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  • About
  • The Global ETD Search service is a free service for researchers to find electronic theses and dissertations. This service is provided by the Networked Digital Library of Theses and Dissertations.
    Our metadata is collected from universities around the world. If you manage a university/consortium/country archive and want to be added, details can be found on the NDLTD website.
231

Search for new physics produced via Vector Boson Fusion in final states with large missing transverse momentum with the ATLAS detector / Recherche de nouvelle physique dans le mode de production VBF dans un état final avec une grande énergie transverse manquante avec le détecteur ATLAS

Perego, Marta Maria 10 April 2018 (has links)
Cette thèse présente des recherches sur la nouvelle physique produite par le processus de Fusion de Bosons Vecteur (VBF) dans les états finaux avec une grand impulsion transverse manquante (Etmiss) en utilisant 36.1 fb⁻¹ de données de collisions proton-proton avec une énergie dans le centre de masse de 13 TeV, recueillies par l'expérience ATLAS au Large Hadron Collider (LHC) au CERN en 2015 et 2016. En particulier, elle se concentre sur la recherche de la désintégration invisible du boson de Higgs produit via le mode VBF. Comme le modèle standard de la physique des particules (MS) prédit une désintégration invisible de Higgs uniquement à travers le mode H->ZZ*->4v avec un rapport d’embranchement BR ~ 0,1%, si une désintégration en particules invisibles du boson de Higgs était observée avec un BR supérieur, ce serait un signe de nouvelle physique. Plusieurs modèles au-delà du modèle standard (BSM) prédisent des désintégrations du boson de Higgs en particules de matière noire (DM, non détectées) ou en particules massives neutres à vie longue. Parmi les recherches H->particules invisibles, la plus sensible est celle où le Higgs est produit via le mode VBF. Son état final est caractérisé par deux jets énergétiques, avec les caractéristiques typiques du mode VBF (c'est-à-dire une grande séparation angulaire et une grande masse invariante des deux jets) et une grande impulsion transverse manquante (Etmiss>180 GeV). Pour sélectionner un échantillon d'événements candidats de signal, une région de signal (SR) est définie pour maximiser la fraction d'événements de signal attendus par rapport à la prédiction du MS (bruit de fond). Les processus MS qui peuvent peupler la SR proviennent principalement des processus Z->vv+jets et W->lv+jets, où le lepton est perdu ou non reconstruit. Leur contribution est estimée avec une approche semi-data driven : des régions dédiées enrichies en événements W->lv/Z->ll sont utilisées pour normaliser les données des estimations de Monte Carlo (MC) en utilisant une technique de fit simultané (méthode du facteur de transfert) et pour les extrapoler à la SR. L'estimation de fond prédit est comparée aux données SR observées. Comme aucun excès n'est trouvé, une limite supérieure sur le BR (H-> invisible) est calculée. L'analyse est ensuite réinterprétée dans le cadre de modèles inspirés du modèle Minimal Dark Matter. Le cas d'un nouveau triplet fermionique électrofaible, avec une hypercharge nulle et avec interactions respectant le nombre B-L, ajouté au MS fournit un bon candidat Dark Matter (WIMP pure). Si on considère l'abondance thermique, la masse du composant neutre est d’environ 3 TeV. Cependant des masses plus faibles sont également envisageables dans le cas de mécanismes de production non thermiques ou lorsque le triplet ne constitue qu'une fraction de l'abondance de DM. Il peut être produit à des collisionneurs proton-proton tels que le LHC et il peut être sondé de différentes manières. Une fois produites, les composantes chargées du triplet se désintègrent dans le composant neutre le plus léger, χ0 , avec en plus des pions très mous, en raison de la petite différence de masse entre les composants neutres et chargés. Ces pions de très faible impulsion ne peuvent pas être reconstruits et sont donc perdus. Le χ0 est reconstruit comme de l’Etmiss dans le détecteur. Par conséquent, lorsqu'il est produit via VBF, il donne lieu à une signature avec deux jets VBF et de l’Etmiss, le même état final que celui qui a été étudié pour l'analyse de VBF H->invisible. Des points de masse différentes (de 90 GeV à 200 GeV) ont été engendrés avec les programmes Monte Carlo Madgraph+Pythia, dans le cadre du logiciel officiel ATLAS, et les limites supérieures sont définies sur la section efficace fiducielle de production. Des extrapolations à des luminosités plus élevées (Run3 et HL-LHC) en utilisant une approche simplifiée sont également présentées. / This thesis presents searches for new physics produced via Vector Boson Fusion (VBF) in final states with large Missing Transverse Momentum (Etmiss) using 36.1 fb⁻¹ of data from proton-proton collisions at center-of-mass-energy of 13 TeV, collected by the ATLAS experiment at the Large Hadron Collider at CERN during 2015 and 2016. In particular, it focuses on the search for the invisible decay of the Higgs boson produced via the vector boson fusion (VBF) process. As the SM predicts an Higgs invisible decay only through H->ZZ*->4v with Branching Ratio BR~0.1%, if an invisibly decaying Higgs boson would be observed with a higher BR, this would be a sign of new physics. Several Beyond the Standard Model (BSM) models predict invisibly decaying Higgs boson where the Higgs can decay into dark matter particles or neutral long-lived massive particles. Among the H->invisible searches the most sensitive one is the one where the Higgs is produced via the VBF process. Its final state is characterized by two energetic jets, with the typical features of the VBF mode (i.e. large angular separation and large invariant mass) and large missing transverse momentum (Etmiss>180 GeV). To select a sample of signal candidate events, a Signal Region (SR) is designed to maximize the fraction of expected signal events with respect to the SM prediction (backgrounds). The SM processes which can populate the SR comes mainly from Z->vv+jets and W->lv+jets processes, where the lepton is lost or not reconstructed. Their contribution is estimated with a semi data driven approach: dedicated regions enriched in W->lv/Z->ll events are used to normalize to data the Monte Carlo (MC) estimates using a simultaneous fitting technique (transfer factor) and to extrapolate them to the SR. The predicted background estimate is compared to the observed SR data. Since no excess is found, an upper limit on the BR(H->inv) is set. The analysis is then reinterpreted in the context of models inspired by the Minimal Dark Matter model. The case of a new electroweak fermionic triplet, with null hypercharge and with interactions respecting the B-L number, added on top of the SM provides a good Dark Matter candidate. As such, it is an example of pure Weakly Interacting Massive Particle (WIMP), meaning that it is a DM particle with SU(2)_L SM interactions which is not mixing with other states (pure).If the thermal abundance is assumed, the mass of the neutral component is around 3 TeV, however smaller masses are also allowed in case of non-thermal production mechanisms or if the triplet constitutes only a fraction of the DM abundance. It can be produced at proton-proton colliders such as the LHC and it can be probed in different ways. Once produced, the charged components of the triplet decays into the lightest neutral component chi0 plus very soft charged pions. chi0 is reconstructed as Etmiss in the detector while the pions, because of the small mass splitting between the neutral and charged components, are so soft that are lost and are not reconstructed. Therefore, when produced via VBF, it gives rise to a signature with two VBF jets and Etmiss, the same final state that has been investigated for the VBF Higgs invisible analysis. Different mass point (from 90 GeV to 200 GeV) have been generated with the Madgraph+Pythia, Monte Carlo programs within the official ATLAS software, and upper limits are set on the fiducial cross section. Extrapolations to higher luminosities using a simplified approach are also presented.
232

Astrophysical aspects of dark matter direct detection / Aspects astrophysiques de la détection directe de matière sombre

Magni, Stefano 13 November 2015 (has links)
Cette thèse traite des aspects astrophysiques de la détection directe (DD) de matière noire sous forme de WIMPs. On se concentre sur les contraintes observationnelles des quantités astrophysiques qui influent sur l'interprétation des résultats expérimentaux de DD.On revoit tout d'abord le formalisme de la DD et on résume les résultats expérimentaux les plus importants ainsi que les méthodes statistiques généralement utilisés pour interpréter les données. On reproduit ensuite les limites expérimentales sur la section efficace spin-indépendante. On résume l'ensemble des hypothèses astrophysiques couramment utilisées dans le modèle de halo standard et on décrit l'influence de ses paramètres sur les limites.Pour inscrire la DD dans un cadre plus général, on résume les concepts les plus importants de la dynamique Galactique. En particulier, on revoit comment modéliser la Galaxie avec des modèles de masse, tout en soulignant les relations entre les différentes quantités astrophysiques. On décrit des procédures qui permettent d'obtenir des distributions dans l'espace des phases de la matière noire qui soient consistantes avec un profil de matière noire et un potentiel Galactique donné. La plus simple procédure étant basée sur l'équation d'Eddington, on discute ses limites d'applicabilité. On revoit dans les détails la littérature récente concernant les déterminations et les incertitudes des quantités astrophysiques liées à la DD et des paramètres Galactiques fondamentaux.Dans la dernière partie de la thèse on s'intéresse aux estimations récentes de la vitesse d'échappement publiées par la collaboration RAVE. On étudie dans les détails les implications de ces résultats sur les expériences de DD. Pour cela on prends en compte les corrélations entre les quantités astrophysiques importantes pour la DD, et en assumant le modèles de masse de RAVE on calcule la distribution de matière noire dans l'espace des phases avec l'équation d'Eddington. Du fait des valeurs plus élevés de la densité locale de matière noire, cette procédure conduit à des limites plus contraignantes par rapport a celles standards. / This thesis deals with the astrophysical aspects of the direct detection of WIMP dark matter (DMDD). In particular, it focuses on the observational constraints on the astrophysical quantities relevant for DMDD, which impact on the interpretation of the experimental results.We review the formalism of DMDD and we summarize some of the main experimental results in this domain and the statistical methods usually employed to interpret the data, reproducing the associated constraints on the parameter space relevant for spin-independent WIMP-nucleon interaction. We summarize the set of astrophysical assumptions usually employed, the Standard Halo Model, and we point out the impact of variations in its parameters on such limits.We outline the main concepts of the dynamics of our galaxy that allow to put the astrophysics related to DMDD in a wider framework. In particular, we review the description of the Galaxy through Milky Way mass models (MWMM), pointing out how the astrophysical quantities are related. We describe some procedures to obtain dark matter phase-space distributions consistent with given dark matter profile and Galactic potential, the simplest being Eddington equation, of which we discuss the limits of applicability. We review in detail the recent literature on the main determinations and uncertainties of the astrophysical quantities relevant for DMDD and of the fundamental Galactic parameters.In the most original part of this thesis we focus on the recent estimates of the local Galactic escape speed published by the RAVE collaboration. We study in detail the implications of these results for the spin-independent interpretation of DMDD experiments. We take into account the correlations between the astrophysical quantities relevant for DMDD calculations, and from the assumed MWMM we compute the dark matter phase-space distribution using Eddington equation, which provides a self-consistent physical connection between the two. This procedure leads to more constraining exclusion curves with respect to the standard ones, due to higher values of the local dark matter density.
233

Dynamics of Warps and Lopsidedness in Spiral Galaxies

Saha, Kanak January 2007 (has links) (PDF)
No description available.
234

Análise da abundância e detecção direta num modelo de matéria escura

Santos, Antonio Carlos Oliveira 25 April 2015 (has links)
Made available in DSpace on 2015-05-14T12:14:17Z (GMT). No. of bitstreams: 1 arquivototal.pdf: 8387291 bytes, checksum: 02ffc69a044d7312934d6910183b8440 (MD5) Previous issue date: 2015-04-25 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / In this work we consider a minimal local abelian gauge group extension with charge B - 3Le anomaly-free. We add a right-handed singlet Majorana fermion plus a neutral and charged scalars, responsible for spontaneous symmetry breaking and a charged singlet scalar to provide a connection between the electron and the Majorana fermion. The aim of this model is provide a low energy theory to Dark matter as a Majorana fermion. There are several evidences of a new kind of a non-baryonic matter but its nature and properties are not well established. So, based in some experiments (in particular those that main focus is the direct detection), we are going to constraint some parameters of the model to test its feasibility in this context. We have used a computational program called micrOMEGAs (based on CalCHEP) to compute the abundance and scattering cross section between dark matter and nucleon and compare with the experimental constraints arising from Planck (abundance) and LUX (scattering cross section). We show that the results support the restrictions imposed by the observations providing future perspectives for this extension, like indirect detection of dark matter. / Nesta dissertação consideramos uma extensão abeliana mínima local, de carga B-3Le, livre de anomalias, onde foi introduzido um férmion de majorana de mão direita juntamente com um novo bóson escalar, responsável pela quebra espontânea da simetria local, e um escalar carregado conectando a família de léptons ao férmion de majorana. Este modelo tem por objetivo fornecer uma teoria de baixas energias para a matéria escura atribuída a um férmion de majorana. Logo, baseado em alguns experimentos (em particular aqueles cujo principal objetivo é a detecção direta de uma possível nova partícula atribuída à esta matéria), iremos vincular os parâmetros de nosso modelo a fim de verificar sua aplicabilidade neste senário. Com isto, utilizaremos o programa computacional micrOMEGAS (que utiliza o CalcHEP) a fim de calcular alguns observáveis do modelo, tais como a abundância e secção transversal de choque do espalhamento elástico entre a matéria escura e o nucleon e, em seguida, comparamos aos dados experimentais do Planck (abundância) e LUX (seção de choque). Resultados preliminares apontam para a validade do modelo diante das restrições impostas pelas observações, possibilitando a perspectiva de aplicação desta extensão em outros contextos, como os da detecção indireta da matéria escura.
235

Gamma-ray lines from the dark side of matter: model-independent approaches / Lignes gammas provenant de la matière noire: approches indépendantes de modèles

Scarna, Tiziana 17 December 2014 (has links)
Lignes spectrales de rayons gammas provenants de la matière noire. <p>Approches indépendantes de modèles/ Gamma-Ray Lines from the Dark Side of Matter: Model-Independent Approaches<p><p> Cette thèse a pour thématique centrale la matière noire, et plus particulièrement un type de signal qu’elle pourrait émettre, à savoir des lignes spectrales de rayons gammas. La nature de la matière noire demeure mystérieuse, et ce que l’on sait de ses propriétés est exposé dans le premier chapitre. En particulier, la pertinence des lignes spectrales de rayons gammas dans l’étude de la matière noire est soulignée. Cette thèse est consacrée à l’étude des connexions possibles entre la phénoménologie de ce type de signal et d’autres manifestations, qu’il s’agisse de détection directe ou indirecte, ou bien de détection dans des collisionneurs tels que le LHC. Le but est d’établir la possibilité de discriminer différents modèles et/ou d’obtenir des contraintes indépendantes.<p>\ / Doctorat en Sciences / info:eu-repo/semantics/nonPublished
236

Dark matter: signs and genesis / Matière noire: signes et genèse

Lopez Honorez, Laura 26 June 2007 (has links)
<p align="justify">The success of Big Bang Nucleosynthesis (BBN) combined with the detailed analysis of the small imperfections of the Cosmic Microwave Background blackbody spectrum lead to the conclusion that most of the matter content of our universe is made of some non-baryonic material, the dark matter!</p><p><p><p align="justify">In this thesis, we review the compiling indications of dark matter and the so-called freeze-out mechanism which may settle the relic density of the species in the framework of the standard Big Bang model. We also examine principally two methods of detection of dark matter, direct and indirect detection searches.</p><p><p><p align="justify">Let us stress that the Standard Model on its own is unable to provide enough aspirants for the role of dark matter. As a consequence, one has to dig into the tremendous domain of physics "Beyond the Standard Model" in order to have a chance to elucidate the problem of the missing mass.</p><p><p><p align="justify">In this thesis in particular, we consider the Inert Doublet Model (IDM) which includes an additional Higgs doublet, enclosing two neutral scalars candidates for dark matter. We invoke the Standard freeze-out mechanism for the production of dark matter. We get then dark matter candidates in two rather separate mass ranges, one between 40 and 80 GeV, the other one between 400 GeV and 1 TeV. We also show that dark matter annihilation at the galactic center can be at the origin of a gamma-ray flux which can be probed by the future GLAST experiment.</p><p><p><p align="justify">We address a low reheating temperature scenario for the genesis of dark matter in a Left-Right symmetric extension of the Standard Model. The candidate for dark matter is a MeV right-handed neutrino and we show that a baryon-dark matter interaction at the galactic center can be the source of the low energy positrons responsible for the 511 keV gamma-ray excess observed by the INTEGRAL experiment in the galactic bulge region.</p><p><p><p align="justify">Finally, prompted by the possibility to explain the baryon and dark matter rather similar abundances by one single "Matter Genesis" mechanism, we study a non-thermal production mechanism for dark matter. The framework is also Left-Right symmetric and dark candidate is a ~3 GeV right handed neutrino.</p> <p><p> / Doctorat en Sciences / info:eu-repo/semantics/nonPublished
237

Dark Matter – Direct Detection and Capture in the Sun / Mörk Materia – Direkt Detektion och Solinfångning

Lind, Erika January 2020 (has links)
Dark matter has been inferred from various observations such as in galaxy clusters, flat galactic rotation curves, gravitational lensing measurements and the cosmic microwave background. Despite overwhelming observational evidence and ongoing searches, a clear signal of dark matter has not yet been detected. Searches for dark matter include direct detection of dark matter scattering off target nuclei in underground detectors and indirect detection of dark matter annihilation- and decay products. A promising way to detect these invisible particles is by capture of dark matter in the Sun. Dark matter from the galactic halo is assumed to scatter off solar nuclei and being captured provided that their velocities are smaller than the Sun's escape velocity. The captured particles are assumed to continuously scatter until reaching thermal equilibrium. As dark matter is accumulated in the Sun, they will start to annihilate. The resulting annihilation products are what we hope to detect on Earth. We review the capture rate of elastic and inelastic dark matter in the Sun and dark matter direct detection. Lower bounds on the solar capture rate for a given dark matter mass can be obtained independently of halo-related properties e.g., the dark matter velocity distribution and local density, if one assumes that a direct detection signal has been observed. These bounds can be compared to solar neutrino flux bounds in detectors to obtain limits on the branching fraction of annihilation of dark matter resulting in neutrinos. Lower bounds for the elastic and exothermic inelastic dark matter are computed assuming the Standard Halo Model. The exothermic bounds are strong and larger than the elastic bounds as well as those that would be obtained in the endothermic case. / Existensen av mörk materia har idag gjorts trolig genom t.ex. observationer av galaktiska kluster, galaktiska rotationskurvor, gravitationslinsmätningar och den kosmiska mikrovågsbakgrunden. Trots ett stort antal observationer, så har vi emellertid inte lyckats detektera en tydlig signal för mörk materia. I sökandet ingår direkt detektion av kollisioner mellan mörk materia och atomkärnor i underjordiska detektorer samt indirekt detektion av dess annihilation- och sönderfallsprodukter. Ett särskilt lovande sätt, på vilket dessa osynliga partiklar kan tänkas detekteras, är genom infångning av mörk materia i solen. Mörk materia från den galaktiska halon antas då spridas på solatomkärnor och infångas förutsatt att deras hastighet är lägre än flykthastigheten från solen. De infångade partiklarna antas därefter kollidera tills dess att de uppnår termisk jämvikt. När mörk materia har ackumulerats i solen så börjar den att annihilera, och det är de resulterande annihilationsprodukterna som vi hoppas kunna detektera här på jorden. Vi undersöker infångning av elastisk och inelastisk mörk materia i solen och direkt detektion av mörk materia. Nedre gränser för solinfångning för en given mörk materiamassa kan erhållas oberoende av halo-relaterade egenskaper som t.ex. mörk materiahastighetsfördelning och lokal densitet, under antagandet att en direkt detektionssignal har observerats. Dessa gränser kan jämföras med flödeshastigheten av neutrinos från solen för att erhålla gränser för övergångssannolikheter för annihilation av mörk materia som resulterar i neutrinos. Nedre gränser för elastisk och exotermisk inelastisk mörk materia är beräknade genom att anta Standard Halo Modellen. De exotermiska gränserna är starka och högre än de elastiska gränserna såväl som de som skulle ha erhållits i det endotermiska fallet.
238

The assembly history of disc galaxies

Miller, Sarah Holmes January 2013 (has links)
We present new measures of the rotation curves of disc galaxies from z~0.2 to z~1.7, using deep exposures from both DEIMOS and LRIS spectrographs on the Keck telescopes in combination with multi-band imaging from the Hubble Space Telescope. We do this with a new modelling code, curvation, which has been optimised to extract the rotation velocity measurements from galaxies at intermediate and high redshift. To this end, we conduct a bulge-to-disc de-composition to allow us to de-project observed velocities to extract a model of the intrinsic rotation curve. We demonstrate the improved accuracy and precision of these measurements via a number of tests, but primarily in recovering an intrinsic scatter of the high redshift Tully-Fisher relation which is similar to that found locally. We show for the first time that the stellar mass Tully-Fisher relation is tightly in place at z~1, the normalisation of which has evolved less than 0.02±0.02 dex in stellar mass from z~1.7 to z~0.2. We do however see evidence for evolution in classic B-band Tully-Fisher relation, which is brighter at z~1 by 0.85±0.28 magnitudes than that at z~0.3. This trend is consistent with what was previously known about the evolving star-formation rates of disc galaxies. We then explore the potential drivers of these trends in the Tully-Fisher relation by estimating the baryonic and dark matter content of our galaxies. We also discover a surprising trend in the bulgeless disc galaxies at high redshift, which may be evolving differently from other rotationally supported galaxies. In the context of work which has been conducted at z~2, we discuss our results of a stellar mass Tully-Fisher relation which is strikingly similar over two-thirds of the age of the Universe.
239

On gravity : a study of analytical and computational approaches to problem solving in collisionless systems

Barber, Jeremy A. January 2014 (has links)
I present an overview of the tools and methods of gravitational dynamics motivated by a variety of dynamics problems. Particular focus will be given to the development of dynamic phase-space configurations as well as the distribution functions of collisionless systems. Chapter 1 is a short review of the descriptions of a gravitational system examining Poisson's equations, the probability distribution of particles, and some of the most popular model groups before working through the challenges of introducing anisotropy into a model. Chapter 2 covers the work of Barber2014b which looks at the relations between quantities in collisionless systems. Analytical methods are employed to describe a model that can violate the GDSAI, a well-known result connecting the density slope to the velocity anisotropy. We prove that this inequality cannot hold for non-separable systems and discuss the result in the context of stability theorems. Chapter 3 discusses the background for theories of gravity beyond Newton and Einstein. It covers the `dark sector' of modern astrophysics, motivates the development of MOND, and looks at some small examples of these MONDian theories in practice. Chapter 4 discusses how to perform detailed numerical simulations covering code methods for generating initial conditions and simulating them accurately in both Newtonian and MONDian approaches. The chapter ends with a quick look at the future of N-body codes. Chapters 5 and 6 contain work from Barber 2012 and Barber 2014a which look at the recent discovery of an attractor in the phase-space of collisionless systems and present a variety of results to demonstrate the robustness of the feature. Attempts are then made to narrow down the necessary and sufficient conditions for the effect while possible mechanisms are discussed. Finally, the epilogue is a short discussion on how best to communicate scientific ideas to others in a lecturing or small group setting. Particular focus is given to ideas of presentation and the relative importance of formality versus personality.
240

Measuring subhalo mass in redMaPPer clusters with CFHT Stripe 82 Survey

Li, Ran, Shan, Huanyuan, Kneib, Jean-Paul, Mo, Houjun, Rozo, Eduardo, Leauthaud, Alexie, Moustakas, John, Xie, Lizhi, Erben, Thomas, Van Waerbeke, Ludovic, Makler, Martin, Rykoff, Eli, Moraes, Bruno 21 May 2016 (has links)
We use the shear catalogue from the CFHT Stripe-82 Survey to measure the subhalo masses of satellite galaxies in redMaPPer clusters. Assuming a Chabrier initial mass function and a truncated NFW model for the subhalo mass distribution, we find that the subhalo mass to galaxy stellar mass ratio increases as a function of projected halo-centric radius r(p), from M-sub/M-star = 4.43(-2.23)(+6.63) at r(p) is an element of [0.1, 0.3] h(-1) Mpc toM(sub)/M-star = 75.40(-19.09)(+19.73) at r(p) is an element of [0.6, 0.9] h(-1) Mpc. We also investigate the dependence of subhalo masses on stellar mass by splitting satellite galaxies into two stellar mass bins: 10 < log (M-star/h(-1) M-circle dot) < 10.5 and 11 < log (M-star/h(-1) M-circle dot) < 12. The best-fitting subhalomass of the more massive satellite galaxy bin is larger than that of the lessmassive satellites: log(M-sub/h(-1) M-circle dot) = 11.14(-0.73)(+0.66) (M-sub/M-star = 19.5(-17.9)(+19.8)) versus log(M-sub/h(-1) M-circle dot) = 12.38(-0.16)(+0.16) (M-sub/M-star = 21.1(-7.7)(+7.4)).

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