PRINCIPLES AND APPLICATIONS OF GRAVITATIONAL LENSING. The precursors of XVIII et XIX centuries. 2 G M r. v e

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Cours de Cosmologie observationnelle Master 010-011 EPFL 18 May

Meylan Laboratoire d Astrophysique Ecole Polytechnique Fédérale

ch The precursors of XVIII et XIX centuries 1783: John Michell in

Soldner in Germany The escape velocity v e at the surface of a

1 Cours de Cosmologie observationnelle Master EPFL 18 May 011 PRINCIPLES AND APPLICATIONS OF GRAVITATIONAL LENSING Georges Meylan Laboratoire d Astrophysique Ecole Polytechnique Fédérale de Lausanne The precursors of XVIII et XIX centuries 1783: John Michell in England 1796: Pierre Simon Laplace in France 1801: Johann von Soldner in Germany The escape velocity v e at the surface of a spherical mass M of radius r : 1 April 011 : gravitational lensing effect by a black hole of 1 m J v e = G M r

2 GM RS ". 95 c M M sol km Schwarzschild radius The phenomenon of gravitational lensing " GM tan = " = v r GM v r deflection angle (Newton) = 4GM c r = R r S deflection angle (Einstein RG) In 1919, during a total solar eclipse, first test of a GR prediction : GR prediction at solar limb = 1.75" confirmed by Eddington (190) The Sun : first gravitational lens 1919 : the Sun : first gravitational lens After the solar eclipse of 1919 and papers in 1930 s subject ~ totally abandoned for about 30 years 1960 s 1970 s Theoretical discussions Inventions of CCDs Discovery of quasars In 1979, first case of a gravitational lens (extragalactic, i.e., at cosmological distance) QSO Walsh, Carswell, Weymann, 1979, Nature, 79, 381 The disruptive action of the lensing galaxy splits the single image of the quasar into two or more componants d i µ = d s = magnification QSO A image QSO QSO B image

QSO 0957+561: first gravitational lens at cosmological distance QSO 0957+561: first gravitational lens at cosmological distance HST/WFPC "(A,B) = 6.1" V A = V B # 17.1 z(source)=1.41 V G =19.

3 QSO : first gravitational lens at cosmological distance QSO : first gravitational lens at cosmological distance HST/WFPC "(A,B) = 6.1" V A = V B # 17.1 z(source)=1.41 V G =19.1 z(lens)=0.36 Image A Image B CIV 1549 Å CIII] 1909 Å MgII 798 Å "(A,B) = 6.1" V A = V B # 17.1 z(source)=1.41 Walsh, Carswell, Weymann 1979, Nature, 79, 381 PKS : first tight pair of quasars All pairs of quasars observed in the Universe do not always proceed from the effect of a gravitational lens z = A B Djorgovski & Meylan, 1987, ApJ, 31, L17

PKS 1145-071: first tight pair of quasars PHL 1: second tight pair of quasars Radio image from VLA I A /I B =.

91 Meylan & Djorgovski (1994) PHL 1: second tight pair of quasars LBQS 149-008 Discovered by Hewett et al.

(1999), Mortlock et al. (1999), and Faure et al. (003) No obvious lensing galaxy Difficult to model as a lens Faure et al.

4 PKS : first tight pair of quasars PHL 1: second tight pair of quasars Radio image from VLA I A /I B =.7 in V I A /I B > 10 4 in radio "(A,B) = 4." KECK U QSO B QSO A KECK V Djorgovski & Meylan, 1987, ApJ, 31, L17 "(A,B) = 4." z 1.91 Meylan & Djorgovski (1994) PHL 1: second tight pair of quasars LBQS Discovered by Hewett et al. (1989), two QSO components (A and B), proposed as a gravitational lens; z =.076 Suggested as a binary QSO by Kochanek et al. (1999), Mortlock et al. (1999), and Faure et al. (003) No obvious lensing galaxy Difficult to model as a lens Faure et al. find no weak lensing distortion in the field Hewett et al. C B "(A,B) = 4." z 1.91 Meylan & Djorgovski (1991) deep Keck and VLT images reveal additional components, one of which (C) is a QSO at the same redshift A CASTLES HST image

I band (Keck) K band (Keck + VLT) QQQ 149-008 : first tight triplet of quasars 8 C 4 B 3 8 D? C 4 B 3 A 1 9 A 9 1 "(A,B) = 4." z =.076 Djorgovski et al.

Keeton s gravlens software Explore the parameter space, seek the best fit solutions Model always produces four QSO images; assume two viable scenarios: Model

5 I band (Keck) K band (Keck + VLT) QQQ : first tight triplet of quasars 8 C 4 B 3 8 D? C 4 B 3 A 1 9 A 9 1 "(A,B) = 4." z =.076 Djorgovski et al. (007) 5 arcsec 5 arcsec Keck Spectra of the QSO Components a1 a1 % a1 a1 a1 a3 a3 % a1 a3 a % a3 % a3 % $ obs (Å) Absorbers: z a1 = 1.51 (A,B), z a = 1.66 (A), z a3 = (B,C) Gravitational Lens Models Assume a singular isothermal sphere + external shear A standard model which reproduces most known lenses Use C. Keeton s gravlens software Explore the parameter space, seek the best fit solutions Model always produces four QSO images; assume two viable scenarios: Model L1: the faint image D is the 4th component Model L: image A is an unresolved blend, "& < 0.05 Both scenarios fail: L1: best reduced ' = 1941 (), image D is the brightest, images B and C about equal, positions off by ~ 0.5 L: best reduced ' = 74, image A is ~ 1. displaced Conclude that the lensing hypothesis is unlikely

What about the lensing galaxy? Our best lensing model L predicts a massive and luminous lens galaxy, which is not seen, even if placed in an optimal position: Observed L: z lens = 0.5 L: z lens = 1.

6 What about the lensing galaxy? Our best lensing model L predicts a massive and luminous lens galaxy, which is not seen, even if placed in an optimal position: Observed L: z lens = 0.5 L: z lens = 1.4 Flux Ratios of the QSO Spectra C Putative lens Putative lens A B K lens > 4 mag K lens = 18.5 mag K lens = 17.1 mag Spectrum Differences Component C has a bluer UV continuum, but redder optical to IR colors: A B C (Due to a contamination by the host galaxy?) (R-K).49 ± ± ± 0.1 (J-K) 1.13 ± ± ± 0.13 Spectrum differences between components A and B are about as expected for a random pair of QSOs at this redshift (Mortlock et al. 1999) Different shape of the C IV line; possibly C III] as well Marginal redshift differences from cross-correlation: "V AB = 80 ± 160 km/s, "V BC = 100 ± 400 km/s While the optical and IR flux ratio is A/B = 5 ± 3, but in X-rays it is A/B = 5.3 ± 1.8 (from ChaMP; Kim et al. 006) Triple QSO vs. Gravitational Lens We are unable to reproduce the observed geometry and intensities of images using plausible range of lensing models No evidence for a massive lensing galaxy in the images No weak lensing distortions in the field (Faure et al.), even if there was a dark, massive lens present Observed spectroscopic and color differences are naturally much easier to explain if these were physically distinct AGN Therefore, we conclude that this is most likely a case of a physical close triple QSO Projected separations are typical for interacting galaxy systems: "& AB = 43 kpc, "& AC = 36 kpc, "& BC = 30 kpc (proper units, for h = 0.7, ( m = 0.3, ( ) = 0.7 cosmology)

8 C R band (VLT) MCS deconvolution 4 QQQ 149-008 : first tight triplet of quasars D? B 3 A 9 3 arcsec 1 Disturbed host galaxy? "(A,B) = 4." z =.

(007) QQQ 149-008 : first tight triplet of quasars "(A,B) = 4." z =.

known to occur with frequencies up to ~ 100 times higher than what may be expected from galaxy clustering alone This can be understood if galaxy

7 8 C R band (VLT) MCS deconvolution 4 QQQ : first tight triplet of quasars D? B 3 A 9 3 arcsec 1 Disturbed host galaxy? "(A,B) = 4." z =.076 Djorgovski et al. (007) QQQ : first tight triplet of quasars "(A,B) = 4." z =.076 Djorgovski et al. (007) Conclusion about LBQS We see this system at a peak epoch of QSO activity and galaxy merging Binary QSOs at comparable redshifts are known to occur with frequencies up to ~ 100 times higher than what may be expected from galaxy clustering alone This can be understood if galaxy interactions are responsible for an onset of QSO activity In this case, we may be witnessing a 3-galaxy interaction, with AGN occurring in all of them Further studies of this system, and discoveries of more such QSO triples may provide useful new insights into a joint hierarchical formation of galaxies and SMBHs For more details, please see astro-ph/

3 directions: - to the lens - to the source - to the image 3 angles: - " # Theoretical bases Friedman-Lemaître-Robertson-Walker metrics The inhomogeneities creating the effect of gravitational lens

8 3 directions: - to the lens - to the source - to the image 3 angles: - " # Theoretical bases Friedman-Lemaître-Robertson-Walker metrics The inhomogeneities creating the effect of gravitational lens are only local perturbations * the luminous path is made of three independent parts : 3 plans: - of the source $ - of the image % - of the observer 3 distances: - D s D d D ds i ii iii Theoretical bases The inhomogeneities creating the effect of gravitational lens are only local perturbations * the luminous path is made of three independent parts : i, ii, iii. In a way similar to a prism, the light rays are deflected (by a very small angle) while they travel through the gravitational field of a point-like mass : " 4G M % = " dz = = c $ # c b R S The deflection happens essentially for " z ~ ± b where "z «D * the mass distribution can be projected along the line of sight and replaced by the surface mass density + (, ). b The lens equation The positions of the source and of the images are related by a non linear equation providing the possibility of multiple images: multiple image positions # corresponding to a unique source position " # = $ "( )

Distances at cosmological scale The three distances D d, D s and D ds are defined in such a way that the relation is true in the space-time of GR : such distances are called angular-diameter

9 Distances at cosmological scale The three distances D d, D s and D ds are defined in such a way that the relation is true in the space-time of GR : such distances are called angular-diameter distances. D " D D (in general) D( z, z i j d $ j ) = # with i s c = H ds (1 " " G G )( G " G 0 i j i 0 0(1 + zi )(1 + z j ) G = i 1/ ( 1+ 0 zi ) j ) Einstein radius in the case of a lens with axial symmetry " = # $ %( #) & "(#) = # $ D ds 4GM(#) D d D s c # Thanks to the axial symmetry, a source on the optical axis (" = 0) creates an image with the shape of a ring with a radius value : # " E = 4GM(" ) E D ds & % c ( $ D d D s ' 1/ Einstein radius King et al. 1998, MNRAS, 95, L41 In many models, # E represents the frontier between the positions of the sources generating either multiple images or a single image. A star as a lens (Einstein s pessimism) of masse M # 1 M at D # 10 Kpc: ) E ' = (( % & M M sol 1/ $ " # ' % & 10 D Kpc A galaxy as a lens (Zwicky s optimism) of masse M # M at D # 1 Gpc: ) E ' M = 0.9(( % 11 & 10 M sol 1/ $ " # ' % & 1 D Gpc $ " # 1/ $ " # 1/ B HST-NICMOS Full Einstein ring in the IR (diameter # 1") z source =?? z lentille = 0.881

MG 0414+0534 HST-ACS image of RXJ 1131-131 A A1 B G C HST-WFPC diameter #.1" z source =.64 z lentille = 0.

Courbin et al. 1999 Sluse et al. (006) Abell 18 HST WFPC z amas = 0.175 z sources ~ 0.7-5.

10 MG HST-ACS image of RXJ A A1 B G C HST-WFPC diameter #.1" z source =.64 z lentille = 0.96 HST imaging: - light profile of the lens - ellipticity and PA - astrometry of quasar images - lensed quasar host - other lensed objects VLT spectroscopy: - lens redshift - chromatic microlensing Courbin et al Sluse et al. (006) Abell 18 HST WFPC z amas = z sources ~ large and small arcs The gravitational lenses classified following three regimes: STRONG: the source is imaged into several components, their shapes and luminosities are strongly perturbed WEAK: one single image of the source, with its shape and luminosity strongly perturbed Kneib et al., 1996, ApJ, 471, amas = 1370 ± 140 km s -1 MICRO: one single image of the source, with only its luminosity strongly perturbed

Adam et al., 1989, A&A, 08, L15 QSO 37+0305: La Croix d Einstein HST-WFPC "(A,B)=1.

04 agissent comme autant de microlentilles, induisant des variations des luminosités

11 Adam et al., 1989, A&A, 08, L15 QSO : La Croix d Einstein HST-WFPC "(A,B)=1.7" B C QSO : La Croix d Einstein z = 1.69 A D z source = 1.69 z lentille = 0.04 galaxie. macro lentille étoiles. micro lentilles QSO : La Croix d Einstein Les étoiles de la galaxie à z = 0.04 agissent comme autant de microlentilles, induisant des variations des luminosités dans les quatre composantes du quasar à z = Moyen très direct de mesurer la taille d un QSO dans le visible slight complication from microlensing

microlensing events Usefulness of gravitational lenses via microlensing C A D B Mass distribution in our Galaxy Constraints on the size of quasar sources Upper limits on ( PM from point masses

12 microlensing events Usefulness of gravitational lenses via microlensing C A D B Mass distribution in our Galaxy Constraints on the size of quasar sources Upper limits on ( PM from point masses (neutron stars, black holes) Search for, and study of, exosolar planets Einstein Cross ESO-VLT June 006 Frequency of binary stars Enormous samples of variable stars A galaxy acting as a lens: Isothermal sphere with central singularity (SIS) Stars considered as the particles of a perfect gas, confined by their own mean gravitational potential, with spherical symmetry : k T p = m m" = kt v dp G M ( r) dr = g r equation of state thermal equilibrium hydrostatic equilibrium A galaxy acting as a lens: Isothermal sphere with central singularity (SIS) " v 1 A simple solution : SIS #( r) = G r % = " v 1 #( ) = G # # v v c 0kms 4 $ = 1.4"" ( 1 surface density deflection angle Multiple images only if the source verifies : " < # E Solutions of the lens equation : # ± = " ± # E )

13 A galaxy acting as a lens: Isothermal sphere with central core (CIS) " A simple solution : CIS v #( r) = G r # v 1 (" ) = G " + rc surface density 1+ 0 # 1 0 = " 0 + D 0 lens equation v Dd Dds D # 4 " c r D defines the number of images c s 1 + r c A galaxy acting as a lens: Isothermal sphere with central core (CIS) " [( # 1/ 0 = 0 # D 1+ 0 ) 1] / 0 multiple images if D > The local properties of the mapping source plane lens plane are described by its jacobian matrix : A. &" /&# The locus of the points # in the lens plane where strongly disturbed images are created is the set of points where the matrix A cannot be locally inverted, i.e., where its jacobian is null * critical lines et caustics. Surface brightness preserved : photons neither created nor distroyed The magnification µ is the ratio of the solid angles of the images and of the sources, with A. &" /&# µ = d" I = det( # $ d" S # % ) &1 d' I+ critical lines and positions of the images (lens plane) caustics and position of the source (source plane) µ = 1 det A d' I- d' S

QSO HE 1104-1805 ESO-MPI.-m IRAC J Courbin et al., 1998, ApJ, 330, 57 "(A,B)=3.

73 HE1104-1805 H1413+117 critical lines caustics The local properties of the application

14 QSO HE ESO-MPI.-m IRAC J Courbin et al., 1998, ApJ, 330, 57 "(A,B)=3.19" z source =.3 z lens = 0.73 HE H critical lines caustics The local properties of the application source plane lens plane are described by its jacobian matrix : A. &" /&# Observations 0.7" After deconvolution 0.3" The deconvolution provides an essential step PG B14+31 The locus of a point where A cannot be locally inverted, zero jacobian: critical lines and caustics. The Hubble constant and the age of the Universe movie

15 Evolution of the Hubble constant H o with time Evolution of the Hubble constant H 0 with time WMAP data do not independantly constrain H 0 (Spergel et al. 003, 006) Data from WMAP Spergel et al. 003 The age of the Universe from the gravitational lenses method based on cosmological distances independant of any local calibrations contrary to the HST Cepheid Key Program Efstathiou, 003: H 0 between 37 and 7

16 obs Time delay between two different light paths with different lengths * * Intrinsic QSO light variations * time delay "/ * * Time delay the travel time of a photon (Refsdal 1964, 1966) t( " ) = (1+ z d ) c D d D s & 1 D ds ' ( ( " # $ ) #%( ) ") * + = t + t geom grav The geometric term t geom represents the time delay induced by the longer light path followed by the deflected photons. The gravitational term t grav represents the time delay due to the relativistic time dilation induced by the gravitational field of the deflector. The term in front of the brackets ensures that the measured quantities correspond to the time delay as measured by the observer. intrinsic variations * time delay "/ * H 0 Measure of the time delay in radio QSO Haarsma et al., 1997, ApJ, 479, 10 Visible: "/ = 417 ± 3 days H 0 via QSO model: redshifts, positions, magnitudes, mass profile $ +1 # H 0 = 98 v ' $ 1.1yr ' "11 & ) & ) km s "1 Mpc "1 % 330km s "1 ( % ( *+ BA Observations: - v (lens) = 79 ± 1 km s -1 "/ BA = 417 ± 3 days H 0 = 67 ± 8 km s -1 Mpc -1 Falco et al. 1997, ApJ, 484, 70

17 H 0 via photometric monitoring for QSO RX H 0 via photometric monitoring for QSO RX Burud et al., Burud et al., 003 "/ AB = 146 days "/ AB = 146 days H 0 = 74 ± 9 km s -1 Mpc -1 H 0 = 74 ± 9 km s -1 Mpc -1 The Hubble constant from quasar time delays intrinsic luminosity fluctuations time delay measurement Hubble constant determination H 0 = 7 ± 8 km s -1 Mpc -1 H 0 = 61 ± 7 km s -1 Mpc -1 age of the Universe 10 gravitational lenses * H 0 = 61 ± 7 km s -1 Mpc -1

COSMOGRAIL COSmological MOnitoring of GRAvItational Lenses COSMOGRAIL COSmological Monitoring GRAvitatIonal Lenses Goal: production of 0 time delays over the next few years For the monitoring: Euler

telescope, Bangalore, India For high-resolution photometry and spectroscopy: ESO-VLT, KECK, GEMINI 8-10 meter-class telescopes Hubble Space Telescope NASA/ESA Hawaii Paranal currently, quasars

18 COSMOGRAIL COSmological MOnitoring of GRAvItational Lenses COSMOGRAIL COSmological Monitoring GRAvitatIonal Lenses Goal: production of 0 time delays over the next few years For the monitoring: Euler Swiss telescope, La Silla, Chile Mercator Belgian-Swiss telescope, La Palma, Canary Islands Maïdanak telescope, Uzbekistan Manchester Robotic telescope, La Palma, Canary Islands Himalayan Chandra telescope, Bangalore, India For high-resolution photometry and spectroscopy: ESO-VLT, KECK, GEMINI 8-10 meter-class telescopes Hubble Space Telescope NASA/ESA Hawaii Paranal currently, quasars observed as frequently as possible Keck Gemini Hawaii Paranal La Silla Cerro Tololo Chili Observations La Palma Spain Himalayan Chandra Telescope India Maidanak Ouzbekistan In order to constrain models we need a good knowledge of: - the position of each image - the luminosity of each image - distance of the source - distance of the lens - masse of the lens

Determination of the redshifts of lensing galaxies with VLT COSMOGRAIL : gravitational lens and time delay SDSS J1650+451 1.5 arcsec Image B Image A Eigenbrod et al. 006b, A&A 451, 759 Vuissoz et al.

19 Determination of the redshifts of lensing galaxies with VLT COSMOGRAIL : gravitational lens and time delay SDSS J arcsec Image B Image A Eigenbrod et al. 006b, A&A 451, 759 Vuissoz et al. 006a, A&A, submitted, see astro-ph/ COSMOGRAIL : gravitational lens and time delay SDSS J QSO RXJ Image B Image A Vuissoz et al. 007, A&A, 464, 845 H 0 = 5 ± 4 km s -1 Mpc -1 Claeskens et al. 006 A&A Sluse et al. 006 A&A

20 Detailed study of gravitational lenses HST imaging: - light profile of the lens - ellipticity and PA - astrometry of quasar images - lensed quasar host - other lensed objects HE Lens with 4 images, z s = 1.69, z l = 0.45, separation =.6 one clear Einstein ring connecting all four images about 10 galaxies within 40 HST IR images NIC VLT spectroscopy: - lens redshift - chromatic microlensing HST-ACS image of RXJ (Sluse et al. 006) 5 seasons with Euler+Mercator+Maidanak (01/04-0/08) 1pt / 5j HE HE measurements seasons from SMARTS (Kochanek et al. 006) 5 seasons with Euler+Mercator+Maidanak (01/04-0/08) 1pt / 5j + measurements seasons from SMARTS (Kochanek et al. 006)

21 Status in 010 : The Hubble constant from quasar time delays HST KP : H 0 = 74. ± 3.6 km s -1 Mpc -1 Lensing : H 0 = 63.4 ± 8.4 km s -1 Mpc time delays * H 0 = 63.4 ± 8.4 km s -1 Mpc -1 Time delays are not so cheap : Conclusions - it takes time to observed for 5 seasons Time delays now with uncertainties smaller than 4 % - including systematic - at least twice better than before - now main uncertainties coming from the slope of the mass profile H ± 8.4 km s -1 Mpc -1 ~ 15 more time delays in hand, however, slow careful interpretation If lenses are on average isothermal, then H ± 6 km s -1 Mpc -1 Convergence and shear You may delay, but time will not. Benjamin Franklin The local properties of the application source plane lens plane are described by its jacobian matrix: A. &" /&# With the convergence 1 and the shear : & 1 A = (1 '* ) $ % 0 0# & cos( ' ) $ 1" % sin ( * sin ( # ' cos( " The convergence 1 has a magnification action on the light rays: the image conserve the shape of the source, but with a different size. The shear induces an anisotropy with intensity and orientation 3.

22 Field of deformation of background galaxies without deformation with deformation Abell 1689 HST ACS (003) Abell 1689 HST ACS z amas = 0.18 ( a = 1848 ± 166 km s -1 Deep HST image t int = 13. hours

23 Abell 1689 HST ACS z = 3.04 Abell 1689 HST ACS (003) z amas = 0.18 ( a = 1848 ± 166 km s -1 Thousands of mirages in this image z = 3.04 Deep HST image t int = 13. heures Reconstruction of the mass distribution via the gravitational distortions Shear as a function of the convergence 1 image colombi IAP weak lensing see lectures by P. Schneider Seitz & Schneider, 1997, A&A, 318, 687

Weak Gravitational Lensing Map the 3D distribution of DM in the Universe

Very sensitive to DE through both geometry and growth Massey et al.

The gravitational lensing phenomenon is ubiquitous everywhere in the

24 Weak Gravitational Lensing Map the 3D distribution of DM in the Universe Measures the mass without assumptions in relation between mass and light Very sensitive to DE through both geometry and growth Massey et al. Nature 007 Based on Cosmos data The shape of a galaxy at ~ 1% accuracy The gravitational lensing phenomenon is ubiquitous everywhere in the Universe on galactic scales as well as on cosmological scales Sarah Bridle Great08

A new astrophysical tool : since 1979, the phenomenon of gravitational lensing is the subject of intense research activities, both theoretical and observational, which have

determination of the total mass of the lensing galaxy Direct determination of cosmological parameters: - Hubble constant H 0 - density parameters ( m and ( ) Study of mass

25 A new astrophysical tool : since 1979, the phenomenon of gravitational lensing is the subject of intense research activities, both theoretical and observational, which have created a new tool for the study of the whole Universe, from nearby planets to the most distant galaxies Usefulness of gravitational lenses via strong and weak lensing Direct determination of the total mass of the lensing galaxy Direct determination of cosmological parameters: - Hubble constant H 0 - density parameters ( m and ( ) Study of mass distribution of dark matter: - in galaxies - in clusters of galaxies - in large scale structures Natural telescopes for the observations of very distant objects at very high redshifts

Gravitational Lensing. A Brief History, Theory, and Applications

Gravitational Lensing. A Brief History, Theory, and Applications Gravitational Lensing A Brief History, Theory, and Applications A Brief History Einstein (1915): light deflection by point mass M due to bending of space-time = 2x Newtonian light tangentially grazing