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A gravitational-wave standard siren measurement of the Hubble constant

2 n o v e m b e r 2017 | v o L 551 | n A T U r e | 85

LeTTer

doi:10.1038/nature24471

A gravitational-wave standard siren measurement of the Hubble constant

The LIGo Scientific Collaboration and The virgo Collaboration *, The 1m2H Collaboration *, The Dark energy Camera GW-em Collaboration and the DeS Collaboration *, The DLT40 Collaboration *, The Las Cumbres observatory Collaboration *, The vInroUGe Collaboration * & The mASTer Collaboration *

*Lists of authors and their affiliations appear in the online version of the paper.

On 17 August 2017, the Advanced LIGO 1 and Virgo 2 detectors observed the gravitational-wave event GW170817—a strong signal from the merger of a binary neutron-star system 3. Less than two seconds after the merger, a γ-ray burst (GRB 170817A) was detected within a region of the sky consistent with the LIGO–Virgo-derived location of the gravitational-wave source 4–6. This sky region was subsequently observed by optical astronomy facilities 7, resulting in the identification 8–13 of an optical transient signal within about ten arcseconds of the galaxy NGC 4993. This detection of GW170817 in both gravitational waves and electromagnetic waves represents the first ‘multi-messenger’ astronomical observation. Such observations enable GW170817 to be used as a ‘standard siren’14–18 (meaning that the absolute distance to the source can be determined directly from the gravitational-wave measurements) to measure the Hubble constant. This quantity represents the local expansion rate of the Universe, sets the overall scale of the Universe and is of fundamental importance to cosmology. Here we report a measurement of the Hubble constant that combines the distance to the source inferred purely from the gravitational-wave signal with the recession velocity inferred from measurements of the redshift using the electromagnetic data. In contrast to previous measurements, ours does not require the use of a cosmic ‘distance ladder’19: the gravitational-wave analysis can be used to estimate the luminosity distance out to cosmological scales directly, without the use of intermediate astronomical distance measurements. We determine the Hubble constant to be about 70 kilometres per second per megaparsec. This value is consistent with existing measurements 20,21, while being completely independent of them. Additional standard siren measurements from future gravitational-wave sources will enable the Hubble constant to be constrained to high precision.

The Hubble constant H 0 measures the mean expansion rate of the Universe. At nearby distances (less than about 50 Mpc) it is well approx-imated by the expression

=v H d (1)H 0where v H is the local ‘Hubble flow’ velocity of a source and d is the distance to the source. At such distances all cosmological distance measures (such as luminosity distance and comoving distance) differ at the order of v H /c , where c is the speed of light. Because v H /c ≈ 1% for GW170817, the differences between the different distance measures are much smaller than the overall errors in distance. Our measurement of

H 0 is similarly insensitive to the values of other cosmological param-eters, such as the matter density Ωm and the dark-energy density ΩΛ.

To obtain the Hubble flow velocity at the position of GW170817, we use the optical identification of the host galaxy NGC 49937. This iden-tification is based solely on the two-dimensional projected offset and is independent of any assumed value of H 0. The position and redshift of this galaxy allow us to estimate the appropriate value of the Hubble flow velocity. Because the source is relatively nearby, the random relative motions of galaxies, known as peculiar velocities, need to be taken into account. The peculiar velocity is about 10% of the measured recessional velocity (see Methods).

The original standard siren proposal 14 did not rely on the unique identification of a host galaxy. By combining information from around 100 independent gravitational-wave detections, each with a set of potential host galaxies, an estimate of H 0 accurate to 5% can be obtained even without the detection of any transient optical counterparts 22. This is particularly relevant, because gravitational-wave networks will detect many binary black-hole mergers over the coming years 23 and these are not expected to be accompanied by electromagnetic counterparts. Alternatively, if an electromagnetic counterpart has been identified but the host galaxy is unknown, then the same statistical method can be applied but using only those galaxies in a narrow beam around the loca-tion of the optical counterpart. However, such statistical analyses are sensitive to several complicating effects, such as the incompleteness of current galaxy catalogues or the need for dedicated follow-up surveys, and to a range of selection effects 24. Here we use the identification of NGC 4993 as the host galaxy of GW170817 to perform a standard siren measurement of the Hubble constant 15–18.

Analysis of the gravitational-wave data associated with GW170817 produces estimates for the parameters of the source, under the assump-tion that general relativity is the correct model of gravity 3. We are most interested in the joint posterior distribution on the luminosity distance and binary orbital inclination angle. For the analysis we fix the location of the gravitational-wave source on the sky to the identified location of the counterpart 8 (see Methods for details).

An analysis of the gravitational-wave data alone finds that

GW170817 occurred at a distance =.?.+.d 438Mpc 6929

(all values are quoted as the maximum posterior value with the minimal-width 68.3% credible interval). The distance quoted here differs from that in other studies 3, because here we assume that the optical counterpart represents the true sky location of the gravitational-wave source instead of mar-ginalizing over a range of potential sky locations. The uncertainty of

approximately 15% is due to a combination of statistical measurement

error from the noise in the detectors, instrumental calibration uncer-tainties 3 and a geometrical factor that depends on the correlation of distance with inclination angle. The gravitational-wave measurement is consistent with the distance to NGC 4993 measured using the Tully–Fisher relation 19,25, d TF = 41.1 ± 5.8 Mpc.

The measurement of the gravitational-wave polarization is crucial for inferring the binary inclination. This inclination, ι, is defined as the

angle between the line-of-sight vector from the source to the detector and the orbital-angular-momentum vector of the binary system. For electromagnetic phenomena it is typically not possible to tell whether a system is orbiting clockwise or anticlockwise (or, equivalently, face-on or face-off), and sources are therefore usually characterized

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by a viewing angle defined as min(ι, 180° ? ι), with ι in the range [0°, 180°]. By contrast, gravitational-wave measurements can identify the sense of the rotation, and so ι ranges from 0° (anticlockwise) to 180° (clockwise). Previous gravitational-wave detections by the Laser Interferometer Gravitational-wave Observatory (LIGO) had large uncertainties in luminosity distance and inclination 23 because the two LIGO detectors that were involved are nearly co-aligned, preventing a precise polarization measurement. In the present case, owing to the addition of the Virgo detector, the cosine of the inclination can be constrained at 68.3% (1σ) confidence to the range [?1.00, ?0.81], corresponding to inclination angles in the range [144°, 180°]. This incli-nation range implies that the plane of the binary orbit is almost, but not quite, perpendicular to our line of sight to the source (ι ≈ 180°), which is consistent with the observation of a coincident γ-ray burst 4–6. We report inferences on cos ι because our prior for it is flat, so the posterior is proportional to the marginal likelihood for it from the gravitation-al-wave observations.

Electromagnetic follow-up observations of the gravitational-wave sky-localization region 7 discovered an optical transient 8–13 in close proximity to the galaxy NGC 4993. The location of the transient was previously observed by the Distance Less Than 40 Mpc (DLT40) survey on 27.99 July 2017 universal time (ut) and no sources were found 10. We estimate the probability of a random chance association between the optical counterpart and NGC 4993 to be 0.004% (Methods). In what follows we assume that the optical counterpart is associated with GW170817, and that this source resides in NGC 4993.

To compute H 0 we need to estimate the background Hubble flow velocity at the position of NGC 4993. In the traditional electro-magnetic calibration of the cosmic ‘distance ladder’19, this step is commonly carried out using secondary distance indicator informa-tion, such as the Tully–Fisher relation 25, which enables the back-ground Hubble flow velocity in the local Universe to be inferred by scaling back from more distant secondary indicators calibrated in quiet Hubble flow. We do not adopt this approach here, however, to preserve more fully the independence of our results from the electromagnetic distance ladder. Instead we estimate the Hubble flow velocity at the position of NGC 4993 by correcting for local peculiar motions.

NGC 4993 is part of a collection of galaxies, ESO 508, which has a center-of-mass recession velocity relative to the frame of the cosmic microwave background (CMB)26 of 27 3,327 ± 72 km s ?1. We correct

the group velocity by 310 km s ?1 owing to the coherent bulk flow 28,29 towards the Great Attractor (Methods). The standard error on our estimate of the peculiar velocity is 69 km s ?1, but recognizing that this value may be sensitive to details of the bulk flow motion that have been imperfectly modelled, in our subsequent analysis we adopt a more conservative estimate 29 of 150 km s ?1 for the uncertainty on the peculiar velocity at the location of NGC 4993 and fold this into our estimate of the uncertainty on v H . From this, we obtain a Hubble velocity v H = 3,017 ± 166 km s ?1.

Once the distance and Hubble-velocity distributions have been determined from the gravitational-wave and electromagnetic data, respectively, we can constrain the value of the Hubble constant. The measurement of the distance is strongly correlated with the measure-ment of the inclination of the orbital plane of the binary. The analy-sis of the gravitational-wave data also depends on other parameters describing the source, such as the masses of the components 23. Here we treat the uncertainty in these other variables by marginalizing over the posterior distribution on system parameters 3, with the exception of the position of the system on the sky, which is taken to be fixed at the location of the optical counterpart.

We carry out a Bayesian analysis to infer a posterior distribution on H 0 and inclination, marginalized over uncertainties in the recessional and peculiar velocities (Methods). In Fig. 1 we show the marginal pos-terior for H 0. The maximum a posteriori value with the minimal 68.3%

credible interval is =.?.+.??H 700km s Mpc 08012011. Our estimate agrees

well with state-of-the-art determinations of this quantity, including CMB measurements from Planck 20 (67.74 ± 0.46 km s ?1 Mpc ?1; ‘TT, TE, EE + lowP + lensing + ext’) and type Ia supernova measure-ments from SHoES 21 (73.24 ± 1.74 km s ?1 Mpc ?1), and with baryon acoustic oscillations measurements from SDSS 30, strong lensing

measurements from H0LiCOW 31

, high-angular-multipole CMB

measurements from SPT 32

and Cepheid measurements from the Hubble Space Telescope key project 19. Our measurement is an inde-pendent determination of H 0. The close agreement indicates that, although each method may be affected by different systematic uncer-tainties, we see no evidence at present for a systematic difference between gravitational-wave-based estimates and established electro-magnetic-based estimates. As has been much remarked on, the Planck and SHoES results are inconsistent at a level greater than about 3σ. Our measurement does not resolve this inconsistency, being broadly consistent with both.

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Figure 1 | GW170817 measurement of H 0. The marginalized posterior density for H 0, p (H 0 | GW170817), is shown by the blue curve. Constraints at 1σ (darker shading) and 2σ (lighter shading) from Planck 20 and SHoES 21 are shown in green and orange, respectively. The maximum a posteriori value and minimal 68.3% credible interval from this posterior

density function is =.?.+.??H 700km s Mpc 08012011. The 68.3% (1σ) and 95.4%

(2σ) minimal credible intervals are indicated by dashed and dotted lines, respectively.50

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Figure 2 | Inference on H 0 and inclination. The posterior density of H 0 and cos ι from the joint gravitational-wave–electromagnetic analysis are shown as blue contours. Shading levels are drawn at every 5% credible level, with the 68.3% (1σ; solid) and 95.4% (2σ; dashed) contours in black. Values of H 0 and 1σ and 2σ error bands are also displayed from Planck 20 and SHoES 21. Inclination angles near 180° (cos ι = ?1) indicate that the orbital angular momentum is antiparallel to the direction from the source to the detector.

2 n o v e m b e r 2017 | v o L 551 | n A T U r e | 87

One of the main sources of uncertainty in our measurement of H 0 is due to the degeneracy between distance and inclination in the gravitational-wave measurements. A face-on or face-off binary far away has a similar gravitational-wave amplitude to that of an edge-on binary closer in. This relationship is captured in Fig. 2, which shows posterior contours in the H 0–cos ι parameter space.

The posterior in Fig. 1 results from the vertical projection of Fig. 2, marginalizing out uncertainties in cos ι to derive constraints on H 0. Alternatively, it is possible to project horizontally, and thereby marginalize out H 0 to derive constraints on cos ι. If instead of deriv-ing H 0 we take the existing constraints 20,21 on H 0 independently as priors, we are able to improve our constraints on cos ι, as shown in Fig. 3 Assuming the Planck value for H 0, the minimal 68.3% credible interval for cos ι is [?1.00, ?0.92] (corresponding to an inclination angle in the range [157°, 177°]). Assuming the SHoES value of H 0, it is [?0.97, ?0.85] (corresponding to an inclination angle in the range [148°, 166°]). We note that the face-off ι = 180° orientation for the SHoES result is just outside the 90% confidence range. It will be particularly interesting to compare these constraints to those from modelling 7 of the short γ-ray burst, afterglow and optical counterpart associated with GW170817.

We have presented a standard siren determination of the Hubble constant, using a combination of a distance estimate from gravita-tional-wave observations and a Hubble velocity estimate from electro-magnetic observations. Our measurement does not use a ‘distance ladder’ and makes no prior assumptions about H 0. We find

=.?.+.??H 700km s Mpc 08012011

, which is consistent with existing meas-urements 20,21. This first gravitational-wave–electromagnetic multi- messenger event demonstrates the potential for cosmological inference from gravitational-wave standard sirens. We expect that additional multi-messenger binary neutron-star events will be detected in the coming years, and combining subsequent independent measurements of H 0 from these future standard sirens will lead to an era of precision gravitational-wave cosmology.

Online Content Methods, along with any additional Extended Data display items and Source Data, are available in the online version of the paper; references unique to these sections appear only in the online paper.

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cos L

p (c o s L )

L (°)

Figure 3 | Constraints on the inclination angle of GW170817. The posterior density on cos ι (p (cos ι)) is shown for various assumptions about the prior distribution of H 0. The analysis of the joint gravitational-wave and electromagnetic data with a 1/H 0 prior density gives the blue curve; using values of H 0 from Planck 20 and SHoES 21 as a prior on H 0 gives the green and red curves, respectively. Choosing a narrow prior on H 0 converts the precise Hubble velocity measurements for the group containing NGC 4993 to a precise distance measurement, breaking the distance inclination degeneracy and leading to strong constraints on the inclination. Minimal 68.3% (1σ) credible intervals are indicated by dashed lines. Because our prior on inclination is flat on cos ι, the densities in this plot are proportional to the marginalized likelihood for cos ι.

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polarization of the CMB from 500 square degrees of SPTpol data. Preprint at https://https://www.sodocs.net/doc/a91237950.html,/abs/1707.09353 (2017).Acknowledgements We acknowledge the support of the United States

National Science Foundation (NSF) for the construction and operation of the LIGO Laboratory and Advanced LIGO as well as the Science and T echnology Facilities Council (STFC) of the United Kingdom, the Max-Planck-Society (MPS), and the State of Niedersachsen/Germany for support of the construction of Advanced LIGO and construction and operation of the GEO600 detector. Additional support for Advanced LIGO was provided by the Australian Research Council. We acknowledge the Italian Istituto Nazionale di Fisica Nucleare (INFN), the French Centre National de la Recherche Scientifique (CNRS) and the Foundation for Fundamental Research on Matter supported by the Netherlands Organisation for Scientific Research for the construction and operation of the Virgo detector and the creation and support of the EGO consortium. We acknowledge research support from these agencies as well as by the Council of Scientific and Industrial Research of India, the Department of Science and T echnology, India, the Science and Engineering Research

Board (SERB), India, the Ministry of Human Resource Development, India, the Spanish Agencia Estatal de Investigación, the Vicepresidència i Conselleria d’Innovació, Recerca i Turisme and the Conselleria d’Educació i Universitat del Govern de les Illes Balears, the Conselleria d’Educació, Investigació, Cultura i Esport de la Generalitat Valenciana, the National Science Centre of Poland, the Swiss National Science Foundation (SNSF), the Russian Foundation for Basic Research, the Russian Science Foundation, the European Commission, the European Regional Development Funds (ERDF), the Royal Society, the Scottish Funding Council, the Scottish Universities Physics Alliance, the Hungarian

Scientific Research Fund (OTKA), the Lyon Institute of Origins (LIO), the National Research, Development and Innovation Office Hungary (NKFI), the National Research Foundation of Korea, Industry Canada and the Province of Ontario through the Ministry of Economic Development and Innovation, the Natural Science and Engineering Research Council Canada, the Canadian Institute for Advanced Research, the Brazilian Ministry of Science, T echnology, Innovations, and Communications, the International Center for Theoretical Physics South American Institute for Fundamental Research (ICTP-SAIFR), the Research

Grants Council of Hong Kong, the National Natural Science Foundation of China (NSFC), the Leverhulme Trust, the Research Corporation, the Ministry of Science and T echnology (MOST), T aiwan and the Kavli Foundation. We acknowledge the support of the NSF , STFC, MPS, INFN, CNRS and the State of Niedersachsen/Germany for provision of computational resources. This paper has been assigned the document number LIGO-P1700296. We thank the University of Copenhagen, DARK Cosmology Centre, and the Niels Bohr International Academy for hosting D.A.C., R.J.F ., A.M.B., E. Ramirez-Ruiz and M.R.S. during the discovery of GW170817/SSS17a. R.J.F ., A.M.B., E. Ramirez-Ruiz and D.E.H. were participating in the Kavli Summer Program in Astrophysics, ‘Astrophysics with gravitational wave detections’. This program was supported by the the Kavli Foundation, Danish National Research Foundation, the Niels Bohr International Academy, and the DARK Cosmology Centre. The UCSC group is supported in part by NSF grant AST–1518052, the Gordon & Betty Moore Foundation, the Heising-Simons Foundation, generous donations from many individuals through a UCSC Giving Day grant, and from fellowships from the Alfred P . Sloan Foundation (R.J.F .), the David and Lucile Packard Foundation (R.J.F . and E. Ramirez-Ruiz) and the Niels Bohr Professorship from the DNRF (E. Ramirez-Ruiz). A.M.B. acknowledges support from a UCMEXUS-CONACYT Doctoral Fellowship. Support for this work was provided by NASA through Hubble Fellowship grants HST–HF–51348.001 and HST–HF–51373.001 awarded by the Space T elescope Science Institute, which is operated by the

Association of Universities for Research in Astronomy, Inc., for NASA, under

contract NAS5–26555. The Berger Time-Domain Group at Harvard is supported in part by the NSF through grants AST-1411763 and AST-1714498, and by NASA through grants NNX15AE50G and NNX16AC22G. Funding for the DES Projects has been provided by the DOE and NSF (USA), MEC/MICINN/MINECO (Spain), STFC (UK), HEFCE (UK). NCSA (UIUC), KICP (U. Chicago), CCAPP (Ohio State), MIFPA (T exas A&M), CNPQ, FAPERJ, FINEP (Brazil), DFG (Germany) and the Collaborating Institutions in the Dark Energy Survey. The Collaborating Institutions are Argonne Lab, UC Santa Cruz, University of Cambridge,

CIEMAT-Madrid, University of Chicago, University College London, DES-Brazil Consortium, University of Edinburgh, ETH Zürich, Fermilab, University of Illinois, ICE (IEEC-CSIC), IFAE Barcelona, Lawrence Berkeley Lab, LMU München and the associated Excellence Cluster Universe, University of Michigan, NOAO, University of Nottingham, Ohio State University, University of Pennsylvania, University of Portsmouth, SLAC National Lab, Stanford University, University of Sussex, T exas A&M University and the OzDES Membership Consortium. Based in part on observations at Cerro T ololo Inter-American Observatory, National Optical Astronomy Observatory, which is operated by the Association of

Universities for Research in Astronomy (AURA) under a cooperative agreement with the National Science Foundation. The DES Data Management System is supported by the NSF under grant numbers AST-1138766 and AST-1536171. The DES participants from Spanish institutions are partially supported by MINECO under grants AYA2015-71825, ESP2015-88861, FPA2015-68048, and Centro de Excelencia SEV-2012-0234, SEV-2016-0597 and MDM-2015-0509. Research leading to these results has received funding from the ERC under the European Union’s Seventh Framework Programme including grants ERC 240672, 291329 and 306478. We acknowledge support from the Australian Research Council Centre of Excellence for All-sky Astrophysics (CAASTRO), through project number CE110001020. This manuscript has been authored by Fermi Research Alliance, LLC under contract number DE-AC02-07CH11359 with the US Department of Energy, Office of Science, Office of High Energy Physics. The United States Government retains and the publisher, by accepting the article for publication, acknowledges that the United States Government retains a non-exclusive, paid-up, irrevocable, world-wide license to publish or reproduce the published form of this manuscript, or allow others to do so, for United States Government purposes. D.J.S. acknowledges support for the DL T40 programme from NSF grant AST-1517649. Support for I. Arcavi was provided by NASA through the Einstein Fellowship Program, grant PF6-170148. G. Hosseinzadeh, D.A.H. and C. McCully are supported by NSF grant AST-1313484. D. Poznanski acknowledges support by Israel Science Foundation grant 541/17. VINROUGE is an European Southern Observatory Large Survey (id: 0198.D-2010). MASTER acknowledges the Lomonosov MSU Development Programme and the Russian Federation Ministry of Education and Science. This research has made use of the NASA/IPAC Extragalactic Database (NED), which is operated by the Jet Propulsion Laboratory, California Institute of T echnology, under contract with NASA.

Author Contributions All authors contributed to the work presented in this paper.

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reviewer Information Nature thanks N. Suntzeff and the other anonymous reviewer(s) for their contribution to the peer review of this work.

The LIGO Scientific Collaboration and The Virgo Collaboration

B. P. Abbott1, R. Abbott1, T. D. Abbott2, F. Acernese3,4, K. Ackley5,6,

C. Adams7, T. Adams8, P. Addesso9,4, R. X. Adhikari1, V. B. Adya10, C. Affeldt10,

M. Afrough11, B. Agarwal12, M. Agathos13, K. Agatsuma14, N. Aggarwal15,

O. D. Aguiar16, L. Aiello17,18, A. Ain19, P. Ajith20, B. Allen10,21,22, G. Allen12,

A. Allocca23,24, P. A. Altin25, A. Amato26, A. Ananyeva1, S.

B. Anderson1,

W. G. Anderson21, S. V. Angelova27, S. Antier28, S. Appert1, K. Arai1,

M. C. Araya1, J. S. Areeda29, N. Arnaud28,30, K. G. Arun31, S. Ascenzi32,33,

G. Ashton10, M. Ast34, S. M. Aston7, P. Astone35, D. V. Atallah36, P. Aufmuth22, C. Aulbert10, K. AultONeal37, C. Austin2, A. Avila-Alvarez29, S. Babak38,

P. Bacon39, M. K. M. Bader14, S. Bae40, P. T. Baker41, F. Baldaccini42,43,

G. Ballardin30, S. W. Ballmer44, S. Banagiri45, J. C. Barayoga1, S. E. Barclay46, B. C. Barish1, D. Barker47, K. Barkett48, F. Barone3,4, B. Barr46, L. Barsotti15, M. Barsuglia39, D. Barta49, J. Bartlett47, I. Bartos50,5, R. Bassiri51, A. Basti23,24, J. C. Batch47, M. Bawaj52,43, J. C. Bayley46, M. Bazzan53,54, B. Bécsy55,

C. Beer10, M. Bejger56, I. Belahcene28, A. S. Bell46, B. K. Berger1,

G. Bergmann10, J. J. Bero57, C. P. L. Berry58, D. Bersanetti59, A. Bertolini14, J. Betzwieser7, S. Bhagwat44, R. Bhandare60, I. A. Bilenko61, G. Billingsley1, C. R. Billman5, J. Birch7, R. Birney62, O. Birnholtz10, S. Biscans1,15,

S. Biscoveanu63,6, A. Bisht22, M. Bitossi30,24, C. Biwer44, M. A. Bizouard28,

J. K. Blackburn1, J. Blackman48, C. D. Blair1,64, D. G. Blair64, R. M. Blair47, S. Bloemen65, O. Bock10, N. Bode10, M. Boer66, G. Bogaert66, A. Bohe38,

F. Bondu67, E. Bonilla51, R. Bonnand8, B. A. Boom14, R. Bork1, V. Boschi30,24, S. Bose68,19, K. Bossie7, Y. Bouffanais39, A. Bozzi30, C. Bradaschia24,

P. R. Brady21, M. Branchesi17,18, J. E. Brau69, T. Briant70, A. Brillet66,

M. Brinkmann10, V. Brisson28, P. Brockill21, J. E. Broida71, A. F. Brooks1,

D. A. Brown44, D. D. Brown72, S. Brunett1, C. C. Buchanan2, A. Buikema15, T. Bulik73, H. J. Bulten74,14, A. Buonanno38,75, D. Buskulic8, C. Buy39,

R. L. Byer51, M. Cabero10, L. Cadonati76, G. Cagnoli26,77, C. Cahillane1,

J. Calderón Bustillo76, T. A. Callister1, E. Calloni78,4, J. B. Camp79,

M. Canepa80,59, P. Canizares65, K. C. Cannon81, H. Cao72, J. Cao82,

C. D. Capano10, E. Capocasa39, F. Carbognani30, S. Caride83, M. F. Carney84, J. Casanueva Diaz28, C. Casentini32,33, S. Caudill21,14, M. Cavaglià11,

F. Cavalier28, R. Cavalieri30,

G. Cella24, C. B. Cepeda1, P. Cerdá-Durán85,

G. Cerretani23,24, E. Cesarini86,33, S. J. Chamberlin63, M. Chan46, S. Chao87, P. Charlton88, E. Chase89, E. Chassande-Mottin39, D. Chatterjee21,

K. Chatziioannou90, B. D. Cheeseboro41, H. Y. Chen91, X. Chen64, Y. Chen48, H.-P. Cheng5, H. Chia5, A. Chincarini59, A. Chiummo30, T. Chmiel84,

H. S. Cho92, M. Cho75, J. H. Chow25, N. Christensen71,66, Q. Chu64,

A. J. K. Chua13, S. Chua70, A. K. W. Chung93, S. Chung64, G. Ciani5,53,54,

R. Ciolfi94,95, C. E. Cirelli51, A. Cirone80,59, F. Clara47, J. A. Clark76,

P. Clearwater96, F. Cleva66, C. Cocchieri11, E. Coccia17,18, P.-F. Cohadon70,

D. Cohen28, A. Colla97,35, C. G. Collette98, L. R. Cominsky99, M. Constancio Jr.16, L. Conti54, S. J. Cooper58, P. Corban7, T. R. Corbitt2, I. Cordero-Carrión100, K. R. Corley50, N. Cornish101, A. Corsi83, S. Cortese30, C. A. Costa16,

M. W. Coughlin71,1, S. B. Coughlin89, J.-P. Coulon66, S. T. Countryman50,

P. Couvares1, P. B. Covas102, E. E. Cowan76, D. M. Coward64, M. J. Cowart7, D. C. Coyne1, R. Coyne83, J. D. E. Creighton21, T. D. Creighton103, J. Cripe2, S. G. Crowder104, T. J. Cullen29,2, A. Cumming46, L. Cunningham46, E. Cuoco30, T. Dal Canton79, G. Dálya55, S. L. Danilishin22,10, S. D’Antonio33,

K. Danzmann22,10, A. Dasgupta105, C. F. Da Silva Costa5, L. E. H. Datrier46, V. Dattilo30, I. Dave60, M. Davier28, D. Davis44, E. J. Daw106, B. Day76, S. De44, D. DeBra51, J. Degallaix26, M. De Laurentis17,4, S. Deléglise70,

W. Del Pozzo58,23,24, N. Demos15, T. Denker10, T. Dent10, R. De Pietri107,108, V. Dergachev38, R. De Rosa78,4, R. T. DeRosa7, C. De Rossi26,30, R. DeSalvo109, O. de Varona10, J. Devenson27, S. Dhurandhar19, M. C. Díaz103, L. Di Fiore4, M. Di Giovanni110,95, T. Di Girolamo50,78,4, A. Di Lieto23,24, S. Di Pace97,35,

I. Di Palma97,35, F. Di Renzo23,24, Z. Doctor91, V. Dolique26, F. Donovan15,

K. L. Dooley11, S. Doravari10, I. Dorrington36, R. Douglas46, M. Dovale álvarez58, T. P. Downes21, M. Drago10, C. Dreissigacker10, J. C. Driggers47, Z. Du82,

M. Ducrot8, P. Dupej46, S. E. Dwyer47, T. B. Edo106, M. C. Edwards71, A. Effler7, H.-B. Eggenstein38,10, P. Ehrens1, J. Eichholz1, S. S. Eikenberry5,

R. A. Eisenstein15, R. C. Essick15, D. Estevez8, Z. B. Etienne41, T. Etzel1,

M. Evans15, T. M. Evans7, M. Factourovich50, V. Fafone32,33,17, H. Fair44,

S. Fairhurst36, X. Fan82, S. Farinon59, B. Farr91, W. M. Farr58,

E. J. Fauchon-Jones36, M. Favata111, M. Fays36, C. Fee84, H. Fehrmann10,

J. Feicht1, M. M. Fejer51, A. Fernandez-Galiana15, I. Ferrante23,24, E. C. Ferreira16, F. Ferrini30, F. Fidecaro23,24, D. Finstad44, I. Fiori30, D. Fiorucci39,

M. Fishbach91, R. P. Fisher44, M. Fitz-Axen45, R. Flaminio26,112, M. Fletcher46, H. Fong90, J. A. Font85,113, P. W. F. Forsyth25, S. S. Forsyth76, J.-D. Fournier66, S. Frasca97,35, F. Frasconi24, Z. Frei55, A. Freise58, R. Frey69, V. Frey28,

E. M. Fries1, P. Fritschel15, V. V. Frolov7, P. Fulda5, M. Fyffe7, H. Gabbard46, B. U. Gadre19, S. M. Gaebel58, J. R. Gair114, L. Gammaitoni42, M. R. Ganija72, S. G. Gaonkar19, C. Garcia-Quiros102,

F. Garufi78,4, B. Gateley47, S. Gaudio37,

G. Gaur115, V. Gayathri116, N. Gehrels79?, G. Gemme59, E. Genin30, A. Gennai24, D. George12, J. George60, L. Gergely117, V. Germain8, S. Ghonge76,

Abhirup Ghosh20, Archisman Ghosh20,14, S. Ghosh65,14,21, J. A. Giaime2,7,

K. D. Giardina7, A. Giazotto24, K. Gill37, L. Glover109, E. Goetz118, R. Goetz5, S. Gomes36, B. Goncharov6, G. González2, J. M. Gonzalez Castro23,24,

A. Gopakumar119, M. L. Gorodetsky61, S. E. Gossan1, M. Gosselin30,

R. Gouaty8, A. Grado120,4, C. Graef46, M. Granata26, A. Grant46, S. Gras15,

C. Gray47, G. Greco121,122, A. C. Green58, E. M. Gretarsson37, P. Groot65,

H. Grote10, S. Grunewald38, P. Gruning28, G. M. Guidi121,122, X. Guo82,

A. Gupta63, M. K. Gupta105, K. E. Gushwa1, E. K. Gustafson1, R. Gustafson118, O. Halim18,17,

B. R. Hall68, E. D. Hall15, E. Z. Hamilton36, G. Hammond46,

M. Haney123, M. M. Hanke10, J. Hanks47, C. Hanna63, M. D. Hannam36, O. A. Hannuksela93, J. Hanson7, T. Hardwick2, J. Harms17,18, G. M. Harry124, I. W. Harry38, M. J. Hart46, C.-J. Haster90, K. Haughian46, J. Healy57,

A. Heidmann70, M. C. Heintze7, H. Heitmann66, P. Hello28, G. Hemming30, M. Hendry46, I. S. Heng46, J. Hennig46, A. W. Heptonstall1, M. Heurs10,22,

S. Hild46, T. Hinderer65, D. Hoak30, D. Hofman26, K. Holt7, D. E. Holz91,

P. Hopkins36, C. Horst21, J. Hough46, E. A. Houston46, E. J. Howell64,

A. Hreibi66, Y. M. Hu10, E. A. Huerta12, D. Huet28,

B. Hughey37, S. Husa102, S. H. Huttner46, T. Huynh-Dinh7, N. Indik10, R. Inta83, G. Intini97,35, H. N. Isa46, J.-M. Isac70, M. Isi1, B. R. Iyer20, K. Izumi47, T. Jacqmin70, K. Jani76,

P. Jaranowski125, S. Jawahar62, F. Jiménez-Forteza102, W. W. Johnson2,

D. I. Jones126, R. Jones46, R. J. G. Jonker14, L. Ju64, J. Junker10, C. V. Kalaghatgi36, V. Kalogera89, B. Kamai1, S. Kandhasamy7, G. Kang40, J. B. Kanner1,

S. J. Kapadia21, S. Karki69, K. S. Karvinen10, M. Kasprzack2, M. Katolik12,

E. Katsavounidis15, W. Katzman7, S. Kaufer22, K. Kawabe47,

F. Kéfélian66,

D. Keitel46, A. J. Kemball12, R. Kennedy106, C. Kent36, J. S. Key127, F. Y. Khalili61, I. Khan17,33, S. Khan10, Z. Khan105,

E. A. Khazanov128, N. Kijbunchoo25, Chunglee Kim129, J. C. Kim130, K. Kim93, W. Kim72, W. S. Kim131, Y.-M. Kim92, S. J. Kimbrell76, E. J. King72, P. J. King47, M. Kinley-Hanlon124, R. Kirchhoff10, J. S. Kissel47, L. Kleybolte34, S. Klimenko5, T. D. Knowles41, P. Koch10,

S. M. Koehlenbeck10, S. Koley14, V. Kondrashov1, A. Kontos15, M. Korobko34, W. Z. Korth1, I. Kowalska73, D. B. Kozak1, C. Kr?mer10, V. Kringel10,

B. Krishnan10, A. Królak132,133, G. Kuehn10, P. Kumar90, R. Kumar105,

S. Kumar20, L. Kuo87, A. Kutynia132, S. Kwang21, B. D. Lackey38, K. H. Lai93, M. Landry47, R. N. Lang134, J. Lange57, B. Lantz51, R. K. Lanza15,

A. Lartaux-Vollard28, P. D. Lasky6, M. Laxen7, A. Lazzarini1, C. Lazzaro54,

P. Leaci97,35, S. Leavey46, C. H. Lee92, H. K. Lee135, H. M. Lee136, H. W. Lee130, K. Lee46, J. Lehmann10, A. Lenon41, M. Leonardi110,95, N. Leroy28,

N. Letendre8, Y. Levin6, T. G. F. Li93, S. D. Linker109, T. B. Littenberg137, J. Liu64, X. Liu21, R. K. L. Lo93, N. A. Lockerbie62, L. T. London36, J. E. Lord44,

M. Lorenzini17,18, V. Loriette138, M. Lormand7, G. Losurdo24, J. D. Lough10, C. O. Lousto57, G. Lovelace29, H. Lück22,10, D. Lumaca32,33, A. P. Lundgren10, R. Lynch15, Y. Ma48, R. Macas36, S. Macfoy27, B. Machenschalk10, M. MacInnis15, D. M. Macleod36, I. Maga?a Hernandez21, F. Maga?a-Sandoval44,

L. Maga?a Zertuche44, R. M. Magee63, E. Majorana35, I. Maksimovic138,

N. Man66, V. Mandic45, V. Mangano46, G. L. Mansell25, M. Manske21,25,

M. Mantovani30, F. Marchesoni52,43, F. Marion8, S. Márka50, Z. Márka50,

C. Markakis12, A. S. Markosyan51, A. Markowitz1, E. Maros1, A. Marquina100, F. Martelli121,122, L. Martellini66, I. W. Martin46, R. M. Martin111,

D. V. Martynov15, K. Mason15,

E. Massera106, A. Masserot8, T. J. Massinger1, M. Masso-Reid46, S. Mastrogiovanni97,35, A. Matas45,

F. Matichard1,15, L. Matone50, N. Mavalvala15, N. Mazumder68, R. McCarthy47, D. E. McClelland25, S. McCormick7,

L. McCuller15, S. C. McGuire139, G. McIntyre1, J. McIver1, D. J. McManus25, L. McNeill6, T. McRae25, S. T. McWilliams41, D. Meacher63, G. D. Meadors38,10, M. Mehmet10, J. Meidam14, E. Mejuto-Villa9,4, A. Melatos96, G. Mendell47,

R. A. Mercer21, E. L. Merilh47, M. Merzougui66, S. Meshkov1, C. Messenger46, C. Messick63, R. Metzdorff70, P. M. Meyers45, H. Miao58, C. Michel26,

H. Middleton58, E. E. Mikhailov140, L. Milano78,4, A. L. Miller5,97,35,

B. B. Miller89, J. Miller15, M. Millhouse101, M.

C. Milovich-Goff109,

O. Minazzoli66,141, Y. Minenkov33, J. Ming38, C. Mishra142, S. Mitra19,

V. P. Mitrofanov61, G. Mitselmakher5, R. Mittleman15, D. Moffa84, A. Moggi24, K. Mogushi11, M. Mohan30, S. R. P. Mohapatra15, M. Montani121,122,

C. J. Moore13,

D. Moraru47, G. Moreno47, S. R. Morriss103, B. Mours8,

C. M. Mow-Lowry58, G. Mueller5, A. W. Muir36, Arunava Mukherjee10,

D. Mukherjee21, S. Mukherjee103, N. Mukund19, A. Mullavey7, J. Munch72,

E. A. Mu?iz44, M. Muratore37, P. G. Murray46, K. Napier76, I. Nardecchia32,33, L. Naticchioni97,35, R. K. Nayak143, J. Neilson109, G. Nelemans65,14,

T. J. N. Nelson7, M. Nery10, A. Neunzert118, L. Nevin1, J. M. Newport124,

G. Newton46?, K. K. Y. Ng93, T. T. Nguyen25, D. Nichols65, A. B. Nielsen10,

S. Nissanke65,14, A. Nitz10, A. Noack10, F. Nocera30, D. Nolting7, C. North36, L. K. Nuttall36, J. Oberling47, G. D. O’Dea109, G. H. Ogin144, J. J. Oh131,

S. H. Oh131, F. Ohme10, M. A. Okada16, M. Oliver102, P. Oppermann10, Richard J. Oram7, B. O’Reilly7, R. Ormiston45, L. F. Ortega5,

R. O’Shaughnessy57, S. Ossokine38, D. J. Ottaway72, H. Overmier7,

B. J. Owen83, A. E. Pace63, J. Page137, M. A. Page64, A. Pai116,145, S. A. Pai60, J. R. Palamos69, O. Palashov128,

C. Palomba35, A. Pal-Singh34, Howard Pan87, Huang-Wei Pan87, B. Pang48, P. T. H. Pang93, C. Pankow89, F. Pannarale36, B. C. Pant60, F. Paoletti24, A. Paoli30, M. A. Papa38,21,10, A. Parida19, W. Parker7,

D. Pascucci46, A. Pasqualetti30, R. Passaquieti23,24, D. Passuello24, M. Patil133, B. Patricelli146,24, B. L. Pearlstone46, M. Pedraza1, R. Pedurand26,147,

L. Pekowsky44, A. Pele7, S. Penn148, C. J. Perez47, A. Perreca1,110,95,

L. M. Perri89, H. P. Pfeiffer90,38, M. Phelps46, O. J. Piccinni97,35, M. Pichot66, F. Piergiovanni121,122, V. Pierro9,4, G. Pillant30, L. Pinard26, I. M. Pinto9,4,

M. Pirello47, M. Pitkin46, M. Poe21, R. Poggiani23,24, P. Popolizio30, E. K. Porter39, A. Post10, J. Powell46,149, J. Prasad19, J. W. W. Pratt37, G. Pratten102,

V. Predoi36, T. Prestegard21, M. Prijatelj10, M. Principe9,4, S. Privitera38,

G. A. Prodi110,95, L. G. Prokhorov61, O. Puncken10, M. Punturo43, P. Puppo35, M. Pürrer38, H. Qi21, V. Quetschke103, E. A. Quintero1, R. Quitzow-James69, F. J. Raab47, D. S. Rabeling25, H. Radkins47, P. Raffai55, S. Raja60, C. Rajan60, B. Rajbhandari83, M. Rakhmanov103, K. E. Ramirez103, A. Ramos-Buades102, P. Rapagnani97,35, V. Raymond38, M. Razzano23,24, J. Read29, T. Regimbau66, L. Rei59, S. Reid62, D. H. Reitze1,5, W. Ren12, S. D. Reyes44, F. Ricci97,35,

P. M. Ricker12, S. Rieger10, K. Riles118, M. Rizzo57, N. A. Robertson1,46,

R. Robie46, F. Robinet28, A. Rocchi33, L. Rolland8, J. G. Rollins1, V. J. Roma69, J. D. Romano103, R. Romano3,4, C. L. Romel47, J. H. Romie7, D. Rosin′ ska150,56, M. P. Ross151, S. Rowan46, A. Rüdiger10, P. Ruggi30, G. Rutins27, K. Ryan47, S. Sachdev1, T. Sadecki47, L. Sadeghian21, M. Sakellariadou152, L. Salconi30,

M. Saleem116, F. Salemi10, A. Samajdar143, L. Sammut6, L. M. Sampson89, E. J. Sanchez1, L. E. Sanchez1, N. Sanchis-Gual85, V. Sandberg47, J. R. Sanders44, B. Sassolas26, B. S. Sathyaprakash63,36, P. R. Saulson44, O. Sauter118,

R. L. Savage47, A. Sawadsky34, P. Schale69, M. Scheel48, J. Scheuer89,

J. Schmidt10, P. Schmidt1,65, R. Schnabel34, R. M. S. Schofield69,

A. Sch?nbeck34, E. Schreiber10, D. Schuette10,22,

B. W. Schulte10,

B. F. Schutz36,10, S. G. Schwalbe37, J. Scott46, S. M. Scott25, E. Seidel12,

D. Sellers7, A. S. Sengupta153, D. Sentenac30, V. Sequino32,33,17, A. Sergeev128, D. A. Shaddock25, T. J. Shaffer47, A. A. Shah137, M. S. Shahriar89,

M. B. Shaner109, L. Shao38, B. Shapiro51, P. Shawhan75, A. Sheperd21,

D. H. Shoemaker15, D. M. Shoemaker76, K. Siellez76, X. Siemens21,

M. Sieniawska56, D. Sigg47, A. D. Silva16, L. P. Singer79, A. Singh38,10,22,

A. Singhal17,35, A. M. Sintes102,

B. J. J. Slagmolen25, B. Smith7, J. R. Smith29, R. J. E. Smith1,6, S. Somala154, E. J. Son131, J. A. Sonnenberg21, B. Sorazu46, F. Sorrentino59, T. Souradeep19, A. P. Spencer46, A. K. Srivastava105,

K. Staats37, A. Staley50, D. Steer39, M. Steinke10, J. Steinlechner34,46,

S. Steinlechner34, D. Steinmeyer10, S. P. Stevenson58,149, R. Stone103,

D. J. Stops58, K. A. Strain46, G. Stratta121,122, S.

E. Strigin61, A. Strunk47,

R. Sturani155, A. L. Stuver7, T. Z. Summerscales156, L. Sun96, S. Sunil105,

J. Suresh19, P. J. Sutton36, B. L. Swinkels30, M. J. Szczepan′ czyk37, M. Tacca14, S. C. Tait46, C. Talbot6, D. Talukder69, D. B. Tanner5, M. Tápai117,

A. Taracchini38, J. D. Tasson71, J. A. Taylor137, R. Taylor1, S. V. Tewari148,

T. Theeg10, F. Thies10, E. G. Thomas58, M. Thomas7, P. Thomas47,

K. A. Thorne7, E. Thrane6, S. Tiwari17,95, V. Tiwari36, K. V. Tokmakov62,

K. Toland46, M. Tonelli23,24, Z. Tornasi46, A. Torres-Forné85, C. I. Torrie1,

D. T?yr?58, F. Travasso30,43, G. Traylor7, J. Trinastic5, M. C. Tringali110,95,

L. Trozzo157,24, K. W. Tsang14, M. Tse15, R. Tso1, L. Tsukada81, D. Tsuna81,

D. Tuyenbayev103, K. Ueno21, D. Ugolini158, C. S. Unnikrishnan119,

A. L. Urban1, S. A. Usman36, H. Vahlbruch22, G. Vajente1, G. Valdes2,

N. van Bakel14, M. van Beuzekom14, J. F. J. van den Brand74,14,

C. Van Den Broeck14,

D. C. Vander-Hyde44, L. van der Schaaf14,

J. V. van Heijningen14, A. A. van Veggel46, M. Vardaro53,54, V. Varma48, S. Vass1, M. Vasúth49, A. Vecchio58, G. Vedovato54, J. Veitch46, P. J. Veitch72,

K. Venkateswara151, G. Venugopalan1, D. Verkindt8, F. Vetrano121,122,

A. Viceré121,122, A. D. Viets21, S. Vinciguerra58, D. J. Vine27, J.-Y. Vinet66,

S. Vitale15, T. Vo44, H. Vocca42,43, C. Vorvick47, S. P. Vyatchanin61, A. R. Wade1, L. E. Wade84, M. Wade84, R. Walet14, M. Walker29, L. Wallace1, S. Walsh38,10,21, G. Wang17,122, H. Wang58, J. Z. Wang63, W. H. Wang103, Y. F. Wang93,

R. L. Ward25, J. Warner47, M. Was8, J. Watchi98, B. Weaver47, L.-W. Wei10,22, M. Weinert10, A. J. Weinstein1, R. Weiss15, L. Wen64, E. K. Wessel12, P. We?els10, J. Westerweck10, T. Westphal10, K. Wette25, J. T. Whelan57, S. E. Whitcomb1, B. F. Whiting5, C. Whittle6, D. Wilken10, D. Williams46, R. D. Williams1,

A. R. Williamson65, J. L. Willis1,159,

B. Willke22,10, M. H. Wimmer10,

W. Winkler10, C. C. Wipf1, H. Wittel10,22, G. Woan46, J. Woehler10, J. Wofford57, K. W. K. Wong93, J. Worden47, J. L. Wright46, D. S. Wu10, D. M. Wysocki57,

S. Xiao1, H. Yamamoto1, C. C. Yancey75, L. Yang160, M. J. Yap25, M. Yazback5, Hang Yu15, Haocun Yu15, M. Yvert8, A. Zadroz· ny132, M. Zanolin37,

T. Zelenova30, J.-P. Zendri54, M. Zevin89, L. Zhang1, M. Zhang140, T. Zhang46, Y.-H. Zhang57, C. Zhao64, M. Zhou89, Z. Zhou89, S. J. Zhu38,10, X. J. Zhu6,

A. B. Zimmerman90, M. E. Zucker1,15 & J. Zweizig1

1LIGO, California Institute of Technology, Pasadena, California 91125, USA. 2Louisiana State University, Baton Rouge, Louisiana 70803, USA. 3Università di Salerno, Fisciano,

I-84084 Salerno, Italy. 4INFN, Sezione di Napoli, Complesso Universitario di Monte Sant’Angelo, I-80126 Napoli, Italy. 5University of Florida, Gainesville, Florida 32611, USA. 6OzGrav, School of Physics and Astronomy, Monash University, Clayton, Victoria 3800, Australia. 7LIGO Livingston Observatory, Livingston, Louisiana 70754, USA. 8Laboratoire d’Annecy-le-Vieux de Physique des Particules (LAPP), Université Savoie Mont Blanc, CNRS/IN2P3, F-74941 Annecy, France. 9University of Sannio at Benevento, I-82100 Benevento, Italy. 10Max Planck Institute for Gravitational Physics (Albert Einstein Institute), D-30167 Hannover, Germany. 11The University of Mississippi, University, Mississippi 38677, USA. 12NCSA, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA. 13University of Cambridge, Cambridge CB2 1TN, UK. 14Nikhef, Science Park, 1098 XG Amsterdam, The Netherlands. 15LIGO, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA. 16Instituto Nacional de Pesquisas Espaciais, 12227-010 S?o José dos Campos, S?o Paulo, Brazil. 17Gran Sasso Science Institute (GSSI), I-67100 L’Aquila, Italy. 18INFN, Laboratori Nazionali del Gran Sasso, I-67100 Assergi, Italy. 19Inter-University Centre for Astronomy and Astrophysics, Pune 411007, India. 20International Centre for Theoretical Sciences, Tata Institute of Fundamental Research, Bengaluru 560089, India. 21University of Wisconsin-Milwaukee, Milwaukee, Wisconsin 53201, USA. 22Leibniz Universit?t Hannover, D-30167 Hannover, Germany.

23Università di Pisa, I-56127 Pisa, Italy. 24INFN, Sezione di Pisa, I-56127 Pisa, Italy.

25OzGrav, Australian National University, Canberra, Australian Capital Territory 0200, Australia. 26Laboratoire des Matériaux Avancés (LMA), CNRS/IN2P3, F-69622 Villeurbanne, France. 27SUPA, University of the West of Scotland, Paisley PA1 2BE, UK.

28LAL, Université Paris-Sud, CNRS/IN2P3, Université Paris-Saclay, F-91898 Orsay, France. 29California State University Fullerton, Fullerton, California 92831, USA. 30European Gravitational Observatory (EGO), I-56021 Cascina, Italy. 31Chennai Mathematical Institute, Chennai 603103, India. 32Università di Roma Tor Vergata, I-00133 Roma, Italy. 33INFN, Sezione di Roma Tor Vergata, I-00133 Roma, Italy. 34Universit?t Hamburg, D-22761 Hamburg, Germany. 35INFN, Sezione di Roma, I-00185 Roma, Italy. 36Cardiff University, Cardiff CF24 3AA, UK. 37Embry-Riddle Aeronautical University, Prescott, Arizona 86301, USA. 38Max Planck Institute for Gravitational Physics (Albert Einstein Institute), D-14476 Potsdam-Golm, Germany. 39APC, AstroParticule et Cosmologie, Université Paris Diderot, CNRS/IN2P3, CEA/Irfu, Observatoire de Paris, Sorbonne Paris Cité, F-75205 Paris Cedex 13, France. 40Korea Institute of Science and Technology Information, Daejeon 34141, South Korea. 41West Virginia University, Morgantown, West Virginia 26506, USA.

42Università di Perugia, I-06123 Perugia, Italy. 43INFN, Sezione di Perugia, I-06123 Perugia, Italy. 44Syracuse University, Syracuse, New York 13244, USA. 45University of Minnesota, Minneapolis, Minnesota 55455, USA. 46SUPA, University of Glasgow, Glasgow G12 8QQ, UK. 47LIGO Hanford Observatory, Richland, Washington 99352, USA. 48Caltech CaRT, Pasadena, California 91125, USA. 49Wigner RCP, RMKI, Konkoly Thege Miklós út

29-33, H-1121 Budapest, Hungary. 50Columbia University, New York, New York 10027, USA. 51Stanford University, Stanford, California 94305, USA. 52Università di Camerino, Dipartimento di Fisica, I-62032 Camerino, Italy. 53Università di Padova, Dipartimento di Fisica e Astronomia, I-35131 Padova, Italy. 54INFN, Sezione di Padova, I-35131 Padova, Italy. 55Institute of Physics, E?tv?s University, Pázmány Péter sétány 1/A, Budapest 1117, Hungary. 56Nicolaus Copernicus Astronomical Center, Polish Academy of Sciences,

00-716 Warsaw, Poland. 57Rochester Institute of Technology, Rochester, New York 14623, USA. 58University of Birmingham, Birmingham B15 2TT, UK. 59INFN, Sezione di Genova, I-16146 Genova, Italy. 60RRCAT, Indore MP 452013, India. 61Faculty of Physics, Lomonosov Moscow State University, Moscow 119991, Russia. 62SUPA, University of Strathclyde, Glasgow G1 1XQ, UK. 63The Pennsylvania State University, University Park, Pennsylvania 16802, USA. 64OzGrav, University of Western Australia, Crawley, Western Australia 6009, Australia. 65Department of Astrophysics/IMAPP, Radboud University Nijmegen, PO Box 9010, 6500 GL Nijmegen, The Netherlands. 66Artemis, Université C?te d’Azur, Observatoire C?te d’Azur, CNRS, CS 34229, F-06304 Nice Cedex 4, France.

67Institut FOTON, CNRS, Université de Rennes 1, F-35042 Rennes, France. 68Washington State University, Pullman, Washington 99164, USA. 69University of Oregon, Eugene, Oregon 97403, USA. 70Laboratoire Kastler Brossel, UPMC-Sorbonne Universités, CNRS, ENS-PSL Research University, Collège de France, F-75005 Paris, France. 71Carleton College, Northfield, Minnesota 55057, USA. 72OzGrav, University of Adelaide, Adelaide, South Australia 5005, Australia. 73Astronomical Observatory Warsaw University, 00-478 Warsaw, Poland. 74VU University Amsterdam, 1081 HV Amsterdam, The Netherlands.

75University of Maryland, College Park, Maryland 20742, USA. 76Center for Relativistic Astrophysics, Georgia Institute of Technology, Atlanta, Georgia 30332, USA. 77Université Claude Bernard Lyon 1, F-69622 Villeurbanne, France. 78Università di Napoli ‘Federico II’, Complesso Universitario di Monte Sant’Angelo, I-80126 Napoli, Italy. 79NASA Goddard Space Flight Center, Greenbelt, Maryland 20771, USA. 80Dipartimento di Fisica, Università degli Studi di Genova, I-16146 Genova, Italy. 81RESCEU, University of Tokyo, Tokyo

113-0033, Japan. 82Tsinghua University, Beijing 100084, China. 83Texas Tech University, Lubbock, Texas 79409, USA. 84Kenyon College, Gambier, Ohio 43022, USA.

85Departamento de Astronomía y Astrofísica, Universitat de València, E-46100 Burjassot, Spain. 86Museo Storico della Fisica e Centro Studi e Ricerche Enrico Fermi, I-00184 Roma, Italy. 87National Tsing Hua University, Hsinchu City, 30013 Taiwan, China. 88Charles Sturt University, Wagga Wagga, New South Wales 2678, Australia. 89Center for Interdisciplinary Exploration and Research in Astrophysics (CIERA), Northwestern University, Evanston, Illinois 60208, USA. 90Canadian Institute for Theoretical Astrophysics, University of Toronto, Toronto, Ontario M5S 3H8, Canada. 91University of Chicago, Chicago, Illinois 60637, USA. 92Pusan National University, Busan 46241, South Korea. 93The Chinese University of Hong Kong, Shatin, Hong Kong. 94INAF, Osservatorio Astronomico di Padova, I-35122 Padova, Italy. 95INFN, Trento Institute for Fundamental Physics and Applications, I-38123 Povo, Italy. 96OzGrav, University of Melbourne, Parkville, Victoria 3010, Australia. 97Università di Roma ‘La Sapienza’, I-00185 Roma, Italy.

98Université Libre de Bruxelles, 1050 Brussels, Belgium. 99Sonoma State University, Rohnert Park, California 94928, USA. 100Departamento de Matemáticas, Universitat de València, E-46100 Burjassot, Spain. 101Montana State University, Bozeman, Montana 59717, USA. 102Universitat de les Illes Balears, IAC3—IEEC, E-07122 Palma de Mallorca, Spain. 103The University of Texas Rio Grande Valley, Brownsville, Texas 78520, USA.

104Bellevue College, Bellevue, Washington 98007, USA. 105Institute for Plasma Research, Bhat, Gandhinagar 382428, India. 106The University of Sheffield, Sheffield S10 2TN, UK. 107Dipartimento di Scienze Matematiche, Fisiche e Informatiche, Università di Parma,

I-43124 Parma, Italy. 108INFN, Sezione di Milano Bicocca, Gruppo Collegato di Parma,

I-43124 Parma, Italy. 109California State University, Los Angeles, 5151 State University Drive, Los Angeles, California 90032, USA. 110Università di Trento, Dipartimento di Fisica, I-38123 Povo, Italy. 111Montclair State University, Montclair, New Jersey 07043, USA.

112National Astronomical Observatory of Japan, 2-21-1 Osawa, Mitaka, Tokyo 181-8588, Japan. 113Observatori Astronòmic, Universitat de València, E-46980 Paterna, Spain.

114School of Mathematics, University of Edinburgh, Edinburgh EH9 3FD, UK. 115University and Institute of Advanced Research, Koba Institutional Area, Gandhinagar Gujarat 382007, India. 116IISER-TVM, CET Campus, Trivandrum Kerala 695016, India.

117University of Szeged, Dóm tér 9, 6720 Szeged, Hungary. 118University of Michigan, Ann Arbor, Michigan 48109, USA. 119Tata Institute of Fundamental Research, Mumbai 400005, India. 120INAF, Osservatorio Astronomico di Capodimonte, I-80131 Napoli, Italy.

121Università degli Studi di Urbino ‘Carlo Bo’, I-61029 Urbino, Italy. 122INFN, Sezione di Firenze, I-50019 Sesto Fiorentino, Italy. 123Physik-Institut, University of Zurich, Winterthurerstrasse 190, 8057 Zurich, Switzerland. 124American University, Washington DC 20016, USA. 125University of Bia?ystok, 15-424 Bia?ystok, Poland. 126University of Southampton, Southampton SO17 1BJ, UK. 127University of Washington Bothell, 18115 Campus Way NE, Bothell, Washington 98011, USA. 128Institute of Applied Physics, Nizhny Novgorod 603950, Russia. 129Korea Astronomy and Space Science Institute, Daejeon 34055, South Korea. 130Inje University Gimhae, South Gyeongsang 50834, South Korea. 131National Institute for Mathematical Sciences, Daejeon 34047, South Korea. 132NCBJ, 05-400 S′ wierk-Otwock, Poland. 133Institute of Mathematics, Polish Academy of Sciences, 00656 Warsaw, Poland. 134Hillsdale College, Hillsdale, Michigan 49242, USA. 135Hanyang

University, Seoul 04763, South Korea. 136Seoul National University, Seoul 08826, South Korea. 137NASA Marshall Space Flight Center, Huntsville, Alabama 35811, USA. 138ESPCI, CNRS, F-75005 Paris, France. 139Southern University and A&M College, Baton Rouge, Louisiana 70813, USA. 140College of William and Mary, Williamsburg, Virginia 23187, USA. 141Centre Scientifique de Monaco, 8 quai Antoine Ier, MC-98000, Monaco. 142Indian Institute of Technology Madras, Chennai 600036, India. 143IISER-Kolkata, Mohanpur, West Bengal 741252, India. 144Whitman College, 345 Boyer Avenue, Walla Walla, Washington 99362 USA. 145Indian Institute of Technology Bombay, Powai, Mumbai, Maharashtra 400076, India. 146Scuola Normale Superiore, Piazza dei Cavalieri 7, I-56126 Pisa, Italy. 147Université de Lyon, F-69361 Lyon, France. 148Hobart and William Smith Colleges, Geneva, New York 14456, USA. 149OzGrav, Swinburne University of Technology, Hawthorn, Victoria 3122, Australia. 150Janusz Gil Institute of Astronomy, University of Zielona Góra, 65-265 Zielona Góra, Poland. 151University of Washington, Seattle, Washington 98195, USA. 152King’s College London, University of London, London WC2R 2LS, UK. 153Indian Institute of Technology, Gandhinagar Ahmedabad Gujarat 382424, India. 154Indian Institute of Technology Hyderabad, Sangareddy, Khandi, Telangana 502285, India.

155International Institute of Physics, Universidade Federal do Rio Grande do Norte, Natal RN 59078-970, Brazil. 156Andrews University, Berrien Springs, Michigan 49104, USA. 157Università di Siena, I-53100 Siena, Italy. 158Trinity University, San Antonio, Texas 78212, USA. 159Abilene Christian University, Abilene, Texas 79699, USA. 160Colorado State University, Fort Collins, Colorado 80523, USA.

The 1M2H Collaboration

R. J. Foley1, D. A. Coulter1, M. R. Drout2, D. Kasen3,4, C. D. Kilpatrick1,

B. F. Madore2, A. Murguia-Berthier1, Y.-

C. Pan1, A. L. Piro2, J. X. Prochaska1, E. Ramirez-Ruiz1,5, A. Rest6, C. Rojas-Bravo1, B. J. Shappee2,7, M. R. Siebert1, J.

D. Simon2 & N. Ulloa8

1Department of Astronomy and Astrophysics, University of California, Santa Cruz, California 95064, USA. 2The Observatories of the Carnegie Institution for Science, 813 Santa Barbara Street, Pasadena, California 91101, USA. 3Nuclear Science Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA. 4Departments

of Physics and Astronomy, University of California, Berkeley, California 94720, USA.

5Dark Cosmology Centre, Niels Bohr Institute, University of Copenhagen, Blegdamsvej 17, 2100 Copenhagen, Denmark. 6Space Telescope Science Institute, 3700 San Martin Drive, Baltimore, Maryland 21218, USA. 7Institute for Astronomy, University of Hawai’i, 2680 Woodlawn Drive, Honolulu, Hawaii 96822, USA. 8Departamento de Física y Astronomía, Universidad de La Serena, La Serena, Chile.

The Dark Energy Camera GW-EM Collaboration and The DES Collaboration

J. Annis1, M. Soares-Santos2,1, D. Brout3, D. Scolnic4, H. T. Diehl1, J. Frieman1,4, E. Berger5, K. D. Alexander5, S. Allam1, E. Balbinot6, P. Blanchard7,

R. E. Butler8,1, R. Chornock9, E. R. Cook10,11, P. Cowperthwaite5,

A. Drlica-Wagner1, M. R. Drout12, F. Durret13, T. Eftekhari7, D. A. Finley1,

W. Fong14, C. L. Fryer15, J. García-Bellido16, M. S.S. Gill17, R. A. Gruendl18,19, C. Hanna20,19, W. Hartley21,22, K. Herner1, D. Huterer23, D. Kasen24,

R. Kessler4, T. S. Li1, H. Lin1, P. A. A. Lopes25, A. C. C. Louren?o25,

R. Margutti26, J. Marriner1, J. L. Marshall10, T. Matheson27, G. E. Medina28, B. D. Metzger29, R. R. Mu?oz28, J. Muir30, M. Nicholl5, P. Nugent31,

A. Palmese21, F. Paz-Chinchón19, E. Quataert32, M. Sako3, M. Sauseda10,

D. J. Schlegel33, L. F. Secco3, N. Smith34, F. Sobreira35,36, A. Stebbins1,

V. A. Villar7, A. K. Vivas37, W. Wester1, P. K. G. Williams7, B. Yanny1, A. Zenteno37, T. M. C. Abbott37, F. B. Abdalla21,38, K. Bechtol11, A. Benoit-Lévy39,21,40,

E. Bertin39,40, S. L. Bridle41, D. Brooks21, E. Buckley-Geer1, D. L. Burke42,17, A. Carnero Rosell36,43, M. Carrasco Kind18,19, J. Carretero44,

F. J. Castander45, C. E. Cunha42, C. B. D’Andrea3, L. N. da Costa36,43, C. Davis42, D. L. DePoy10, S. Desai46, J. P. Dietrich47,48, J. Estrada1, E. Fernandez44, B. Flaugher1,

P. Fosalba45, E. Gaztanaga45, D. W. Gerdes49,23, T. Giannantonio50–52,

D. A. Goldstein53,31, D. Gruen42,17, G. Gutierrez1, W. G. Hartley21,22,

K. Honscheid54,55, B. Jain3, D. J. James56, T. Jeltema57, M. W. G. Johnson19, S. Kent1,4, E. Krause42, R. Kron1,4, K. Kuehn58, S. Kuhlmann59, N. Kuropatkin1, O. Lahav21, M. Lima60,36, M. A. G. Maia36,43, M. March3, C. J. Miller49,23,

R. Miquel61,44, E. Neilsen1, B. Nord1, R. L. C. Ogando36,43, A. A. Plazas62,

A. K. Romer63, A. Roodman42,17, E. S. Rykoff42,17, E. Sanchez64, V. Scarpine1, M. Schubnell23, I. Sevilla-Noarbe64, M. Smith65, R. C. Smith37, E. Suchyta66, G. Tarle23, D. Thomas67, R. C. Thomas31, M. A. Troxel54,55, D. L. Tucker1,

V. Vikram59, A. R. Walker37, J. Weller47,68,52 & Y. Zhang1

1Fermi National Accelerator Laboratory, PO Box 500, Batavia, Illinois 60510, USA.

2Department of Physics, Brandeis University, Waltham, Massachusetts, USA. 3Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA. 4Kavli Institute for Cosmological Physics, University of Chicago, Chicago, Illinois 60637, USA. 5Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, Cambridge, Massachusetts 02138, USA. 6Department of Physics, University of Surrey, Guildford GU2 7XH, UK. 7Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, Cambridge, Massachusetts 02138, USA. 8Department of Astronomy, Indiana University, 727 East Third Street, Bloomington, Indiana 47405, USA. 9Astrophysical Institute, Department of Physics and Astronomy, 251B Clippinger Lab, Ohio University, Athens, Ohio 45701, USA. 10George P. and Cynthia Woods Mitchell Institute for Fundamental Physics and Astronomy, and Department of Physics and Astronomy, Texas A&M University, College Station, Texas 77843, USA. 11LSST, 933 North Cherry Avenue, Tucson, Arizona 85721, USA. 13The Observatories of the Carnegie Institution for Science, 813 Santa Barbara Street, Pasadena, California 91101, USA. 14Institut d’Astrophysique de Paris (UMR7095: CNRS and UPMC), 98 bis Bd Arago, F-75014 Paris, France. 15Center

for Interdisciplinary Exploration and Research in Astrophysics (CIERA) and Department of Physics and Astronomy, Northwestern University, Evanston, Illinois 60208, USA. 17Center for Theoretical Astrophysics, Los Alamos National Laboratory, Los Alamos, New Mexico 87544. 18Instituto de Fisica Teorica UAM/CSIC, Universidad Autonoma de Madrid, 28049 Madrid, Spain. 19SLAC National Accelerator Laboratory, Menlo Park, California 94025, USA. 20Department of Astronomy, University of Illinois, 1002 West Green Street, Urbana, Illinois 61801, USA. 21National Center for Supercomputing Applications, 1205 West Clark Street, Urbana, Illinois 61801, USA. 22Department of Physics and Astronomy and Astrophysics,The Pennsylvania State University, University Park, Pennsylvania 16802, USA. 23Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT, UK. 24Department of Physics, ETH Zurich, Wolfgang-Pauli-Strasse 16, CH-8093 Zurich, Switzerland. 25Department of Physics, University of Michigan,

Ann Arbor, Michigan 48109, USA. 26Departments of Physics and Astronomy, and Theoretical Astrophysics Center, University of California, Berkeley, California 94720-7300, USA. 27Observatòrio do Valongo, Universidade Federal do Rio de Janeiro, Ladeira do Pedro Ant?nio 43, Rio de Janeiro, RJ 20080-090, Brazil. 28Center for Interdisciplinary Exploration and Research in Astrophysics (CIERA) and Department of Physics and Astronomy, Northwestern University, Evanston, Illinois 60208, USA. 29National Optical Astronomy Observatory, 950 North Cherry Avenue, Tucson, Arizona 85719, USA.

30Departamento de Astronomonía, Universidad de Chile, Camino del Observatorio 1515, Las Condes, Santiago, Chile. 31Department of Physics and Columbia Astrophysics Laboratory, Columbia University, New York, New York 10027, USA. 32Department of Physics, University of Michigan, 450 Church Street, Ann Arbor, Michigan 48109-1040, USA. 33Lawrence Berkeley National Laboratory, 1 Cyclotron Road, Berkeley, California 94720, USA. 34Department of Astronomy and Theoretical Astrophysics Center, University of California, Berkeley, California 94720-3411, USA. 35Physics Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720-8160, USA. 36Steward Observatory, University of Arizona, 933 North Cherry Avenue, Tucson, Arizona 85721, USA. 37Instituto de Física Gleb Wataghin, Universidade Estadual de Campinas, Campinas SP 13083-859, Brazil. 38Laboratório Interinstitucional de e-Astronomia — LIneA, Rua Gal. José Cristino 77, Rio de Janeiro, RJ 20921-400, Brazil. 39Cerro Tololo Inter-American Observatory, National Optical Astronomy Observatory, Casilla 603, La Serena, Chile. 40Department

of Physics and Electronics, Rhodes University, PO Box 94, Grahamstown 6140, South Africa. 41CNRS, UMR 7095, Institut d’Astrophysique de Paris, F-75014 Paris, France.

42Sorbonne Universités, UPMC Université Paris 06, UMR 7095, Institut d’Astrophysique de Paris, F-75014 Paris, France. 43Jodrell Bank Center for Astrophysics, School of Physics and Astronomy, University of Manchester, Oxford Road, Manchester M13 9PL, UK. 44Kavli Institute for Particle Astrophysics and Cosmology, PO Box 2450, Stanford University, Stanford, California 94305, USA. 45Observatório Nacional, Rua General José Cristino 77, Rio de Janeiro, RJ 20921-400, Brazil. 46Institut de Física d’Altes Energies (IFAE), The Barcelona Institute of Science and Technology, Campus UAB, 08193 Bellaterra, Spain.

47Institute of Space Sciences, IEEC-CSIC, Campus UAB, Carrer de Can Magrans, 08193 Barcelona, Spain. 48Department of Physics, IIT Hyderabad, Kandi, Telangana 502285, India. 49Excellence Cluster Universe, Boltzmannstrasse 2, 85748 Garching, Germany.

50Faculty of Physics, Ludwig-Maximilians-Universit?t, Scheinerstrasse 1, 81679 Munich, Germany. 51Department of Astronomy, University of Michigan, Ann Arbor, Michigan 48109, USA. 52Institute of Astronomy, University of Cambridge, Madingley Road, Cambridge CB3 0HA, UK. 53Kavli Institute for Cosmology, University of Cambridge, Madingley Road, Cambridge CB3 0HA, UK. 54Universit?ts-Sternwarte, Fakult?t für Physik, Ludwig-Maximilians Universit?t München, Scheinerstrasse 1, 81679 München, Germany. 55Department of Astronomy, University of California, Berkeley, 501 Campbell Hall, Berkeley, California 94720, USA. 56Center for Cosmology and Astro-Particle Physics, The Ohio State University, Columbus, Ohio 43210, USA. 57Department of Physics, The Ohio State University, Columbus, Ohio 43210, USA. 58Astronomy Department, University of Washington, Box 351580, Seattle, Washington 98195, USA. 59Santa Cruz Institute

for Particle Physics, Santa Cruz, California 95064, USA. 60Australian Astronomical Observatory, North Ryde, New South Wales 2113, Australia. 61Argonne National Laboratory, 9700 South Cass Avenue, Lemont, Illinois 60439, USA. 62Departamento de

Física Matemática, Instituto de Física, Universidade de S?o Paulo, CP 66318, S?o Paulo, SP 05314-970, Brazil. 63Institució Catalana de Recerca i Estudis Avan?ats, E-08010 Barcelona, Spain. 64Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Drive, Pasadena, California 91109, USA. 65Department of Physics and Astronomy, Pevensey Building, University of Sussex, Brighton BN1 9QH, UK. 66Centro de Investigaciones Energéticas, Medioambientales y Tecnológicas (CIEMAT), Madrid, Spain. 67School of Physics and Astronomy, University of Southampton, Southampton SO17

1BJ, UK. 68Computer Science and Mathematics Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831. 69Institute of Cosmology and Gravitation, University of Portsmouth, Portsmouth PO1 3FX, UK. 70Max Planck Institute for Extraterrestrial Physics, Giessenbachstrasse, 85748 Garching, Germany.

The DLT40 Collaboration

J. B. Haislip1, V. V. Kouprianov1, D. E. Reichart1, L. Tartaglia2,3, D. J. Sand2, S. Valenti3 & S. Yang3,4,5

1Department of Physics and Astronomy, University of North Carolina at Chapel Hill, Chapel Hill, North Carolina 27599, USA. 2Department of Astronomy and Steward Observatory, University of Arizona, 933 North Cherry Ave, Tucson, Arizona 85719, USA.

3Department of Physics, University of California, 1 Shields Avenue, Davis, California 95616-5270, USA. 4Department of Physics and Astronomy, University of Padova, Via 8 Febbraio, I-35122 Padova, Italy. 5INAF Osservatorio Astronomico di Padova, Vicolo della Osservatorio 5, I-35122 Padova, Italy.

The Las Cumbres Observatory Collaboration

Iair Arcavi1,2, Griffin Hosseinzadeh1,2, D. Andrew Howell1,2, Curtis McCully1,2, Dovi Poznanski3 & Sergiy Vasylyev1,2

1Department of Physics, University of California, Santa Barbara, California 93106-9530, USA. 2Las Cumbres Observatory, 6740 Cortona Drive, Suite 102, Goleta, California 93117-5575, USA. 3School of Physics and Astronomy, Tel Aviv University, Tel Aviv 69978, Israel.

The VINrOUGE Collaboration

N. R. Tanvir1, A. J. Levan2, J. Hjorth3, Z. Cano4, C. Copperwheat5,

A. de Ugarte-Postigo4, P. A. Evans1, J. P. U. Fynbo3, C. González-Fernández6, J. Greiner7, M. Irwin6, J. Lyman2, I. Mandel8, R. McMahon6,

B. Milvang-Jensen3, P. O’Brien1, J. P. Osborne1, D. A. Perley5, E. Pian9, E. Palazzi9, E. Rol10,

S. Rosetti1, S. Rosswog11, A. Rowlinson12,13, S. Schulze14, D. T. H. Steeghs2, C. C. Th?ne4, K. Ulaczyk2, D. Watson3 & K. Wiersema1,2

1Department of Physics and Astronomy, University of Leicester, University Road, Leicester LE1 7RH, UK. 2Department of Physics, University of Warwick, Coventry CV4 7AL, UK.

3DARK, Niels Bohr Institute, University of Copenhagen, Juliane Maries Vej 30, 2100 Copenhagen ?, Denmark. 4Instituto de Astrofísica de Andalucía (IAA-CSIC), Glorieta

de la Astronomía, 18008 Granada, Spain. 5Astrophysics Research Institute, Liverpool John Moores University, IC2, Liverpool Science Park, 146 Brownlow Hill, Liverpool L3

5RF, UK. 6Institute of Astronomy, University of Cambridge, Madingley Road, Cambridge CB3 0HA, UK. 7Max-Planck-Institut für extraterrestrische Physik, 85740 Garching, Giessenbachstrasse 1, Germany. 8Birmingham Institute for Gravitational Wave Astronomy and School of Physics and Astronomy, University of Birmingham, Birmingham B15

2TT, UK. 9INAF, Institute of Space Astrophysics and Cosmic Physics, Via Gobetti 101,

I-40129 Bologna, Italy. 10School of Physics and Astronomy, and Monash Centre for Astrophysics, Monash University, Clayton, Victoria 3800, Australia. 11The Oskar Klein Centre, Department of Astronomy, AlbaNova, Stockholm University, SE-106 91 Stockholm, Sweden. 12Anton Pannekoek Institute, University of Amsterdam, Science Park 904,

1098 XH Amsterdam, The Netherlands. 13ASTRON, the Netherlands Institute for Radio Astronomy, Postbus 2, 7990 AA Dwingeloo, The Netherlands. 14Department of Particle Physics and Astrophysics, Weizmann Institute of Science, 76100 Rehovot, Israel.

The MASTEr Collaboration

V. M. Lipunov1,2, E. Gorbovskoy2, V. G. Kornilov1,2, N. Tyurina2, P. Balanutsa2, D. Vlasenko1,2, I. Gorbunov2, R. Podesta3, H. Levato4, C. Saffe4,

D. A. H.Buckley5, N. M. Budnev6, O. Gress6,2, V. Yurkov7, R. Rebolo8 &

M. Serra-Ricart8

1M. V. Lomonosov Moscow State University, Physics Department, Leninskie gory, GSP-1, Moscow 119991, Russia. 2M. V. Lomonosov Moscow State University, Sternberg Astronomical Institute, Universitetsky 13, Moscow 119234, Russia. 3Observatorio Astronomico Felix Aguilar (OAFA), National University of San Juan, San Juan, Argentina.

4Instituto de Ciencias Astronomicas,de la Tierra y del Espacio (ICATE), San Juan, Argentina. 5South African Astrophysical Observatory, PO Box 9, 7935 Observatory,

Cape Town, South Africa. 6Irkutsk State University, Applied Physics Institute, 20 Gagarin boulevard, 664003 Irkutsk, Russia. 7Blagoveschensk State Pedagogical University, Lenin street 104, Amur Region, Blagoveschensk 675000, Russia. 8Instituto de Astrofacuteisica de Canarias Via Lactea, E-38205La Laguna, Spain.

METHODS

Probability of optical counterpart association with NGC 4993. We calculate the probability that an NGC 4993-like galaxy (or brighter) is misidentified as the host by asking how often the centre of one or more such galaxies falls by random chance within a given angular radius θ of the counterpart. Assuming Poisson counting statistics this probability is given by P= 1 ? exp[?πθ2S(

Finding the Hubble velocity of NGC 4993. In previous electromagnetic deter-minations of the cosmic ‘distance ladder’, the Hubble flow velocity of the local c alibrating galaxies has generally been estimated using redshift-independent s econdary galaxy distance indicators, such as the Tully–Fisher relation or type Ia supernovae, calibrated with more distant samples that can be assumed to sit in quiet Hubble flow19. We do not adopt this approach for NGC 4993, however, so that our inference of the Hubble constant is fully independent of the e lectromagnetic distance scale. Instead we estimate the Hubble flow velocity at the position of NGC 4993 by correcting its measured recessional velocity for local peculiar motions.

NGC 4993 resides in a group of galaxies whose center-of-mass recession v elocity relative to the CMB frame26 is27 3,327 ± 72 km s?1. We assume that all of the g alaxies in the group are at the same distance and therefore have the same Hubble flow velocity, which we assign to be the Hubble velocity of GW170817. This assumption is accurate to within 1% given that the radius of the group is approxi-mately 0.4 Mpc. To calculate the Hubble flow velocity of the group, we correct its measured recessional velocity by the peculiar velocity caused by the local gravita-tional field. This is a large correction28,29; typical peculiar velocities are 300 km s?1, equivalent to about 10% of the total recessional velocity at a distance of 40 Mpc. We use the 6dF galaxy redshift survey peculiar velocity map28,36, which used more than 8,000 Fundamental Plane galaxies to map the peculiar velocity field in the southern hemisphere out to redshift z≈ 0.055. We weight the peculiar v elocity corrections from this catalogue with a Gaussian kernel centered on the sky p osition of NGC 4993 and with a width of 8h?1 Mpc; the kernel width is i ndependent of H0 and is equivalent to a width of 800 km s?1 in velocity space, typical of the widths used in the catalogue itself. There are ten galaxies in the 6dF peculiar v elocity catalogue within one kernel width of NGC 4993. In the CMB frame26, the weighted radial component of the peculiar velocity and associated uncertainty is ?v p?= 310 ± 69 km s?1.

We verified the robustness of this peculiar velocity correction by comparing it with the velocity field reconstructed from the 2MASS redshift survey29,37. This exploits the linear relationship between the peculiar velocity and mass d ensity fields smoothed on scales larger than about 8h?1 Mpc, and the constant of p roportionality can be determined by comparison with radial peculiar velocities of individual galaxies estimated from, for example, Tully–Fisher and type Ia super-novae distances. Using these reconstructed peculiar velocities, which have a larger associated uncertainty29 of 150 km s?1, at the position of NGC 4993 we find a Hubble velocity in the CMB frame of v H= 3,047 km s?1—in excellent agreement with the result derived using 6dF. We adopt this larger uncertainty on the peculiar velocity correction in recognition that the peculiar velocity estimated from the 6dF data may represent an imperfect model of the true bulk flow at the location of NGC 4993. For our inference of the Hubble constant we therefore use a Hubble velocity v H= 3,017 ± 166 km s?1 with 68.3% uncertainty.

Finally, we emphasize again the independence of our Hubble-constant i nference from the electromagnetic distance scale, but note the consistency of our g ravitational-wave distance estimate to NGC 4993 with the Tully–Fisher distance estimate derived by scaling back the Tully–Fisher relation calibrated with more distant galaxies in quiet Hubble flow25. This consistency also strongly supports the robustness of our estimate for the Hubble velocity of NGC 4993.

Summary of the model. Given observed data from a set of gravitational-wave detectors, x GW, parameter estimation is used to generate a posterior on the p arameters that determine the waveform of the gravitational-wave signal. Parameters are inferred within a Bayesian framework38 by comparing strain m easurements3 in the two LIGO detectors and the Virgo detector with the gravi-tational waveforms expected from the inspiral of two point masses39 under general relativity. We use algorithms for removing short-lived detector noise artefacts3,40 and use approximate point-particle waveform models39,41,42. We have verified that the systematic changes in the results presented here from incorporating non-point-mass (tidal) effects43,44 and from different data processing methods are much smaller than the statistical uncertainties in the measurement of H0 and the orbital inclination angle of the binary.

From this analysis we can obtain the parameter estimation likelihood of the observed gravitational-wave data, marginalized over all parameters that charac-terize the gravitational-wave signal except d and cosι:

∫λλλ

ιι

|=|

p x d p x d p

(,cos)(,cos,)()d

GW GW

The other waveform parameters are denoted by λ, with p(λ) denoting the c orresponding prior.

Given perfect knowledge of the Hubble flow velocity of the gravitational-wave source v H, this posterior distribution can be readily converted into a posterior on cosι and H0=v H/d:

ιιι

|∝/|=//ιp H x v H p x d v H p v H p

(,cos)()(,cos)()(cos)

d

0GW H0

2

GW H0H0

where p d(d) and pι(cosι) are the prior distributions on distance and inclina-tion. For the Hubble velocity v H= 3,017 km s?1, the maximum a posteriori distance from the gravitational-wave measurement of 43.8 Mpc corresponds to H0= 68.9 km s?1 Mpc?1, so this procedure would be expected to generate a pos-terior on H0 that peaks close to that value.

Although the above analysis is conceptually straightforward, it makes several assumptions. In practice, the Hubble flow velocity cannot be determined exactly and must be corrected for uncertain peculiar velocities. This correction does not explicitly set a prior on H0, but instead inherits a /H

104 prior from the usual p d(d) ∝ d2 prior used in gravitational-wave parameter estimation. In addition, the logic in this model is that a redshift has been obtained first and the distance is then measured using gravitational waves. Because gravitational-wave detectors cannot be pointed, we cannot target particular galaxies or redshifts for gravitational-wave sources. In practice, we wait for a gravitational-wave event to trigger the analysis and this introduces potential selection effects that we must consider. We see below that the simple analysis described above does give results that are consistent with a more careful analysis for this first detection. However, the simple analysis cannot be readily extended to include second and subsequent detections, so we now describe a more general framework that does not suffer from these limitations. We suppose that we have observed a gravitational-wave event, which generated data x GW in our detectors, and that we have also measured a recessional velocity for the host v r and the peculiar velocity field ?v p? in the vicinity of the host. These observations are statistically independent and so the combined likelihood is

ιι

??|=||??|

p x v v d v H p x d p v d v H p v v

(,,,cos,,)(,cos)(,,)()(2) GW r p p0GW r p0p p

The quantity p(v r | d, v p, H0) is the likelihood of the recessional velocity measure-ment, which we model as

σ

|=+

p v d v H N v H d v

(,,)[,]()

v

r p0p0

2

r

r

where N[μ, σ2](x) is the normal (Gaussian) probability density with mean μ and standard deviation σ evaluated at x. The measured recessional velocity v r= 3,327 km s?1, with uncertainty σ=?

72kms

v

1

r

, is the mean velocity and s tandard error for the members of the group hosting NGC 4993 taken from 2MASS27, corrected to the CMB frame26. We take a similar Gaussian likelihood for the m easured peculiar velocity ?v p?= 310 km s?1, with uncertainty σ=?

150kms

v

1

p

:

σ

??|=??

p v v N v v

()[,]()

v

p p p

2

p

p

From the likelihood in equation (2) we derive the posterior

ιι

ι

|??∝||

×??|

N

p H d v x v v p H p x d p v d v H

p v v p d p v p

(,,cos,,,)()(,cos)(,,)

()()()(cos)

(3)

0p GW r p

s0

GW r p0

p p p

where p(H0), p(d), p(v p) and p(cosι) are the parameter prior probabilities. Our standard analysis assumes a volumetric prior, p(d) ∝ d2, on the Hubble distance, but we explore sensitivity to this choice below. We take a flat-in-log(H0) prior, p(H0) ∝ 1/H0, and impose a flat (that is, isotropic) prior on cosι and a flat prior on v p for v p ∈ [?1,000, 1,000] km s?1. These priors characterize our beliefs about the cosmological population of gravitational-wave events and their hosts before we make any additional measurements or account for selection biases. The full statistical model is summarized graphically in Extended Data Fig. 1. This model with these priors is our canonical analysis.

In equation (3), the term N s(H0) encodes selection effects23,45,46. These arise because of the finite sensitivity of our detectors. Although all events in the Universe generate a response in the detector, we will be able to identify, and hence use, only

signals that generate a response of sufficiently high amplitude. The decision about whether to include an event in the analysis is a property of the data only, in this case {x GW , v r , ?v p ?}, but the fact that we condition our analysis on a signal being detected, that is, the data exceeding these thresholds, means that the likelihood must be renormalized to become the likelihood for detected events. This is the role of

λλλιιι=

||??|×??

N H p x d p v d v H p v v p p d p v p d v x v v ()[(,cos ,)(,,)()

()()()(cos )]d d d dcos d d d (4)

s 0detectable

GW r p 0p p p p GW r p where the integral is over the full prior ranges of the parameters {d , v p , cos ι, λ} and over datasets that would be selected for inclusion in the analysis (that is, that exceed the specified thresholds). If the integral was over all datasets then it would evaluate to 1, but because the range is restricted there can be a non-trivial dependence on parameters characterizing the population of sources, in this case H 0.

In our analysis, there are in principle selection effects in both the

g ravitational-wave data and the electromagnetic data. However, around the time of detection of GW170817, the LIGO–Virgo detector network had a detection horizon of approximately 190 Mpc for binary neutron-star events 3, within which electromagnetic measurements are largely complete. For example, the counterpart associated with GW170817 had a brightness of about 17 mag in the I band at 40 Mpc (refs 8–13); this source would be about 22 mag at 400 Mpc, and there-fore still detectable by survey telescopes such as DECam well beyond the grav-itational-wave horizon. Even the dimmest theoretical light curves for k ilonovae

are expected to peak at about 22.5 mag at the LIGO–Virgo horizon 47

. We there-fore expect that gravitational-wave selection effects are dominant and ignore e lectromagnetic selection effects. The fact that the fraction of binary neutron-star events that will have observed kilonova counterparts is presently unknown does not modify these conclusions, because we can restrict our analysis to only

g ravitational-wave events with kilonova counterparts.For the gravitational-wave data, the decision about whether or not to a nalyse an event is determined largely by the signal-to-noise ratio ρ of the event. A r easonable model for the selection process is a cut in signal-to-noise ratio; that is, events with ρ > ρ* are analysed 48. In that model, the integral over x GW in equation (4) can be replaced by an integral over signal-to-noise ratio from ρ* to ∞, and p (x GW | d , cos ι, λ) replaced by p (ρ | d , cos ι, λ) in the integrand. This distribution depends on the noise properties of the operating detectors and on the intrinsic strain amplitude of the source. The former are clearly independent of the popula-tion parameters, whereas the latter scales as a function of the source parameters divided by the luminosity distance. The dependence on source parameters is on redshifted parameters, which introduces an explicit redshift dependence. However, within the approximately 190-Mpc horizon redshift corrections are at most about 5%, and the Hubble constant measurement is a weak function of these, m eaning that the overall effect is even smaller. At present, whether or not a p articular event in the population ends up being analysed can therefore be regarded as a function of d only. When gravitational-wave selection effects dominate, only the terms in equation (4) arising from the gravitational-wave measurement matter. Because these are a function of d only and we set a prior on d , there is no explicit H 0 dependence in these terms. Hence, N s (H 0) is a constant and can be ignored. This would not be the case if we set a prior on the redshifts of potential sources instead of their distances, because then changes in H 0 would modify the range of d etectable redshifts. As the LIGO–Virgo detectors improve in sensitivity, the redshift d ependence in the g ravitational-wave selection effects will become more important, as will electromagnetic selection effects. However, at that point we will also have to consider deviations in the cosmological model from the simple Hubble flow described in equation (1).

Marginalizing equation (3) over d , v p and cos ι then yields

∫ιιι

|??∝||??|×p H x v v p H p x d p v d v H p v v p d p v p d v (,,)()

[(,cos )(,,)()

()()(cos )]d d dcos 0GW r p 0GW r p 0p p p p The posterior computed in this way is shown in Fig. 1 and has a maximum a

p osteriori value and minimal 68.3% credible interval of .?.+.??700kms Mpc 8012011.

The posterior mean is 78 km s ?1 Mpc ?1 and the standard deviation is 15 km s ?1 Mpc ?1. Various other summary statistics are given in Extended Data Table 1.

Robustness to prior specification. Our canonical analysis uses a uniform

v olumetric prior on distance, p (d ) ∝ d 2. The distribution of galaxies is not

c ompletely uniform owing to clustering, so we explore sensitivity to this prior choice. We are free to place priors on any two of the three variables {

d , H 0, z },

where z = H 0d /c is the Hubble flow redshift of NGC 4993. A choice of prior for two of these variables induces a prior on the third that may or may not correspond to a natural choice for that parameter. A prior on z could be obtained from galaxy catalogue observations 49, but must be corrected for incompleteness. When setting a prior on H 0 and z , the posterior becomes

ιιι|??∝|=/|×??|N p H z v x v v p H H p x d cz H p v z v p v v p z p v p (,,cos ,,,)()

()

(,cos )(,)

()()()(cos )

0p GW r p 0s 0GW 0r p p p p but now

ιιι=

|=/|×??|??

N H p x d cz H p v z v p v v p z p v p z v x v v ()[(,cos )(,)

()()()(cos )]d d dcos d d d r p s 0detectable

GW 0p p p p GW r p When gravitational-wave selection effects dominate, the integral is effectively

∫∫ιιιιιι=

|=/=|//N H p x d cz H p z p z x p x d p dH c p H c d x ()(,cos )()(cos )d dcos d (,cos )()(cos )()d dcos d s 0GW 0GW GW 00GW

which has an H 0 dependence, unless p (z ) takes a special, H 0-dependent form, p (z ) = f (z /H 0)/H 0. However, if the redshift prior is volumetric, p (z ) ∝ z 2, then the selection-effect term is proportional to H 03, which cancels a similar correction to the likelihood and gives a posterior on H 0 that is identical to the canonical analysis.For a single event, any choice of prior can be mapped to our canonical analysis with a different prior on H 0. For any reasonable prior choices on d or z , we would expect to gradually lose sensitivity to the particular prior choice as further observed events are added to the analysis. However, to illustrate the uncertainty that comes from the prior choice for this first event, we compare in Extended Data Fig. 2 and Extended Data Table 1 the results from the canonical prior choice p (d ) ∝ d 2 to those from two other choices: using a flat prior on z , and assuming a velocity correction due to the peculiar velocity of NGC 4993 that is a Gaussian with width 250 km s ?1. (To do the first of these, the posterior samples from gravitational-wave parameter estimation have to be re-weighted, because they are generated with

the d 2

prior used in the canonical analysis. We first ‘undo’ the default prior before applying the desired new prior.)

The choice of a flat prior on z is motivated by the simple model described above, in which we imagine first making a redshift measurement for the host and then use that as a prior for analysing the gravitational-wave data. Setting priors on distance and redshift, the simple analysis gives the same result as the canonical analysis, but now we set a prior on redshift and H 0 and obtain a different result. This is to be expected because we are making different assumptions about the u nderlying

p opulation, and it arises for similar reasons as the different biases in peculiar v elocity measurements based on redshift-selected or distance-selected samples 50. As can be seen in Extended Data Table 1, the results change by less than 1σ, as measured by the statistical error of the canonical analysis.

By increasing the uncertainty in the peculiar velocity prior, we test the assump-tions in our canonical analysis that (1) NGC 4993 is a member of the nearby group of galaxies, and (2) that this group has a center-of-mass velocity close to the Hubble flow. The results in Extended Data Table 1 summarize changes in the values of H 0 and in the error bars.

We conclude that the effect of a reasonable change to the prior is small relative to the statistical uncertainties for this event.

Incorporating additional constraints on H 0. By including previous measure-ments 20,21 of H 0 we can constrain the orbital inclination more precisely. We do this

by setting the H 0 prior in equation (3) to μσμσ|=p H N (,)[,]H H H H 022

0000

, where for ShoES 21 μ=.??7324kms Mpc H 110 and σ=.??174km s Mpc H 110, and for Planck 20 μ=.??6774kms Mpc H 110 and σ=.??046kms Mpc H 110. The posterior on cos ι is then

∫ιμσιμσ|??∝||??|×|p x v v p x d p v d v H p v v p H p d p v d v H (cos ,,,,)[(,cos )(,,)()

(,)()()]d d d H H H H GW r p 2

GW r p 0p p 02

p p 000

00

This posterior is shown in Fig. 3.

Data and code availability. The publicly available codes and data can be found at the LIGO Open Science Center (https://https://www.sodocs.net/doc/a91237950.html,).

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Extended Data Figure 1 | Graphical model illustrating the statistical relationships between the data and parameters. Open circles indicate parameters that require a prior; filled circles describe measured data, which are conditioned on in the analysis. Here we assume that we have measurements of the gravitational-wave data x GW, a recessional velocity (that is, redshift) v r, and the mean peculiar velocity in the neighborhood of NGC 4993 ?v p?. Arrows flowing into a node indicate that the conditional probability density for the node depends on the source parameters; for example, the conditional distribution for the observed gravitational-wave data p(x GW | d, cosι) depends on the distance and inclination of the source (and additional parameters, here marginalized out).

Extended Data Figure 2 | Using different assumptions compared to our canonical analysis. The posterior distribution on H0 discussed in the main text is shown in black, the alternative flat prior on z (discussed in Methods) gives the distribution shown in blue, and the increased uncertainty (250 km s?1) applied to our peculiar velocity measurement (also discussed in Methods) is shown in pink. Minimal 68.3% (1σ) credible intervals are shown by dashed lines.

Extended Data T able 1 | Summary of constraints on the Hubble constant, binary inclination and distance

We give both 1σ (68.3%) and 90% credible intervals for each quantity. ‘Symm.’ refers to a symmetric interval (for example, median and 5%–95% range); ‘MAP’ refers to maximum a posteriori intervals (for example, MAP value and smallest range enclosing 90% of the posterior). Values given for ι are derived from arccosine-transforming the corresponding values for cosι, so the ‘MAP’ values differ from those that would be derived from the posterior on ι.

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