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P. Jovanovic/L. Popovic: Gravitational Lensing Statistics and Cosmology


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P. Jovanovic/L. Popovic: Gravitational Lensing Statistics and Cosmology

  2. 2. Outline <ul><li>Observational cosmology: basics and parameters </li></ul><ul><li>Cosmological experiments: </li></ul><ul><li>Cosmic Microwave Background Radiation (CMBR) </li></ul><ul><li>Type Ia supernovae </li></ul><ul><li>Gravitational lensing </li></ul><ul><ul><li>Strong: detection of distant galaxies </li></ul></ul><ul><ul><li>Weak: detection of dark matter </li></ul></ul><ul><ul><li>Time delay: determination of H 0 </li></ul></ul><ul><ul><li>Statistics: constraining Ω 0 and Ω Λ </li></ul></ul><ul><ul><li>Problems with gravitational lensing statistics </li></ul></ul><ul><li>Conclusions </li></ul>
  3. 3. Cosmology basics <ul><li>The current models of cosmology are based on the field equations of general relativity : </li></ul><ul><li>Friedmann-Lemaître-Robertson-Walker (FLRW) metric: a solution of the Einstein field equations in the case of a simply connected, homogeneous, isotropic expanding or contracting universe: </li></ul><ul><li>r , ϕ , ϑ - comoving polar coordinates </li></ul><ul><li>k - the scalar curvature of the 3-space: k = 0, > 0, or < 0 corresponds to flat, closed, or open universe </li></ul><ul><li>a(t) - the dimensionless scale factor of the universe </li></ul><ul><li>Λ CDM model uses the FLRW metric, the Friedmann equations and the cosmological equation of state to describe the universe </li></ul>
  4. 4. Cosmological parameters <ul><li>H - the Hubble constant </li></ul><ul><li>ρ - the mass density of the universe </li></ul><ul><li>Λ - the cosmological constant </li></ul><ul><li>k - the curvature of space </li></ul><ul><li>a - the expansion factor of universe </li></ul><ul><li>dimensionless density parameters : </li></ul><ul><li>where the subscript “ 0 ” indicate the quantities which in general evolve with time and which are referring to the present epoch </li></ul><ul><li>several observational techniques are used for their estimation </li></ul>
  5. 5. Wilkinson Microwave Anisotropy Probe (WMAP) The &quot;angular spectrum&quot; of the fluctuations in the WMAP full-sky map, showing the relative brightness of the &quot;spots&quot; in the map vs. the size of the spots. The shape of this curve contain a wealth of information about the history of the universe
  6. 6. Supernova Cosmology Project <ul><li>Type Ia supernovae: the standard candles </li></ul><ul><li>Intrinsic luminosity is known </li></ul><ul><li>Apparent luminosity can be measured </li></ul><ul><li>The ratio of above two luminosities can provide the luminosity-distance ( d L ) of a SN </li></ul><ul><li>The red shift z can be measured independently from spectroscopy </li></ul><ul><li>Using d L (z) or equivalently the magnitude( z ) one can draw a Hubble diagram </li></ul>
  7. 7. Constraining the cosmological parameters <ul><li>Riess et al. 2004, ApJ , 607, 665 </li></ul><ul><li>Tonry et al. 2003, ApJ , 594, 1 </li></ul>
  8. 8. Content of the Universe
  9. 9. Gravitational lensing
  10. 10. Einstein Ring Radius of a gravitational lens
  11. 11. Examples: QSO 2237+030 ( z= 1.695), also known as “Einstein cross” and lensing galaxy ZW2237+030 ( z= 0.0394) RXJ1131-1231 PG 1115+080
  12. 12. Strong lensing: detection of distant galaxies <ul><li>The orange arc : an elliptical galaxy at z= 0.7, </li></ul><ul><li>the blue arcs : star forming galaxies at z= 1 - 2.5 </li></ul><ul><li>the red arc and the red dot : the farthest known galaxy at z~ 7 (13 billion ly away, i.e. only 750 million years after the big bang </li></ul>
  13. 13. Weak lensing: detection of dark matter unlensed lensed
  14. 14. Distribution of dark matter
  15. 15. The Hubble constant from gravitational lens time delays Kochanek & Schechter, 2003, astro-ph/0306040
  16. 16. Courbin, 2003, astro-ph/0304497 HST Key Project : determination of the H 0 by the systematic observations of Cepheid variable stars in several galaxies using HST
  17. 17. Gravitational lensing statistics <ul><li>More details about history and basics in the book: P. Schneider, C. Kochanek and J. Wambsganss, 2006, “Gravitational Lensing: Strong, Weak and Micro”, Saas-Fee Advanced Courses, Springer Berlin Heidelberg ( ) </li></ul><ul><li>Optical depth for gravitational lensing, i.e. the probability to observe such effects (Turner et al. 1984, ApJ , 284, 1; Turner, 1990, ApJ , 365, L43): </li></ul><ul><li>where z S and z L are the source and lens redshifts, σ is lens velocity dispersion,  ( σ ; z L ) is the velocity function, A is the cross section for multiple imaging, B is the magnification bias, dV is the differential comoving volume element </li></ul><ul><li>The Current State : lens statistics constraints on   and  0 are in good agreement with results from Type Ia supernovae </li></ul><ul><li>for a spatially flat universe:   = 0.72 - 0.78 (Mitchell et al. 2005, ApJ , 622, 81) </li></ul>
  18. 18. Likelihood contours at the 68%, 90%, 95%, and 99% confidence levels. The dotted line marks spatially flat cosmologies The separation distribution of the 12 CLASS lenses Mitchell et al. 2005, ApJ , 622, 81 Differential (thick) and cumulative (thin) probability along the line of spatially flat cosmologies
  19. 19. Gravitational macrolensing optical depth <ul><li>The effective optical depth is related to the number N GL (z) of multiply imaged quasars within a sample of N QSO (z) quasars with redshifts z by: </li></ul>Zakharov, Popovi ć and Jovanovi ć , 2004, A&A , 881
  20. 20. Distribution of all QSOs and lensed QSOs in Veron & Veron Catalogue <ul><li>Veron-Cetty & Veron, 2006, A&A , 455, 773: a sample of 85221 ( N QSO ) quasars among which 69 ( N GL ) are gravitationally lensed </li></ul>
  21. 21. The ratio of lensed to total number of quasars and optical depth for three different flat cosmological models as a function of quasar redshift
  22. 22. Optical depth of cosmologically distributed gravitational microlenses (Zakharov, Popovi ć and Jovanovi ć , 2004, A&A , 881)
  23. 23. Optical depth of cosmologically distributed gravitational microlenses for three different values of  L
  24. 25. Problems with gravitational lensing statistics <ul><li>Small number of observed gravitational lenses (~100) is insufficient for reliable statistics. Solution not later than 2015: LSST, SNAP, SKA and JWST projects will drastically increase the number of detected gravitational lenses </li></ul>Large Synoptic Survey Telescope (LSST): 2013 SuperNova/Acceleration Probe (SNAP): 2013 Square Kilometre Array (SKA): 2015 James Webb Space Telescope (JWST): 2013 <ul><li>Extinction by dust in the lens galaxies leads to artificially low number of observed lenses </li></ul><ul><li>Galaxy evolution: decrease of lensing population for higher redshifts would lower the number of observed lenses </li></ul><ul><li>Ellipticity and clustering: mass distributions of lenses is not circularly symmetric </li></ul><ul><li>Cosmology </li></ul>
  25. 26. Conclusions <ul><li>We demonstrated constraining the cosmological parameters by gravitational lens statistics on a sample of lensed quasars from Veron & Veron catalogue of quasars and active nuclei </li></ul><ul><li>Obtained results are in satisfactory agreement with those obtained from CLASS and SDSS surveys (Mitchell et al. 2005, ApJ , 622, 81) </li></ul><ul><li>Optical depth of cosmologically distributed gravitational microlenses also depends on assumed cosmological model (Zakharov, Popovi ć and Jovanovi ć , 2004, A&A , 881) </li></ul>