th><th>m<sub>1</sub> ∈ [2.5, 5]M<sub>☉</sub></th><th>m<sub>1</sub> ∈ [2.5, 100]M<sub>☉</sub></th><th>m<sub>1</sub> ∈ [1, 100]M<sub>☉</sub></th></tr><tr><th></th><th>m<sub>2</sub> ∈ [1, 2.5]M<sub>☉</sub></th><th>m<sub>2</sub> ∈ [1, 2.5]M<sub>☉</sub></th><th>m<sub>2</sub> ∈ [2.5, 100]M<sub>☉</sub></th><th>m<sub>2</sub> ∈ [1, 2.5]M<sub>☉</sub></th><th>m<sub>2</sub> ∈ [2.5, 5]M<sub>☉</sub></th><th>m<sub>2</sub> ∈ [1, 100]M<sub>☉</sub></th></tr></thead><tbody><tr><th>PDB (pair)</th><td>170<sup>+270</sup><sub>-120</sub></td><td>27<sup>+31</sup><sub>-17</sub></td><td>25<sup>+10</sup><sub>-7.0</sub></td><td>19<sup>+28</sup><sub>-13</sub></td><td>9.3<sup>+15.7</sup><sub>-7.2</sub></td><td>240<sup>+270</sup><sub>-140</sub></td></tr><tr><th>PDB (ind)</th><td>44<sup>+96</sup><sub>-34</sub></td><td>73<sup>+67</sup><sub>-37</sub></td><td>22<sup>+8.0</sup><sub>-6.0</sub></td><td>12<sup>+18</sup><sub>-9.0</sub></td><td>9.7<sup>+11.3</sup><sub>-7.0</sub></td><td>150<sup>+170</sup><sub>-71</sub></td></tr><tr><th>MS</th><td>660<sup>+1040</sup><sub>-530</sub></td><td>49<sup>+91</sup><sub>-38</sub></td><td>37<sup>+24</sup><sub>-13</sub></td><td>3.7<sup>+35.3</sup><sub>-3.4</sub></td><td>0.12<sup>+24.88</sup><sub>-0.12</sub></td><td>770<sup>+1030</sup><sub>-530</sub></td></tr><tr><th>BGP</th><td>98.0<sup>+260.0</sup><sub>-85.0</sub></td><td>32.0<sup>+62.0</sup><sub>-24.0</sub></td><td>33.0<sup>+16.0</sup><sub>-10.0</sub></td><td>1.7<sup>+30.0</sup><sub>-1.7</sub></td><td>5.2<sup>+12.0</sup><sub>-4.1</sub></td><td>180.0<sup>+270.0</sup><sub>-110.0</sub></td></tr><tr><th>MERGED</th><td>10 - 1700</td><td>7.8 - 140</td><td>16 - 61</td><td>0.02 - 39</td><td>9.4 × 10<sup>-5</sup> - 25</td><td>72 - 1800</td></tr></tbody></table>

tion, as well as the results of FM model applied to BBH. This representation emphasizes the importance of asymmetric binaries to the overall merger rate $dR/dm_1$ for masses between $1M☉$ and $10M☉$. The inferred merger rates further illustrate a falloff in event rate at masses above the BNS scale, with additional peaks associated with both unequal mass binaries consistent with NSBH systems as well as approximately equal mass BBH binaries. The rate of events with at least one component between 2.5–5M☉ (i.e. in the purported mass gap) is constrained to be lower than the rate of BNS-like events, but is consistent with the rate of BBH-like events. As further emphasis, Fig. 4 shows the merger rate versus mass for all binaries and also restricting to binaries with $q \simeq 1$ (e.g., the diagonal bins in the BGP model). The rate for approximately equal mass binaries is significantly lower. In other words, because asymmetric mergers like NSBH occur at a much higher rate than BBH but a much lower rate than BNS, in a joint analysis they significantly impact the marginal merger rate $dR/dm_1$ at the lowest masses.

This result highlights another feature: the compact binary population has (at least) three dominant populations: BNS-like systems; significantly asymmetric binaries with small $m_2$, comparable to the typical masses of NSs (i.e., including NSBHs as well as GW190814); and the main BBH population with $q$ preferentially more symmetric than 1/4 (i.e., including GW190412 but not GW190814).

For binaries containing lower mass gap-scale objects, our inferences about the merger rate and its dependence on mass are consistent despite considerable modeling uncertainty. For binaries containing objects between $2.5M☉$ and $5M☉$ and having massive BH-scale primaries ($> 5M☉$), the mass distribution and merger rate is informed by a few events (GW190814 in particular), thus subject to considerable uncertainty in the inferred component mass distributions. Likewise, for binaries con-

taining objects between $2.5M☉$ and $5M☉$ and having NS-scale companions, the merger rate is marginally informed by a few events that may not be associated with this region (i.e., GW200115), exacerbating uncertainty in the inferred NS and BH mass distributions. Providing multiple results for these two source classes explores our systematic uncertainty. The models presented in this section are subject to different sources of systematic uncertainty. For example, MS employs a Gaussian distribution to model components in BNSs, whereas PDB uses a single power law with a sharp turn on at low masses to model all objects below the inferred lower edge of the mass gap. These differences result in considerably different BNS rates due to the limited number of detections in the NS mass range. In particular, differences in pairing function shift the rate inference and add statistical uncertainty in the BNS region. MS and PDB (pair) all assume independent pairing of component masses; PDB (ind) models the pairing of component masses as a power law in mass ratio; and BGP uses a piecewise-constant gaussian process over both component masses. We can therefore directly compare PDB (ind) and PDB (pair) to understand the impact of assuming independent pairing. Independent pairing implies an equal number of equal mass and asymmetric mass mergers, while there have been relatively few unequal mass observations. Thus, a large fraction of PDB (ind)'s assumed population has gone undetected, resulting in low overall rate. On the other hand, PDB (pair) finds more support for equal mass binaries than asymmetric binaries and produces a higher rate.

### C. Characterizing suppressed merger rates between NS and BH Masses

Figures 3 and 4 show a reduction in the rate above NS masses. It was shown using GWTC-2 that the merger
<figure><img src="image_4.png" /><figcaption>FIG. 3. Rate density versus component masses for different models inferred from events with FAR < 0.25 yr⁻¹, illustrating consistency on large, coarse-grained scales, but some disagreement and systematics in areas with few observed events. *Top left panel:* Rate density computed with the FM model assuming no redshift evolution, for binary black holes only. Modulations along lines of constant chirp mass are apparent. *Top right panel:* Rate density inferred with the BGP model using all compact objects. This model can reproduce observations with localized regions of relatively enhanced rate density. In the binary black hole region, some regions of enhanced density are commensurate with the FM result. *Bottom left panel:* Rate density inferred with MS. For mergers involving NS, this model reproduces observations with broad distributions, consistent with smoothing the BGP result. For mergers involving typical BH, this model strongly favors equal-mass mergers. *Bottom right panel:* Rate density inferred with PDB. This model is also consistent with smoothing the FM result, producing features similar to MS, albeit with less structure in the mass ratio distribution for BBH, and by construction lacking a peak near 30*M*<sub>☉</sub>.</figcaption></figure>

rate between $3M_{\odot}$ and $7M_{\odot}$ is suppressed relative to an unbroken power-law extending from higher masses [11]. With additional observations, as well as models and sensitivity estimates that span the full mass range of CBCs, we can now produce a comprehensive perspective on merger rates versus mass throughout the low-mass interval 1–10$M_{\odot}$. In so doing, we find a dropoff in merger rates above NS-scale masses. As a result, in the detection-weighted population, objects with NS-scale mass components are well-separated from objects with BH-scale masses. However, we are unable to confidently infer an absence or presence of a subsequent rise in merger rates from lower mass gap masses. The pur-

ported lower mass gap [28–31] between the NS and black hole populations would produce such a rise, such that the mass gap produces an extended local minimum in the merger rate versus mass. We therefore neither find evidence for nor rule out the existence of a two-sided lower mass gap.

Figure 5 shows the differential rate as a function of component mass inferred from all three models. The PDB model infers the location of this drop-off to occur at $M_{\text{low}}^{\text{gap}} = 2.1_{-0.6}^{+0.8}M_{\odot}$, as shown by black vertical lines. While the other models do not explicitly infer the location of the drop-off, they do clearly show a reduction in the rate at a similar location. The prominence of this
<figure><img src="image_5.png" /></figure>

FIG. 4. Impact of asymmetric binaries on the primary mass distribution, illustrating how the depth and extent of a mass gap in any one-dimensional distribution depends on the choice of slicing or marginalization over the remaining dimension. Differential merger rate as a function of primary mass for the BGP model when considering only the diagonal $q \simeq 1$ bins in Fig. 3 i.e. $m_1 \frac{dN}{dm_1 \frac{dq}{dV_c} dt} \bigg|_{q \approx 1}$ and the population of compact binaries across all mass bins. The rate for approximately equal mass binaries is significantly lower highlighting the contribution of asymmetric mergers like NSBHs to the marginal distribution over primary mass. The plot uses the BGP population model inferred from events passing a FAR threshold of $< 0.25\text{yr}^{-1}$. Solid curves represent the median rate densities and shaded areas denote 90% credible regions.

<figure><img src="image_6.png" /></figure>

FIG. 5. Differential merger rate as a function of component mass for the PDB, MS, and BGP model. Three independent methods with different modeling assumptions agree on the merger rate versus mass, while illustrating the importance of modeling systematics on the overall rate for objects with NS-scale masses. Shaded areas denote 90% credible regions, while vertical black lines denote the median (solid) and 90% credible intervals (dashed) of the lower boundary of the mass gap, $M_{\text{low}}^{\text{gap}}$, in the PDB model rate dropoff location.

drop-off can be characterized by comparing the rate of mergers with both masses below $2.5M_{\odot}$ (BNS) to that of mergers with at least one component mass between 2.5 and $5M_{\odot}$ (in the mass gap). For this comparison, we find that the differential merger rate of systems with at least one component in the mass gap is one to two orders of magnitude lower than the BNS rate. Thus, even in the absence of any prior knowledge of the difference between NSs and BHs, the gravitational-wave data suggest two distinct populations of compact objects. This is consistent with results initially found for GWTC-1 by [108] and for GWTC-2 by [109].

A subsequent rise in the mass distribution above the putative mass gap is less clearly discernible. The PDB model explicitly parametrizes the mass gap with both low and high-mass transitions $M_{\text{low/high}}^{\text{gap}}$ and a gap depth $A$ (where $A=0$ corresponds to no gap and $A=1$ to a lower mass gap containing no events). While the posterior on $A$ peaks around 0.77, i.e. corresponding to a relatively empty mass gap, it has broad support between 0 and 1, indicating an inability to unambiguously differentiate between the presence or absence of a lower mass gap. Additionally, the Bayes factor for a model with no gap ($A=0$) or a completely empty gap ($A=1$), relative to the parametrized model, are 0.073 and 1.4, respectively. This lack of clear preference indicates an inability to resolve the absence or existence of a clear gap-like feature in this part of the mass spectrum.

A subsequent rise in the mass distribution at $M_{\text{high}}^{\text{gap}}$ is also less clear to discern. The models infer mass distributions with similar support for both a mildly pronounced gap and a flat transition above $M_{\text{high}}^{\text{gap}}$. Both of these are consistent with the finding in [11] of a deviation from a single power law below primary masses of $\sim 7M_{\odot}$.

We find that if a lower mass gap does exist, it may not be totally empty. While the merger rates show a fall-off above around $2.5M_{\odot}$ in Fig. 5, the rate does not fall to zero. Furthermore, the component masses of 6 events have at least 5% posterior support between $M_{\text{low}}^{\text{gap}}$ and $M_{\text{high}}^{\text{gap}}$ when using a population-informed prior [109]. GW190814 stands out as having considerable support for its secondary being within the mass gap or below the dropoff in the rate at $M_{\text{low}}^{\text{gap}}$: $P(m_{2,\text{GW190814}} \in [M_{\text{low}}^{\text{gap}}, M_{\text{high}}^{\text{gap}}]) = 0.76$. This event has a mass ratio $q = 0.112^{+0.008}_{-0.009}$ [23], hinting at either a potential subpopulation of low-$q$, low-$m_2$ BBHs, or a handful of NSBHs with high NS masses. The former possibility is examined in Sec. VIE, and the latter is discussed in Sec. VC. For both the NSBH systems, there is a $\sim 10\%$ probability of the secondary lying in the mass gap and, for GW200115 the primary has a 70% probability of $m_1 < M_{\text{high}}^{\text{gap}}$. Finally, GW190924-021846, which is the BBH event with the lowest total mass, we find roughly equal support for the secondary being either within ($m_2 < M_{\text{high}}^{\text{gap}}$) or above ($m_2 < M_{\text{high}}^{\text{gap}}$) the mass gap.

The inferred depth of the gap does depend heavily on the assumed pairing function: a model in which objects
are randomly paired with other objects regardless of mass
ratio predicts a more prominent gap than one with a
power-law-in-mass-ratio pairing function as in Eq. (11).
Similarly, a change of the pairing function will impact
the classification of various components as below, in or
above the mass gap. Consequently, we do not rely on
this methodology for event classification in Sec. V, and
instead use EOS-informed limits on the maximum al-
lowed NS mass, and perform leave-one-out analyses with
respect to known subpopulations. The lower mass gap-
related results stated here are obtained using a random
pairing model.

Though we report on our analysis with FAR<
0.25 yr⁻¹, to assess the stability of our results to thresh-
old choices we have repeated our analyses using all
events with previously reported parameter inferences be-
low 1 yr⁻¹ (i.e., excluding GW190531). Even though
such an analysis includes all five candidate NSBH, our
key conclusions remain largely unchanged: the derived
merger rates versus mass are consistent with the error
bars shown in Figs. 4, and 5, and the merger rates re-
ported in Table II are consistent. In particular, we draw
similar conclusions about the merger rate between 2M☉
and 10M☉: suppressed but likely filled, without evidence
for or against a true two-sided mass gap.

V. MASS DISTRIBUTION OF NEUTRON
STARS IN BINARIES

In this section, we characterize the astrophysical pop-
ulation of NSs using data from the gravitational wave
events that are likely to contain at least one NS. Be-
cause of the paucity of low-mass compact binary mergers
observed to date, and the difficulty in ascertaining the
presence of a NS in these systems, modeling the NS pop-
ulation observed in gravitational waves has been chal-
lenging. In our previous population analysis through
Gravitational Wave Transient Catalog 2 (GWTC-2) [11],
the rate density of BNS and NSBH mergers was esti-
mated, but the shape of the mass distribution of the
NSs in these compact binaries was not inferred. The
BNS events GW170817 and GW190425 were included in
a joint study of the Galactic and gravitational wave pop-
ulations of BNSs in [131], which linked the two observed
populations via a bimodal birth mass distribution. The
confident BNS and NSBH detections made to date were
analyzed in a study of the gravitational wave population
in [100], which found the observed NS masses to be con-
sistent with a uniform distribution.

We begin by classifying the observed low-mass com-
pact binaries as BNSs, NSBHs or BBHs. The classifi-
cations are based on a comparison of their component
masses with an EOS-informed estimate of the maximum
NS mass, and are corroborated against the location of
the lower mass gap between NSs and BHs as inferred in
the previous section. Then, adopting these source classi-
fications as definite and considering the BNS and NSBH

detections below a FAR threshold of 0.25 yr⁻¹, we infer
the shape of the NS mass distribution in compact bina-
ries. In contrast to Sec. IV, we do not attempt to deter-
mine the overall rate of such mergers, nor do we attempt
to infer the mass distribution of BHs in coalescing NSBH
systems. Our analysis makes a comparison with the ob-
served Galactic population of NSs, and we additionally
investigate the impact on the population of the event
GW190814, a lower mass-gap merger whose secondary
may possibly be a NS, but is more likely a low-mass BH.

A. Events containing NSs

The gravitational-wave signal of a compact binary
merger involving a NS differs from that of a BBH due to
matter effects in the waveform, most notably the phas-
ing of the gravitational waveform during the inspiral due
to the tidal deformation of the NS [132]. Since none of
the observations in O3b [1] yield an informative measure-
ment of tidal deformability, the gravitational-wave data
do not identify which sources contain a NS. Nonetheless,
we can establish whether their components are consistent
with NSs by comparing their masses to the maximum NS
mass, M<sub>max</sub>, following the method described in [7].

The precise value of M<sub>max</sub> is unknown because of un-
certainty in the NS EOS. Mass measurements for the
heaviest known pulsars [133, 134] set a lower bound of
~ 2 M<sub>☉</sub> on M<sub>max</sub>, while basic causality considerations
imply that M<sub>max</sub> ≲ 3 M<sub>☉</sub> [135, 136]. While individual
nuclear theory models for the EOS can produce maxi-
mum masses as large as ~ 3 M<sub>☉</sub>, astrophysical inferences
of the EOS generally predict that the maximum mass of
a nonrotating NS, the TOV mass M<sub>max,TOV</sub>, is between
2.2M<sub>☉</sub> and 2.5 M<sub>☉</sub> [9, 122–124, 137]. Similarly, studies of
GW170817’s merger remnant suggest that M<sub>max,TOV</sub> ≲
2.3 M<sub>☉</sub> [125–130]. Rapid rotation can sustain a max-
imum mass up to ~ 20% larger than M<sub>max,TOV</sub> [138].
However, the astrophysical processes that form compact
binaries may prevent the EOS-supported M<sub>max</sub> from be-
ing realized in the population.

We can therefore identify objects as NS candidates
based on their mass using estimates of M<sub>max</sub>, as long
as we assume a clean separation between the NS and
BH mass spectra. Of the events with FAR less than
0.25 yr<sup>-1</sup>, five have at least one component mass with
support below 3 M<sub>☉</sub>, making them potentially consis-
tent with a BNS or NSBH merger. These events are
listed in Table III, and their component mass posteriors
are compared to two estimates of M<sub>max</sub> in Fig. 6.

For each of these observed low-mass events, we calcu-
late in Table III the probability that at least one of the
component masses is less than the maximum NS mass,
marginalizing over statistical uncertainties and assuming
a uniform component mass prior. We adopt a threshold
probability of 50% for classification as a NS. Our fiducial
maximum NS mass estimate is taken to be M<sub>max,TOV</sub>
from the EOS inference of [9], which is based on pulsar
timing, gravitational wave and x-ray observations of NSs. That study finds $M_{max,TOV} = 2.21^{+0.31}_{-0.21} M_\odot$, and the corresponding posterior distribution is shown for comparison in Fig. 6. Four of the FAR < 0.25 yr⁻¹ events have $P(m < M_{max,TOV}) > 0.5$ for at least one component, and we deem them either BNSs (if $m_1 < M_{max,TOV}$) or NSBHs (if only $m_2 < M_{max,TOV}$). The fifth event, GW190814, has $P(m < M_{max,TOV}) = 0.06$ and is therefore classified as a BBH. These source classifications do not change if, instead of $M_{max,TOV}$, we compare against the rotating NS maximum mass, $M_{max}(\chi)$, as calculated from an empirical relation involving the TOV mass and the component spin $\chi$ [139]. This allows for the possibility that one or more of the low-mass components is rapidly rotating.

We draw similar conclusions about each event if we interpret the sharp decrease in merger rate near $2.5 M_\odot$ seen in the PDB analysis as the separation between NS and BH mass ranges. (This interpretation does not imply that $M_{max,TOV}$ and $M_{low}^{gap}$ need to agree: $M_{low}^{gap}$ could be below $M_{max,TOV}$ if the heaviest NSs the EOS can support are not realized in nature, or $M_{low}^{gap}$ could be above $M_{max,TOV}$ if the lower mass gap occurs within the BH mass spectrum.) Following [109], we compare the component mass measurements against the inferred $M_{low}^{gap}$ parameter from the PDB model, as shown in Fig. 6, and list the probabilities $P(m < M_{low}^{gap})$ in Table III. The same four events are consistent with BNSs or NSBHs.

Fig. 6 also plots the component mass posteriors for two FAR < 1 yr⁻¹ events from Table I that may contain NSs, if astrophysical in origin. In particular, GW190426 and GW190917 have masses consistent with NSBH systems [3, 4]. This classification is confirmed by the $P(m < M_{max,TOV})$ and $P(m < M_{low}^{gap})$ probabilities calculated for them in Table III.

## B. Mass distribution

Using the FAR < 0.25 yr⁻¹ events classified as BNSs or NSBHs in Table III, we infer the mass distribution of NSs in merging compact binaries. We adopt the POWER and PEAK parametric mass models described in Sec. III and implement a selection function based on a semi-analytic approximation of the integrated network sensitivity VT, fixing the redshift evolution of the population and ignoring spins when estimating the detection fraction. The population hyper-parameters are sampled from uniform prior distributions, subject to the condition $m_{min} \le \mu \le m_{max}$ in the PEAK model, except that we assume that the maximum mass in the NS population, $m_{max}$, does not exceed $M_{max,TOV}$. This is consistent with our use of the nonrotating maximum NS mass to classify the events, and amounts to an assumption that the NSs observed via inspiral gravitational waves are not rotationally supported. In practice, this means imposing a prior proportional to the cumulative distribution function of $M_{max,TOV}$, as shown in the inset of Fig. 7 and

<figure><img src="image_7.png" /></figure>

FIG. 6. Masses for events with at least one candidate neutron star. Upper panel: one-dimensional posterior distributions for the masses of the candidate NSs, as compared to estimates of the maximum NS mass based on the dense-matter EOS [9] ($M_{max,TOV}$) and on the inferred location of the lower mass gap in Sec. IV's PDB analysis ($M_{low}^{gap}$). Primary components are shown dash-dotted. GW190814's secondary component lies above both estimates of the maximum NS mass. Lower panel: two-dimensional 50% (shaded) and 90% (unshaded) credible regions for the binary masses of each candidate NS merger. The marginal events GW190426 and GW190917 are shown dotted. The 90% credible intervals of the maximum NS mass posterior inferred from the EOS and from the lower mass gap location are also plotted. GW190814 occupies a distinct region of the $m_1-m_2$ plane compared to the events deemed BNSs or NSBHs.

detailed in Appendix B 1.

The inferred mass distributions for these two models are plotted in Fig. 7. The posterior population distribution for the POWER model has $\alpha = -2.1^{+5.2}_{-6.9}$, consistent with a uniform mass distribution, although the median distribution is a decreasing function of mass. The power-law hyper-parameter is most strongly constrained relative to the flat $\alpha \in [-12, 4]$ prior on the low end. The two bumps in the 90% credible interval visible in Fig. 7 correspond respectively to the minimum and maximum mass cutoffs of the population model realizations with $\alpha < 0$ and $\alpha > 0$. The median inferred PEAK distribution is relatively flat, and the peak width and location are almost entirely unconstrained relative to the prior: $\sigma = 1.1^{+0.8}_{-0.8} M_\odot$ and $\mu = 1.5^{+0.4}_{-0.3} M_\odot$ for a uniform $\sigma \in [0.01, 2.00] M_\odot$ and $\mu \in [1, 3] M_\odot$ prior subject to $m_{min} \le \mu \le m_{max}$. Thus, the gravitational wave observations to date do not support a NS mass distribution with a pronounced single peak. This contrasts with
<table><caption>TABLE III. Classifications for low-mass events from Table I. The probability that a component is compatible with a NS is measured by the fraction of its mass posterior lying below an estimate [9] of the maximum nonrotating NS mass, $M_{max,TOV}$, marginalized over statistical uncertainties. We adopt a 50% threshold for classification as a NS, assuming a clean separation between NS and BH mass spectra. Probabilities are reported relative to a uniform prior on the component mass. They refer to the secondary component of all events except GW170817 and GW190425, in which case the secondary is securely below the maximum NS mass and the probability for the primary is given. The probabilities are similar and the classifications are unchanged when the component masses are compared to $M_{low}^{gap}$, the location of the lower mass gap between NSs and BHs inferred from Sec. IV's PDB analysis of the FAR < 0.25 yr$^{-1}$ events.</caption><thead><tr><th>Name</th><th>FAR<sub>min</sub> (yr<sup>-1</sup>)</th><th>P(m &lt; M<sub>max,TOV</sub>)</th><th>P(m &lt; M<sub>low</sub><sup>gap</sup>)</th><th>Classification</th></tr></thead><tbody><tr><td>GW170817</td><td>&lt; 1 &times; 10<sup>-5</sup></td><td>0.99</td><td>0.97</td><td>BNS</td></tr><tr><td>GW190425</td><td>3.38&times;10<sup>-02</sup></td><td>0.67</td><td>0.71</td><td>BNS</td></tr><tr><td>GW190814</td><td>&lt; 1 &times; 10<sup>-5</sup></td><td>0.06</td><td>0.24</td><td>BBH</td></tr><tr><td>GW200105</td><td>2.04&times;10<sup>-01</sup></td><td>0.94</td><td>0.73</td><td>NSBH</td></tr><tr><td>GW200115</td><td>&lt; 1 &times; 10<sup>-5</sup></td><td>0.93</td><td>0.96</td><td>NSBH</td></tr><tr><td>GW190426</td><td>9.12&times;10<sup>-01</sup></td><td>0.82</td><td>-</td><td>NSBH</td></tr><tr><td>GW190917</td><td>6.56&times;10<sup>-01</sup></td><td>0.56</td><td>-</td><td>NSBH</td></tr></tbody></table>

the Galactic BNS subpopulation, whose mass distribution is sharply peaked around $1.35 M_{\odot}$ [39, 40, 140], as shown for comparison in Fig. 7. The mass distribution of NSs observed in gravitational waves is broader and has greater support for high-mass NSs. This latter point is also true compared to the Galactic NS population as a whole, whose mass distribution has a double-peaked shape [141–143].

The minimum NS mass in the gravitational wave population is inferred to be $1.2_{-0.2}^{+0.1} M_{\odot}$ and $1.1_{-0.1}^{+0.2} M_{\odot}$ in the POWER and PEAK models, respectively. The lower bound on $m_{min}$ is a prior boundary motivated by the sensitivity model, as the gravitational-wave searches target sources above $1 M_{\odot}$. The maximum mass in the population is found to be $2.0_{-0.3}^{+0.3} M_{\odot}$ for the POWER model and $2.0_{-0.2}^{+0.2} M_{\odot}$ for the PEAK model, relative to the EOS-informed $m_{max}$ prior. These values are consistent with the maximum mass inferred from the Galactic NS population, $2.2_{-0.2}^{+0.8} M_{\odot}$ [142], as can be seen in the inset of Fig. 7. The maximum mass is the best-constrained hyper-parameter in the population models. Its upper bound is more tightly constrained than the Galactic $m_{max}$ in Fig. 7 as a result of the imposed $m_{max} \le M_{max,TOV}$ prior, which begins tapering above $2 M_{\odot}$, and the strong selection bias of gravitational-wave observations towards heavier masses, which renders the non-observation of heavier NSs informative. Nonetheless, the statistical uncertainty in $m_{max}$ remains large, and it is expected that approximately 50 BNS detections will be needed before the maximum mass in the NS population can be measured to within $0.1 M_{\odot}$ [144].

The $m_{max}$ value inferred from gravitational waves is also as large as $M_{max,TOV}$ within statistical uncertainties. This would not be the case if, for instance, the astrophysical processes that form coalescing compact binaries prevented $2 M_{\odot}$ NSs from pairing with other compact objects. Such a scenario is compatible with the EOS-informed $m_{max}$ prior that we impose. However, we find

there is no evidence that the NS mass spectrum observed with gravitational waves is limited by the astrophysical formation channel: NSs as heavy as can be supported by the EOS can end up in merging compact binaries.

Moreover, we infer a consistent maximum mass if we adopt a uniform $m_{max}$ prior instead of the EOS-informed one. This relaxes the assumption that the observed NS masses must be below the nonrotating maximum mass, and accounts for the possibility that rapid rotation may cause a NS's mass to exceed $M_{TOV}$. Specifically, we find $m_{max} = 2.1_{-0.4}^{+0.8} M_{\odot}$ in the POWER model and $2.0_{-0.2}^{+0.8} M_{\odot}$ in the PEAK model. The upper error bar on $m_{max}$ extends to much higher values in this case because it is no longer subject to the tapering EOS-informed prior, which has little support above $2.5 M_{\odot}$. We also obtain consistent results if we expand the event list to include the two marginal NSBH detections listed in Table III, as described in Appendix C2.

### C. Outlier events

The mass-based event classification carried out above deemed GW190814 to be a BBH merger on the basis of the maximum NS mass the EOS can support. We now further demonstrate that it is an outlier from the population of BNSs and NSBHs observed with gravitational waves.

If we dispense with its $M_{max,TOV}$-based classification, and include GW190814 as a NSBH in the population analysis, the inferred maximum mass is shifted up to $2.8_{-0.2}^{+0.2} M_{\odot}$ in the POWER model and $2.7_{-0.2}^{+0.3} M_{\odot}$ in the PEAK model (cf. $m_{max} = 2.1_{-0.4}^{+0.8} M_{\odot}$ in the POWER model and $m_{max} = 2.0_{-0.2}^{+0.8} M_{\odot}$ in the PEAK model without GW190814). These values are obtained relative to a uniform $m_{max}$ prior, since we are no longer consistently enforcing $m \le M_{max,TOV}$; all results in this subsection refer to this prior. The $m_{max}$ posterior has support up
<figure><img src="image_8.png" /></figure>

FIG. 7. Inferred neutron star mass distribution. The median mass distribution (solid) and 90% credible interval (shading) inferred for the POWER (respectively, PEAK) population model is shown in blue (orange), as compared to the mass distribution of NSs in Galactic BNSs [41] (dot-dashed black) and the mass distribution of all Galactic NSs [142] (solid black). The inferred gravitational-wave population has a greater prevalence of high-mass NSs. The inset shows the posterior distribution for the maximum mass in the NS population for both models, as compared to the Galactic $m_{max}$. The EOS-informed $m_{max}$ prior, which is proportional to the cumulative distribution function of $M_{max,TOV}$, is also shown in the inset (dashed). It enforces $m \le M_{max,TOV}$ using the maximum Tolman-Oppenheimer-Volkoff mass estimate from [9]. The maximum mass in the gravitational-wave population is as large as $M_{max,TOV}$ within statistical uncertainties.

to $3 M_{\odot}$, where the prior truncates and the models' fixed BH mass distribution begins. The inferred NS mass distributions with GW190814 are similar, but flatter and broader, than those depicted in Fig. 7.

To test whether GW190814 hails from the same population as GW170817, GW190425, GW200105 and GW200115, we examine the PEAK model's posterior predictive distribution for secondary masses with and without GW190814 in the event list. Figure 8 compares GW190814's measured $m_2 = 2.59_{-0.09}^{+0.08} M_{\odot}$ against the prediction for the largest observed secondary mass, $\max_5(m_2)$, after two BNS observations and three NSBH observations. That is, we draw two pairs of masses from the posterior predictive distribution for BNSs and three secondary masses from the posterior predictive distribution for NSBHs, take the largest of the five secondaries, and build up the plotted distributions by performing this procedure repeatedly. The probability of observing a secondary mass at least as large as the mean of GW190814's

$m_2$ in the population is only 0.2% according to the PEAK model fit that excludes GW190814. (We characterize GW190814's $m_2$ by its mean, since it is measured so precisely.) The equivalent probability relative to the PEAK model fit that includes GW190814 is 3.3%; we expect a rigorous, fully self-consistent calculation of a p-value to lie between these two numbers [145]. Hence, GW190814's secondary component is an outlier from the secondaries in BNS and NSBH systems. In the next section, we also establish GW190814 as an outlier from the BBH population observed in gravitational waves, corroborating our previous analysis [11]. These findings reinforce that it represents a distinct subpopulation of merging compact binaries.

<figure><img src="image_9.png" /></figure>

FIG. 8. Comparison between GW190814's secondary component and the largest secondary mass in the observed BNS and NSBH population. The PEAK model is fit to the population including (respectively, excluding) GW190814. The predicted distribution of the largest secondary mass, $\max_5(m_2)$, observed after five detections—two BNSs and three NSBHs—is shown in orange (blue). The shaded region represents the 90% credible interval of the posterior distribution for the mass of GW190814's secondary component. GW190814's $m_2$ is a 0.2%-level outlier from the rest of the observed population of NS secondaries.

## VI. MASS DISTRIBUTION OF BLACK HOLES IN BINARIES

We find two key new conclusions about the black hole mass distribution using the GWTC-3 dataset to infer a population: that the mass distribution has a structure, reflected in clustering of detected events, and that observations are consistent with a continuous, monoton-
ically decreasing mass distribution at masses > 50$M_{\odot}$, providing inconclusive evidence for an upper mass gap. Adopting previous coarse-grained models, we find conclusions consistent with our analysis of GWTC-2 [25]. For the purposes of this section, given our large BBH sample, we adopt a FAR threshold of 1 yr$^{-1}$, but we do not include the previously identified outliers GW190917 (a NSBH) and GW190814 (an extreme mass ratio binary) in the BBH population unless otherwise noted. Additionally, unlike the redshift-independent results described in Sec. IV, the new analyses described in this section all account for a redshift-dependent BBH merger rate accounting to Eq. (7). Specifically, in this Section we present results for the PP model to broadly characterize the mass spectrum and corroborate results found in GWTC-2, as well as the cubic spline power law perturbation PS model and the binned Gaussian process BGP, as both can capture smaller-scale features in the mass distribution. All three models are described in detail in Section III C. We report on the same BGP analysis as performed in Sec. IV, with FAR < 0.25 yr$^{-1}$ and without allowing for redshift dependence; by contrast, the PS, PP, and FM models allow for redshift dependence and use FAR < 1 yr$^{-1}$. Table IV summarizes our results for the overall BBH merger rate, as well as merger rates over restricted mass intervals.

## A. Broad features of the mass spectrum

The events from GWTC-3 are broadly consistent with the previously identified population [11]. Figure 9 compares some of the expectations from our previous analysis of GWTC-2 BBHs with the comprehensive sample of GWTC-3 BBH events. The panels compare the observed and expected fractions of all events detected below a threshold in primary mass $m_1$, effective inspiral spin $\chi_{\text{eff}}$, or source redshift. The panels also show the Wilson score interval [146], a frequentist estimate of the uncertainty in the cumulative distribution $F$, which is approximately $\pm 1.68\sqrt{F(1-F)/N_{\text{obs}}}$ when $F$ is significantly different from 0 or 1.

All the cumulative distributions in Figure 9 are broadly consistent with our prior expectations based on coarse-grained models used in our previous work. For this reason, we begin by presenting the inferred coarse-grained mass distribution of black hole binaries, making use of the PP model [11] which best fitted the population from GWTC-2.

Figure 10 shows our inference on the astrophysical primary mass (left) and mass ratio (right) distributions, using the fiducial mass model, compared to what was previously found in GWTC-2 (black). We find a power-law slope for the primary mass, $\alpha = 3.5_{-0.56}^{+0.6}$, supplemented by a Gaussian peak at $34_{-4.0}^{+2.6}M_{\odot}$. On the upper end, the mass of the 99th percentile, $m_{99\%}$, is found to be $44_{-5.1}^{+9.2}M_{\odot}$. The mass ratio distribution is modelled as a power law $q^{\beta_q}$ with $\beta_q = 1.1_{-1.3}^{+1.7}$

In contrast to our GWTC-2 population fit, the inferred mass spectrum decays more rapidly; the $m_{99\%}$ is considerably lower than $60_{-13}^{+14}M_{\odot}$, as was found with GWTC-2. These results are expected, given that the new observations in GWTC-3 contain a greater fraction of lower mass systems (see, e.g., Fig. 1). The fraction of BBH mergers with primary masses within the Gaussian component of the fiducial model is found to be $\lambda = 0.038_{-0.026}^{+0.058}$ ($0.1_{-0.071}^{+0.14}$ in GWTC-2), but still rules out zero. This result further highlights that the fraction of higher mass binaries has decreased in GWTC-3. Both the mean and the standard deviation of the Gaussian component are consistent with previous inferences. Furthermore, the inferred mass ratio distribution is less peaked towards equal mass binaries ($\beta_q = 1.1_{-1.3}^{+1.7}$) compared to GWTC-2 ($\beta_q = 1.3_{-1.5}^{+2.4}$), a result driven by the discovery of binaries with support for substantially unequal masses (see, e.g., Fig. 9).

We previously used several other phenomenological models to interpret sources in GWTC-2. Using this broader suite of models, we draw similar conclusions to those presented above: the mass distribution is inconsistent with the single power law and has a feature at $\sim 35-40 M_{\odot}$. The peak’s location is also well-separated from the largest black holes predicted by the other component: the over-density and maximum mass are still not associated. The odd ratios discriminating between these models are modest, of order one in three to one in ten. Despite for presentation purposes adopting the PP for illustrating consistency with GWTC-2 results, we cannot decisively differentiate between a peak near $35M_{\odot}$ versus a more generic transition towards a lower merger rate at higher mass; see Appendix D1 for details.

In Table IV, we provide BBH merger rates for the full population, as well as split based upon the primary mass at $m_1 < 20M_{\odot}$, $m_1 \in [20, 50]M_{\odot}$ and $m_1 > 50M_{\odot}$ to capture the broad features of the mass spectrum: the high rate at low masses, a peak around $35-45M_{\odot}$ and the falling merger rate at high masses.

## B. Mass distribution has substructure

With new discoveries in O3, we are now confident the mass distribution has substructure, with localized peaks in the component mass distribution. For example, we find overdensities in the merger rate (> 100.0% credibility) as a function of primary mass, when compared to a power law, at $m_1 = 10_{-0.59}^{+0.29}M_{\odot}$ and $m_1 = 35_{-2.9}^{+1.7}M_{\odot}$. At best, we have modest confidence (less than 10:1 odds) in additional structure. These signs of substructure were identified in O3a [47] and are corroborated by consistent observations in O3b.

We arrive at these conclusions through multiple independent analyses. Each of these model agnostic approaches attempts to reconstruct the mass distributions with minimal constraints imposed. Specifically, we employ a flexible mixture model (introduced in Section III C
<figure><img src="image_10.png" /><figcaption>FIG. 9. The empirical cumulative density function $\hat{F} = \sum_k P_k(x)/N$ of observed binary parameter distributions (derived from the single-event cumulative distributions $P_k(x)$ for each parameter $x$) are shown in blue for primary mass (left), effective inspiral spin (center), and redshift (right). All binaries used in this study with FAR< 1/4yr are included, and each is analyzed using our fiducial noninformative prior. For comparison, the gray bands show the expected observed distributions, based on our previous analysis of GWTC-2 BBH. Solid lines show the medians, while the shading indicates a 90% credible interval on the empirical cumulative estimate and selection-weighted reconstructed population, respectively. GW190814 is excluded from this analysis.</figcaption></figure>

<figure><img src="image_11.png" /><figcaption>FIG. 10. The astrophysical BBH primary mass (left) and mass ratio (right) distributions for the fiducial PP model, showing the differential merger rate as a function of primary mass or mass ratio. The solid blue curve shows the posterior population distribution (PPD) with the shaded region showing the 90% credible interval. The black solid and dashed lines show the PPD and 90% credible interval from analyzing GWTC-2 as reported in [11]. The vertical gray band in the primary mass plot shows 90% credible intervals on the location of the mean of the Gaussian peak for the fiducial model.</figcaption></figure>

<table><caption>TABLE IV. Merger rates in Gpc$^{-3}$ yr$^{-1}$ for BBH binaries, quoted at the 90% credible interval, for the PP model and for three non-parametric models (BINNED GAUSSIAN PROCESS, FLEXIBLE MIXTURES, POWER LAW + SPLINE). Rates are given for three ranges of primary mass, $m_1$ as well as for the entire BBH population. Despite differences in methods, the results are consistent among the models. BGP assumes a non-evolving merger rate in redshift. The merger rate for PP, FM, and PS is quoted at a redshift value of 0.2, the value where the relative error in merger rate is smallest.</caption><thead><tr><th></th><th>m<sub>1</sub> &isin; [5, 20]M<sub>&odot;</sub></th><th>m<sub>1</sub> &isin; [20, 50]M<sub>&odot;</sub></th><th>m<sub>1</sub> &isin; [50, 100]M<sub>&odot;</sub></th><th>All BBH</th></tr><tr><th></th><th>m<sub>2</sub> &isin; [5, 20]M<sub>&odot;</sub></th><th>m<sub>2</sub> &isin; [5, 50]M<sub>&odot;</sub></th><th>m<sub>2</sub> &isin; [5, 100]M<sub>&odot;</sub></th><th></th></tr></thead><tbody><tr><th>PP</th><td>23.6<sup>+13.7</sup><sub>-9.0</sub></td><td>4.5<sup>+1.7</sup><sub>-1.3</sub></td><td>0.2<sup>+0.1</sup><sub>-0.1</sub></td><td>28.3<sup>+13.9</sup><sub>-9.1</sub></td></tr><tr><th>BGP</th><td>20.0<sup>+11.0</sup><sub>-8.0</sub></td><td>6.3<sup>+3.0</sup><sub>-2.2</sub></td><td>0.75<sup>+1.1</sup><sub>-0.46</sub></td><td>33.0<sup>+16.0</sup><sub>-10.0</sub></td></tr><tr><th>FM</th><td>21.1<sup>+11.6</sup><sub>-7.8</sub></td><td>4.3<sup>+2.0</sup><sub>-1.4</sub></td><td>0.2<sup>+0.2</sup><sub>-0.1</sub></td><td>26.5<sup>+11.7</sup><sub>-8.6</sub></td></tr><tr><th>PS</th><td>27<sup>+12</sup><sub>-8.8</sub></td><td>3.5<sup>+1.5</sup><sub>-1.1</sub></td><td>0.19<sup>+0.16</sup><sub>-0.09</sub></td><td>31<sup>+13</sup><sub>-9.2</sub></td></tr><tr><th>MERGED</th><td>13.3 &ndash; 39</td><td>2.5 &ndash; 6.3</td><td>0.099 &ndash; 0.4</td><td>17.9 &ndash; 44</td></tr></tbody></table>
and labelled FM in tables and figures), a cubic spline power law perturbation (PS), and a binned Gaussian process (BGP). Figure 11 shows the inferred rate $d\mathcal{R}/dm_1$ as a function of primary mass for each of the non-parametric models. There is a clear presence of structure beyond an unbroken single power law found when using these more flexible models, with a global maximum of the merger rate at larger masses at around $10M_\odot$ followed by a fall off to lower rates. Modulating this extended decline, the PS, FM and even BGP show indications of additional structure. As the BGP likely cannot resolve small-scale features, we assess these features' details and significance with the remaining two models.

Figure 12 shows the results of the spline perturbation model, where 1000 posterior draws of the spline function $f(m_1)$ are illustrated, where $\exp f(m_1)$ modulates an underlying power-law distribution. The inferred perturbation $f(m_1)$ strongly disfavors zero at both the $10M_\odot$ and $35M_\odot$ peak, finding $f \le 0$ at 0.216%, and < 0.0325% credibilities respectively. Additionally for the drop in merger rate at $14M_\odot$, the PS model finds $f \le 0$ at 96.1% credibility.

### C. Inconclusive evidence for upper mass gap

Stellar evolution models predict a lack of black holes with masses from $50_{-10}^{+20}M_\odot$ to $\sim 120M_\odot$ due to pair production instability [147–153]. The high-mass event GW190521 could have a component lying within this mass gap [22, 154]. Other analyses of this event with independent parameter inferences have argued this event could have both components outside this gap [155–157]. We define a gap as a rapid decline in merger rate at some cutoff mass, followed by a rapid rise in the distribution at a significantly higher mass. Repeating similar analyses with the full O3 data set, we find no evidence for such a gap. Following [155], we extend our PP mass model to allow for masses > 100 $M_\odot$, and to include a zero-rate mass interval, parameterized with the lower edge and width of the gap. With this extended model, we find minimal posterior support for the gap to start at < 75 $M_\odot$ (3.1% credibility). When it does, the gap width is constrained to be < 35 $M_\odot$. The majority of the posterior support has the gap start above 75 $M_\odot$, consistent with the inferred maximum mass cutoff from the PP model without a gap. This allows both component masses of the most massive BBH in the catalog, GW190521, to fall below the cutoff, leaving no observations with masses larger than the start of the gap. We are not able to determine whether or not the mass distribution exhibits a rise again at higher masses. We find a slight preference ($\ln B = 0.06$) for the PP model without a gap over one with the gap included, thus we report inconclusive evidence for a zero-rate upper mass gap. Inconclusive support for a zero-rate gap challenges classical conclusions for the pair-instability mass gap. The pair-instability mass gap could start higher than theory expects, or the high-mass binaries in our catalog could

be formed in a way that avoids pair-instability.

### D. Evolution of rate with redshift

The observation of BBH mergers offers us the means of not only measuring the local merger rate per comoving volume but also the *evolution* of this merger rate as we look back towards larger redshifts $z$. Given the limited range of redshift to which our searches are sensitive, we parametrize the merger rate per comoving volume as a simple power law, with $\mathcal{R}(z) \propto (1+z)^\kappa$ [96].

In our previous study [11], the redshift distribution was weakly constrained, exhibiting a preference for a rate that increased with redshift but still consistent with a non-evolving merger rate. Here, in addition to new events observed in O3b, we leverage updated pipelines and our improved sensitivity models to update our inference of $\kappa$. As discussed further in Appendix C 5, these sensitivity model refinements indicate a lower search sensitivity to high-redshift BBH mergers than previously concluded. We now confidently claim to see evolution of the BBH merger rate with redshift in our population with a FAR < 1 $\text{yr}^{-1}$, inferring that $\kappa > 0$ at 99.6% credibility. While the exact distribution of $\kappa$ does depend on the chosen mass model, we can rule out a redshift-independent merger rate at similar credible levels when adopting any of the parameterized mass distribution models used in [11].

Figure 13 shows the marginal posterior on $\kappa$ given GWTC-3 in blue, obtained while using the PP and DE-Fault mass and spin models. The dashed distribution, meanwhile, shows the previously published measurement of $\kappa$ obtained with GWTC-2. In Fig. 13 we also show our corresponding constraints on $\mathcal{R}(z)$ itself as a function of redshift. The dark blue line traces our median estimate on $\mathcal{R}(z)$ at each redshift, while the dark and light shaded regions show central 90% and 50% credible bounds. Our best measurement of the BBH merger rate occurs at $z \approx 0.2$, at which $\mathcal{R}(z = 0.2) = 19-42 \text{ Gpc}^{-3} \text{yr}^{-1}$. For comparison, the dashed black line in Fig. 13 is proportional to the Madau–Dickinson star formation rate model [158], whose evolution at low redshift corresponds to $\kappa_{SFR} = 2.7$. While the rate evolution remains consistent with the Madau–Dickinson star formation rate model, it is not expected for these two rates to agree completely due to the time delays from star formation to merger [159–167].

In most plausible formation scenarios (e.g., if BBHs arise from stellar progenitors), we do not expect $\mathcal{R}(z)$ to continue growing with arbitrarily high $z$. Instead, we anticipate that $\mathcal{R}(z)$ will reach a maximum beyond which it turns over and falls to zero. Even in cases where the peak redshift $z_p$ at which $\mathcal{R}(z)$ is maximized lies beyond the LIGO–Virgo detection horizon, a sufficiently tight upper limit on the stochastic gravitational-wave background due to distant compact binary mergers [168–170] can be leveraged to bound $z_p$ from above, potentially yielding a
<figure><img src="image_12.png" /></figure>

FIG. 11. The differential merger rate for the primary mass predicted using three non-parametric models compared to the fiducial PP model. Solid curves are the medians and the colored bands are the 90% credible intervals. These models offer increased flexibility compared to phenomenological models in predicting the population. The PS applies a perturbation to the primary mass in a modified version of our fiducial PP model that does not include the Gaussian peak. FM models the chirp mass, mass ratio, and aligned spin distribution as a weighted sum of mixture components. Both of these models incorporate a single parameter redshift evolution of the merger rate [Eq. (7)]. The BGP models the two-dimensional mass distribution as a binned Gaussian Process which is piecewise constant in $log m_i$, illustrating the same analysis as presented in Sec. IV with FAR < 0.25 yr$^{-1}$. All three models infer a local maximum in the merger rate at around $10M_\odot$ and $35M_\odot$.

<figure><img src="image_13.png" /></figure>

FIG. 12. The cubic spline function, $f(m_1)$, describing the perturbations to an underlying power law inferred with the PS model. The thin grey lines show 1000 draws from the posterior while the black lines show the knot locations (vertical) and the 90% credible region of the posterior. The dashed blue lines mark the 90% credible bounds of the Gaussian priors (centered on zero) imposed on each knot's height. The shaded region covers any masses less than the 95th percentile of the marginal posterior distribution on $m_{min}$. Because the low mass region of the mass distribution is cut off and there are no observations there, the posterior in this region resembles the prior of the cubic spline function.

joint measurement of $\kappa$ and $z_p$ [171]. As demonstrated in [172], our current instruments are not yet sensitive enough to enable a meaningful joint constraint on $\kappa$ and $z_p$, even with the inclusion of new events in GWTC-3.

As heavy BBHs are primarily believed to arise from low-metallicity stellar progenitors [173–175], one might wonder if more massive BBHs are observed at systemat-

ically higher redshifts than less massive systems. Moreover, any metallicity dependence in the physics of stars, such as the maximum black hole mass imposed by pair instability supernovae (PISN) [148, 152, 176], could yield redshift-dependent features in the black hole mass distribution [177, 178]. Such a redshift dependence would confound efforts to leverage the PISN mass gap as a probe of cosmology. Previous investigations [179] demonstrated using GWTC-2 that redshift dependence of the maximum BBH mass would be required to fit the observations if the BBH mass distribution has a sharp upper cutoff. However, if the distribution decays smoothly at high masses, for example as a power-law, the data are consistent with no redshift dependence of the cutoff location.

We revisit this question using the latest BBH detections among GWTC-3, finding that these conclusions remain unchanged. Specifically, by modelling the high-mass tail of the distribution with a separate power-law index, we find no evidence that the distribution is redshift dependent, suggesting that the high-mass structure in the BBH mass distribution remains consistent across redshift.

E. Outliers in the BBH Population

While we inferred the population of most BBH and binaries involving NS, some systems (particularly with significantly asymmetric masses) lie at the boundary between these categories [23, 145]. So far, we have simply excluded these events from our BBH analysis. To demonstrate this choice is internally self-consistent and
<figure><img src="image_14.png" /><figcaption>FIG. 13. Constraints on the evolution of the BBH merger rate with redshift. Top: Posterior on the power-law index $\kappa$ governing the BBH rate evolution, which is presumed to take the form $R(z) \propto (1+z)^{\kappa}$. The blue histogram shows our latest constraints using GWTC-3 ($\kappa = 2.9_{-1.8}^{+1.7}$), while the dashed distribution shows our previous constraints under GWTC-2. Bottom: Central 50% (dark blue) and 90% (light blue) credible bounds on the BBH merger rate $R(z)$. The dashed line, for reference, is proportional to the rate of cosmic star formation [158]; we infer that $R(z)$ remains consistent with evolution tracing star formation.</figcaption></figure>

well-motivated, we show that these events are outliers from our recovered BBH population. Specifically, we repeat the population analysis using the PP model, highlighting the extent to which the population changes when including these events.

For a population consisting of all potential BBH events in O3, including GW190917 and GW190814, the mass distribution must extend to lower masses. In Fig. 14 we plot the recovered distribution for the minimum BH mass, $m_{\min}$, that characterizes the primary mass scale above which black holes follow the parameterized power law distribution. The minimum mass is $m_{\min} = 2.3_{-0.23}^{+0.27} M_{\odot}$, with an extremely sharp turn-on of $\delta_m = 0.39_{-0.36}^{+1.3} M_{\odot}$. By contrast, if we remove the two low-mass events, we find a minimum BH mass of

<figure><img src="image_15.png" /><figcaption>FIG. 14. The posterior distribution on the minimum mass truncation hyper-parameter, $m_{\min}$, inferred with the PP model. The posteriors are shown both including and excluding the two BBH mergers containing low mass secondaries, GW190814 and GW190917. The cutoff at $m_{\min} = 2 M_{\odot}$ corresponds to the lower bound of the prior distribution. The inclusion of either of these two events significantly impacts the distribution. The shaded regions indicate the 90% credible interval on the $m_2$ posterior distribution for the two outlier events, GW190814 (purple) and GW190917 (grey).</figcaption></figure>

$m_{\min} = 5.0_{-1.7}^{+0.86} M_{\odot}$, which is consistent with a mass gap, and a broader turn-on of $\delta_m = 4.9_{-3.2}^{+3.4} M_{\odot}$. It is the secondary masses, $m_2$ of these events that are in tension with the remainder of the population, as demonstrated in Fig. 14 where the secondary masses are shown by the shaded regions. A single minimum mass is imposed upon all BH, therefore the secondary masses of low-mass or asymmetric binaries have the strongest impact on our inference of $m_{\min}$.

These analyses imply two key results about the compact binary population. First, the binary black hole population excluding highly asymmetric systems such as GW190814 is well-defined, and the analyses carried out in this section are well-suited to characterizing the bulk of the BBH population. Second, the existence of GW190814 implies the existence of a subpopulation of highly asymmetric binaries, disconnected from the BBH population but potentially connected to the recently-identified population of NSBH.

## VII. SPIN DISTRIBUTION OF BLACK HOLES IN BINARIES

Compared to our previous work [11], we find two key new conclusions for black hole spins: that the spin distribution broadens above $30M_{\odot}$, and that the mass ratio and spin are correlated. Adopting previous coarse-grained models, we find consistent conclusions as our analysis of GWTC-2; notably, we still conclude that a fraction of events probably have negative $\chi_{\text{eff}}$.

The component spins of binary black holes may offer vital clues as to the evolutionary pathways that produce merging BBHs [180–187]. The magnitudes of
BBH spins are expected to be influenced by the nature of angular momentum transport in stellar progenitors [173, 188, 189], processes like tides [181, 190, 191] and mass transfer that operate in binaries, and the environment in which the binary itself is formed. Their directions, meanwhile, may tell us about the physical processes by which binaries are most often constructed; we expect BBHs born from isolated stellar evolution to possess spins preferentially aligned with their orbital angular momenta, while binaries that are dynamically assembled in dense environments are predicted to exhibit isotropically oriented spins [183, 185].

Figure 15 illustrates our constraints on the component spin magnitudes (left) and spin tilts (right) of BBHs under the DEFAULT spin model. Using GWTC-3, we make similar conclusions regarding the spin magnitude distribution as made previously with GWTC-2. In particular, spin magnitudes appear concentrated below $\chi_i \lesssim 0.4$, with a possible tail extending towards large or maximal values. Our understanding of the spin tilt distribution, in contrast, has evolved with the addition of new BBHs in GWTC-3. As in GWTC-2, we again exclude the case of perfect spin-orbit alignment (corresponding to $\zeta = 1$ and $\sigma_t = 0$). With GWTC-3, however, we more strongly favor a broad or isotropic distribution of spin tilts. This shift is seen in the right-hand side of Fig. 15: whereas the $\cos\theta$ distribution inferred from GWTC-2 was consistent with tilts concentrated preferentially around $\cos\theta = 1$, evidence for this concentration is now diminished, with O3b results preferring a flatter distribution across $\cos\theta$.

Figure 16 illustrates our updated constraints on the $\chi_{\text{eff}}$ and $\chi_p$ distributions under the GAUSSIAN spin model. As above, our previous results obtained with GWTC-2 are shown in blue, while black curves show our updated measurements with O3b. Measurement of the $\chi_{\text{eff}}$ distribution with GWTC-2 suggested an effective inspiral spin distribution of non-vanishing width centered at $\chi_{\text{eff}} \approx 0.05$, while the $\chi_p$ distribution appeared incompatible with a narrow distribution at $\chi_p = 0$, bolstering the conclusion above that the BBH population exhibits a range of non-vanishing spin-tilt misalignment angles. These conclusions are further strengthened when updating our analysis with GWTC-3. We again infer a $\chi_{\text{eff}}$ distribution compatible with small but non-vanishing spins, with a mean centered at $0.06_{-0.05}^{+0.04}$. Our updated constraints on the effective precessing spin distribution reaffirm the need for non-vanishing $\chi_p$ among the BBH population. The $\chi_p$ measurements made previously with GWTC-2 were consistent with both a broad underlying distribution or a very narrow distribution centered around $\chi_p \approx 0.3$; this latter possibility is the source of the apparent jaggedness seen in the GWTC-2 result. We draw similar conclusions with GWTC-3, finding that $\chi_p$ measurements can be explained either by a broad distribution centered at $\chi_p = 0$, or a narrow distribution centered at $\chi_p \approx 0.2$. If we include GW190814 in our sample (which is otherwise excluded by default from our BBH analyses) support for this second mode is diminished,

leaving a zero-centered $\chi_p$ distribution with standard deviation $0.16_{-0.08}^{+0.15}$.

In addition to the distributions of effective inspiral spins and component spins $\chi_1$ and $\chi_2$ associated with the more and less massive components of BBHs, respectively, we also explore the distributions of the more and less rapidly spinning components among the BBH population [192]. For a given binary, we define $\chi_A = \max_{|\chi|} (\chi_1, \chi_2)$ and $\chi_B = \min_{|\chi|} (\chi_1, \chi_2)$ as the component spins with the larger and smaller magnitudes, respectively. As discussed in Sec. IX, some models for stellar evolution and explosion predict that isolated black holes are born effectively non-rotating and that binary black hole systems primarily acquire spin through tidal spin-up of the secondary component by the first-born (non-spinning) black hole. If this is the case, then we expect to observe a non-vanishing distribution of $\chi_A$ but a distribution of $\chi_B$ concentrated at or near zero. Figure 17 shows the resulting distributions of these spin-sorted magnitudes $\chi_A$ (blue) and $\chi_B$ (green), as implied by the DEFAULT model constraints on component spin magnitudes and tilt angles. Light and dark shaded regions show 50% and 90% credible bounds on each parameter, while the dark lines trace the expectation value of $p(\chi)$ as a function of spin-sorted $\chi$. The $\chi_A$ distribution, by definition, is concentrated at larger values than the peak seen in Fig. 15 (at $\chi \approx 0.2$). Across the BBH population, these more rapidly spinning components exhibit a distribution that likely peaks near $\chi_A \approx 0.4$, with 1st and 99th percentiles at $0.07_{-0.03}^{+0.05}$ and $0.8_{-0.08}^{+0.08}$, respectively. Less rapidly spinning components, meanwhile, are centered at or below $\chi_B \lesssim 0.2$, with 99% of values occurring below $0.54_{-0.08}^{+0.09}$.

One significant question explored in our previous study [11] was the degree to which BBHs exhibit extreme spin-orbit misalignment, with tilt angles exceeding $\theta \ge 90^\circ$ and thus negative effective inspiral spins. Such steeply tilted spins are unlikely for BBH formation from isolated stellar progenitors [193], and hence would serve as a strong indicator of dynamical interaction during BBH evolution. Our GWTC-2 study [11] interpreted the results of the DEFAULT and GAUSSIAN spin analyses as indicating the presence of extremely misaligned spins. As seen in Fig. 15, the component spin-tilt distribution is non-vanishing below $\cos\theta = 0$. Similarly, in Fig. 16 the $\chi_{\text{eff}}$ distribution has significant support at $\chi_{\text{eff}} < 0$. To check whether this requirement for negative $\chi_{\text{eff}}$ was a true feature of the data or an extrapolation of the Gaussian population model (which assumes the existence of extended tails), we extended the Gaussian model to truncate the effective inspiral spin on the range $\chi_{\text{eff,min}} \le \chi_{\text{eff}} \le 1$ (rather than $-1 \le \chi_{\text{eff}} \le 1$) and hierarchically measured the lower truncation bound $\chi_{\text{eff,min}}$. We found $\chi_{\text{eff,min}} < 0$ at 99.1% credibility, concluding that the data required the presence of negative effective inspiral spins. We obtain consistent results if we perform an identical check with GWTC-3; Fig. 18 illustrates our updated posterior on $\chi_{\text{eff,min}}$, now inferred to be negative