THE REDSHIFT of the LENSED OBJECT in the EINSTEIN RING B0218+3571 Judith G
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Gravitational Lensing in Quasar Samples
Astronomy and Astrophysics Review ManuscriptNr will b e inserted by hand later Gravitational Lensing in Quasar Samples JeanFrancois Claeskens and Jean Surdej Institut dAstrophysique et de Geophysique Universite de Liege Avenue de Cointe B Liege Belgium Received April Accepted Summary The rst cosmic mirage was discovered approximately years ago as the double optical counterpart of a radio source This phenomenon had b een predicted some years earlier as a consequence of General Relativity We present here a summary of what we have learnt since The applications are so numerous that we had to concentrate on a few selected asp ects of this new eld of research This review is fo cused on strong gravitational lensing ie the formation of multiple images in QSO samples It is intended to give an uptodate status of the observations and to present an overview of its most interesting p otential applications in cosmology and astrophysics as well as numerous imp ortant results achieved so far The rst Section follows an intuitive approach to the basics of gravitational lensing and is develop ed in view of our interest in multiply imaged quasars The astrophysical and cosmo logical applications of gravitational lensing are outlined in Section and the most imp ortant results are presented in Section Sections and are devoted to the observations Finally conclusions are summarized in the last Section We have tried to avoid duplication with existing and excellent intro ductions to the eld of gravitational lensing For this reason we did not concentrate -
The Gravitational Lens Effect of Galaxies and Black Holes
.f .(-L THE GRAVITATIONAL LENS EFFECT of GALAXIES and BLACK HOLES by Igor Bray, B.Sc. (Hons.) A thesis submitted in accordance with the requirements of the Degree of Doctor of Philosophy. Department of lr{athematical Physics The University of Adelaide South Australia January 1986 Awo.c(sd rt,zb to rny wife Ann CONTENTS STATEMENT ACKNOWLEDGEMENTS lt ABSTRACT lll PART I Spheroidal Gravitational Lenses I Introduction 1.1 Spherical gravitational lenses I 1.2 Spheroidal gravitational lenses 12 2 Derivationof I("o). ......16 3 Numerical Investigation 3.1 Evaluations oI l(zs) 27 3.2 Numericaltechniques 38 3.3 Numerical results 4L PART II Kerr Black llole As A Gravitational Lens 4 Introduction 4.1 Geodesics in the Kerr space-time 60 4.2 The equations of motion 64 5 Solving the Equations of Motion 5.1 Solution for 0 in the case m - a'= 0 68 5.2 Solution for / in the case m: a = O 76 5.3 Relating À and 7 to the position of the ìmage .. .. .82 5.4 Solution for 0 ... 89 5.5 Solution for / 104 5.6 Solution for ú. .. ..109 5.7 Quality of the approximations 115 6 Numerical investigation . .. ... tt7 References 122 STATEMENT This thesis contains no material which has been accepted for the award of any degree, and to the best of my knowledge and belief, contains no material previously published or written by another person except where due reference is made in the text. The author consents to the thesis being made available for photocopying and loan if applicable if accepted for the award of the degree. -
Gravitational Lensing
Gravitational Lensing Diana Streng Phy 495 December 2006 Topics Light deflection, and how spacetime curvature dictates gravitational lensing (GL) A brief history about the GL phenomenon Types of GL Effects Applications Preliminary Notes ¾ 1 parsec = “the distance from the Earth to a star that has a parallax of 1 arcsecond” = 3.08567758×1016 m = 3.26156378 light years Preliminary Notes 1 Arcminute = (1/60) of 1 degree Æ 1’ 1 Arcsecond = (1/60) of 1 arcminute Æ 1” = (1/3600) of 1 degree Hubble’s Law v = H 0d where H0 = 70 km/s/Mpc v Redshift 1+ λ − λ z = obs emit = c λ v emit 1− c Gravitational Lensing Gravitational Lensing A product of Einstein’s general theory of relativity, but first predicted by A. Einstein in 1912 Occurs in any accelerated frame of reference. Details governed by spacetime curvature. Early thoughts on Gravitational Lensing… “Of course there is not hope in observing this phenomenon directly. First, we shall scarcely ever approach closely enough to such a central line. Second, the angle beta will defy the resolving power of our instruments.” -- Albert Einstein, in his letter to Science magazine, 1936 Timeline 1919 – Arthur Eddington – multiple images may occur during a solar eclipse. 1936 – R.W. Mandl wrote Einstein on the possibility of G.L. by single stars. Einstein published discussion in Science magazine, volume 84, No. 2188, December 4, 1936, pg. 506-507 1937 – Fritz Zwicky considered G.L. by galaxies and calculated Deflection angles Image strengths (Timeline) 1963 – Realistic scenarios for using G.L. Quasi-stellar objects Distant galaxies Determining distances and masses in lensing systems. -
No Sign of Gravitational Lensing in the Cosmic Microwave Background
Perspectives No sign of gravitational lensing in the ., WFPC2, HST, NASA ., WFPC2, HST, cosmic microwave et al background Ron Samec ravitational lensing is a Ggravitational-optical effect whereby a background object like a distant quasar is magnified, distorted Andrew Fruchter (STScI) Image by and brightened by a foreground galaxy. It is alleged that the cluster of galaxies Abell 2218, distorts and magnifies It is one of the consequences of general light from galaxies behind it. relativity and is so well understood that fectly smooth black body spectrum of sioned by Hoyle and Wickramasinghe it now appears in standard optics text 5,6 books. Objects that are too far to be 2.725 K with very tiny fluctuations in and by Hartnett. They showed that seen are ‘focused’ by an intervening the pattern on the 70 μK level. These a homogeneous cloud mixture of car- concentration of matter and bought ‘bumps’ or patterns in the CMB are bon/silicate dust and iron or carbon into view to the earth based astronomer. supposedly the ‘seeds’ from which whiskers could produce such a back- One of the most interesting photos of the galaxies formed. Why is it so ground radiation. If the CMB is not the effects of gravitational lensing smooth? Alan Guth ‘solved’ this puz- of cosmological origin, all the ad hoc ideas that have been added to support is shown in the HST image of Abell zle by postulating that the universe was the big bang theory (like inflation) 2218 by Andrew Fruchter1 (Space originally a very tiny entity in thermal fall apart. -
First Results from the High-Cadence Monitoring of M31 with Pan-STARRS 1
PAndromeda: first results from the high-cadence monitoring of M31 with Pan-STARRS 1 C.-H. Lee – ASIAA seminar 29 Feb. 2012 PIs: S. Seitz, R. Bender A. Rifeser, J. Koppenhoefer, U. Hopp, C. Goessl, R. P. Saglia, J. Snigula (Max Planck Institute for Extraterrestrial Physics, Germany) W. E. Sweeney (Institute for Astronomy, University of Hawaii, USA) and the PS1 Science Consortium Outline 1. Introduction to microlensing 2. Pan-STARRS and PAndromeda 3. First results from PAndromeda 4. Prospects - Breaking the microlensing degeneracy - Beyond microlensing Introduction Image1 Image2 Observer Lens Source Credit: NASA, ESA, and Johan Richard (Caltech, USA) Microlensing Basics Angular Einstein ring radius Image Credit: Gould (2000) Position of the image Amplification of the image Image Credit: Scott Gaudi Searching for Dark Matter Paczynski(1986) proposed to use microlensing to search for massive compact halo object (MACHO) as dark matter candidates Triggered numerous experiments towards Galactic Bulge and Magellanic Clouds Thousands of events have been detected since 1993. OGLE and MOA report ~1000 events/yr nowadays Results from LMC/SMC M < 0.1 solar mass: - f < 10% (MACHO, EROS, OGLE) M between 0.1-1 solar mass: - f ~ 20% (MACHO 2000, Bennett 2005) - self-lensing (EROS 2007, OGLE II-III, 2009-2011) Caveats of LMC/SMC lensing experiments: - Single line-of-sight - Unknown self-lensing (star lensed by star) rate => M31 provides a solution to both 1 and 2 M31 microlensing 1. Why M31? - Various lines of sight - Asymmetric halo-lensing signal 2. Previous studies on M31 - POINT-AGAPE (2005): evidence for a MACHO signal - MEGA (2006): self-lensing and upper limit for f - WeCAPP (2008): PA-S3/GL1, a bright candidate attributed to MACHO lensing Too few events to constrain f => requires large area survey Outline 1. -
Gravitational Lensing in a Black-Bounce Traversable Wormhole
Gravitational lensing in black-bounce spacetimes J. R. Nascimento,1, ∗ A. Yu. Petrov,1, y P. J. Porf´ırio,1, z and A. R. Soares1, x 1Departamento de F´ısica, Universidade Federal da Para´ıba, Caixa Postal 5008, 58051-970, Jo~aoPessoa, Para´ıba, Brazil In this work, we calculate the deflection angle of light in a spacetime that interpolates between regular black holes and traversable wormholes, depending on the free parameter of the metric. Afterwards, this angular deflection is substituted into the lens equations which allows to obtain physically measurable results, such as the position of the relativistic images and the magnifications. I. INTRODUCTION The angular deflection of light when passing through a gravitational field was one of the first predictions of the General Relativity (GR). Its confirmation played a role of a milestone for GR being one of the most important tests for it [1,2]. Then, gravitational lenses have become an important research tool in astrophysics and cosmology [3,4], allowing studies of the distribution of structures [5,6], dark matter [7] and some other topics [8{15]. Like as in the works cited earlier, the prediction made by Einstein was developed in the weak field approximation, that is, when the light ray passes at very large distance from the source which generates the gravitational lens. Under the phenomenological point of view, the recent discovery of gravitational waves by the LIGO-Virgo collaboration [16{18] opened up a new route of research, that is, to explore new cosmological observations by probing the Universe with gravitational waves, in particular, studying effects of gravitational lensing in the weak field approximation (see e.g. -
Gravitational Lensing and Optical Geometry • Marcus C
Gravitational Lensing and OpticalGravitational Geometry • Marcus C. Werner Gravitational Lensing and Optical Geometry A Centennial Perspective Edited by Marcus C. Werner Printed Edition of the Special Issue Published in Universe www.mdpi.com/journal/universe Gravitational Lensing and Optical Geometry Gravitational Lensing and Optical Geometry: A Centennial Perspective Editor Marcus C. Werner MDPI • Basel • Beijing • Wuhan • Barcelona • Belgrade • Manchester • Tokyo • Cluj • Tianjin Editor Marcus C. Werner Duke Kunshan University China Editorial Office MDPI St. Alban-Anlage 66 4052 Basel, Switzerland This is a reprint of articles from the Special Issue published online in the open access journal Universe (ISSN 2218-1997) (available at: https://www.mdpi.com/journal/universe/special issues/ gravitational lensing optical geometry). For citation purposes, cite each article independently as indicated on the article page online and as indicated below: LastName, A.A.; LastName, B.B.; LastName, C.C. Article Title. Journal Name Year, Article Number, Page Range. ISBN 978-3-03943-286-8 (Hbk) ISBN 978-3-03943-287-5 (PDF) c 2020 by the authors. Articles in this book are Open Access and distributed under the Creative Commons Attribution (CC BY) license, which allows users to download, copy and build upon published articles, as long as the author and publisher are properly credited, which ensures maximum dissemination and a wider impact of our publications. The book as a whole is distributed by MDPI under the terms and conditions of the Creative Commons license CC BY-NC-ND. Contents About the Editor .............................................. vii Preface to ”Gravitational Lensing and Optical Geometry: A Centennial Perspective” ..... ix Amir B. -
Inner Dark Matter Distribution of the Cosmic Horseshoe (J1148+1930) with Gravitational Lensing and Dynamics?
A&A 631, A40 (2019) Astronomy https://doi.org/10.1051/0004-6361/201935042 & c S. Schuldt et al. 2019 Astrophysics Inner dark matter distribution of the Cosmic Horseshoe (J1148+1930) with gravitational lensing and dynamics? S. Schuldt1,2, G. Chirivì1,2, S. H. Suyu1,2,3 , A. Yıldırım1,4, A. Sonnenfeld5, A. Halkola6, and G. F. Lewis7 1 Max-Planck-Institut für Astrophysik, Karl-Schwarzschild Str. 1, 85741 Garching, Germany e-mail: [email protected] 2 Physik Department, Technische Universität München, James-Franck Str. 1, 85741 Garching, Germany e-mail: [email protected] 3 Institute of Astronomy and Astrophysics, Academia Sinica, 11F of ASMAB, No.1, Section 4, Roosevelt Road, Taipei 10617, Taiwan 4 Max Planck Institute for Astronomy, Königstuhl 17, 69117 Heidelberg, Germany 5 Kavli Institute for the Physics and Mathematics of the Universe, The University of Tokyo, 5-1-5 Kashiwanoha, Kashiwa 277-8583, Japan 6 Pyörrekuja 5 A, 04300 Tuusula, Finland 7 Sydney Institute for Astronomy, School of Physics, A28, The University of Sydney, Sydney, NSW 2006, Australia Received 10 January 2019 / Accepted 19 August 2019 ABSTRACT We present a detailed analysis of the inner mass structure of the Cosmic Horseshoe (J1148+1930) strong gravitational lens system observed with the Hubble Space Telescope (HST) Wide Field Camera 3 (WFC3). In addition to the spectacular Einstein ring, this systems shows a radial arc. We obtained the redshift of the radial arc counterimage zs;r = 1:961 ± 0:001 from Gemini observations. To disentangle the dark and luminous matter, we considered three different profiles for the dark matter (DM) distribution: a power law profile, the Navarro, Frenk, and White (NFW) profile, and a generalized version of the NFW profile. -
Strong Gravitational Lensing by Schwarzschild Black Holes
STRONG GRAVITATIONAL LENSING BY SCHWARZSCHILD BLACK HOLES G. S. Bisnovatyi-Kogan1,2,3 and O. Yu. Tsupko1,3 The properties of the relativistic rings which show up in images of a source when a black hole lies between the source and observer are examined. The impact parameters are calculated, along with the distances of closest approach of the rays which form a relativistic ring, their angular sizes, and their "magnification" factors, which are much less than unity. Keywords: strong gravitational lensing: Schwarzschild black hole 1. Introduction One of the basic approximations in the theory of gravitational lensing [1, 2] is the approximation of weak lensing, i.e., small deflection angles. In the case of Schwarzschild lensing by a point mass, this approximation means that the impact parameters for incident photons are much greater than the Schwarzschild radius of the lensing system. In most astrophysical situations involving gravitational lensing, the weak lensing condition is well satisfied and it is possible to limit oneself to that case. In some cases, however, strong lensing effects and those associated with large deflection angles are of interest. Some effects associated with taking the motion of photons near the gravitational radius of a black hole into account, have been discussed before [3, 4]. An explicit analytic expression for the deflection angle in a Schwarzschild metric have been derived in the strong field limit [5, 6]. In this paper we investigate effects arising from the strong distortion of isotropic radiation from a star by the gravitational field of a black hole. (1) Space Research Institute, Russian Academy of Sciences, Russia; e-mail: [email protected] (2) Joint Institute for Nuclear Research, Dubna, Russia (3) Moscow Engineering Physics Institute, Moscow, Russia; e-mail: [email protected] 2. -
Testing Gravity and Dark Energy with Gravitational Lensing
Testing gravity and dark energy with gravitational lensing by Emma Beynon THE THESIS IS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE AWARD OF THE DEGREE OF DOCTOR OF PHILOSOPHY OF THE UNIVERSITY OF PORTSMOUTH September, 2012 Copyright c Copyright 2012 by Emma Beynon. All rights reserved. The copyright of this thesis rests with the Author. Copies (by any means) either in full, or of extracts, may not be made without the prior written consent from the Author. i Abstract Forthcoming wide field weak lensing surveys, such as DES and Euclid, present the pos- sibility of using lensing as a tool for precision cosmology. This means exciting times are ahead for cosmological constraints for different gravity and dark energy models, but also presents possible new challenges in modelling, both non-standard physics and the lensing itself. In this thesis I look at how well DES and Euclid will be able to discriminate between different cosmological models and utilise lensing’s combination of geometry and growth information to break degeneracies between models that fit geometrical probes, but may fail to fit the observed growth. I have focussed mainly on the non-linear structure growth regime, as these scales present the greatest lensing signal, and therefore greatest discrim- inatory power. I present the predicted discriminatory power for modified gravities models, DGP and f(R), including non-linear scales for DES and Euclid. Using the requirement that mod- ified gravities must tend to general relativity on small scales, we use the fitting formula proposed by Hu & Sawicki to calculate the non-linear power spectrum for our lens- ing predictions. -
Discovery of a High-Redshift Einstein Ring The
A&A 436, L21–L25 (2005) Astronomy DOI: 10.1051/0004-6361:200500115 & c ESO 2005 Astrophysics Editor Discovery of a high-redshift Einstein ring the , , , to R. A. Cabanac1 2 3, D. Valls-Gabaud3 4, A. O. Jaunsen2,C.Lidman2, and H. Jerjen5 1 Dep. de Astronomía y Astrofísica, Pontificia Universidad Católica de Chile, Casilla 306, Santiago, Chile e-mail: [email protected] 2 European Southern Observatory, Alonso de Cordova 3107, Casilla 19001, Santiago, Chile Letter 3 Canada-France-Hawaii Telescope, 65-1238 Mamalahoa Highway, Kamuela, HI 96743, USA 4 CNRS UMR 5572, LATT, Observatoire Midi-Pyrénées, 14 Av. E. Belin, 31400 Toulouse, France 5 Research School of Astronomy and Astrophysics, ANU, Mt. Stromlo Observatory, Weston ACT 2611, Australia Received 24 December 2004 / Accepted 26 April 2005 Abstract. We report the discovery of a partial Einstein ring of radius 1. 48 produced by a massive (and seemingly isolated) elliptical galaxy. The spectroscopic follow-up at the VLT reveals a 2L galaxy at z = 0.986, which is lensing a post-starburst galaxy at z = 3.773. This unique configuration yields a very precise measure of the mass of the lens within the Einstein radius, . ± . × 11 −1 / / = − . ± . (8 3 0 4) 10 h70 M. The fundamental plane relation indicates an evolution rate of dlog(M L)B dz 0 57 0 04, similar to other massive ellipticals at this redshift. The source galaxy shows strong interstellar absorption lines indicative of large gas- phase metallicities, with fading stellar populations after a burst. Higher resolution spectra and imaging will allow the detailed study of an unbiased representative of the galaxy population when the universe was just 12% of its current age. -
Doing Physics with Quaternions
Doing Physics with Quaternions Douglas B. Sweetser ©2005 doug <[email protected]> All righs reserved. 1 INDEX Introduction 2 What are Quaternions? 3 Unifying Two Views of Events 4 A Brief History of Quaternions Mathematics 6 Multiplying Quaternions the Easy Way 7 Scalars, Vectors, Tensors and All That 11 Inner and Outer Products of Quaternions 13 Quaternion Analysis 23 Topological Properties of Quaternions 28 Quaternion Algebra Tool Set Classical Mechanics 32 Newton’s Second Law 35 Oscillators and Waves 37 Four Tests of for a Conservative Force Special Relativity 40 Rotations and Dilations Create the Lorentz Group 43 An Alternative Algebra for Lorentz Boosts Electromagnetism 48 Classical Electrodynamics 51 Electromagnetic Field Gauges 53 The Maxwell Equations in the Light Gauge: QED? 56 The Lorentz Force 58 The Stress Tensor of the Electromagnetic Field Quantum Mechanics 62 A Complete Inner Product Space with Dirac’s Bracket Notation 67 Multiplying quaternions in Polar Coordinate Form 69 Commutators and the Uncertainty Principle 74 Unifying the Representations of Integral and Half−Integral Spin 79 Deriving A Quaternion Analog to the Schrödinger Equation 83 Introduction to Relativistic Quantum Mechanics 86 Time Reversal Transformations for Intervals Gravity 89 Unified Field Theory by Analogy 101 Einstein’s vision I: Classical unified field equations for gravity and electromagnetism using Riemannian quaternions 115 Einstein’s vision II: A unified force equation with constant velocity profile solutions 123 Strings and Quantum Gravity 127 Answering Prima Facie Questions in Quantum Gravity Using Quaternions 134 Length in Curved Spacetime 136 A New Idea for Metrics 138 The Gravitational Redshift 140 A Brief Summary of Important Laws in Physics Written as Quaternions 155 Conclusions 2 What Are Quaternions? Quaternions are numbers like the real numbers: they can be added, subtracted, multiplied, and divided.