Bernard Fort

Institut d’astrophysique de Paris

Gravitational lenses in the Universe

ESO-Vitacura November 14, 2006

Part 1: Strong Lensingmultiple images regime

Historical lensing observations Fermat principle and lens equations

Lensing by a point mass

Lensing by mass distributions

Galaxy and cluster lensing: astrophysical applications

Weak lensing principles

Lensing mass reconstruction

The flexion regime

The cosmic shear: an overview

Part 2: weak and highly

singly magnified image regime

November 16, 2006

Deflection of light

Metric for the weak field approximation

gravitational achromatic lens

Fermat principle+

Equivalent to an optical index n <1

1801 Soldner: are the apparent positions of stars

affected by their mutual light deflection?

hyperbolic passage of a photon bulet with v = c:

tan (/2) = GM/(c2r)

1911 Einstein: finds the correct General Relativity answer

= 4GM/(c2r)

=> and predicts 2 x the newton value

A short history of lensing

Light deflection by the sun

= 4 G Mo / (c2 r) = 1.75 ‘’

1919, Eddington

measures = 1.6“

at the edge of the sun, confirming GR

r

Mo

r

1937 Zwicky: galaxies can act as lenses 1964 Refsdal: time delay and Ho 1979 Walsh & Weyman: double QSO 0957+561 CCD cameras 1887 giant arcs in cluster and first Einstein ring1993 Macho and Eros microlensing 1995 the weak lensing regime 2000 cosmic shear measurements 2005 discovery of an extrasolar earth like planet 2010-15 the golden age of lensing

History of lensing

Discovery of the double quasar (Walsh et al. 1984)

Lensing by Galaxies: HST Images

An Einstein gravitational ring

The Giant arc in A370

The second giant arc

Cl 2244

The cosmic optical bench

(or multiple thin lenses)

SL

Calculating the deflection angle

geometrical term

n

deflection angle

=

equation 1

for weak gravitational field

light propagation time is reduced inpresence of a gravitational field

Fermat principle yields the deflection angle

are very small => Born's approximation can be used

to remember

The thin lens equation

A

Cosmic optical bench ~ Natural optical telescope

O S

L

Dol

Time delay and thin lens

tgeom. = Dol /(2 c) = (Dos Dol / Dls) ()^2 / (2c)

tgrav. = - (2/c^2) (Dol ) dz

Fermat’s principle: (tgeom. + tgrav.) = 0

gives: – 2 (Dls/Dos) (Dol ) (Dol )

identifying with: Dos + Dls = Dos

gives: () = (2 / c^2) (Dol )

From Blanford and Kochanek lectures «gravitational lenses », 1986

Point mass M

equation 2

Total deviation for a 2D mass distribution

O S

LGpcs Gpcs

kpcs

Surface mass density

equation 3

m

(1)

equation 3

Thin lens equation

A

SO

L

Uniform sheet of constant mass density o g/cm2

= (1-o/crit)

If o = crit = 0 for any

The plan focuses any beams onto the observer

~ - / 2~ o / 2

/ 2

equation 4

Reduced quantities

critical density (g/cm2)

convergence =reduced surface density

deflection angle

Reduced thin lens equation

A

Non-linear projection through the reduced deflection angle

s) i)

( 5) (6)

But non linear lens

From the Liege university lensing team

Caustic surfacesenvelopes of families of rays ~ focal surfaces

The 2D Poisson equation

3D Poisson equation

Using Green's function of the2D Laplacian operator gives the potential from the mass distribution

(3) equation 7

(10) (8)

Light Travel Time and Image Formation

1 image

3 images

detour

Time dilation

Total light travel time

=source

O L S

Multiple images formation

Convergence+ shear

~

Local image properties

A = Jacobian matrix of the projection through the lens equation

If the potential gradient does not vary on the image size

(9)

to remember

convergence

complex shear

projection matrix

(10)

(9)

Magnification matrix M

(10)

Etherington theorem

The elementary surface brightness (flux / dx.dy) on each position the source is conserved on the conjugated point of the projected image (but seeing effects).

consequence: one can detect the presence of a lense only from the magnification and distortion of a geometrical shape. A lens in front of a uniform brightness distribution (or random distribution of points) cannot be seen.

Magnification Abs

surface magnification

Two eingen values 2 caustic lines

(11)

(12)

from (10)

Convergence map only

Shear map: (amplitude and direction)

Map of a circular sources grid

Ar_1 r,rr 00 1 1rrr

Ax_, y_1 x,xx, yx,yx, yx,yx, y1 y,yx, y

r_1 r,rr1 1rrr̂1

Cylindrical projected potential

radial caustic tangential caustic

1 r,rr 0 1 1rrr 0

Solving the lens equation for a point mass M

Point mass lens equation

-2 -1 1 2

-2

-1

1

2

3

s = |i – 1 / i|

ri1,ri2

1/r projected potential Ln (r)

rs

with angular radial coordinates in e unit

two images but one is

very demagnified

Einstein radius e

(13)

ring configuration for point mass or spherical potential

Source, lens, observer perfectly aligned

~ 1-3” for a lens galaxy

~ 10-50” for a cluster of galaxies

Magnification for a point mass

In[66]:= PlotAbsr,r, 3, 3

-3 -2 -1 1 2 3

2

4

6

8

10

Out[66]= Graphics

f1/f2 =

Multi-site observations

Lensing by moving star mass

note that f1 / f2 = (2 / 1)4

12

DM = MACHOS ?

Nature of DM

Microlensing by MACHOS(dark stars, BH,.. )

t

Microlenlensing event by the binary star MACHO 98

Microlensing an observational challenge!

Data mining: Need to distinguish

microlensing from numerous variable

stars.

Candidate MACHOs: Late M stars, Brown Dwarfs, planets Primordial Black Holes Ancient Cool White Dwarfs

<10-20% of the galactic halo is made of compact objects of ~ 0.5 M

MACHO: 11.9 million stars toward the LMC observed for 7 yr >17 events

EROS-2: 17.5 million stars toward LMC for 5 yr >10 events (+2 events from EROS-1)

To be updated!

Dark Halo: Microlensing results

searching hearth like planet

Ar_1 r,rr 00 1 1rrr

Ax_, y_1 x,xx, yx,yx, yx,yx, y1 y,yx, y

r_1 r,rr1 1rrr̂1

Spherical potential

radial caustic tangential caustic

1 r,rr 0 1 1rrr 0

Spherical isothermal potentials

SIS particules in thermal equilibrium everywhere (DM, stars)

_ 2

2 G _

ReRe

4 2 Dls Dol

c2 Dos

2 k T

m

3Dr_ ^2

G M

deviation = constante

(13)

X-section ~ 4

to remember for SIS

central singularity

isothermal potential with core radius: SISrc

_oe^2 c^2

new Einstein radius e

e^2 c^2

deviation ~ if << c = constante if >> c

(14)

-3 -2 -1 1 2 3

-2

-1.5

-1

-0.5

0.5

1

1.5

2

Re

Isothermal potential with a core radius

Equivalent to a flat rotation curve

Parity changes

SIS

Universal Cold DM density profile

Numerical simulations gives:

~ 1

Navarro, Franck and White potential 1998

with

(15)

(16)

with galaxy & cluster potentials

also ellipsoidal dark matter halos

M(r >) converges

Central part:

DM+stars

effective deviation angle

Elliptical potential

q ~ ellipticity parameter

/Local surface magnification

Back to caustics and critical lines with projected elliptical potential

Locus of caustics lines in the source plan projected into critical lines in the image plan where become infinite

= 0 = 0

images for a non-singular elliptical lens.

Radial arc

Cusp arc

Einstein Cross

Fold arc

Singly magnified image

From Kneib et al 1993

rays

caustics

Caustics (focal surfaces)

rays: critical points of path length (Fermat-Hamilton)

field point

x . , z

initial wavefront, h(t)

t

path length

t;x, z

z h t 2 x t 2

t 0 and t2 0

t 0

rays and caustics

caustics are physical catastrophes described by the theory of Thom and Arnold

1 t;x t3 xt

variable

parameter

smooth function

1

t

x<01

t

x=0

1

t

x>0

critical points: ∂1/∂t=0

Multiple images of the sun on Villarica lake

images are places on the water where the distance sun-water-eye is stationary

Multiple caustics with merging

Caustics images drawn by a distant distant sun on the bottom of a swimming pool (a reverse light propagation with the sun as an observer )

Light curve of OGLE235

a binary system with a big jupiter like satellite

Binary events was first suggested by Mao & Paczynski, 1991, ApJL, 374, 40

Aplication of lensing in cosmology

Newtonian gravitational potentialCosmology Cosmology geometry Newtonian potential

Image magnification

Beyond z=6 with Strong Gravitational Lenses

From Kneib et al 2005

Measuring Ho from time delay

Cuevad Tello et al; 200670 +/- 10

Image location potential modelingdelay Ho

RCS1 giant arc sample from Gladders et al 2005

Some arcs have Einstein radius up to 50 "

A1689, RCS 0224

Specific X-ray Cluster surveys

Modeling A370

From Kneib et al 1993

LENSTOOL (strong and weak regime 1993 - 2006)people who wrote part of this project ( in chronological order ): Jean-Paul Kneib (1993), Henri Bonnet , Ghyslain Golse, David Sand, Eric Jullo, Phil Marshall

GRAVLENS 2005- Software for Gravitational Lensing by Chuck Keeton

Lensview 2006: Software for modelling resolved gravitational lens images B. Wayth & R. Webster

Many others: Rigaud, Kovner, Kochanek, Barthelmann, Gavazzi,Valls-Gabaud, Soyu..

Modelling softwares

Cf: seminar Marceau Limousin November 15

Probing the density profile of DM halos

inside ~ 10 kpcs ?10 < r < 2-300 kpcs r -2 r > 2-300 kpcs, maybe r -3

Cf. seminar Marceau Limousin Nov 15,2006

Results with MS2137-23

elliptic halo => collisionless DM, Miralda-escude 96; coupling a dual modeling SL-WL with a dynamical study of stars: profile compatible with NFW simulations for r > 10 kpcs; triaxial ellipsoïd projection effect (potential twist from radial to tangential images); MOND does not work ; Bartelmann 98, Gavazzi et al. 2002, 03, 04,..)

Testing DM halo shape with several arc systems

Several multiple image systems can probe a dark matter twist of ellipticity

Gavazzi et al 2004

Internal potential

external potential

Detection of dark Matter clumps

• Bonnet et al in Cl0024+1654 (WL)

• Weinberg & Kamionsky 2003 theoretical predictions for non virialized cluster mass still in the merging process.

Simulations: CDM halos are lumpy

(Bradac et al. 2002)

Substructure complicated catastrophes!

Dalal and Kochanek 2002

Fraction of the observed image brightnesses deviating from the

best smooth model fit?

(Dark) halo sub-structures can explain QSO anomalies !

Sub-halo analysis with simulations

The Einstein cross

No Dark Matter at the center of the galaxy!

Coupling lensing and stellar dynamics

Lens modelling give the mass at rEinstein andDM

Stars see the potential for r < reff Jeans equation

M* / Lv anisotropy= (M* / L, , v

anisotropyspectro

observation

(~ potential slope

from Koopmann & Treu 2005

SLACS

Lensing -> recovers the Ellipticals fundamental planeFor isolated E (external shear perturbation < 0.035)

<L/*> = 1.01 +/- 0.065 rms

(r) ~ r - 2.01 +/- 0.03 near Einstein Radius (~Flat Rot.Curve)

PA and ellipticity of light and DM trace each other ( M*~75%)

No evolution (<10%) of parameters with z (but more galaxies around <ZL>~0.2)

A SL2S cosmological tests with rings ?

Hypothesis: Treu's results

<L/*> =1. +/- 0.065

r(r) ~ r - 2.01+/-0.03 at Re ~ Flat Rot. Curve (DM light-conspiracy)

Re/L = Dol Dls /D os

Re/* = G (, or w0,w1)Log r

Re

Lens modeling

VLT spectroscopy

Simulations: CDM halos are lumpy

typical galaxy,~1012 Mo

should contain many sub-haloscorresponding to smallest satellite galaxies. Where

are they?

(Moore et al. 1999; Klypin et al. 1999)

QSO image anomalies

Fact

• In 4-image lenses, the image positions can be fit by smooth lens models:

positions determined by itrue i

smooth

• The flux ratios cannot; brightnesses determined by

ijtrue = ij

smooth + ijsub

• Interpretation• Flux ratios are perturbed by substructure in the lens

potential. (Mao & Schneider 1998; Metcalf & Madau 2001; Dalal & Kochanek 2002).

Is there Halo Sub-Structure?(e.g. Dalal and Kochanek 2001,2002)

1 image

3 images

B1555 radio

Images A and B should be equally bright!

Micro-lensing by stars? Maybe

Halo Sub-structure ?

Testing rotation curves

(Sanders & McGaugh 2002)

SIS mass distribution:

~ 1-3” for a lens galaxy ~ 10-50” for a cluster of galaxies

Where are the intermediate mass lenses ?

(3’’<< 7’’) ?

Cf ESO seminar Bernard Fort November 24

Does it exist cosmic strings lenses?

SNAPJoint Dark Energy Mission: NASA (75%) & DOE (25%) launch 2014-2015

6 years survey: super novae and weak lensing SNAP: 2m telescope, instrument FOV 1 deg2

Imaging / spectro. one deep field (15 deg2), one large field (~300 deg2 ?) ~ 1Billlion $

• DUNE (Dark Universe Explorer): similar survey but

1.2-1.5m telescope and imaging only instrument FOV 1 deg2

~ 300 M€

•Prediction snap n ~ 4000 and 14000 strong lenses

JWSTJWST: Le successeur de Hubble dans l’Infrarouge

• Un miroir de 6,6 m

• Lancement en 2011 mission de 5 à 10 ans

INSTRUMENT MIRISpectro-imageur, 5-28 μm

Participation française focalisée autour du banc optique de l’imageur (détecteur intégré au RAL, UK)

Responsabilité managériale de la partie française

Responsabilité « système » de l’ensemble