The Sloan Digital Sky Survey Quasar Lens Search. Iii. Constraints on Dark Energy from the Third Data Release Quasar Lens Catalog
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The Astronomical Journal, 135:512–519, 2008 February doi:10.1088/0004-6256/135/2/512 c 2008. The American Astronomical Society. All rights reserved. Printed in the U.S.A. THE SLOAN DIGITAL SKY SURVEY QUASAR LENS SEARCH. III. CONSTRAINTS ON DARK ENERGY FROM THE THIRD DATA RELEASE QUASAR LENS CATALOG Masamune Oguri1,2, Naohisa Inada3,4, Michael A. Strauss2, Christopher S. Kochanek5, Gordon T. Richards6, Donald P. Schneider7, Robert H. Becker8,9, Masataka Fukugita10, Michael D. Gregg8,9, Patrick B. Hall11, Joseph F. Hennawi12,DavidE.Johnston13,14, Issha Kayo15, Charles R. Keeton16, Bartosz Pindor17,Min-SuShin2, Edwin L. Turner2, Richard L. White18, Donald G. York19, Scott F. Anderson20, Neta A. Bahcall2, Robert J. Brunner21, Scott Burles22, Francisco J. Castander23, Kuenley Chiu24, Alejandro Clocchiatti25, Daniel Eisenstein26, Joshua A. Frieman19,27,28, Yozo Kawano15, Robert Lupton2, Tomoki Morokuma29, Hans-Walter Rix30, Ryan Scranton31, and Erin Scott Sheldon32 1 Kavli Institute for Particle Astrophysics and Cosmology, Stanford University, 2575 Sand Hill Road, Menlo Park, CA 94025, USA 2 Princeton University Observatory, Peyton Hall, Princeton, NJ 08544, USA 3 Institute of Astronomy, Faculty of Science, University of Tokyo, 2-21-1 Osawa, Mitaka, Tokyo 181-0015, Japan 4 Cosmic Radiation Laboratory, RIKEN (The Physical and Chemical Research Organization), 2-1 Hirosawa, Wako, Saitama 351-0198, Japan 5 Department of Astronomy, The Ohio State University, Columbus, OH 43210, USA 6 Department of Physics, Drexel University, 3141 Chestnut Street, Philadelphia, PA 19104, USA 7 Department of Astronomy and Astrophysics, The Pennsylvania State University, 525 Davey Laboratory, University Park, PA 16802, USA 8 IGPP-LLNL, L-413, 7000 East Avenue, Livermore, CA 94550, USA 9 Department of Physics, University of California at Davis, 1 Shields Avenue, Davis, CA 95616, USA 10 Institute for Cosmic Ray Research, University of Tokyo, 5-1-5 Kashiwa, Kashiwa City, Chiba 277-8582, Japan 11 Department of Physics and Astronomy, York University, 4700 Keele Street, Toronto, Ontario, M3J 1P3, Canada 12 Department of Astronomy, University of California at Berkeley, 601 Campbell Hall, Berkeley, CA 94720-3411, USA 13 Jet Propulsion Laboratory, 4800 Oak Grove Drive, Pasadena, CA 91109, USA 14 California Institute of Technology, 1200 East California Blvd, Pasadena, CA 91125, USA 15 Department of Physics and Astrophysics, Nagoya University, Chikusa-ku, Nagoya 464-8602, Japan 16 Department of Physics and Astronomy, Rutgers University, Piscataway, NJ 08854, USA 17 Space Research Centre, University of Leicester, Leicester LE1 7RH, UK 18 Space Telescope Science Institute, 3700 San Martin Drive, Baltimore, MD 21218, USA 19 Dept. of Astronomy and Astrophysics, and The Enrico Fermi Institute, 5640 So. Ellis Avenue, The University of Chicago, Chicago, IL 60637, USA 20 Astronomy Department, Box 351580, University of Washington, Seattle, WA 98195, USA 21 Department of Astronomy, University of Illinois, 1002 West Green Street, Urbana, IL 61801, USA 22 Kavli Institute for Astrophysics and Space Research and Department of Physics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA 23 Institut d’Estudis Espacials de Catalunya/CSIC, Gran Capita 2-4, 08034 Barcelona, Spain 24 School of Physics, University of Exeter, Stocker Road, Exeter EX4 4QL, UK 25 Departamento de Astronom´ıa y Astrof´ısica, Pontificia Universidad Catolica´ de Chile, Casilla 306, Santiago 22, Chile 26 Steward Observatory, University of Arizona, 933 North Cherry Avenue, Tucson, AZ 85721, USA 27 Kavli Institute for Cosmological Physics, University of Chicago, Chicago, IL 60637, USA 28 Center for Particle Astrophysics, Fermilab, P.O. Box 500, Batavia, IL 60510, USA 29 National Astronomical Observatory, 2-21-1 Osawa, Mitaka, Tokyo 181-8588, Japan 30 Max Planck Institute for Astronomy, Koenigsstuhl 17, 69117 Heidelberg, Germany 31 University of Pittsburgh, Department of Physics and Astronomy, 3941 O’Hara Street, Pittsburgh, PA 15260, USA 32 Center for Cosmology and Particle Physics, Department of Physics, New York University, 4 Washington Place, New York, NY 10003, USA Received 2007 August 5; accepted 2007 October 29; published 2008 January 15 ABSTRACT We present cosmological results from the statistics of lensed quasars in the Sloan Digital Sky Survey (SDSS) Quasar Lens Search. By taking proper account of the selection function, we compute the expected number of quasars lensed by early-type galaxies and their image separation distribution assuming a flat universe, which is then compared with seven lenses found in the SDSS Data Release 3 to derive constraints on dark energy under strictly controlled criteria. =− Ω = +0.11 +0.13 For a cosmological constant model (w 1) we obtain Λ 0.74−0.15(stat.)−0.06(syst.). Allowing w to be a free Ω = +0.07 +0.03 =− ± +0.3 parameter we find M 0.26−0.06(stat.)−0.05(syst.)andw 1.1 0.6(stat.)−0.5(syst.) when combined with the constraint from the measurement of baryon acoustic oscillations in the SDSS luminous red galaxy sample. Our results are in good agreement with earlier lensing constraints obtained using radio lenses, and provide additional confirmation of the presence of dark energy consistent with a cosmological constant, derived independently of type Ia supernovae. Key words: cosmological parameters – cosmology: theory – gravitational lensing Online-only material: color figure There are many models that explain the acceleration, including 1. INTRODUCTION a classical cosmological constant, decaying scalar fields, and The accelerating expansion of the universe is one of the topological defects (e.g., see Peebles & Ratra 2003,fora central problems in modern cosmology. This acceleration is review). In addition it might also be explained by long-range usually attributed to the dominant presence of a negative- modifications of the gravitational force law (e.g., Carroll et al. pressure component that is often referred to as dark energy. 2004). 512 No. 2, 2008 SDSS QUASAR LENS SEARCH. III. 513 The dark energy is characterized by its cosmological density brighter than i = 19.1. In this paper, we use a subsample of ΩDE, and its equation of state w, which is defined as the pressure this optical lens sample to constrain cosmological parameters, divided by the density of dark energy. In particular, measuring in particular the dark energy abundance and equation of state. w is a useful test of models for dark energy. Since w determines This paper is organized as follows. In Section 2 we briefly the expansion rate of the universe and the cosmological distance summarize our statistical lens sample. Section 3 describes how to a given redshift, not only ΩDE but also the value of w and the expected number of lensed quasars is computed. We present its time dependence can be inferred from distance (or volume) our results in Section 4, and summarize in Section 5.Wede- measurements on cosmological scales. One powerful way to note the present matter density as ΩM . The present dark energy constrain w is via observations of distant type-Ia supernovae that density is described as ΩDE,orΩΛ if the cosmological constant make use of luminosity-decline rate correlations to standardize w =−1 is assumed. We use the Hubble constant in dimension- −1 −1 their luminosities (Riess et al. 1998; Perlmutter et al. 1999): less form h = H0/(100 km s Mpc ). Throughout the paper since the standardized luminosities of type-Ia supernovae have we assume a flat universe ΩM + ΩDE = 1. Magnitudes quoted small scatter, they serve as an excellent standard candle to in the paper are corrected for Galactic extinction (Schlegel et al. measure cosmological distances. Another probe of dark energy 1998). is the fluctuation spectrum of the cosmic microwave background (CMB; de Bernardis et al. 2000; Spergel et al. 2003, 2007). 2. LENSED QUASAR SAMPLE The integrated Sachs–Wolfe effect, which can be detected by correlating the CMB map with the large-scale distribution of Our lensed quasar sample is constructed from the SDSS galaxies, allows a direct detection of the dark energy component DR3 spectroscopic quasar catalog (Schneider et al. 2005). The (e.g., Rassat et al. 2007). Additional constraints on dark energy properties of the SDSS are presented in a series of technical come from baryon acoustic oscillations in the galaxy power papers. Gunn et al. (2006) describes the dedicated wide-field spectrum (Eisenstein et al. 2005;Coleetal.2005; Percival et al. 2.5-m telescope. Details of the photometric survey are given 2007) and X-ray clusters of galaxies (Allen et al. 2004; 2007; in Fukugita et al. (1996), Gunn et al. (1998), Lupton et al. Rapetti et al. 2005). Since different methods involve different (1999, 2001), Hogg et al. (2001), Smith et al. (2002), Pier et al. systematics and degeneracies with the cosmological parameters, (2003), Ivezicetal.(´ 2004), Tucker et al. (2006), and Lupton it is of great importance to use as many independent observations (2007). Blanton et al. (2003) present the tiling algorithm of the as possible in studying dark energy. spectroscopic survey. Spectroscopic quasar targets are selected The statistics of strong lensing offer an alternative constraint according to an algorithm described in Richards et al. (2002). on dark energy (Turner 1990; Fukugita et al. 1990,butsee Details of each public data set are given in a series of data also Keeton 2002). The probability that a distant object is release papers (Stoughton et al. 2002; Abazajian et al. 2003, strongly lensed is proportional to the number of possible