Astronomy

What actually determines the angular uncertainty of the source of a detected gravitational wave?

What actually determines the angular uncertainty of the source of a detected gravitational wave?


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This answer and comments got me thinking. Astrometry 101 tells us that while we can use $lambda/D$ as an estimator of resolution, if we can assume a point source we can determine the centroid or position to far higher precision.

For example, GAIA's design targets for precision were roughly 7, 20, and 200 micro-arcseconds for visual magnitudes 10, 15, and 20, respectively whereas $lambda/D$ gives 70,000 x 200,000 micro-arcseconds for its rectangular mirror.

The limitations are both instrumental beyond just the aperture or baseline, and connected to the nature of the signal, and that's were determining the direction of a gravitational wave source is very different than determining the direction of a star's light.

Question: For gravitational waves then, what actually determines the angular uncertainty of the source direction? Does it turn out to be baseline-limited (e.g. $lambda/D$) or instrument-limited, or limited by the very short-lived and chirped nature of the signal? Or is it something else, perhaps in the modeling and reconstruction of the event itself?

From ligo.caltech.edu's Gravitational-Wave Observatories Across the Globe just for background:


Quantum Astronomy: Information in the Universe

This is a short addition to the four-part series on Quantum Astronomy previously written for SPACE.com. Here, we add some details resulting from the process of submitting a paper to the scientific literature. If you?d like to read the technical paper it is entitled, ?Quantum Uncertainty Considerations for Gravitational Lens Interferometry? by Doyle and Carico, and can be downloaded at the Web site:? http://www.bentham.org/open/toaaj/openaccess2.htm.

Having written about four dozen articles now for SPACE.com and I can say that none have given me as much feedback as the series on quantum astronomy? I think people intuit that quantum physics is still redefining how we think of science and what we think the fundamental nature of reality may be, and thus enjoy participating in this amazing modern adventure.

To quickly summarize the preceding series on the quantum astronomy, in the first article we looked at the double-slit experiment and how it appears to indicate that a single particle of light (a photon) travels through two slits (apertures) to make an interference pattern, apparently being in two places at once, and yet still be detected as a small particle when it registers on a detector screen. In the second article we looked at the uncertainty principle which requires that certain pairs of measurable quantities (position and momentum, for example) cannot both be measured accurately simultaneously. Time and energy are another such set of ?complimentary pairs? so that if one measures the energy of a particle really well, one cannot tell very accurately at what time the particle had that energy. This uncertainty principle can be manipulated?one might say that one can trade off one kind of information for another, as long as ignorance is conserved.?

In the third article we noted that waves associated with particles in quantum physics are waves of probability (not waves like ocean waves, although they do share many characteristics). So what one can know or cannot know about, for example, which path a photon took to a detector, actually determines what one will detect?for example whether an interference pattern is detected or not. If one cannot tell which path a photon took to a detector, one can get interference, but not otherwise. And finally, in the fourth article, we discussed doing a cosmic-scale double-slit experiment, first proposed by John Wheeler of Princeton University, where a decision about which path a photon takes around a gravitational lens (a galaxy aligned so it can bend light from a more distance quasar) can be decided long after?even billions of years after?the photon had supposedly already left the source and traveled along one path or the other. This was called the ?cosmic-scale delayed-choice? experiment.

To review this experiment, John Wheeler (a colleague of Einstein?s) proposed that light from a quasar about 7 billion light years away is split by a gravitational lens, and so we have light traveling to us along two paths?A (the shorter path) and B (the longer path, that encounters more of the gravitational lensing galaxy and whose path is ?bent? toward us). If a fiber optics cable (trillions of miles long would be needed) could be used to make the distance along the shorter path A equal to the distance along path B, then one could get an interference pattern rather than just an image of A superimposed on an image of B at the detector. But, interestingly, at the detection rate of one photon at a time, that would mean one could decide to have the photon travel both paths at the last moment rather than just path A (or B) ? deciding this 7 billion years after the photon supposedly left the quasar! Thus this experiment really meant delayed-choice, to the point where John Wheeler could talk about his hypothetical experiment in terms of altering ?history.? But it could only be thought at the time (such thought-only experiments were dubbed ?gedanken? experiments by Albert Einstein).

Changing this experiment from a gedanken experiment to a performable experiment,? my colleague Dr. David Carico and I proposed that one might actually utilize the uncertainty principle itself to replace the trillions-of-miles-long fiber optics cable. This notion was based on the idea that, since knowability or unknowability is the important consideration (rather than actual distances involved),? we proposed not so much to make the two paths a photon traveled equal, but rather to just render any difference in the length of the two paths unmeasureable (i.e., unknowable). We proposed that by knowing the energy of the photon very well (by using a narrow band radio filter, for example) that the time that the photon actually had that energy would be unknowable (since time is the complimentary pair of energy). So, if the unknowability in the time is unmeasureably longer than the delay time between the light paths of the gravitational lens itself, then the two paths are, essentially, ?unmeasureably equal,? and one cannot tell which path the photon took. If one persists in thinking classically, the photon can then be said to have taken both paths then. To put it in physics-ese, we have used the uncertainty principle as a quantum eraser ? it erases the quantum nature of a photon, making it a probability wave again, which can ?exist? (if probability wave can be said to exist) along both possible paths again.

We did have to go through some mighty refereeing to get this paper in print, however. One of the biggest doubts about this experiment working was related to using it on extended objects in the sky. It was aid that one may measure a point source ?traveling? along two paths then, but what if the source is a whole extended galaxy? Well, even galaxies can be thought of as being made up of a lot of ?point? sources, so we argued that the technique would still nevertheless apply, as long as one could not tell what the extent of the actual galaxy (angular size on the sky) was. We did this by introducing what is called a ?Mach-Zehnder Interferometer?(MZI) which,? unlike a double-slit set-up, cannot tell the angular extent of a photon source because it does not produce an interference pattern ? it only indicates whether interference is taking place or not. (For those familiar with the MZI, the gravitational lens itself is the first beam splitter in the system and has an effective refractive index so can change the phase of the light. For those of you not familiar with the MZI, thanks for hanging in there so far!)?

We also talked with many physicists about this idea and all were encouraging. Freeman Dyson of Princeton Institute for Advanced Studies told us, ?I think you?re OK.? Andre Linde of Stanford University said, ?These things are tricky.? Daniel Greenberger of City College of New York said, ?I think it is worth a try.? And John Wheeler (at a scientific meeting on the occasion of his 90th birthday) said, ?That?s very interesting. I hope you succeed.? Of course the actual referees for our paper were more detailed and the process did drag on for a couple of years. Scientists are usually very friendly and happy to discuss new ideas, but when something is going into the refereed scientific literature, that is a whole ?nother story.

One referee wrote, ?The validity of the claim that interference would be observed between extended sources if observed through a sufficiently narrow band filter is absolutely critical?.if it is right the implications would be extremely profound, and extend far beyond the narrow confines of measuring time delays in lensed systems, as it would completely undermine the conventional understanding of how interferometry works.? I have to confess that as I read this at this point I thought ?Gulp.? But I also realized that?barring anything we and the referees and editors overlooked?on the other hand, if this experiment did not work it would be a more radical departure for physics than if it did. This is because it would imply that the quantum uncertainty principle itself did not apply in some circumstances?did not, for example, extend over macroscopic distances. So, with this argument, our paper was finally accepted.

The great quantum physicist, Richard Feynman, once said (to paraphrase) If you think you understand quantum physics then you don?t understand enough to understand that you don?t understand it! And Einstein himself once wrote, ?I have thought a hundred times as much about the quantum problems as I have about general relativity theory.? We can relate. And you are also most welcome to join Einstein?s ?hundred times? club. You, too, may begin thinking of the universe, not so much in terms of material objects, but rather in terms of information. And as quantum measurement begins to leave the laboratory and extend throughout space I think we?re all in for a lot of surprises. And a lot of fun too.


Precision interferometry for gravitational wave detection: Current status and future trends

Abstract

Gravitational wave detectors rely on ultra-high precision interferometry to detect dynamic strains arising from fluctuations in space-time from cataclysmic astrophysical events. The resulting displacements occur on the sub-attometer and smaller levels. To achieve this unprecedented level of measurement precision, kilometer length-scale interferometers have been developed and refined in the past 20 years. Gravitational wave interferometers make use of a broad array of technologies: the world's most stable high power lasers, the most precisely figured mirrors, ultraquiet vibration isolation systems, and sophisticated hierarchical feedback systems. This article explores the physics, engineering, and optical techniques underlying gravitational wave interferometers, and attempts to give the reader a sense of the breadth of science and technology needed to make interferometers perform at these unparalleled levels.


What actually determines the angular uncertainty of the source of a detected gravitational wave? - Astronomy

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The Highest Energy Neutrino Alerts

After the discovery of high-energy astrophysical neutrinos in 2013, IceCube has learned to identify astrophysical neutrinos and measure their directions within seconds of their observation.

There are currently two different real-time analyses that reconstruct the highest energy neutrinos and send immediate alerts. Information about these events is shared as a GCN alert within a minute after detection.

These alerts are coordinated by the GCN/TAN network—the Gamma-Ray Burst Coordinates Network and the Transient Astronomy Network—that was initially created to facilitate follow-up observations of GRBs by spaceborne detectors. Currently, they include many other instruments and also track non-GRB transients- such as the flaring of active galaxies.

IceCube HESE alerts announce the detection of a single high-energy neutrino that interacts inside the instrumented volume of ice. Uncertainty in the location depends on the energy of the neutrino and the specific pattern of Cherenkov light in the detector. Muon tracks, a common signature for muon neutrinos, point with a typical error of 1.5 degrees. The pointing resolution for cascades, a common signature for electron and tau neutrinos, is only 10 degrees but is being improved. The frequency of these alerts is three to four times per year. The first alert was sent in April 2016.

IceCube EHE alerts announce the detection of a single extremely high-energy neutrino coming from the Northern Hemisphere, i.e., one that reaches IceCube after passing through Earth, thus filtering out all background. Uncertainty in the location depends mainly on the energy since these are always track signatures. Typical pointing errors are less than 0.5 degrees. They occur four to six times per year. The first alert was sent in July 2016.


Author information

Affiliations

LIGO, California Institute of Technology, Pasadena, 91125, California, USA

B. P. Abbott, R. Abbott, R. X. Adhikari, A. Ananyeva, S. B. Anderson, S. Appert, K. Arai, M. C. Araya, J. C. Barayoga, B. C. Barish, B. K. Berger, G. Billingsley, S. Biscans, J. K. Blackburn, C. D. Blair, R. Bork, A. F. Brooks, S. Brunett, C. Cahillane, T. A. Callister, C. B. Cepeda, M. W. Coughlin, P. Couvares, D. C. Coyne, P. Ehrens, J. Eichholz, T. Etzel, J. Feicht, E. M. Fries, S. E. Gossan, K. E. Gushwa, E. K. Gustafson, A. W. Heptonstall, M. Isi, B. Kamai, J. B. Kanner, V. Kondrashov, W. Z. Korth, D. B. Kozak, A. Lazzarini, A. Markowitz, E. Maros, T. J. Massinger, F. Matichard, G. McIntyre, J. McIver, S. Meshkov, L. Nevin, M. Pedraza, A. Perreca, E. A. Quintero, D. H. Reitze, N. A. Robertson, J. G. Rollins, S. Sachdev, E. J. Sanchez, L. E. Sanchez, P. Schmidt, R. J. E. Smith, R. Taylor, C. I. Torrie, R. Tso, A. L. Urban, G. Vajente, S. Vass, G. Venugopalan, A. R. Wade, L. Wallace, A. J. Weinstein, S. E. Whitcomb, R. D. Williams, J. L. Willis, C. C. Wipf, S. Xiao, H. Yamamoto, L. Zhang, M. E. Zucker & J. Zweizig

Louisiana State University, Baton Rouge, 70803, Louisiana, USA

T. D. Abbott, C. Austin, C. C. Buchanan, T. R. Corbitt, J. Cripe, T. J. Cullen, J. A. Giaime, G. González, T. Hardwick, W. W. Johnson, M. Kasprzack & G. Valdes

Università di Salerno, Fisciano, I-84084, Salerno, Italy

F. Acernese, F. Barone & R. Romano

INFN, Sezione di Napoli, Complesso Universitario di Monte S.Angelo, Napoli, I-80126, Italy

F. Acernese, F. Barone, E. Calloni, M. De Laurentis, R. De Rosa, L. Di Fiore, T. Di Girolamo, F. Garufi, A. Grado, L. Milano & R. Romano

University of Florida, Gainesville, 32611, Florida, USA

K. Ackley, I. Bartos, C. R. Billman, H.-P. Cheng, H. Chia, G. Ciani, C. F. Da Silva Costa, S. S. Eikenberry, P. Fulda, R. Goetz, S. Klimenko, A. L. Miller, G. Mitselmakher, G. Mueller, L. F. Ortega, D. H. Reitze, D. B. Tanner, J. Trinastic, B. F. Whiting & M. Yazback

OzGrav, School of Physics and Astronomy, Monash University, Clayton, 3800, Victoria, Australia

K. Ackley, S. Biscoveanu, B. Goncharov, P. D. Lasky, Y. Levin, L. McNeill, L. Sammut, R. J. E. Smith, C. Talbot, E. Thrane, C. Whittle & X. J. Zhu

LIGO Livingston Observatory, Livingston, 70754, Louisiana, USA

C. Adams, S. M. Aston, J. Betzwieser, J. Birch, K. Bossie, P. Corban, M. J. Cowart, R. T. DeRosa, A. Effler, T. M. Evans, V. V. Frolov, M. Fyffe, J. A. Giaime, K. D. Giardina, J. Hanson, M. C. Heintze, K. Holt, T. Huynh-Dinh, S. Kandhasamy, W. Katzman, M. Laxen, M. Lormand, S. McCormick, A. Mullavey, T. J. N. Nelson, D. Nolting, Richard J. Oram, B. O’Reilly, H. Overmier, W. Parker, A. Pele, J. H. Romie, D. Sellers, B. Smith, A. L. Stuver, M. Thomas, K. A. Thorne & G. Traylor

Laboratoire d’Annecy-le-Vieux de Physique des Particules (LAPP), Université Savoie Mont Blanc, CNRS/IN2P3, Annecy, F-74941, France

T. Adams, R. Bonnand, D. Buskulic, M. Ducrot, D. Estevez, V. Germain, R. Gouaty, N. Letendre, F. Marion, A. Masserot, B. Mours, L. Rolland, D. Verkindt, M. Was & M. Yvert

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

P. Addesso, E. Mejuto-Villa, V. Pierro, I. M. Pinto & M. Principe

Max Planck Institute for Gravitational Physics (Albert Einstein Institute), Hannover, D-30167, Germany

V. B. Adya, C. Affeldt, B. Allen, G. Ashton, C. Aulbert, C. Beer, G. Bergmann, O. Birnholtz, O. Bock, N. Bode, M. Brinkmann, M. Cabero, C. D. Capano, S. L. Danilishin, K. Danzmann, T. Denker, T. Dent, O. de Varona, S. Doravari, M. Drago, C. Dreissigacker, H.-B. Eggenstein, H. Fehrmann, H. Grote, M. M. Hanke, M. Heurs, Y. M. Hu, N. Indik, J. Junker, K. S. Karvinen, S. Khan, R. Kirchhoff, P. Koch, S. M. Koehlenbeck, C. Krämer, V. Kringel, B. Krishnan, G. Kuehn, J. Lehmann, J. D. Lough, H. Lück, A. P. Lundgren, B. Machenschalk, G. D. Meadors, M. Mehmet, Arunava Mukherjee, M. Nery, A. B. Nielsen, A. Nitz, A. Noack, F. Ohme, P. Oppermann, M. A. Papa, A. Post, M. Prijatelj, O. Puncken, S. Rieger, A. Rüdiger, F. Salemi, J. Schmidt, E. Schreiber, D. Schuette, B. W. Schulte, B. F. Schutz, A. Singh, M. Steinke, D. Steinmeyer, T. Theeg, F. Thies, S. Walsh, L.-W. Wei, M. Weinert, P. Weßels, J. Westerweck, T. Westphal, D. Wilken, B. Willke, M. H. Wimmer, W. Winkler, H. Wittel, J. Woehler, D. S. Wu & S. J. Zhu

The University of Mississippi, University, Mississippi, 38677, USA

M. Afrough, M. Cavaglià, C. Cocchieri, K. L. Dooley & K. Mogushi

NCSA, University of Illinois at Urbana-Champaign, Urbana, 61801, Illinois, USA

B. Agarwal, G. Allen, D. George, E. A. Huerta, M. Katolik, A. J. Kemball, C. Markakis, W. Ren, P. M. Ricker, E. Seidel & E. K. Wessel

University of Cambridge, Cambridge, CB2 1TN, UK

M. Agathos, A. J. K. Chua & C. J. Moore

Nikhef, Science Park, Amsterdam, 1098 XG, The Netherlands

K. Agatsuma, M. K. M. Bader, A. Bertolini, B. A. Boom, H. J. Bulten, S. Caudill, Archisman Ghosh, S. Ghosh, R. J. G. Jonker, S. Koley, J. Meidam, G. Nelemans, S. Nissanke, M. Tacca, K. W. Tsang, N. van Bakel, M. van Beuzekom, J. F. J. van den Brand, C. Van Den Broeck, L. van der Schaaf, J. V. van Heijningen & R. Walet

LIGO, Massachusetts Institute of Technology, Cambridge, 02139, Massachusetts, USA

N. Aggarwal, L. Barsotti, S. Biscans, A. Buikema, N. Demos, F. Donovan, R. A. Eisenstein, R. C. Essick, M. Evans, A. Fernandez-Galiana, P. Fritschel, S. Gras, E. D. Hall, E. Katsavounidis, A. Kontos, R. K. Lanza, R. Lynch, M. MacInnis, D. V. Martynov, K. Mason, F. Matichard, N. Mavalvala, L. McCuller, J. Miller, R. Mittleman, S. R. P. Mohapatra, D. H. Shoemaker, M. Tse, S. Vitale, R. Weiss, Hang Yu, Haocun Yu & M. E. Zucker

Instituto Nacional de Pesquisas Espaciais, 12227-010 São José dos Campos, São Paulo, Brazil

O. D. Aguiar, M. Constancio Jr., C. A. Costa, E. C. Ferreira, M. A. Okada & A. D. Silva

Gran Sasso Science Institute (GSSI), L’Aquila, I-67100, Italy

L. Aiello, M. Branchesi, E. Coccia, M. De Laurentis, V. Fafone, O. Halim, J. Harms, I. Khan, M. Lorenzini, V. Sequino, A. Singhal, S. Tiwari & G. Wang

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

L. Aiello, M. Branchesi, E. Coccia, O. Halim, J. Harms & M. Lorenzini

Inter-University Centre for Astronomy and Astrophysics, Pune, 411007, India

A. Ain, S. Bose, S. Dhurandhar, B. U. Gadre, S. G. Gaonkar, S. Mitra, N. Mukund, A. Parida, J. Prasad, T. Souradeep & J. Suresh

International Centre for Theoretical Sciences, Tata Institute of Fundamental Research, Bengaluru, 560089, India

P. Ajith, Abhirup Ghosh, Archisman Ghosh, B. R. Iyer & S. Kumar

University of Wisconsin-Milwaukee, Milwaukee, 53201, Wisconsin, USA

B. Allen, W. G. Anderson, P. R. Brady, P. Brockill, S. Caudill, D. Chatterjee, J. D. E. Creighton, T. P. Downes, S. Ghosh, C. Horst, S. J. Kapadia, S. Kwang, X. Liu, I. Magaña Hernandez, M. Manske, R. A. Mercer, D. Mukherjee, M. A. Papa, M. Poe, T. Prestegard, H. Qi, L. Sadeghian, A. Sheperd, X. Siemens, J. A. Sonnenberg, K. Ueno, A. D. Viets & S. Walsh

Leibniz Universität Hannover, Hannover, D-30167, Germany

B. Allen, P. Aufmuth, A. Bisht, S. L. Danilishin, K. Danzmann, M. Heurs, S. Kaufer, H. Lück, D. Schuette, A. Singh, H. Vahlbruch, L.-W. Wei, B. Willke & H. Wittel

Università di Pisa, Pisa, I-56127, Italy

A. Allocca, A. Basti, G. Cerretani, W. Del Pozzo, A. Di Lieto, F. Di Renzo, I. Ferrante, F. Fidecaro, J. M. Gonzalez Castro, R. Passaquieti, R. Poggiani, M. Razzano & M. Tonelli

INFN, Sezione di Pisa, Pisa, I-56127, Italy

A. Allocca, A. Basti, M. Bitossi, V. Boschi, C. Bradaschia, G. Cella, G. Cerretani, W. Del Pozzo, A. Di Lieto, F. Di Renzo, I. Ferrante, F. Fidecaro, F. Frasconi, A. Gennai, A. Giazotto, J. M. Gonzalez Castro, G. Losurdo, A. Moggi, F. Paoletti, R. Passaquieti, D. Passuello, B. Patricelli, R. Poggiani, M. Razzano, M. Tonelli & L. Trozzo

OzGrav, Australian National University, Canberra, 0200, Australian Capital Territory, Australia

P. A. Altin, J. H. Chow, P. W. F. Forsyth, N. Kijbunchoo, G. L. Mansell, M. Manske, D. E. McClelland, D. J. McManus, T. McRae, T. T. Nguyen, D. S. Rabeling, S. M. Scott, D. A. Shaddock, B. J. J. Slagmolen, R. L. Ward, K. Wette & M. J. Yap

Laboratoire des Matériaux Avancés (LMA), CNRS/IN2P3, Villeurbanne, F-69622, France

A. Amato, G. Cagnoli, J. Degallaix, C. De Rossi, V. Dolique, R. Flaminio, M. Granata, D. Hofman, C. Michel, R. Pedurand, L. Pinard & B. Sassolas

SUPA, University of the West of Scotland, Paisley, PA1 2BE, UK

S. V. Angelova, J. Devenson, S. Macfoy, G. Rutins & D. J. Vine

LAL, Université Paris-Sud, CNRS/IN2P3, Université Paris-Saclay, Orsay, F-91898, France

S. Antier, N. Arnaud, I. Belahcene, M. A. Bizouard, V. Brisson, J. Casanueva Diaz, F. Cavalier, D. Cohen, M. Davier, V. Frey, P. Gruning, P. Hello, D. Huet, A. Lartaux-Vollard, N. Leroy & F. Robinet

California State University Fullerton, Fullerton, 92831, California, USA

J. S. Areeda, A. Avila-Alvarez, T. J. Cullen, G. Lovelace, J. Read, J. R. Smith & M. Walker

European Gravitational Observatory (EGO), Cascina, I-56021, Italy

N. Arnaud, G. Ballardin, M. Bitossi, V. Boschi, A. Bozzi, F. Carbognani, R. Cavalieri, A. Chiummo, S. Cortese, E. Cuoco, V. Dattilo, C. De Rossi, F. Ferrini, I. Fiori, E. Genin, M. Gosselin, G. Hemming, D. Hoak, M. Mantovani, M. Mohan, F. Nocera, A. Paoli, A. Pasqualetti, G. Pillant, P. Popolizio, P. Ruggi, L. Salconi, D. Sentenac, B. L. Swinkels, F. Travasso & T. Zelenova

Chennai Mathematical Institute, Chennai, 603103, India

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

S. Ascenzi, C. Casentini, V. Fafone, D. Lumaca, I. Nardecchia & V. Sequino

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

S. Ascenzi, C. Casentini, E. Cesarini, S. D’Antonio, V. Fafone, I. Khan, D. Lumaca, Y. Minenkov, I. Nardecchia, A. Rocchi & V. Sequino

Universität Hamburg, Hamburg, D-22761, Germany

M. Ast, L. Kleybolte, M. Korobko, A. Pal-Singh, A. Sawadsky, R. Schnabel, A. Schönbeck, J. Steinlechner & S. Steinlechner

INFN, Sezione di Roma, Roma, I-00185, Italy

P. Astone, A. Colla, S. Di Pace, I. Di Palma, S. Frasca, G. Intini, P. Leaci, E. Majorana, S. Mastrogiovanni, A. L. Miller, L. Naticchioni, C. Palomba, O. J. Piccinni, P. Puppo, P. Rapagnani, F. Ricci & A. Singhal

Cardiff University, Cardiff, CF24 3AA, UK

D. V. Atallah, I. Dorrington, S. Fairhurst, E. J. Fauchon-Jones, M. Fays, S. Gomes, E. Z. Hamilton, M. D. Hannam, P. Hopkins, C. V. Kalaghatgi, C. Kent, L. T. London, R. Macas, D. M. Macleod, A. W. Muir, C. North, L. K. Nuttall, F. Pannarale, V. Predoi, B. S. Sathyaprakash, B. F. Schutz, P. J. Sutton, V. Tiwari & S. A. Usman

Embry-Riddle Aeronautical University, Prescott, 86301, Arizona, USA

K. AultONeal, S. Gaudio, K. Gill, E. M. Gretarsson, B. Hughey, M. Muratore, J. W. W. Pratt, S. G. Schwalbe, K. Staats, M. J. Szczepańczyk & M. Zanolin

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

S. Babak, A. Bohe, A. Buonanno, V. Dergachev, H.-B. Eggenstein, S. Grunewald, I. W. Harry, B. D. Lackey, G. D. Meadors, J. Ming, S. Ossokine, M. A. Papa, H. P. Pfeiffer, S. Privitera, M. Pürrer, V. Raymond, L. Shao, A. Singh, A. Taracchini, S. Walsh & S. J. Zhu

APC, AstroParticule et Cosmologie, Université Paris Diderot, CNRS/IN2P3, CEA/Irfu, Observatoire de Paris, Sorbonne Paris Cité, F-75205, Paris Cedex 13, France

P. Bacon, M. Barsuglia, Y. Bouffanais, C. Buy, E. Capocasa, E. Chassande-Mottin, D. Fiorucci, E. K. Porter & D. Steer

Korea Institute of Science and Technology Information, Daejeon, 34141, South Korea

West Virginia University, Morgantown, 26506, West Virginia, USA

P. T. Baker, B. D. Cheeseboro, Z. B. Etienne, T. D. Knowles, A. Lenon & S. T. McWilliams

Università di Perugia, Perugia, I-06123, Italy

F. Baldaccini, L. Gammaitoni & H. Vocca

INFN, Sezione di Perugia, Perugia, I-06123, Italy

F. Baldaccini, M. Bawaj, F. Marchesoni, M. Punturo, F. Travasso & H. Vocca

Syracuse University, Syracuse, 13244, New York, USA

S. W. Ballmer, S. Bhagwat, C. Biwer, D. A. Brown, D. Davis, S. De, H. Fair, D. Finstad, R. P. Fisher, J. E. Lord, F. Magaña-Sandoval, L. Magaña Zertuche, E. A. Muñiz, L. Pekowsky, S. D. Reyes, J. R. Sanders, P. R. Saulson, D. C. Vander-Hyde & T. Vo

University of Minnesota, Minneapolis, 55455, Minnesota, USA

S. Banagiri, M. Fitz-Axen, V. Mandic, A. Matas, P. M. Meyers & R. Ormiston

SUPA, University of Glasgow, Glasgow, G12 8QQ, UK

S. E. Barclay, B. Barr, J. C. Bayley, A. S. Bell, M. Chan, A. Cumming, L. Cunningham, L. E. H. Datrier, R. Douglas, P. Dupej, M. Fletcher, H. Gabbard, C. Graef, A. Grant, G. Hammond, M. J. Hart, K. Haughian, M. Hendry, I. S. Heng, J. Hennig, S. Hild, J. Hough, E. A. Houston, S. H. Huttner, H. N. Isa, R. Jones, D. Keitel, S. Leavey, K. Lee, V. Mangano, I. W. Martin, M. Masso-Reid, C. Messenger, P. G. Murray, G. Newton, D. Pascucci, B. L. Pearlstone, M. Phelps, M. Pitkin, J. Powell, N. A. Robertson, R. Robie, S. Rowan, J. Scott, B. Sorazu, A. P. Spencer, J. Steinlechner, K. A. Strain, S. C. Tait, K. Toland, Z. Tornasi, A. A. van Veggel, J. Veitch, D. Williams, G. Woan, J. L. Wright & T. Zhang

LIGO Hanford Observatory, Richland, 99352, Washington, USA

D. Barker, J. Bartlett, J. C. Batch, R. M. Blair, F. Clara, J. C. Driggers, S. E. Dwyer, B. Gateley, C. Gray, J. Hanks, K. Izumi, K. Kawabe, P. J. King, J. S. Kissel, M. Landry, R. McCarthy, G. Mendell, E. L. Merilh, D. Moraru, G. Moreno, J. Oberling, C. J. Perez, M. Pirello, F. J. Raab, H. Radkins, C. L. Romel, K. Ryan, T. Sadecki, V. Sandberg, R. L. Savage, T. J. Shaffer, D. Sigg, A. Strunk, P. Thomas, C. Vorvick, J. Warner, B. Weaver & J. Worden

Caltech CaRT, Pasadena, 91125, California, USA

K. Barkett, J. Blackman, Y. Chen, Y. Ma, B. Pang, M. Scheel & V. Varma

Wigner RCP, RMKI, Konkoly Thege Miklós út 29-33, Budapest, H-1121, Hungary

Columbia University, New York, 10027, New York, USA

I. Bartos, K. R. Corley, S. T. Countryman, T. Di Girolamo, M. Factourovich, S. Márka, Z. Márka, L. Matone & A. Staley

Stanford University, Stanford, 94305, California, USA

R. Bassiri, E. Bonilla, R. L. Byer, C. E. Cirelli, D. DeBra, M. M. Fejer, B. Lantz, A. S. Markosyan & B. Shapiro

Dipartimento di Fisica, Università di Camerino, Camerino, I-62032, Italy

Dipartimento di Fisica e Astronomia, Università di Padova, Padova, I-35131, Italy

M. Bazzan, G. Ciani & M. Vardaro

INFN, Sezione di Padova, Padova, I-35131, Italy

M. Bazzan, G. Ciani, L. Conti, C. Lazzaro, M. Vardaro, G. Vedovato & J.-P. Zendri

Institute of Physics, Eötvös University, Pázmány P. s. 1/A, Budapest, 1117, Hungary

B. Bécsy, G. Dálya, Z. Frei & P. Raffai

Nicolaus Copernicus Astronomical Center, Polish Academy of Sciences, Warsaw, 00-716, Poland

M. Bejger, D. Rosińska & M. Sieniawska

Rochester Institute of Technology, Rochester, 14623, New York, USA

J. J. Bero, J. Healy, J. Lange, C. O. Lousto, R. O’Shaughnessy, M. Rizzo, J. T. Whelan, J. Wofford, D. M. Wysocki & Y.-H. Zhang

University of Birmingham, Birmingham, B15 2TT, UK

C. P. L. Berry, S. J. Cooper, W. Del Pozzo, M. Dovale álvarez, W. M. Farr, A. Freise, S. M. Gaebel, A. C. Green, H. Miao, H. Middleton, C. M. Mow-Lowry, S. P. Stevenson, D. J. Stops, E. G. Thomas, D. Töyrä, A. Vecchio, S. Vinciguerra & H. Wang

INFN, Sezione di Genova, Genova, I-16146, Italy

D. Bersanetti, M. Canepa, A. Chincarini, A. Cirone, S. Farinon, G. Gemme, L. Rei & F. Sorrentino

RRCAT, Indore, 452013, MP, India

R. Bhandare, I. Dave, J. George, S. A. Pai, B. C. Pant, S. Raja & C. Rajan

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

I. A. Bilenko, M. L. Gorodetsky, F. Y. Khalili, V. P. Mitrofanov, L. G. Prokhorov, S. E. Strigin & S. P. Vyatchanin

SUPA, University of Strathclyde, Glasgow, G1 1XQ, UK

R. Birney, S. Jawahar, N. A. Lockerbie, S. Reid & K. V. Tokmakov

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

S. Biscoveanu, S. J. Chamberlin, A. Gupta, C. Hanna, R. M. Magee, D. Meacher, C. Messick, A. E. Pace, B. S. Sathyaprakash & J. Z. Wang

OzGrav, University of Western Australia, Crawley, 6009, Western Australia, Australia

C. D. Blair, D. G. Blair, X. Chen, Q. Chu, S. Chung, D. M. Coward, E. J. Howell, L. Ju, J. Liu, M. A. Page, L. Wen & C. Zhao

Department of Astrophysics/IMAPP, Radboud University Nijmegen, PO Box 9010, Nijmegen, 6500, GL, The Netherlands

S. Bloemen, P. Canizares, S. Ghosh, P. Groot, T. Hinderer, G. Nelemans, D. Nichols, S. Nissanke, P. Schmidt & A. R. Williamson

Artemis, Université Côte d’Azur, Observatoire Côte d’Azur, CNRS, CS 34229, Nice, F-06304, Cedex 4, France

M. Boer, G. Bogaert, A. Brillet, N. Christensen, F. Cleva, J.-P. Coulon, J.-D. Fournier, H. Heitmann, A. Hreibi, F. Kéfélian, N. Man, L. Martellini, M. Merzougui, O. Minazzoli, M. Pichot, T. Regimbau & J.-Y. Vinet

Institut FOTON, CNRS, Université de Rennes 1, Rennes, F-35042, France

Washington State University, Pullman, 99164, Washington, USA

S. Bose, B. R. Hall & N. Mazumder

University of Oregon, Eugene, 97403, Oregon, USA

J. E. Brau, R. Frey, S. Karki, J. R. Palamos, R. Quitzow-James, V. J. Roma, P. Schale, R. M. S. Schofield & D. Talukder

Laboratoire Kastler Brossel, UPMC-Sorbonne Universités, CNRS, ENS-PSL Research University, Collège de France, Paris, F-75005, France

T. Briant, S. Chua, P.-F. Cohadon, S. Deléglise, A. Heidmann, J.-M. Isac, T. Jacqmin & R. Metzdorff

Carleton College, Northfield, 55057, Minnesota, USA

J. E. Broida, N. Christensen, M. W. Coughlin, M. C. Edwards & J. D. Tasson

OzGrav, University of Adelaide, Adelaide, 5005, South Australia, Australia

D. D. Brown, H. Cao, M. R. Ganija, W. Kim, E. J. King, J. Munch, D. J. Ottaway & P. J. Veitch

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

VU University Amsterdam, Amsterdam, 1081 HV, The Netherlands

H. J. Bulten & J. F. J. van den Brand

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

A. Buonanno, M. Cho, P. Shawhan & C. C. Yancey

Center for Relativistic Astrophysics, Georgia Institute of Technology, Atlanta, 30332, Georgia, USA

L. Cadonati, J. Calderón Bustillo, J. A. Clark, E. E. Cowan, B. Day, S. S. Forsyth, S. Ghonge, K. Jani, S. J. Kimbrell, K. Napier, D. M. Shoemaker & K. Siellez

Université Claude Bernard Lyon 1, Villeurbanne, F-69622, France

Università di Napoli ‘Federico II’, Complesso Universitario di Monte S.Angelo, Napoli, I-80126, Italy

E. Calloni, R. De Rosa, T. Di Girolamo, F. Garufi & L. Milano

NASA Goddard Space Flight Center, Greenbelt, 20771, Maryland, USA

J. B. Camp, T. Dal Canton, N. Gehrels & L. P. Singer

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

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

K. C. Cannon, L. Tsukada & D. Tsuna

Tsinghua University, Beijing, 100084, China

Texas Tech University, Lubbock, 79409, Texas, USA

S. Caride, A. Corsi, R. Coyne, R. Inta, B. J. Owen & B. Rajbhandari

Kenyon College, Gambier, 43022, Ohio, USA

M. F. Carney, T. Chmiel, C. Fee, D. Moffa, L. E. Wade & M. Wade

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

P. Cerdá-Durán, J. A. Font, N. Sanchis-Gual & A. Torres-Forné

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

National Tsing Hua University, Hsinchu City, Taiwan, 30013, China

S. Chao, L. Kuo, Howard Pan & Huang-Wei Pan

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

Center for Interdisciplinary Exploration and Research in Astrophysics (CIERA), Northwestern University, Evanston, 60208, Illinois, USA

E. Chase, S. B. Coughlin, V. Kalogera, B. B. Miller, C. Pankow, L. M. Perri, L. M. Sampson, J. Scheuer, M. S. Shahriar, M. Zevin, M. Zhou & Z. Zhou

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

K. Chatziioannou, H. Fong, C.-J. Haster, P. Kumar, H. P. Pfeiffer & A. B. Zimmerman

University of Chicago, Chicago, 60637, Illinois, USA

H. Y. Chen, Z. Doctor, B. Farr, M. Fishbach & D. E. Holz

Pusan National University, Busan, 46241, South Korea

The Chinese University of Hong Kong, Shatin, Hong Kong

A. K. W. Chung, O. A. Hannuksela, K. Kim, K. H. Lai, T. G. F. Li, R. K. L. Lo, K. K. Y. Ng, P. T. H. Pang, Y. F. Wang & K. W. K. Wong

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

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

R. Ciolfi, M. Di Giovanni, M. Leonardi, A. Perreca, G. A. Prodi, S. Tiwari & M. C. Tringali

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

P. Clearwater, A. Melatos & L. Sun

Università di Roma ‘La Sapienza’, Roma, I-00185, Italy

A. Colla, S. Di Pace, I. Di Palma, S. Frasca, G. Intini, P. Leaci, S. Mastrogiovanni, A. L. Miller, L. Naticchioni, O. J. Piccinni, P. Rapagnani & F. Ricci

Université Libre de Bruxelles, Brussels, 1050, Belgium

Sonoma State University, Rohnert Park, 94928, California, USA

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

I. Cordero-Carrión & A. Marquina

Montana State University, Bozeman, 59717, Montana, USA

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

P. B. Covas, C. Garcia-Quiros, S. Husa, F. Jiménez-Forteza, M. Oliver, G. Pratten, A. Ramos-Buades & A. M. Sintes

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

T. D. Creighton, M. C. Díaz, S. R. Morriss, S. Mukherjee, V. Quetschke, M. Rakhmanov, K. E. Ramirez, J. D. Romano, R. Stone, D. Tuyenbayev & W. H. Wang

Bellevue College, Bellevue, 98007, Washington, USA

Institute for Plasma Research, Bhat, Gandhinagar, 382428, India

A. Dasgupta, M. K. Gupta, Z. Khan, R. Kumar, A. K. Srivastava & S. Sunil

The University of Sheffield, Sheffield, S10 2TN, UK

E. J. Daw, T. B. Edo, R. Kennedy & E. Massera

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

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

California State University, Los Angeles, 5151 State University Drive, Los Angeles, 90032, California, USA

R. DeSalvo, L. Glover, S. D. Linker, M. C. Milovich-Goff, J. Neilson, G. D. O’Dea & M. B. Shaner

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

M. Di Giovanni, M. Leonardi, A. Perreca, G. A. Prodi & M. C. Tringali

Montclair State University, Montclair, 07043, New Jersey, USA

National Astronomical Observatory of Japan, 2-21-1 Osawa, Mitaka, Tokyo, 181-8588, Japan

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

School of Mathematics, University of Edinburgh, Edinburgh, EH9 3FD, UK

University and Institute of Advanced Research, Koba Institutional Area, Gandhinagar, 382007, Gujarat, India

IISER-TVM, CET Campus, Trivandrum, 695016, Kerala, India

V. Gayathri, A. Pai & M. Saleem

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

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

E. Goetz, R. Gustafson, A. Neunzert, K. Riles & O. Sauter

Tata Institute of Fundamental Research, Mumbai, 400005, India

A. Gopakumar & C. S. Unnikrishnan

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

Università degli Studi di Urbino ‘Carlo Bo’, Urbino, I-61029, Italy

G. Greco, G. M. Guidi, F. Martelli, M. Montani, F. Piergiovanni, G. Stratta, F. Vetrano & A. Viceré

INFN, Sezione di Firenze, Sesto Fiorentino, I-50019, Italy

G. Greco, G. M. Guidi, F. Martelli, M. Montani, F. Piergiovanni, G. Stratta, F. Vetrano, A. Viceré & G. Wang

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

American University, Washington, 20016, DC, USA

G. M. Harry, M. Kinley-Hanlon & J. M. Newport

University of Białystok, Białystok, 15-424, Poland

University of Southampton, Southampton, SO17 1BJ, UK

University of Washington Bothell, 18115 Campus Way NE, Bothell, Washington, 98011, USA

Institute of Applied Physics, Nizhny Novgorod, 603950, Russia

E. A. Khazanov, O. Palashov & A. Sergeev

Korea Astronomy and Space Science Institute, Daejeon, 34055, South Korea

Inje University Gimhae, South Gyeongsang, 50834, South Korea

National Institute for Mathematical Sciences, Daejeon, 34047, South Korea

W. S. Kim, J. J. Oh, S. H. Oh & E. J. Son

NCBJ, Świerk-Otwock, 05-400, Poland

A. Królak, A. Kutynia & A. Zadrożny

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

Hillsdale College, Hillsdale, 49242, Michigan, USA

Hanyang University, Seoul, 04763, South Korea

Seoul National University, Seoul, 08826, South Korea

NASA Marshall Space Flight Center, Huntsville, 35811, Alabama, USA

T. B. Littenberg, J. Page, A. A. Shah & J. A. Taylor

ESPCI, CNRS, Paris, F-75005, France

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

College of William and Mary, Williamsburg, 23187, Virginia, USA

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

Indian Institute of Technology Madras, Chennai, 600036, India

IISER-Kolkata, Mohanpur, 741252, West Bengal, India

Whitman College, 345 Boyer Avenue, Walla Walla, Washington, 99362, USA

Indian Institute of Technology Bombay, Powai, Mumbai, 400076, Maharashtra, India

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

Université de Lyon, Lyon, F-69361, France

Hobart and William Smith Colleges, Geneva, 14456, New York, USA

OzGrav, Swinburne University of Technology, Hawthorn, 3122, Victoria, Australia

Janusz Gil Institute of Astronomy, University of Zielona Góra, Zielona Góra, 65-265, Poland

University of Washington, Seattle, 98195, Washington, USA

King’s College London, University of London, London, WC2R 2LS, UK

Indian Institute of Technology, Gandhinagar Ahmedabad, 382424, Gujarat, India

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

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

Andrews University, Berrien Springs, 49104, Michigan, USA

Università di Siena, Siena, I-53100, Italy

Trinity University, San Antonio, 78212, Texas, USA

Abilene Christian University, Abilene, 79699, Texas, USA

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

Department of Astronomy and Astrophysics, University of California, Santa Cruz, 95064, California, USA

R. J. Foley, D. A. Coulter, C. D. Kilpatrick, A. Murguia-Berthier, Y.-C. Pan, J. X. Prochaska, E. Ramirez-Ruiz, C. Rojas-Bravo & M. R. Siebert

The Observatories of the Carnegie Institution for Science, 813 Santa Barbara Street, Pasadena, 91101, California, USA

M. R. Drout, B. F. Madore, A. L. Piro, B. J. Shappee & J. D. Simon

Hubble and Carnegie-Dunlap Fellow

Nuclear Science Division, Lawrence Berkeley National Laboratory, Berkeley, 94720, California, USA

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

Dark Cosmology Centre, Niels Bohr Institute, University of Copenhagen, Blegdamsvej 17, Copenhagen, 2100, Denmark

Space Telescope Science Institute, 3700 San Martin Drive, Baltimore, 21218, Maryland, USA

Institute for Astronomy, University of Hawai’i, 2680 Woodlawn Drive, Honolulu, 96822, Hawaii, USA

Hubble and Carnegie-Princeton Fellow

Departamento de Física y Astronomía, Universidad de La Serena, La Serena, Chile

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

J. Annis, M. Soares-Santos, H. T. Diehl, J. Frieman, S. Allam, R. E. Butler, A. Drlica-Wagner, D. A. Finley, K. Herner, T. S. Li, H. Lin, J. Marriner, A. Stebbins, W. Wester, B. Yanny, E. Buckley-Geer, J. Estrada, B. Flaugher, G. Gutierrez, S. Kent, R. Kron, N. Kuropatkin, E. Neilsen, B. Nord, V. Scarpine, D. L. Tucker & Y. Zhang

Department of Physics, Brandeis University, Waltham, Massachusetts, USA

Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, 19104, Pennsylvania, USA

D. Brout, M. Sako, L. F. Secco, C. B. D’Andrea, B. Jain & M. March

Kavli Institute for Cosmological Physics, University of Chicago, Chicago, 60637, Illinois, USA

D. Scolnic, J. Frieman, R. Kessler, S. Kent & R. Kron

Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, Cambridge, 02138, Massachusetts, USA

E. Berger, K. D. Alexander, P. Cowperthwaite & M. Nicholl

Department of Physics, University of Surrey, Guildford, GU2 7XH, UK

Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, Cambridge, 02138, Massachusetts, USA

P. Blanchard, T. Eftekhari, V. A. Villar & P. K. G. Williams

Department of Astronomy, Indiana University, 727 East Third Street, Bloomington, 47405, Indiana, USA

Department of Physics and Astronomy, Astrophysical Institute, 251B Clippinger Lab, Ohio University, Athens, 45701, Ohio, USA

and Department of Physics and Astronomy, George P. and Cynthia Woods Mitchell Institute for Fundamental Physics and Astronomy, Texas A&M University, College Station, 77843, Texas, USA

E. R. Cook, J. L. Marshall, M. Sauseda & D. L. DePoy

LSST, 933 North Cherry Avenue, Tucson, 85721, Arizona, USA

Hubble and Carnegie-Dunlap Fellow

The Observatories of the Carnegie Institution for Science, 813 Santa Barbara Street, Pasadena, 91101, California, USA

Institut d’Astrophysique de Paris (UMR7095: CNRS and UPMC), 98 bis Bd Arago, Paris, F-75014, France

Center for Interdisciplinary Exploration and Research in Astrophysics (CIERA) and Department of Physics and Astronomy, Northwestern University, Evanston, 60208, Illinois, USA

Center for Theoretical Astrophysics, Los Alamos National Laboratory, Los Alamos, 87544, New Mexico

Instituto de Fisica Teorica UAM/CSIC, Universidad Autonoma de Madrid, Madrid, 28049, Spain

SLAC National Accelerator Laboratory, Menlo Park, California, 94025, USA

M. S. S. Gill, D. L. Burke, D. Gruen, A. Roodman & E. S. Rykoff

Department of Astronomy, University of Illinois, 1002 West Green Street, Urbana, 61801, Illinois, USA

R. A. Gruendl & M. Carrasco Kind

National Center for Supercomputing Applications, 1205 West Clark Street, Urbana, 61801, Illinois, USA

R. A. Gruendl, C. Hanna, F. Paz-Chinchón, M. Carrasco Kind & M. W. G. Johnson

Department of Physics and Astronomy and Astrophysics,The Pennsylvania State University, University Park, Pennsylvania, 16802, USA

Department of Physics and Astronomy, University College London, Gower Street, London, WC1E 6BT, UK

W. Hartley, A. Palmese, F. B. Abdalla, A. Benoit-Lévy, D. Brooks, W. G. Hartley & O. Lahav

Department of Physics, ETH Zurich, Wolfgang-Pauli-Strasse 16, Zurich, CH-8093, Switzerland

Department of Physics, University of Michigan, Ann Arbor, 48109, Michigan, USA

D. Huterer, D. W. Gerdes, C. J. Miller, M. Schubnell & G. Tarle

Departments of Physics and Astronomy, and Theoretical Astrophysics Center, University of California, Berkeley, 94720-7300, California, USA

Observatòrio do Valongo, Universidade Federal do Rio de Janeiro, Ladeira do Pedro Antônio 43, Rio de Janeiro, RJ 20080-090, Brazil

P. A. A. Lopes & A. C. C. Lourenço

Center for Interdisciplinary Exploration and Research in Astrophysics (CIERA) and Department of Physics and Astronomy, Northwestern University, Evanston, 60208, Illinois, USA

National Optical Astronomy Observatory, 950 North Cherry Avenue, Tucson, 85719, Arizona, USA

Departamento de Astronomonía, Universidad de Chile, Camino del Observatorio 1515, Las Condes, Santiago, Chile

Department of Physics and Columbia Astrophysics Laboratory, Columbia University, New York, 10027, New York, USA

Department of Physics, University of Michigan, 450 Church Street, Ann Arbor, 48109-1040, Michigan, USA

Lawrence Berkeley National Laboratory, 1 Cyclotron Road, Berkeley, 94720, California, USA

P. Nugent, D. A. Goldstein & R. C. Thomas

Department of Astronomy and Theoretical Astrophysics Center, University of California, Berkeley, 94720-3411, California, USA

Physics Division, Lawrence Berkeley National Laboratory, Berkeley, 94720-8160, California, USA

Steward Observatory, University of Arizona, 933 North Cherry Avenue, Tucson, 85721, Arizona, USA

Instituto de Física Gleb Wataghin, Universidade Estadual de Campinas, Campinas, SP 13083-859, Brazil

Laboratório Interinstitucional de e-Astronomia — LIneA, Rua Gal. José Cristino 77, Rio de Janeiro, RJ 20921-400, Brazil

F. Sobreira, A. Carnero Rosell, L. N. da Costa, M. Lima, M. A. G. Maia & R. L. C. Ogando

Cerro Tololo Inter-American Observatory, National Optical Astronomy Observatory, Casilla, La Serena, 603, Chile

A. K. Vivas, A. Zenteno, T. M. C. Abbott, R. C. Smith & A. R. Walker

Department of Physics and Electronics, Rhodes University, PO Box 94, Grahamstown, 6140, South Africa

CNRS, UMR 7095, Institut d’Astrophysique de Paris, Paris, F-75014, France

Sorbonne Universités, UPMC Université Paris 06, UMR 7095, Institut d’Astrophysique de Paris, Paris, F-75014, France

Jodrell Bank Center for Astrophysics, School of Physics and Astronomy, University of Manchester, Oxford Road, Manchester, M13 9PL, UK

Kavli Institute for Particle Astrophysics and Cosmology, PO Box 2450, Stanford University, Stanford, 94305, California, USA

D. L. Burke, C. E. Cunha, C. Davis, D. Gruen, E. Krause, A. Roodman & E. S. Rykoff

Observatório Nacional, Rua Gal. José Cristino 77, Rio de Janeiro, RJ 20921-400, Brazil

A. Carnero Rosell, L. N. da Costa, M. A. G. Maia & R. L. C. Ogando

Institut de Física d’Altes Energies (IFAE), The Barcelona Institute of Science and Technology, Campus UAB, Bellaterra, 08193, Spain

J. Carretero, E. Fernandez & R. Miquel

Institute of Space Sciences, IEEC-CSIC, Campus UAB, Carrer de Can Magrans, Barcelona, 08193, Spain

F. J. Castander, P. Fosalba & E. Gaztanaga

Department of Physics, IIT Hyderabad, Kandi, 502285, Telangana, India

Excellence Cluster Universe, Boltzmannstrasse 2, Garching, 85748, Germany

Faculty of Physics, Ludwig-Maximilians-Universität, Scheinerstrasse 1, Munich, 81679, Germany

Department of Astronomy, University of Michigan, Ann Arbor, 48109, Michigan, USA

Institute of Astronomy, University of Cambridge, Madingley Road, Cambridge, CB3 0HA, UK

Kavli Institute for Cosmology, University of Cambridge, Madingley Road, Cambridge, CB3 0HA, UK

Universitäts-Sternwarte, Fakultät für Physik, Ludwig-Maximilians Universität München, Scheinerstrasse 1, München, 81679, Germany

Department of Astronomy, University of California, Berkeley, 501 Campbell Hall, Berkeley, 94720, California, USA

Center for Cosmology and Astro-Particle Physics, The Ohio State University, Columbus, 43210, Ohio, USA

Department of Physics, The Ohio State University, Columbus, 43210, Ohio, USA

Astronomy Department, University of Washington, Box 351580, Seattle, 98195, Washington, USA

Santa Cruz Institute for Particle Physics, Santa Cruz, 95064, California, USA

Australian Astronomical Observatory, North Ryde, 2113, New South Wales, Australia

Argonne National Laboratory, 9700 South Cass Avenue, Lemont, 60439, Illinois, USA

Departamento de Física Matemática, Instituto de Física, Universidade de São Paulo, São Paulo, CP 66318, SP 05314-970, Brazil

Institució Catalana de Recerca i Estudis Avançats, Barcelona, E-08010, Spain

Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Drive, Pasadena, 91109, California, USA

Department of Physics and Astronomy, Pevensey Building, University of Sussex, Brighton, BN1 9QH, UK

Centro de Investigaciones Energéticas, Medioambientales y Tecnológicas (CIEMAT), Madrid, Spain

E. Sanchez & I. Sevilla-Noarbe

School of Physics and Astronomy, University of Southampton, Southampton, SO17 1BJ, UK

Computer Science and Mathematics Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee, 37831

Institute of Cosmology and Gravitation, University of Portsmouth, Portsmouth, PO1 3FX, UK

Max Planck Institute for Extraterrestrial Physics, Giessenbachstrasse, Garching, 85748, Germany

Department of Physics and Astronomy, University of North Carolina at Chapel Hill, Chapel Hill, 27599, North Carolina, USA

J. B. Haislip, V. V. Kouprianov & D. E. Reichart

Department of Astronomy and Steward Observatory, University of Arizona, 933 North Cherry Ave, Tucson, 85719, Arizona, USA

Department of Physics, University of California, 1 Shields Avenue, Davis, 95616-5270, California, USA

L. Tartaglia, S. Valenti & S. Yang

Department of Physics and Astronomy, University of Padova, Via 8 Febbraio, Padova, 2-35122, Italy

INAF Osservatorio Astronomico di Padova, Vicolo della Osservatorio 5, Padova, I-35122, Italy

Department of Physics, University of California, Santa Barbara, 93106-9530, California, USA

Iair Arcavi, Griffin Hosseinzadeh, D. Andrew Howell, Curtis McCully & Sergiy Vasylyev

Las Cumbres Observatory, 6740 Cortona Drive, Suite 102, Goleta, 93117-5575, California, USA

Iair Arcavi, Griffin Hosseinzadeh, D. Andrew Howell, Curtis McCully & Sergiy Vasylyev

School of Physics and Astronomy, Tel Aviv University, Tel Aviv 69978, Israel

Department of Physics and Astronomy, University of Leicester, University Road, Leicester, LE1 7RH, UK

N. R. Tanvir, P. A. Evans, P. O’Brien, J. P. Osborne, S. Rosetti & K. Wiersema

Department of Physics, University of Warwick, Coventry, CV4 7AL, UK

A. J. Levan, J. Lyman, D. T. H. Steeghs, K. Ulaczyk & K. Wiersema

DARK, Niels Bohr Institute, University of Copenhagen, Juliane Maries Vej 30, Copenhagen Ø, 2100, Denmark

J. Hjorth, J. P. U. Fynbo, B. Milvang-Jensen & D. Watson

Instituto de Astrofísica de Andalucía (IAA-CSIC), Glorieta de la Astronomía, Granada, 18008, Spain

Z. Cano, A. de Ugarte-Postigo & C. C. Thöne

Astrophysics Research Institute, Liverpool John Moores University, IC2, Liverpool Science Park, 146 Brownlow Hill, Liverpool, L3 5RF, UK

C. Copperwheat & D. A. Perley

Institute of Astronomy, University of Cambridge, Madingley Road, Cambridge, CB3 0HA, UK

C. González-Fernández, M. Irwin & R. McMahon

Max-Planck-Institut für extraterrestrische Physik, Garching, 85740, Giessenbachstrasse 1, Germany

Birmingham Institute for Gravitational Wave Astronomy and School of Physics and Astronomy, University of Birmingham, Birmingham, B15 2TT, UK

INAF, Institute of Space Astrophysics and Cosmic Physics, Via Gobetti 101, Bologna, I-40129, Italy

School of Physics and Astronomy, and Monash Centre for Astrophysics, Monash University, Clayton, 3800, Victoria, Australia

Department of Astronomy, The Oskar Klein Centre, AlbaNova, Stockholm University, Stockholm, SE-106 91, Sweden

Anton Pannekoek Institute, University of Amsterdam, Science Park 904, Amsterdam, 1098 XH, The Netherlands

ASTRON, the Netherlands Institute for Radio Astronomy, Postbus 2, Dwingeloo, 7990 AA, The Netherlands

Department of Particle Physics and Astrophysics, Weizmann Institute of Science, Rehovot, 76100, Israel

Physics Department, M. V. Lomonosov Moscow State University, Leninskie gory, GSP-1, Moscow, 119991, Russia

V. M. Lipunov, V. G. Kornilov & D. Vlasenko

M. V. Lomonosov Moscow State University, Sternberg Astronomical Institute, Universitetsky pr., 13, Moscow, 119234, Russia

V. M. Lipunov, E. Gorbovskoy, V. G. Kornilov, N. Tyurina, P. Balanutsa, D. Vlasenko, I. Gorbunov & O. Gress

Observatorio Astronomico Felix Aguilar (OAFA), National University of San Juan, San Juan, Argentina

Instituto de Ciencias Astronomicas,de la Tierra y del Espacio (ICATE), San Juan, Argentina

South African Astrophysical Observatory, PO Box 9, 7935 Observatory, Cape Town, South Africa

Irkutsk State University, Applied Physics Institute, 20 Gagarin boulevard, Irkutsk, 664003, Russia

Blagoveschensk State Pedagogical University, Lenin street 104, Amur Region, 675000, Blagoveschensk, Russia

Instituto de Astrofacuteisica de Canarias Via Lactea, Laguna, E-38205La, Spain

Consortia

The LIGO Scientific Collaboration and The Virgo Collaboration

  • B. P. Abbott
  • , R. Abbott
  • , T. D. Abbott
  • , F. Acernese
  • , K. Ackley
  • , C. Adams
  • , T. Adams
  • , P. Addesso
  • , R. X. Adhikari
  • , V. B. Adya
  • , C. Affeldt
  • , M. Afrough
  • , B. Agarwal
  • , M. Agathos
  • , K. Agatsuma
  • , N. Aggarwal
  • , O. D. Aguiar
  • , L. Aiello
  • , A. Ain
  • , P. Ajith
  • , B. Allen
  • , G. Allen
  • , A. Allocca
  • , P. A. Altin
  • , A. Amato
  • , A. Ananyeva
  • , S. B. Anderson
  • , W. G. Anderson
  • , S. V. Angelova
  • , S. Antier
  • , S. Appert
  • , K. Arai
  • , M. C. Araya
  • , J. S. Areeda
  • , N. Arnaud
  • , K. G. Arun
  • , S. Ascenzi
  • , G. Ashton
  • , M. Ast
  • , S. M. Aston
  • , P. Astone
  • , D. V. Atallah
  • , P. Aufmuth
  • , C. Aulbert
  • , K. AultONeal
  • , C. Austin
  • , A. Avila-Alvarez
  • , S. Babak
  • , P. Bacon
  • , M. K. M. Bader
  • , S. Bae
  • , P. T. Baker
  • , F. Baldaccini
  • , G. Ballardin
  • , S. W. Ballmer
  • , S. Banagiri
  • , J. C. Barayoga
  • , S. E. Barclay
  • , B. C. Barish
  • , D. Barker
  • , K. Barkett
  • , F. Barone
  • , B. Barr
  • , L. Barsotti
  • , M. Barsuglia
  • , D. Barta
  • , J. Bartlett
  • , I. Bartos
  • , R. Bassiri
  • , A. Basti
  • , J. C. Batch
  • , M. Bawaj
  • , J. C. Bayley
  • , M. Bazzan
  • , B. Bécsy
  • , C. Beer
  • , M. Bejger
  • , I. Belahcene
  • , A. S. Bell
  • , B. K. Berger
  • , G. Bergmann
  • , J. J. Bero
  • , C. P. L. Berry
  • , D. Bersanetti
  • , A. Bertolini
  • , J. Betzwieser
  • , S. Bhagwat
  • , R. Bhandare
  • , I. A. Bilenko
  • , G. Billingsley
  • , C. R. Billman
  • , J. Birch
  • , R. Birney
  • , O. Birnholtz
  • , S. Biscans
  • , S. Biscoveanu
  • , A. Bisht
  • , M. Bitossi
  • , C. Biwer
  • , M. A. Bizouard
  • , J. K. Blackburn
  • , J. Blackman
  • , C. D. Blair
  • , D. G. Blair
  • , R. M. Blair
  • , S. Bloemen
  • , O. Bock
  • , N. Bode
  • , M. Boer
  • , G. Bogaert
  • , A. Bohe
  • , F. Bondu
  • , E. Bonilla
  • , R. Bonnand
  • , B. A. Boom
  • , R. Bork
  • , V. Boschi
  • , S. Bose
  • , K. Bossie
  • , Y. Bouffanais
  • , A. Bozzi
  • , C. Bradaschia
  • , P. R. Brady
  • , M. Branchesi
  • , J. E. Brau
  • , T. Briant
  • , A. Brillet
  • , M. Brinkmann
  • , V. Brisson
  • , P. Brockill
  • , J. E. Broida
  • , A. F. Brooks
  • , D. A. Brown
  • , D. D. Brown
  • , S. Brunett
  • , C. C. Buchanan
  • , A. Buikema
  • , T. Bulik
  • , H. J. Bulten
  • , A. Buonanno
  • , D. Buskulic
  • , C. Buy
  • , R. L. Byer
  • , M. Cabero
  • , L. Cadonati
  • , G. Cagnoli
  • , C. Cahillane
  • , J. Calderón Bustillo
  • , T. A. Callister
  • , E. Calloni
  • , J. B. Camp
  • , M. Canepa
  • , P. Canizares
  • , K. C. Cannon
  • , H. Cao
  • , J. Cao
  • , C. D. Capano
  • , E. Capocasa
  • , F. Carbognani
  • , S. Caride
  • , M. F. Carney
  • , J. Casanueva Diaz
  • , C. Casentini
  • , S. Caudill
  • , M. Cavaglià
  • , F. Cavalier
  • , R. Cavalieri
  • , G. Cella
  • , C. B. Cepeda
  • , P. Cerdá-Durán
  • , G. Cerretani
  • , E. Cesarini
  • , S. J. Chamberlin
  • , M. Chan
  • , S. Chao
  • , P. Charlton
  • , E. Chase
  • , E. Chassande-Mottin
  • , D. Chatterjee
  • , K. Chatziioannou
  • , B. D. Cheeseboro
  • , H. Y. Chen
  • , X. Chen
  • , Y. Chen
  • , H.-P. Cheng
  • , H. Chia
  • , A. Chincarini
  • , A. Chiummo
  • , T. Chmiel
  • , H. S. Cho
  • , M. Cho
  • , J. H. Chow
  • , N. Christensen
  • , Q. Chu
  • , A. J. K. Chua
  • , S. Chua
  • , A. K. W. Chung
  • , S. Chung
  • , G. Ciani
  • , R. Ciolfi
  • , C. E. Cirelli
  • , A. Cirone
  • , F. Clara
  • , J. A. Clark
  • , P. Clearwater
  • , F. Cleva
  • , C. Cocchieri
  • , E. Coccia
  • , P.-F. Cohadon
  • , D. Cohen
  • , A. Colla
  • , C. G. Collette
  • , L. R. Cominsky
  • , M. Constancio Jr.
  • , L. Conti
  • , S. J. Cooper
  • , P. Corban
  • , T. R. Corbitt
  • , I. Cordero-Carrión
  • , K. R. Corley
  • , N. Cornish
  • , A. Corsi
  • , S. Cortese
  • , C. A. Costa
  • , M. W. Coughlin
  • , S. B. Coughlin
  • , J.-P. Coulon
  • , S. T. Countryman
  • , P. Couvares
  • , P. B. Covas
  • , E. E. Cowan
  • , D. M. Coward
  • , M. J. Cowart
  • , D. C. Coyne
  • , R. Coyne
  • , J. D. E. Creighton
  • , T. D. Creighton
  • , J. Cripe
  • , S. G. Crowder
  • , T. J. Cullen
  • , A. Cumming
  • , L. Cunningham
  • , E. Cuoco
  • , T. Dal Canton
  • , G. Dálya
  • , S. L. Danilishin
  • , S. D’Antonio
  • , K. Danzmann
  • , A. Dasgupta
  • , C. F. Da Silva Costa
  • , L. E. H. Datrier
  • , V. Dattilo
  • , I. Dave
  • , M. Davier
  • , D. Davis
  • , E. J. Daw
  • , B. Day
  • , S. De
  • , D. DeBra
  • , J. Degallaix
  • , M. De Laurentis
  • , S. Deléglise
  • , W. Del Pozzo
  • , N. Demos
  • , T. Denker
  • , T. Dent
  • , R. De Pietri
  • , V. Dergachev
  • , R. De Rosa
  • , R. T. DeRosa
  • , C. De Rossi
  • , R. DeSalvo
  • , O. de Varona
  • , J. Devenson
  • , S. Dhurandhar
  • , M. C. Díaz
  • , L. Di Fiore
  • , M. Di Giovanni
  • , T. Di Girolamo
  • , A. Di Lieto
  • , S. Di Pace
  • , I. Di Palma
  • , F. Di Renzo
  • , Z. Doctor
  • , V. Dolique
  • , F. Donovan
  • , K. L. Dooley
  • , S. Doravari
  • , I. Dorrington
  • , R. Douglas
  • , M. Dovale álvarez
  • , T. P. Downes
  • , M. Drago
  • , C. Dreissigacker
  • , J. C. Driggers
  • , Z. Du
  • , M. Ducrot
  • , P. Dupej
  • , S. E. Dwyer
  • , T. B. Edo
  • , M. C. Edwards
  • , A. Effler
  • , H.-B. Eggenstein
  • , P. Ehrens
  • , J. Eichholz
  • , S. S. Eikenberry
  • , R. A. Eisenstein
  • , R. C. Essick
  • , D. Estevez
  • , Z. B. Etienne
  • , T. Etzel
  • , M. Evans
  • , T. M. Evans
  • , M. Factourovich
  • , V. Fafone
  • , H. Fair
  • , S. Fairhurst
  • , X. Fan
  • , S. Farinon
  • , B. Farr
  • , W. M. Farr
  • , E. J. Fauchon-Jones
  • , M. Favata
  • , M. Fays
  • , C. Fee
  • , H. Fehrmann
  • , J. Feicht
  • , M. M. Fejer
  • , A. Fernandez-Galiana
  • , I. Ferrante
  • , E. C. Ferreira
  • , F. Ferrini
  • , F. Fidecaro
  • , D. Finstad
  • , I. Fiori
  • , D. Fiorucci
  • , M. Fishbach
  • , R. P. Fisher
  • , M. Fitz-Axen
  • , R. Flaminio
  • , M. Fletcher
  • , H. Fong
  • , J. A. Font
  • , P. W. F. Forsyth
  • , S. S. Forsyth
  • , J.-D. Fournier
  • , S. Frasca
  • , F. Frasconi
  • , Z. Frei
  • , A. Freise
  • , R. Frey
  • , V. Frey
  • , E. M. Fries
  • , P. Fritschel
  • , V. V. Frolov
  • , P. Fulda
  • , M. Fyffe
  • , H. Gabbard
  • , B. U. Gadre
  • , S. M. Gaebel
  • , J. R. Gair
  • , L. Gammaitoni
  • , M. R. Ganija
  • , S. G. Gaonkar
  • , C. Garcia-Quiros
  • , F. Garufi
  • , B. Gateley
  • , S. Gaudio
  • , G. Gaur
  • , V. Gayathri
  • , N. Gehrels
  • , G. Gemme
  • , E. Genin
  • , A. Gennai
  • , D. George
  • , J. George
  • , L. Gergely
  • , V. Germain
  • , S. Ghonge
  • , Abhirup Ghosh
  • , Archisman Ghosh
  • , S. Ghosh
  • , J. A. Giaime
  • , K. D. Giardina
  • , A. Giazotto
  • , K. Gill
  • , L. Glover
  • , E. Goetz
  • , R. Goetz
  • , S. Gomes
  • , B. Goncharov
  • , G. González
  • , J. M. Gonzalez Castro
  • , A. Gopakumar
  • , M. L. Gorodetsky
  • , S. E. Gossan
  • , M. Gosselin
  • , R. Gouaty
  • , A. Grado
  • , C. Graef
  • , M. Granata
  • , A. Grant
  • , S. Gras
  • , C. Gray
  • , G. Greco
  • , A. C. Green
  • , E. M. Gretarsson
  • , P. Groot
  • , H. Grote
  • , S. Grunewald
  • , P. Gruning
  • , G. M. Guidi
  • , X. Guo
  • , A. Gupta
  • , M. K. Gupta
  • , K. E. Gushwa
  • , E. K. Gustafson
  • , R. Gustafson
  • , O. Halim
  • , B. R. Hall
  • , E. D. Hall
  • , E. Z. Hamilton
  • , G. Hammond
  • , M. Haney
  • , M. M. Hanke
  • , J. Hanks
  • , C. Hanna
  • , M. D. Hannam
  • , O. A. Hannuksela
  • , J. Hanson
  • , T. Hardwick
  • , J. Harms
  • , G. M. Harry
  • , I. W. Harry
  • , M. J. Hart
  • , C.-J. Haster
  • , K. Haughian
  • , J. Healy
  • , A. Heidmann
  • , M. C. Heintze
  • , H. Heitmann
  • , P. Hello
  • , G. Hemming
  • , M. Hendry
  • , I. S. Heng
  • , J. Hennig
  • , A. W. Heptonstall
  • , M. Heurs
  • , S. Hild
  • , T. Hinderer
  • , D. Hoak
  • , D. Hofman
  • , K. Holt
  • , D. E. Holz
  • , P. Hopkins
  • , C. Horst
  • , J. Hough
  • , E. A. Houston
  • , E. J. Howell
  • , A. Hreibi
  • , Y. M. Hu
  • , E. A. Huerta
  • , D. Huet
  • , B. Hughey
  • , S. Husa
  • , S. H. Huttner
  • , T. Huynh-Dinh
  • , N. Indik
  • , R. Inta
  • , G. Intini
  • , H. N. Isa
  • , J.-M. Isac
  • , M. Isi
  • , B. R. Iyer
  • , K. Izumi
  • , T. Jacqmin
  • , K. Jani
  • , P. Jaranowski
  • , S. Jawahar
  • , F. Jiménez-Forteza
  • , W. W. Johnson
  • , D. I. Jones
  • , R. Jones
  • , R. J. G. Jonker
  • , L. Ju
  • , J. Junker
  • , C. V. Kalaghatgi
  • , V. Kalogera
  • , B. Kamai
  • , S. Kandhasamy
  • , G. Kang
  • , J. B. Kanner
  • , S. J. Kapadia
  • , S. Karki
  • , K. S. Karvinen
  • , M. Kasprzack
  • , M. Katolik
  • , E. Katsavounidis
  • , W. Katzman
  • , S. Kaufer
  • , K. Kawabe
  • , F. Kéfélian
  • , D. Keitel
  • , A. J. Kemball
  • , R. Kennedy
  • , C. Kent
  • , J. S. Key
  • , F. Y. Khalili
  • , I. Khan
  • , S. Khan
  • , Z. Khan
  • , E. A. Khazanov
  • , N. Kijbunchoo
  • , Chunglee Kim
  • , J. C. Kim
  • , K. Kim
  • , W. Kim
  • , W. S. Kim
  • , Y.-M. Kim
  • , S. J. Kimbrell
  • , E. J. King
  • , P. J. King
  • , M. Kinley-Hanlon
  • , R. Kirchhoff
  • , J. S. Kissel
  • , L. Kleybolte
  • , S. Klimenko
  • , T. D. Knowles
  • , P. Koch
  • , S. M. Koehlenbeck
  • , S. Koley
  • , V. Kondrashov
  • , A. Kontos
  • , M. Korobko
  • , W. Z. Korth
  • , I. Kowalska
  • , D. B. Kozak
  • , C. Krämer
  • , V. Kringel
  • , B. Krishnan
  • , A. Królak
  • , G. Kuehn
  • , P. Kumar
  • , R. Kumar
  • , S. Kumar
  • , L. Kuo
  • , A. Kutynia
  • , S. Kwang
  • , B. D. Lackey
  • , K. H. Lai
  • , M. Landry
  • , R. N. Lang
  • , J. Lange
  • , B. Lantz
  • , R. K. Lanza
  • , A. Lartaux-Vollard
  • , P. D. Lasky
  • , M. Laxen
  • , A. Lazzarini
  • , C. Lazzaro
  • , P. Leaci
  • , S. Leavey
  • , C. H. Lee
  • , H. K. Lee
  • , H. M. Lee
  • , H. W. Lee
  • , K. Lee
  • , J. Lehmann
  • , A. Lenon
  • , M. Leonardi
  • , N. Leroy
  • , N. Letendre
  • , Y. Levin
  • , T. G. F. Li
  • , S. D. Linker
  • , T. B. Littenberg
  • , J. Liu
  • , X. Liu
  • , R. K. L. Lo
  • , N. A. Lockerbie
  • , L. T. London
  • , J. E. Lord
  • , M. Lorenzini
  • , V. Loriette
  • , M. Lormand
  • , G. Losurdo
  • , J. D. Lough
  • , C. O. Lousto
  • , G. Lovelace
  • , H. Lück
  • , D. Lumaca
  • , A. P. Lundgren
  • , R. Lynch
  • , Y. Ma
  • , R. Macas
  • , S. Macfoy
  • , B. Machenschalk
  • , M. MacInnis
  • , D. M. Macleod
  • , I. Magaña Hernandez
  • , F. Magaña-Sandoval
  • , L. Magaña Zertuche
  • , R. M. Magee
  • , E. Majorana
  • , I. Maksimovic
  • , N. Man
  • , V. Mandic
  • , V. Mangano
  • , G. L. Mansell
  • , M. Manske
  • , M. Mantovani
  • , F. Marchesoni
  • , F. Marion
  • , S. Márka
  • , Z. Márka
  • , C. Markakis
  • , A. S. Markosyan
  • , A. Markowitz
  • , E. Maros
  • , A. Marquina
  • , F. Martelli
  • , L. Martellini
  • , I. W. Martin
  • , R. M. Martin
  • , D. V. Martynov
  • , K. Mason
  • , E. Massera
  • , A. Masserot
  • , T. J. Massinger
  • , M. Masso-Reid
  • , S. Mastrogiovanni
  • , A. Matas
  • , F. Matichard
  • , L. Matone
  • , N. Mavalvala
  • , N. Mazumder
  • , R. McCarthy
  • , D. E. McClelland
  • , S. McCormick
  • , L. McCuller
  • , S. C. McGuire
  • , G. McIntyre
  • , J. McIver
  • , D. J. McManus
  • , L. McNeill
  • , T. McRae
  • , S. T. McWilliams
  • , D. Meacher
  • , G. D. Meadors
  • , M. Mehmet
  • , J. Meidam
  • , E. Mejuto-Villa
  • , A. Melatos
  • , G. Mendell
  • , R. A. Mercer
  • , E. L. Merilh
  • , M. Merzougui
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The Dark Energy Camera GW-EM Collaboration and the DES Collaboration

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The DLT40 Collaboration

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The Las Cumbres Observatory Collaboration

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The VINROUGE Collaboration

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The MASTER Collaboration

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Contributions

All authors contributed to the work presented in this paper.


Gravitational wave astronomy — Potential and possible realisation

Since the pioneering work of Joseph Weber more than a decade ago there has been a continuing effort towards the development of more sensitive gravitational wave detectors. There are a number of interesting astrophysical sources of gravitational waves including coalescing compact binary star systems, stellar collapses and rotating neutron stars, and to detect all of these is likely to require a strain sensitivity better than 10 −22 over a bandwidth of a few hundred Hz at frequencies at or below 1kHz. To achieve such sensitivity requires considerable experimental ingenuity however work in a number of laboratories suggests that such performance should be attainable using laser interferometry between freely suspended masses separated by a distance of the order of a kilometre. This paper includes a review of possible sources and outlines methods of detection currently being developed or planned, with particular emphasis on long baseline laser interferometers.


Contents

Albert Einstein originally predicted the existence of gravitational waves in 1916, [24] [25] on the basis of his theory of general relativity. [26] General relativity interprets gravity as a consequence of distortions in space-time, caused by mass. Therefore, Einstein also predicted that events in the cosmos would cause "ripples" in space-time – distortions of space-time itself – which would spread outward, although they would be so minuscule that they would be nearly impossible to detect by any technology foreseen at that time. [13] It was also predicted that objects moving in an orbit would lose energy for this reason (a consequence of the law of conservation of energy), as some energy would be given off as gravitational waves, although this would be insignificantly small in all but the most extreme cases. [27]

One case where gravitational waves would be strongest is during the final moments of the merger of two compact objects such as neutron stars or black holes. Over a span of millions of years, binary neutron stars, and binary black holes lose energy, largely through gravitational waves, and as a result, they spiral in towards each other. At the very end of this process, the two objects will reach extreme velocities, and in the final fraction of a second of their merger a substantial amount of their mass would theoretically be converted into gravitational energy, and travel outward as gravitational waves, [28] allowing a greater than usual chance for detection. However, since little was known about the number of compact binaries in the universe and reaching that final stage can be very slow, there was little certainty as to how often such events might happen. [29]

Observation Edit

Gravitational waves can be detected indirectly – by observing celestial phenomena caused by gravitational waves – or more directly by means of instruments such as the Earth-based LIGO or the planned space-based LISA instrument. [30]

Indirect observation Edit

Evidence of gravitational waves was first deduced in 1974 through the motion of the double neutron star system PSR B1913+16, in which one of the stars is a pulsar that emits electro-magnetic pulses at radio frequencies at precise, regular intervals as it rotates. Russell Hulse and Joseph Taylor, who discovered the stars, also showed that over time, the frequency of pulses shortened, and that the stars were gradually spiralling towards each other with an energy loss that agreed closely with the predicted energy that would be radiated by gravitational waves. [31] [32] For this work, Hulse and Taylor were awarded the Nobel Prize in Physics in 1993. [33] Further observations of this pulsar and others in multiple systems (such as the double pulsar system PSR J0737-3039) also agree with General Relativity to high precision. [34] [35]

Direct observation Edit

Direct observation of gravitational waves was not possible for the many decades after they were predicted due to the minuscule effect that would need to be detected and separated from the background of vibrations present everywhere on Earth. A technique called interferometry was suggested in the 1960s and eventually technology developed sufficiently for this technique to become feasible.

In the present approach used by LIGO, a laser beam is split and the two halves are recombined after travelling different paths. Changes to the length of the paths or the time taken for the two split beams, caused by the effect of passing gravitational waves, to reach the point where they recombine are revealed as "beats". Such a technique is extremely sensitive to tiny changes in the distance or time taken to traverse the two paths. In theory, an interferometer with arms about 4 km long would be capable of revealing the change of space-time – a tiny fraction of the size of a single proton – as a gravitational wave of sufficient strength passed through Earth from elsewhere. This effect would be perceptible only to other interferometers of a similar size, such as the Virgo, GEO 600 and planned KAGRA and INDIGO detectors. In practice at least two interferometers would be needed because any gravitational wave would be detected at both of these but other kinds of disturbance would generally not be present at both. This technique allows the sought-after signal to be distinguished from noise. This project was eventually founded in 1992 as the Laser Interferometer Gravitational-Wave Observatory (LIGO). The original instruments were upgraded between 2010 and 2015 (to Advanced LIGO), giving an increase of around 10 times their original sensitivity. [36]

Initial LIGO operations between 2002 and 2010 did not detect any statistically significant events that could be confirmed as gravitational waves. This was followed by a multi-year shut-down while the detectors were replaced by much improved "Advanced LIGO" versions. [37] In February 2015, the two advanced detectors were brought into engineering mode, in which the instruments are operating fully for the purpose of testing and confirming they are functioning correctly before being used for research, [38] with formal science observations due to begin on 18 September 2015. [39]

Throughout the development and initial observations by LIGO, several "blind injections" of fake gravitational wave signals were introduced to test the ability of the researchers to identify such signals. To protect the efficacy of blind injections, only four LIGO scientists knew when such injections occurred, and that information was revealed only after a signal had been thoroughly analyzed by researchers. [40] On 14 September 2015, while LIGO was running in engineering mode but without any blind data injections, the instrument reported a possible gravitational wave detection. The detected event was given the name GW150914. [41]

Event detection Edit

GW150914 was detected by the LIGO detectors in Hanford, Washington state, and Livingston, Louisiana, USA, at 09:50:45 UTC on 14 September 2015. [4] [11] The LIGO detectors were operating in "engineering mode", meaning that they were operating fully but had not yet begun a formal "research" phase (which was due to commence three days later on 18 September), so initially there was a question as to whether the signals had been real detections or simulated data for testing purposes before it was ascertained that they were not tests. [42]

The chirp signal lasted over 0.2 seconds, and increased in frequency and amplitude in about 8 cycles from 35 Hz to 250 Hz. [3] The signal is in the audible range and has been described as resembling the "chirp" of a bird [4] astrophysicists and other interested parties the world over excitedly responded by imitating the signal on social media upon the announcement of the discovery. [4] [43] [44] [45] (The frequency increases because each orbit is noticeably faster than the one before during the final moments before merging.)

The trigger that indicated a possible detection was reported within three minutes of acquisition of the signal, using rapid ('online') search methods that provide a quick, initial analysis of the data from the detectors. [3] After the initial automatic alert at 09:54 UTC, a sequence of internal emails confirmed that no scheduled or unscheduled injections had been made, and that the data looked clean. [40] [46] After this, the rest of the collaborating team was quickly made aware of the tentative detection and its parameters. [47]

More detailed statistical analysis of the signal, and of 16 days of surrounding data from 12 September to 20 October 2015, identified GW150914 as a real event, with an estimated significance of at least 5.1 sigma [3] or a confidence level of 99.99994%. [48] Corresponding wave peaks were seen at Livingston seven milliseconds before they arrived at Hanford. Gravitational waves propagate at the speed of light, and the disparity is consistent with the light travel time between the two sites. [3] The waves had traveled at the speed of light for more than a billion years. [49]

At the time of the event, the Virgo gravitational wave detector (near Pisa, Italy) was offline and undergoing an upgrade had it been online it would likely have been sensitive enough to also detect the signal, which would have greatly improved the positioning of the event. [4] GEO600 (near Hannover, Germany) was not sensitive enough to detect the signal. [3] Consequently, neither of those detectors was able to confirm the signal measured by the LIGO detectors. [4]

Astrophysical origin Edit

The event happened at a luminosity distance of 440 +160
−180 megaparsecs [1] : 6 (determined by the amplitude of the signal), [4] or 1.4 ± 0.6 billion light years, corresponding to a cosmological redshift of 0.093 +0.030
−0.036 (90% credible intervals). Analysis of the signal along with the inferred redshift suggested that it was produced by the merger of two black holes with masses of 35 +5
−3 times and 30 +3
−4 times the mass of the Sun (in the source frame), resulting in a post-merger black hole of 62 +4
−3 solar masses. [1] : 6 The mass–energy of the missing 3.0 ± 0.5 solar masses was radiated away in the form of gravitational waves. [3]

During the final 20 milliseconds of the merger, the power of the radiated gravitational waves peaked at about 3.6 × 10 49 watts or 526dBm – 50 times greater [50] than the combined power of all light radiated by all the stars in the observable universe. [3] [4] [15] [16]

Across the 0.2-second duration of the detectable signal, the relative tangential (orbiting) velocity of the black holes increased from 30% to 60% of the speed of light. The orbital frequency of 75 Hz (half the gravitational wave frequency) means that the objects were orbiting each other at a distance of only 350 km by the time they merged. The phase changes to the signal's polarization allowed calculation of the objects' orbital frequency, and taken together with the amplitude and pattern of the signal, allowed calculation of their masses and therefore their extreme final velocities and orbital separation (distance apart) when they merged. That information showed that the objects had to be black holes, as any other kind of known objects with these masses would have been physically larger and therefore merged before that point, or would not have reached such velocities in such a small orbit. The highest observed neutron star mass is two solar masses, with a conservative upper limit for the mass of a stable neutron star of three solar masses, so that a pair of neutron stars would not have had sufficient mass to account for the merger (unless exotic alternatives exist, for example, boson stars), [2] [3] while a black hole-neutron star pair would have merged sooner, resulting in a final orbital frequency that was not so high. [3]

The decay of the waveform after it peaked was consistent with the damped oscillations of a black hole as it relaxed to a final merged configuration. [3] Although the inspiral motion of compact binaries can be described well from post-Newtonian calculations, [51] the strong gravitational field merger stage can only be solved in full generality by large-scale numerical relativity simulations. [52] [53] [54]

In the improved model and analysis, the post-merger object is found to be a rotating Kerr black hole with a spin parameter of 0.68 +0.05
−0.06 , [1] i.e. one with 2/3 of the maximum possible angular momentum for its mass.

The two stars which formed the two black holes were likely formed about 2 billion years after the Big Bang with masses of between 40 and 100 times the mass of the Sun. [55] [56]

Location in the sky Edit

Gravitational wave instruments are whole-sky monitors with little ability to resolve signals spatially. A network of such instruments is needed to locate the source in the sky through triangulation. With only the two LIGO instruments in observational mode, GW150914's source location could only be confined to an arc on the sky. This was done via analysis of the 6.9 +0.5
−0.4 ms time-delay, along with amplitude and phase consistency across both detectors. This analysis produced a credible region of 150 deg 2 with a probability of 50% or 610 deg 2 with a probability of 90% located mainly in the Southern Celestial Hemisphere, [2] : 7 : fig 4 in the rough direction of (but much farther than) the Magellanic Clouds. [4] [11]

Coincident gamma-ray observation Edit

The Fermi Gamma-ray Space Telescope reported that its Gamma-Ray Burst Monitor (GBM) instrument detected a weak gamma-ray burst above 50 keV, starting 0.4 seconds after the LIGO event and with a positional uncertainty region overlapping that of the LIGO observation. The Fermi team calculated the odds of such an event being the result of a coincidence or noise at 0.22%. [58] However a gamma ray burst would not have been expected, and observations from the INTEGRAL telescope's all-sky SPI-ACS instrument indicated that any energy emission in gamma-rays and hard X-rays from the event was less than one millionth of the energy emitted as gravitational waves, which "excludes the possibility that the event is associated with substantial gamma-ray radiation, directed towards the observer". If the signal observed by the Fermi GBM was genuinely astrophysical, INTEGRAL would have indicated a clear detection at a significance of 15 sigma above background radiation. [59] The AGILE space telescope also did not detect a gamma-ray counterpart of the event. [60]

A follow-up analysis by an independent group, released in June 2016, developed a different statistical approach to estimate the spectrum of the gamma-ray transient. It concluded that Fermi GBM's data did not show evidence of a gamma ray burst, and was either background radiation or an Earth albedo transient on a 1-second timescale. [61] [62] A rebuttal of this follow-up analysis, however, pointed out that the independent group misrepresented the analysis of the original Fermi GBM Team paper and therefore misconstrued the results of the original analysis. The rebuttal reaffirmed that the false coincidence probability is calculated empirically and is not refuted by the independent analysis. [63] [64]

Black hole mergers of the type thought to have produced the gravitational wave event are not expected to produce gamma-ray bursts, as stellar-mass black hole binaries are not expected to have large amounts of orbiting matter. Avi Loeb has theorised that if a massive star is rapidly rotating, the centrifugal force produced during its collapse will lead to the formation of a rotating bar that breaks into two dense clumps of matter with a dumbbell configuration that becomes a black hole binary, and at the end of the star's collapse it triggers a gamma-ray burst. [65] [66] Loeb suggests that the 0.4 second delay is the time it took the gamma-ray burst to cross the star, relative to the gravitational waves. [66] [67]

Other follow-up observations Edit

The reconstructed source area was targeted by follow-up observations covering radio, optical, near infra-red, X-ray, and gamma-ray wavelengths along with searches for coincident neutrinos. [2] However, because LIGO had not yet started its science run, notice to other telescopes was delayed. [ citation needed ]

The ANTARES telescope detected no neutrino candidates within ±500 seconds of GW150914. The IceCube Neutrino Observatory detected three neutrino candidates within ±500 seconds of GW150914. One event was found in the southern sky and two in the northern sky. This was consistent with the expectation of background detection levels. None of the candidates were compatible with the 90% confidence area of the merger event. [68] Although no neutrinos were detected, the lack of such observations provided a limit on neutrino emission from this type of gravitational wave event. [68]

Observations by the Swift Gamma-Ray Burst Mission of nearby galaxies in the region of the detection, two days after the event, did not detect any new X-ray, optical or ultraviolet sources. [69]

Announcement Edit

The announcement of the detection was made on 11 February 2016 [4] at a news conference in Washington, D.C. by David Reitze, the executive director of LIGO, [6] with a panel comprising Gabriela González, Rainer Weiss and Kip Thorne, of LIGO, and France A. Córdova, the director of NSF. [4] Barry Barish delivered the first presentation on this discovery to a scientific audience simultaneously with the public announcement. [70]

The initial announcement paper was published during the news conference in Physical Review Letters, [3] with further papers either published shortly afterwards [19] or immediately available in preprint form. [71]

Awards and recognition Edit

In May 2016, the full collaboration, and in particular Ronald Drever, Kip Thorne, and Rainer Weiss, received the Special Breakthrough Prize in Fundamental Physics for the observation of gravitational waves. [72] Drever, Thorne, Weiss, and the LIGO discovery team also received the Gruber Prize in Cosmology. [73] Drever, Thorne, and Weiss were also awarded the 2016 Shaw Prize in Astronomy [74] [75] and the 2016 Kavli Prize in Astrophysics. [76] Barish was awarded the 2016 Enrico Fermi Prize from the Italian Physical Society (Società Italiana di Fisica). [77] In January 2017, LIGO spokesperson Gabriela González and the LIGO team were awarded the 2017 Bruno Rossi Prize. [78]

The 2017 Nobel Prize in Physics was awarded to Rainer Weiss, Barry Barish and Kip Thorne "for decisive contributions to the LIGO detector and the observation of gravitational waves". [79]

The observation was heralded as inaugurating a revolutionary era of gravitational-wave astronomy. [80] Prior to this detection, astrophysicists and cosmologists were able to make observations based upon electromagnetic radiation (including visible light, X-rays, microwave, radio waves, gamma rays) and particle-like entities (cosmic rays, stellar winds, neutrinos, and so on). These have significant limitations – light and other radiation may not be emitted by many kinds of objects, and can also be obscured or hidden behind other objects. Objects such as galaxies and nebulae can also absorb, re-emit, or modify light generated within or behind them, and compact stars or exotic stars may contain material which is dark and radio silent, and as a result there is little evidence of their presence other than through their gravitational interactions. [81] [82]

Expectations for detection of future binary merger events Edit

On 15 June 2016, the LIGO group announced an observation of another gravitational wave signal, named GW151226. [83] The Advanced LIGO was predicted to detect five more black hole mergers like GW150914 in its next observing campaign from November 2016 until August 2017 (it turned out to be seven), and then 40 binary star mergers each year, in addition to an unknown number of more exotic gravitational wave sources, some of which may not be anticipated by current theory. [11]

Planned upgrades are expected to double the signal-to-noise ratio, expanding the volume of space in which events like GW150914 can be detected by a factor of ten. Additionally, Advanced Virgo, KAGRA, and a possible third LIGO detector in India will extend the network and significantly improve the position reconstruction and parameter estimation of sources. [3]

Laser Interferometer Space Antenna (LISA) is a proposed space based observation mission to detect gravitational waves. With the proposed sensitivity range of LISA, merging binaries like GW150914 would be detectable about 1000 years before they merge, providing for a class of previously unknown sources for this observatory if they exist within about 10 megaparsecs. [19] LISA Pathfinder, LISA's technology development mission, was launched in December 2015 and it demonstrated that the LISA mission is feasible. [84]

A current model predicts LIGO will detect approximately 1000 black hole mergers per year after it reaches full sensitivity planned for 2020. [55] [56]

Lessons for stellar evolution and astrophysics Edit

The masses of the two pre-merger black holes provide information about stellar evolution. Both black holes were more massive than previously discovered stellar-mass black holes, which were inferred from X-ray binary observations. This implies that the stellar winds from their progenitor stars must have been relatively weak, and therefore that the metallicity (mass fraction of chemical elements heavier than hydrogen and helium) must have been less than about half the solar value. [19]

The fact that the pre-merger black holes were present in a binary star system, as well as the fact that the system was compact enough to merge within the age of the universe, constrains either binary star evolution or dynamical formation scenarios, depending on how the black hole binary was formed. A significant number of black holes must receive low natal kicks (the velocity a black hole gains at its formation in a core-collapse supernova event), otherwise the black hole forming in a binary star system would be ejected and an event like GW would be prevented. [19] The survival of such binaries, through common envelope phases of high rotation in massive progenitor stars, may be necessary for their survival. [ clarification needed ] The majority of the latest black hole model predictions comply with these added constraints. [ citation needed ]

The discovery of the GW merger event increases the lower limit on the rate of such events, and rules out certain theoretical models that predicted very low rates of less than 1 Gpc −3 yr −1 (one event per cubic gigaparsec per year). [3] [19] Analysis resulted in lowering the previous upper limit rate on events like GW150914 from

140 Gpc −3 yr −1 to 17 +39
−13 Gpc −3 yr −1 . [85]

Impact on future cosmological observation Edit

Measurement of the waveform and amplitude of the gravitational waves from a black hole merger event makes accurate determination of its distance possible. The accumulation of black hole merger data from cosmologically distant events may help to create more precise models of the history of the expansion of the universe and the nature of the dark energy that influences it. [86] [87]

The earliest universe is opaque since the cosmos was so energetic then that most matter was ionized and photons were scattered by free electrons. [88] However, this opacity would not affect gravitational waves from that time, so if they occurred at levels strong enough to be detected at this distance, it would allow a window to observe the cosmos beyond the current visible universe. Gravitational-wave astronomy therefore may some day allow direct observation of the earliest history of the universe. [3] [18] [19] [20] [21]

Tests of general relativity Edit

The inferred fundamental properties, mass and spin, of the post-merger black hole were consistent with those of the two pre-merger black holes, following the predictions of general relativity. [7] [8] [9] This is the first test of general relativity in the very strong-field regime. [3] [18] No evidence could be established against the predictions of general relativity. [18]

The opportunity was limited in this signal to investigate the more complex general relativity interactions, such as tails produced by interactions between the gravitational wave and curved space-time background. Although a moderately strong signal, it is much smaller than that produced by binary-pulsar systems. In the future stronger signals, in conjunction with more sensitive detectors, could be used to explore the intricate interactions of gravitational waves as well as to improve the constraints on deviations from general relativity. [18]

Speed of gravitational waves and limit on possible mass of graviton Edit

The speed of gravitational waves (vg) is predicted by general relativity to be the speed of light (c). [89] The extent of any deviation from this relationship can be parameterized in terms of the mass of the hypothetical graviton. The graviton is the name given to an elementary particle that would act as the force carrier for gravity, in quantum theories about gravity. It is expected to be massless if, as it appears, gravitation has an infinite range. (This is because the more massive a gauge boson is, the shorter is the range of the associated force as with the infinite range of electromagnetism, which is due to the massless photon, the infinite range of gravity implies that any associated force-carrying particle would also be massless.) If the graviton were not massless, gravitational waves would propagate below lightspeed, with lower frequencies (ƒ) being slower than higher frequencies, leading to dispersion of the waves from the merger event. [18] No such dispersion was observed. [18] [28] The observations of the inspiral slightly improve (lower) the upper limit on the mass of the graviton from Solar System observations to 2.1 × 10 −58 kg , corresponding to 1.2 × 10 −22 eV/c 2 or a Compton wavelength (λg) of greater than 10 13 km, roughly 1 light-year. [3] [18] Using the lowest observed frequency of 35 Hz, this translates to a lower limit on vg such that the upper limit on 1-vg /c is


Black Holes

The Schwarzschild solution has often been stated to be an 'exact solution to the Einstein field equations' that describes the gravitational field surrounding a spherical mass and has become a pillar of contemporary physics. The core premise of the Einstein field equations relates local space-time curvature surrounding a primary body, whereas, the Schwarzschild solution employs a weak field approximation whereby gravity is linearized and secondary bodies are free falling in a flat Euclidean space surrounding a spherical primary mass.

Furthermore, the Schwarzschild solution diverges from tenets of relativity in the following ways:
(i) It employs a flat Euclidean space surrounding a spherical primary mass.
(ii) It employs a novel feature the Schwarzschild radius, Rs, of the black hole event horizon, not found in General Relativity.
(iii) It employs the Hamiltonian energy of a system.
(iv) It does not employ the Lorentz factor of Special and General Relativity.
(v) The Schwarzschild solution has been verified empirically, however, the cosmological equations of the Einstein Field Equation have not been verified and remain speculative.

The conclusion can be drawn that the Schwarzschild solution has been verified and is a distinct physical model, rather than as a simplification or derivation from relativity.


Gravitational Waves and Gravitational-wave Sourcestwo ☆,☆☆

The recent discovery of gravitational-wave burst GW150914 marks the coming of a new era of gravitational-wave astronomy, which provides a new window to study the physics of strong gravitational field, extremely massive stars, extremely high energy processes, and extremely early universe. In this article, we introduce the basic characters of gravitational waves in the Einstein's general relativity, their observational effects and main generation mechanisms, including the rotation of neutron stars, evolution of binary systems, and spontaneous generation in the inflation universe. Different sources produce the gravitational waves at quite different frequencies, which can be detected by different methods. In the lowest frequency range (f < 10 −15 Hz), the detection is mainly dependent of the observation of B-mode polarization of cosmic microwave background radiation. In the middle frequency range (10 −9 < f < 10 −6 Hz), the gravitational waves are detected by analyzing the timing residuals of millisecond pulsars. And in the high frequency range (10 − 4 < f < 10 4 Hz), they can be detected by the space-based and ground-based laser interferometers. In particular, we focus on the main features, detection methods, detection status, and the future prospects for several important sources, including the continuous sources (e.g., the spinning neutron stars, and stable binary systems), the burst sources (e.g., the supernovae, and the merge of binary system), and the stochastic backgrounds generated by the astrophysical and cosmological process. In addition, we forecast the potential breakthroughs in gravitational-wave astronomy in the near future, and the Chinese projects which might involve in these discoveries.