Can the UN Secretary-General Say No : Revisiting the Peking Formula

The study explores the extent to which the U.N. Secretary-General can uphold his or her own views when confronted with adverse stances from powerful States. More specifically, it analyzes a particular modus operandi originally developed by Dag Hammarskjold, known as the “Peking formula”. This form of good offices is discussed in two contexts, namely the 1954-1955 Sino-American hostage crisis when it was first used and the more recent attempts of Javier Perez de Cuéllar and Kofi Annan at solving the subsequent Iraq crises. Drawing upon these two case-studies, the author offers a theoretical account of the complex interactions between law and politics underlying the good offices role of the U.N. Secretary-General

Model of gravitational waves from precessing black-hole binaries through merger and ringdown

We present phenompnr, a frequency-domain phenomenological model of the gravitational-wave signal from binary-black-hole mergers that is tuned to numerical relativity (NR) simulations of precessing binaries. In many current waveform models, e.g., the “phenom” and “eobnr” families that have been used extensively to analyse LIGO-Virgo GW observations, analytic approximations are used to add precession effects to models of nonprecessing (aligned-spin) binaries, and it is only the aligned-spin models that are fully tuned to NR results. In phenompnr we incorporate precessing-binary numerical relativity results in two ways: (i) we produce the first numerical relativity-tuned model of the signal-based precession dynamics through merger and ringdown, and (ii) we extend a previous aligned-spin model, phenomd, to include the effects of misaligned spins on the signal in the coprecessing frame. The numerical relativity calibration has been performed on 40 simulations of binaries with mass ratios between 1 ∶ 1 and 1 ∶ 8 , where the larger black hole has a dimensionless spin magnitude of 0.4 or 0.8, and we choose five angles of spin misalignment with the orbital angular momentum. phenompnr has a typical mismatch accuracy within 0.1% up to mass ratio 1 ∶ 4 and within 1% up to mass ratio 1 ∶ 8

Catalog of precessing black-hole-binary numerical-relativity simulations

We present a public catalog of numerical-relativity binary-black-hole simulations. The catalog contains datasets from 80 distinct configurations of precessing binary-black-hole systems, with mass ratios up to m 2 / m 1 = 8 , dimensionless spin magnitudes on the larger black hole up to | → S 2 | / m 2 2 = 0.8 (the small black hole is nonspinning), and a range of five values of spin misalignment for each mass-ratio/spin combination. We discuss the physical properties of the configurations in our catalog, and assess the accuracy of the initial configuration of each simulation and of the gravitational waveforms. We perform a careful analysis of the errors due to the finite resolution of our simulations and the finite distance from the source at which we extract the waveform data and provide a conservative estimate of the mismatch accuracy. We find that the upper limit on the mismatch uncertainty of our waveforms (including multipoles ℓ ≤ 5 ) is 0.4%. In doing this we present a consistent approach to combining mismatch uncertainties from multiple error sources. We compare this release to previous catalogs and discuss how these new simulations complement the existing public datasets. In particular, this is the first catalog to uniformly cover this parameter space of single-spin binaries and there was previously only sparse coverage of the precessing-binary parameter space for mass ratios ≳ 5 . We discuss applications of these new data, and the most urgent directions for future simulation work

Effects of waveform model systematics on the interpretation of GW150914

PAPER Effects of waveform model systematics on the interpretation of GW150914 B P Abbott1, R Abbott1, T D Abbott2, M R Abernathy3, F Acernese4,5, K Ackley6, C Adams7, T Adams8, P Addesso9,144, R X Adhikari1, V B Adya10, C Affeldt10, M Agathos11, K Agatsuma11, N Aggarwal12, O D Aguiar13, L Aiello14,15, A Ain16, P Ajith17, B Allen10,18,19, A Allocca20,21, P A Altin22, A Ananyeva1, S B Anderson1, W G Anderson18, S Appert1, K Arai1, M C Araya1, J S Areeda23, N Arnaud24, K G Arun25, S Ascenzi15,26, G Ashton10, M Ast27, S M Aston7, P Astone28, P Aufmuth19, C Aulbert10, A Avila-Alvarez23, S Babak29, P Bacon30, M K M Bader11, P T Baker31, F Baldaccini32,33, G Ballardin34, S W Ballmer35, J C Barayoga1, S E Barclay36, B C Barish1, D Barker37, F Barone4,5, B Barr36, L Barsotti12, M Barsuglia30, D Barta38, J Bartlett37, I Bartos39, R Bassiri40, A Basti20,21, J C Batch37, C Baune10, V Bavigadda34, M Bazzan41,42, C Beer10, M Bejger43, I Belahcene24, M Belgin44, A S Bell36, B K Berger1, G Bergmann10, C P L Berry45, D Bersanetti46,47, A Bertolini11, J Betzwieser7, S Bhagwat35, R Bhandare48, I A Bilenko49, G Billingsley1, C R Billman6, J Birch7, R Birney50, O Birnholtz10, S Biscans1,12, A Bisht19, M Bitossi34, C Biwer35, M A Bizouard24, J K Blackburn1, J Blackman51, C D Blair52, D G Blair52, R M Blair37, S Bloemen53, O Bock10, M Boer54, G Bogaert54, A Bohe29, F Bondu55, R Bonnand8, B A Boom11, R Bork1, V Boschi20,21, S Bose16,56, Y Bouffanais30, A Bozzi34, C Bradaschia21, P R Brady18, V B Braginsky49,145, M Branchesi57,58, J E Brau59, T Briant60, A Brillet54, M Brinkmann10, V Brisson24, P Brockill18, J E Broida61, A F Brooks1, D A Brown35, D D Brown45, N M Brown12, S Brunett1, C C Buchanan2, A Buikema12, T Bulik62, H J Bulten11,63, A Buonanno29,64, D Buskulic8, C Buy30, R L Byer40, M Cabero10, L Cadonati44, G Cagnoli65,66, C Cahillane1, J Calderón Bustillo44, T A Callister1, E Calloni5,67, J B Camp68, K C Cannon69, H Cao70, J Cao71, C D Capano10, E Capocasa30, F Carbognani34, S Caride72, J Casanueva Diaz24, C Casentini15,26, S Caudill18, M Cavaglià73, F Cavalier24, R Cavalieri34, G Cella21, C B Cepeda1, L Cerboni Baiardi57,58, G Cerretani20,21, E Cesarini15,26, S J Chamberlin74, M Chan36, S Chao75, P Charlton76, E Chassande-Mottin30, B D Cheeseboro31, H Y Chen77, Y Chen51, H-P Cheng6, A Chincarini47, A Chiummo34, T Chmiel78, H S Cho79, M Cho64, J H Chow22, N Christensen61, Q Chu52, A J K Chua80, S Chua60, S Chung52, G Ciani6, F Clara37, J A Clark44, F Cleva54, C Cocchieri73, E Coccia14,15, P-F Cohadon60, A Colla28,81, C G Collette82, L Cominsky83, M Constancio Jr13, L Conti42, S J Cooper45, T R Corbitt2, N Cornish84, A Corsi72, S Cortese34, C A Costa13, M W Coughlin61, S B Coughlin85, J-P Coulon54, S T Countryman39, P Couvares1, P B Covas86, E E Cowan44, D M Coward52, M J Cowart7, D C Coyne1, R Coyne72, J D E Creighton18, T D Creighton87, J Cripe2, S G Crowder88, T J Cullen23, A Cumming36, L Cunningham36, E Cuoco34, T Dal Canton68, S L Danilishin36, S D'Antonio15, K Danzmann10,19, A Dasgupta89, C F Da Silva Costa6, V Dattilo34, I Dave48, M Davier24, G S Davies36, D Davis35, E J Daw90, B Day44, R Day34, S De35, D DeBra40, G Debreczeni38, J Degallaix65, M De Laurentis5,67, S Deléglise60, W Del Pozzo45, T Denker10, T Dent10, V Dergachev29, R De Rosa5,67, R T DeRosa7, R DeSalvo91, J Devenson50, R C Devine31, S Dhurandhar16, M C Díaz87, L Di Fiore5, M Di Giovanni92,93, T Di Girolamo5,67, A Di Lieto20,21, S Di Pace28,81, I Di Palma28,29,81, A Di Virgilio21, Z Doctor77, V Dolique65, F Donovan12, K L Dooley73, S Doravari10, I Dorrington94, R Douglas36, M Dovale Álvarez45, T P Downes18, M Drago10, R W P Drever1,146, J C Driggers37, Z Du71, M Ducrot8, S E Dwyer37, T B Edo90, M C Edwards61, A Effler7, H-B Eggenstein10, P Ehrens1, J Eichholz1, S S Eikenberry6, R A Eisenstein12, R C Essick12, Z Etienne31, T Etzel1, M Evans12, T M Evans7, R Everett74, M Factourovich39, V Fafone14,15,26, H Fair35, S Fairhurst94, X Fan71, S Farinon47, B Farr77, W M Farr45, E J Fauchon-Jones94, M Favata95, M Fays94, H Fehrmann10, M M Fejer40, A Fernández Galiana12, I Ferrante20,21, E C Ferreira13, F Ferrini34, F Fidecaro20,21, I Fiori34, D Fiorucci30, R P Fisher35, R Flaminio65,96, M Fletcher36, H Fong97, S S Forsyth44, J-D Fournier54, S Frasca28,81, F Frasconi21, Z Frei98, A Freise45, R Frey59, V Frey24, E M Fries1, P Fritschel12, V V Frolov7, P Fulda6,68, M Fyffe7, H Gabbard10, B U Gadre16, S M Gaebel45, J R Gair99, L Gammaitoni32, S G Gaonkar16, F Garufi5,67, G Gaur100, V Gayathri101, N Gehrels68, G Gemme47, E Genin34, A Gennai21, J George48, L Gergely102, V Germain8, S Ghonge17, Abhirup Ghosh17, Archisman Ghosh11,17, S Ghosh11,53, J A Giaime2,7, K D Giardina7, A Giazotto21, K Gill103, A Glaefke36, E Goetz10, R Goetz6, L Gondan98, G González2, J M Gonzalez Castro20,21, A Gopakumar104, M L Gorodetsky49, S E Gossan1, M Gosselin34, R Gouaty8, A Grado5,105, C Graef36, M Granata65, A Grant36, S Gras12, C Gray37, G Greco57,58, A C Green45, P Groot53, H Grote10, S Grunewald29, G M Guidi57,58, X Guo71, A Gupta16, M K Gupta89, K E Gushwa1, E K Gustafson1, R Gustafson106, J J Hacker23, B R Hall56, E D Hall1, G Hammond36, M Haney104, M M Hanke10, J Hanks37, C Hanna74, M D Hannam94, J Hanson7, T Hardwick2, J Harms57,58, G M Harry3, I W Harry29, M J Hart36, M T Hartman6, C-J Haster45,97, K Haughian36, J Healy107, A Heidmann60, M C Heintze7, H Heitmann54, P Hello24, G Hemming34, M Hendry36, I S Heng36, J Hennig36, J Henry107, A W Heptonstall1, M Heurs10,19, S Hild36, D Hoak34, D Hofman65, K Holt7, D E Holz77, P Hopkins94, J Hough36, E A Houston36, E J Howell52, Y M Hu10, E A Huerta108, D Huet24, B Hughey103, S Husa86, S H Huttner36, T Huynh-Dinh7, N Indik10, D R Ingram37, R Inta72, H N Isa36, J-M Isac60, M Isi1, T Isogai12, B R Iyer17, K Izumi37, T Jacqmin60, K Jani44, P Jaranowski109, S Jawahar110, F Jiménez-Forteza86, W W Johnson2, D I Jones111, R Jones36, R J G Jonker11, L Ju52, J Junker10, C V Kalaghatgi94, V Kalogera85, S Kandhasamy73, G Kang79, J B Kanner1, S Karki59, K S Karvinen10, M Kasprzack2, E Katsavounidis12, W Katzman7, S Kaufer19, T Kaur52, K Kawabe37, F Kéfélian54, D Keitel86, D B Kelley35, R Kennedy90, J S Key112, F Y Khalili49, I Khan14, S Khan94, Z Khan89, E A Khazanov113, N Kijbunchoo37, Chunglee Kim114, J C Kim115, Whansun Kim116, W Kim70, Y-M Kim114,117, S J Kimbrell44, E J King70, P J King37, R Kirchhoff10, J S Kissel37, B Klein85, L Kleybolte27, S Klimenko6, P Koch10, S M Koehlenbeck10, S Koley11, V Kondrashov1, A Kontos12, M Korobko27, W Z Korth1, I Kowalska62, D B Kozak1, C Krämer10, V Kringel10, B Krishnan10, A Królak118,119, G Kuehn10, P Kumar97, R Kumar89, L Kuo75, A Kutynia118, B D Lackey29,35, M Landry37, R N Lang18, J Lange107, B Lantz40, R K Lanza12, A Lartaux-Vollard24, P D Lasky120, M Laxen7, A Lazzarini1, C Lazzaro42, P Leaci28,81, S Leavey36, E O Lebigot30, C H Lee117, H K Lee121, H M Lee114, K Lee36, J Lehmann10, A Lenon31, M Leonardi92,93, J R Leong10, N Leroy24, N Letendre8, Y Levin120, T G F Li122, A Libson12, T B Littenberg123, J Liu52, N A Lockerbie110, A L Lombardi44, L T London94, J E Lord35, M Lorenzini14,15, V Loriette124, M Lormand7, G Losurdo21, J D Lough10,19, G Lovelace23, H Lück10,19, A P Lundgren10, R Lynch12, Y Ma51, S Macfoy50, B Machenschalk10, M MacInnis12, D M Macleod2, F Magaña-Sandoval35, E Majorana28, I Maksimovic124, V Malvezzi15,26, N Man54, V Mandic125, V Mangano36, G L Mansell22, M Manske18, M Mantovani34, F Marchesoni33,126, F Marion8, S Márka39, Z Márka39, A S Markosyan40, E Maros1, F Martelli57,58, L Martellini54, I W Martin36, D V Martynov12, K Mason12, A Masserot8, T J Massinger1, M Masso-Reid36, S Mastrogiovanni28,81, F Matichard1,12, L Matone39, N Mavalvala12, N Mazumder56, R McCarthy37, D E McClelland22, S McCormick7, C McGrath18, S C McGuire127, G McIntyre1, J McIver1, D J McManus22, T McRae22, S T McWilliams31, D Meacher54,74, G D Meadors10,29, J Meidam11, A Melatos128, G Mendell37, D Mendoza-Gandara10, R A Mercer18, E L Merilh37, M Merzougui54, S Meshkov1, C Messenger36, C Messick74, R Metzdorff60, P M Meyers125, F Mezzani28,81, H Miao45, C Michel65, H Middleton45, E E Mikhailov129, L Milano5,67, A L Miller6,28,81, A Miller85, B B Miller85, J Miller12, M Millhouse84, Y Minenkov15, J Ming29, S Mirshekari130, C Mishra17, S Mitra16, V P Mitrofanov49, G Mitselmakher6, R Mittleman12, A Moggi21, M Mohan34, S R P Mohapatra12, M Montani57,58, B C Moore95, C J Moore80, D Moraru37, G Moreno37, S R Morriss87, B Mours8, C M Mow-Lowry45, G Mueller6, A W Muir94, Arunava Mukherjee17, D Mukherjee18, S Mukherjee87, N Mukund16, A Mullavey7, J Munch70, E A M Muniz23, P G Murray36, A Mytidis6, K Napier44, I Nardecchia15,26, L Naticchioni28,81, G Nelemans11,53, T J N Nelson7, M Neri46,47, M Nery10, A Neunzert106, J M Newport3, G Newton36, T T Nguyen22, A B Nielsen10, S Nissanke11,53, A Nitz10, A Noack10, F Nocera34, D Nolting7, M E N Normandin87, L K Nuttall35, J Oberling37, E Ochsner18, E Oelker12, G H Ogin131, J J Oh116, S H Oh116, F Ohme10,94, M Oliver86, P Oppermann10, Richard J Oram7, B O'Reilly7, R O'Shaughnessy107, D J Ottaway70, H Overmier7, B J Owen72, A E Pace74, J Page123, A Pai101, S A Pai48, J R Palamos59, O Palashov113, C Palomba28, A Pal-Singh27, H Pan75, C Pankow85, F Pannarale94, B C Pant48, F Paoletti21,34, A Paoli34, M A Papa10,18,29, H R Paris40, W Parker7, D Pascucci36, A Pasqualetti34, R Passaquieti20,21, D Passuello21, B Patricelli20,21, B L Pearlstone36, M Pedraza1, R Pedurand65,132, L Pekowsky35, A Pele7, S Penn133, C J Perez37, A Perreca1, L M Perri85, H P Pfeiffer97, M Phelps36, O J Piccinni28,81, M Pichot54, F Piergiovanni57,58, V Pierro9, G Pillant34, L Pinard65, I M Pinto9, M Pitkin36, M Poe18, R Poggiani20,21, P Popolizio34, A Post10, J Powell36, J Prasad16, J W W Pratt103, V Predoi94, T Prestegard18,125, M Prijatelj10,34, M Principe9, S Privitera29, G A Prodi92,93, L G Prokhorov49, O Puncken10, M Punturo33, P Puppo28, M Pürrer29, H Qi18, J Qin52, S Qiu120, V Quetschke87, E A Quintero1, R Quitzow-James59, F J Raab37, D S Rabeling22, H Radkins37, P Raffai98, S Raja48, C Rajan48, M Rakhmanov87, P Rapagnani28,81, V Raymond29, M Razzano20,21, V Re26, J Read23, T Regimbau54, L Rei47, S Reid50, D H Reitze1,6, H Rew129, S D Reyes35, E Rhoades103, F Ricci28,81, K Riles106, M Rizzo107, N A Robertson1,36, R Robie36, F Robinet24, A Rocchi15, L Rolland8, J G Rollins1, V J Roma59, J D Romano87, R Romano4,5, J H Romie7, D Rosińska43,134, S Rowan36, A Rüdiger10, P Ruggi34, K Ryan37, S Sachdev1, T Sadecki37, L Sadeghian18, M Sakellariadou135, L Salconi34, M Saleem101, F Salemi10, A Samajdar136, L Sammut120, L M Sampson85, E J Sanchez1, V Sandberg37, J R Sanders35, B Sassolas65, B S Sathyaprakash74,94, P R Saulson35, O Sauter106, R L Savage37, A Sawadsky19, P Schale59, J Scheuer85, E Schmidt103, J Schmidt10, P Schmidt1,51, R Schnabel27, R M S Schofield59, A Schönbeck27, E Schreiber10, D Schuette10,19, B F Schutz29,94, S G Schwalbe103, J Scott36, S M Scott22, D Sellers7, A S Sengupta137, D Sentenac34, V Sequino15,26, A Sergeev113, Y Setyawati11,53, D A Shaddock22, T J Shaffer37, M S Shahriar85, B Shapiro40, P Shawhan64, A Sheperd18, D H Shoemaker12, D M Shoemaker44, K Siellez44, X Siemens18, M Sieniawska43, D Sigg37, A D Silva13, A Singer1, L P Singer68, A Singh10,19,29, R Singh2, A Singhal14, A M Sintes86, B J J Slagmolen22, B Smith7, J R Smith23, R J E Smith1, E J Son116, B Sorazu36, F Sorrentino47, T Souradeep16, A P Spencer36, A K Srivastava89, A Staley39, M Steinke10, J Steinlechner36, S Steinlechner27,36, D Steinmeyer10,19, B C Stephens18, S P Stevenson45, R Stone87, K A Strain36, N Straniero65, G Stratta57,58, S E Strigin49, R Sturani130, A L Stuver7, T Z Summerscales138, L Sun128, S Sunil89, P J Sutton94, B L Swinkels34, M J Szczepańczyk103, M Tacca30, D Talukder59, D B Tanner6, M Tápai102, A Taracchini29, R Taylor1, T Theeg10, E G Thomas45, M Thomas7, P Thomas37, K A Thorne7, E Thrane120, T Tippens44, S Tiwari14,93, V Tiwari94, K V Tokmakov110, K Toland36, C Tomlinson90, M Tonelli20,21, Z Tornasi36, C I Torrie1, D Töyrä45, F Travasso32,33, G Traylor7, D Trifirò73, J Trinastic6, M C Tringali92,93, L Trozzo21,139, M Tse12, R Tso1, M Turconi54, D Tuyenbayev87, D Ugolini140, C S Unnikrishnan104, A L Urban1, S A Usman94, H Vahlbruch19, G Vajente1, G Valdes87, N van Bakel11, M van Beuzekom11, J F J van den Brand11,63, C Van Den Broeck11, D C Vander-Hyde35, L van der Schaaf11, J V van Heijningen11, A A van Veggel36, M Vardaro41,42, V Varma51, S Vass1, M Vasúth38, A Vecchio45, G Vedovato42, J Veitch45, P J Veitch70, K Venkateswara141, G Venugopalan1, D Verkindt8, F Vetrano57,58, A Viceré57,58, A D Viets18, S Vinciguerra45, D J Vine50, J-Y Vinet54, S Vitale12, T Vo35, H Vocca32,33, C Vorvick37, D V Voss6, W D Vousden45, S P Vyatchanin49, A R Wade1, L E Wade78, M Wade78, M Walker2, L Wallace1, S Walsh10,29, G Wang14,58, H Wang45, M Wang45, Y Wang52, R L Ward22, J Warner37, M Was8, J Watchi82, B Weaver37, L-W Wei54, M Weinert10, A J Weinstein1, R Weiss12, L Wen52, P Weßels10, T Westphal10, K Wette10, J T Whelan107, B F Whiting6, C Whittle120, D Williams36, R D Williams1, A R Williamson94, J L Willis142, B Willke10,19, M H Wimmer10,19, W Winkler10, C C Wipf1, H Wittel10,19, G Woan36, J Woehler10, J Worden37, J L Wright36, D S Wu10, G Wu7, W Yam12, H Yamamoto1, C C Yancey64, M J Yap22, Hang Yu12, Haocun Yu12, M Yvert8, A Zadrożny118, L Zangrando42, M Zanolin103, J-P Zendri42, M Zevin85, L Zhang1, M Zhang129, T Zhang36, Y Zhang107, C Zhao52, M Zhou85, Z Zhou85, S J Zhu10,29, X J Zhu52, M E Zucker1,12, J Zweizig1 (LIGO Scientific Collaboration, Virgo Collaboration), M Boyle143, T Chu97, D Hemberger51, I Hinder29, L E Kidder143, S Ossokine29, M Scheel51, B Szilagyi51, S Teukolsky143 and A Vano Vinuales94 Hide full author list Published 12 April 2017 • © 2017 IOP Publishing Ltd Classical and Quantum Gravity, Volume 34, Number 10 Focus Issue: Gravitational Waves Article PDF Figures References Citations PDF 258 Total downloads Cited by 1 articles Article has an altmetric score of 3 Turn on MathJax Get permission to re-use this article Share this article Article information Abstract Parameter estimates of GW150914 were obtained using Bayesian inference, based on three semi-analytic waveform models for binary black hole coalescences. These waveform models differ from each other in their treatment of black hole spins, and all three models make some simplifying assumptions, notably to neglect sub-dominant waveform harmonic modes and orbital eccentricity. Furthermore, while the models are calibrated to agree with waveforms obtained by full numerical solutions of Einstein's equations, any such calibration is accurate only to some non-zero tolerance and is limited by the accuracy of the underlying phenomenology, availability, quality, and parameter-space coverage of numerical simulations. This paper complements the original analyses of GW150914 with an investigation of the effects of possible systematic errors in the waveform models on estimates of its source parameters. To test for systematic errors we repeat the original Bayesian analysis on mock signals from numerical simulations of a series of binary configurations with parameters similar to those found for GW150914. Overall, we find no evidence for a systematic bias relative to the statistical error of the original parameter recovery of GW150914 due to modeling approximations or modeling inaccuracies. However, parameter biases are found to occur for some configurations disfavored by the data of GW150914: for binaries inclined edge-on to the detector over a small range of choices of polarization angles, and also for eccentricities greater than ~0.05. For signals with higher signal-to-noise ratio than GW150914, or in other regions of the binary parameter space (lower masses, larger mass ratios, or higher spins), we expect that systematic errors in current waveform models may impact gravitational-wave measurements, making more accurate models desirable for future observations

An improved analysis of GW150914 using a fully spin-precessing waveform model

This paper presents updated estimates of source parameters for GW150914, a binary black-hole coalescence event detected by the Laser Interferometer Gravitational-wave Observatory (LIGO) on September 14, 2015 [1]. Reference presented parameter estimation [2] of the source using a 13-dimensional, phenomenological precessing-spin model (precessing IMRPhenom) and a 11-dimensional nonprecessing effective-one-body (EOB) model calibrated to numerical-relativity simulations, which forces spin alignment (nonprecessing EOBNR). Here we present new results that include a 15-dimensional precessing-spin waveform model (precessing EOBNR) developed within the EOB formalism. We find good agreement with the parameters estimated previously [2], and we quote updated component masses of $35^{+5}_{-3}\mathrm{M}_\odot$ and $30^{+3}_{-4}\mathrm{M}_\odot$ (where errors correspond to 90% symmetric credible intervals). We also present slightly tighter constraints on the dimensionless spin magnitudes of the two black holes, with a primary spin estimate $0.65$ and a secondary spin estimate $0.75$ at 90% probability. Reference [2] estimated the systematic parameter-extraction errors due to waveform-model uncertainty by combining the posterior probability densities of precessing IMRPhenom and nonprecessing EOBNR. Here we find that the two precessing-spin models are in closer agreement, suggesting that these systematic errors are smaller than previously quoted

Directly comparing GW150914 with numerical solutions of Einstein's equations for binary black hole coalescence

We compare GW150914 directly to simulations of coalescing binary black holes in full general relativity, including several performed specifically to reproduce this event. Our calculations go beyond existing semianalytic models, because for all simulations – including sources with two independent, precessing spins – we perform comparisons which account for all the spin-weighted quadrupolar modes, and separately which account for all the quadrupolar and octopolar modes. Consistent with the posterior distributions reported in LVC-PE[1] (at the 90% credible level), we find the data are compatible with a wide range of nonprecessing and precessing simulations. Followup simulations performed using previously-estimated binary parameters most resemble the data, even when all quadrupolar and octopolar modes are included. Comparisons including only the quadrupolar modes constrain the total redshifted mass Mz ∈ [64M� − 82M�], mass ratio 1/q = m2/m1 ∈ [0.6, 1], and effective aligned spin χeff ∈ [−0.3, 0.2], where χeff = (S1/m1 + S2/m2) · Lˆ /M. Including both quadrupolar and octopolar modes, we find the mass ratio is even more tightly constrained. Even accounting for precession, simulations with extreme mass ratios and effective spins are highly inconsistent with the data, at any mass. Several nonprecessing and precessing simulations with similar mass ratio and χeff are consistent with the data. Though correlated, the components’ spins (both in magnitude and directions) are not significantly constrained by the data: the data is consistent with simulations with component spin magnitudes a1,2 up to at least 0.8, with random orientations. Further detailed followup calculations are needed to determine if the data contain a weak imprint from transverse (precessing) spins. For nonprecessing binaries, interpolating between simulations, we reconstruct a posterior distribution consistent with previous results. The final black hole’s redshifted mass is consistent with Mf,z in the range 64.0M� − 73.5M� and the final black hole’s dimensionless spin parameter is consistent with af = 0.62 − 0.73. As our approach invokes no intermediate approximations to general relativity and can strongly reject binaries whose radiation is inconsistent with the data, our analysis provides a valuable complement to LVC-PE[1]

Legal Techniques for Dealing with Scientific Uncertainty in Environmental Law

This Article analyzes how scientific uncertainty is handled in international environmental law. It identifies ten legal techniques used for this purpose (i.e., precautionary reasoning; framework-protocol approach; advisory scientific bodies; law-making by treaty bodies; managerial approaches to compliance; prior informed consent; environmental impact assessment and monitoring; provisional measures; evidence; and facilitated liability) and links them to four different stages of development of environmental regimes (i.e., advocacy, design, implementation, and reparation). These techniques are illustrated by reference to some fifteen environmental treaties and other instruments as well as through a detailed case study focusing on the climate change regime

International enviromental law

Ixxv.; 438 hal.; ill.; 19 c