Transcript Gravitational lenses in the Universe Bernard Fort Institut d’astrophysique de Paris ESO-Vitacura November 14, 2006

Gravitational lenses in the Universe
Bernard Fort
Institut d’astrophysique de Paris
ESO-Vitacura November 14, 2006
Part 1: Strong Lensing
multiple 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
Part 2:
weak and highly
singly magnified image regime
Weak lensing principles
Lensing mass reconstruction
The flexion regime
The cosmic shear: an overview
November 16, 2006
Deflection of light
Metric for the weak field approximation
Equivalent to an optical index n <1
+
Fermat principle
gravitational achromatic lens
A short history of lensing
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
Light deflection by the sun
1919, Eddington
measures  = 1.6“
at the edge of the
sun, confirming GR
r
r
Mo
 = 4 G Mo / (c2 r) = 1.75 ‘’
History of lensing
1937
1964
1979
1887
1993
1995
2000
2005
Zwicky: galaxies can act as lenses
Refsdal: time delay and Ho
Walsh & Weyman: double QSO 0957+561
CCD cameras
giant arcs in cluster and first Einstein ring
Macho and Eros microlensing
the weak lensing regime
cosmic shear measurements
discovery of an extrasolar earth like planet
2010-15 the golden age 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
SL
(or multiple thin lenses)
Calculating the deflection angle
n
geometrical term
=
deflection angle
equation 1
to remember
for weak gravitational field
light propagation time is reduced in
presence of a gravitational field
Fermat principle yields the
deflection angle
 are very small => Born's approximation can be used
The thin lens equation
A
Cosmic optical bench ~ Natural optical telescope
Time delay and thin lens
Dol q
q
O

S
L
tgeom. =
 Dol q /(2 c) = (Dos Dol / Dls) (q-b)^2 / (2c)
tgrav. =
- (2/c^2)
Fermat’s principle:
q
f (Dol q) dz
(tgeom. + tgrav.) = 0
gives:
b=q – 2 (Dls/Dos)
(Dol q) y(Dol
identifying with:
b Dos + (q) Dls = q Dos
gives:
(q) = (2 / c^2)
(Dolq)y(Dol
q)
q)
From Blanford and Kochanek lectures «gravitational lenses », 1986
Point mass M
equation 2
Total deviation for a 2D mass distribution
L
Gpcs
Gpcs
S
O
kpcs
Surface mass density
Dm
equation 3
(1)
equation 3
Thin lens equation
A
Uniform sheet of constant mass density
So g/cm2
q
~ So / 2
~ - So / 2
 ~2q. So / 2
O
b = q (1-So/Scrit)
S
L
equation 4
If So = Scrit b= 0 for any q
The plan focuses any beams onto the observer
Reduced quantities
critical density (g/cm2)
convergence =
reduced surface density
deflection angle
Reduced thin lens equation
A
( 5)
(qs)
(qi)
Non-linear projection through the reduced deflection angle
(6)
But non linear lens (q)=q

q
From the Liege university lensing team
Caustic surfaces
envelopes of families of rays ~ focal surfaces
The 2D Poisson equation
3D Poisson equation
Using Green's function of the
2D Laplacian operator gives the
potential from the mass distribution
(3)
(10)
equation 7
(8)
Light Travel Time and Image Formation
detour
3 images
=source
Time dilation
Total light travel time
1 image
Multiple images formation
Convergence
+ shear
O
~
L
S
Local image properties
If the potential gradient does not vary on the image size
A = Jacobian matrix of the projection bq through
the lens equation
(9)
to remember
projection matrix
(10)
convergence
complex shear
(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 m=Abs[dq/db]
from (10)
surface magnification
Two eingen values
(11)
2 caustic lines
(12)
Convergence map only
Shear map: (amplitude and direction)
Map of a circular sources grid
Cylindrical projected potential
1
A x_, y_
1
A r_
r_
1
r,r
r,r
r
0
r,r
radial caustic
1
x,y
x, y
x, y
x,x
r
0
1
y,y
0
1 r
1
r
x, y
x, y
x,y
1
1 r
r
r
r
r
^ 1
tangential caustic
1
1 r
r
r
0
Solving the lens equation for a point mass M
two images but one is
1/r
projected potential Ln (r)
very demagnified
rs
Einstein radius qe
ri1,ri2
(13)
Point mass lens equation
qs = |qi – 1 / qi|
with angular radial coordinates in qe unit
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
f1/f2 =
Lensing by moving star mass
1
2
Multi-site observations
note that
f1 / f2 = (q2 / q1)4
Nature of DM
DM = MACHOS ?
Microlensing by MACHOS
(dark stars, BH,.. )
t
Microlenlensing event by the binary star MACHO 98
Microlensing an observational challenge!
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
Data mining: Need
to distinguish
microlensing from
numerous variable
stars.
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
Spherical potential
1
A x_, y_
1
A r_
r_
1
r,r
r,r
r
0
r,r
radial caustic
1
x,y
x, y
x, y
x,x
r
0
1
y,y
0
1 r
1
r
x, y
x, y
x,y
1
1 r
r
r
r
r
^ 1
tangential caustic
1
1 r
r
r
0
Spherical isothermal potentials
SIS
particules in thermal
equilibrium everywhere (DM, stars)
3D r_
2
kT
GM
m
^ 2
(13)
2
_
2G
_
Re
Re
deviation  = constante
4
2
Dls Dol
c2 Dos
X-section ~ s4
to remember for SIS
central singularity
isothermal potential with core radius: SISrc
_
o
e
new Einstein radius e
^2
c ^2
e^ 2
deviation  ~ q
if q << qc
= constante if q>> qc
(14)
c^2
Isothermal potential with a core radius
SIS
Re
Parity changes
Equivalent to a flat rotation curve
Universal Cold DM density profile
Numerical simulations gives:
(15)
~1
with
(16)
Navarro, Franck and White potential 1998
with galaxy & cluster potentials
Central part:
DM+stars
M(r >) converges
also ellipsoidal dark matter halos
Elliptical potential
q ~ ellipticity parameter
effective deviation angle
Back to caustics and critical lines with
projected elliptical potential
Local surface magnification
=0
/
=0
Locus of caustics lines in the source plan projected into
critical lines in the image plan where m become infinite
images for a non-singular elliptical lens.
Singly magnified image
Radial arc
Cusp arc
Einstein Cross
From Kneib et al 1993
Fold arc
rays and caustics
t f = 0
rays: critical points of path length (Fermat-Hamilton)
field point
x
.,z
caustics
path length
f (t; x, z ) =
rays
2
t
( z - h(t ))  ( x - t )2
initial wavefront, h(t)
Caustics (focal surfaces)
tf = 0 and
2
t f
=0
caustics are physical catastrophes described by the theory of
Thom and Arnold
3
(
)
1 t; x = t  xt
smooth function
variable
parameter
x<0
1
x=0
t
1
x>0
t
critical points: ∂1/∂t=0
1
t
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
Image magnification
CosmologyCosmology
geometry
Newtonian
potential
Newtonian gravitational
potentia
Beyond z=6 with Strong Gravitational Lenses
From Kneib et al 2005
Measuring Ho from time delay
Cuevad Tello et al; 2006
70 +/- 10
delay
Ho
Image location
potential modeling
RCS1 giant arc sample from Gladders et al
2005
Specific X-ray
Cluster surveys
Some arcs have
Einstein radius
up to 50 "
A1689, RCS 0224
Modeling A370
From Kneib et al 1993
Modelling softwares
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..
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
Internal potential
external potential
Several multiple image
systems can probe a dark
matter twist of ellipticity
Gavazzi et al 2004
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
Substructure  complicated catastrophes!
(Bradac et al. 2002)
Sub-halo analysis with simulations
Dalal and Kochanek 2002
(Dark) halo sub-structures can
explain QSO anomalies !
Fraction of the observed image
brightnesses deviating from the
best smooth model fit?
The Einstein cross
No Dark Matter at the center of the galaxy!
Coupling lensing and stellar dynamics
Lens modelling give the mass at rEinstein and S*SDM
Stars see the potential for r < reff
(~ potential slope g)
Jeans equation
c(s(M* / L,g,nv anisotropy)= s(M* / L, g, nv anisotropy)- s*spectro
observation
from Koopmann & Treu 2005
SLACS
Lensing -> recovers the Ellipticals fundamental plane
For isolated E (external shear perturbation < 0.035)
<sL/s*> = 1.01 +/- 0.065 rms
r(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
<sL/s*> =1. +/- 0.065
r(r) ~ r - 2.01+/-0.03 at Re
~ Flat Rot. Curve
(DM light-conspiracy)
Re
Re/sL = Dol Dls /D os
Re/s* = G (W,L, or w0,w1)
Lens modeling
Log r
VLT spectroscopy
Simulations: CDM halos are lumpy
(Moore et al. 1999;
Klypin et al. 1999)
typical galaxy,
~1012 Mo
should contain
many sub-halos
corresponding to
smallest satellite
galaxies. Where
are they?
QSO image anomalies
Fact
• In 4-image lenses, the image positions can be fit by
smooth lens models:
positions determined by fitrue  fismooth
• The flux ratios cannot; brightnesses determined by
fijtrue = fijsmooth + fijsub
• 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)
B1555 radio
3
images
1
image
Images A and B should be
equally bright!
Micro-lensing by stars? Maybe
Halo Sub-structure ?
Testing rotation curves
(Sanders & McGaugh 2002)
Where are the intermediate mass lenses ?
SIS mass distribution:
(3’’<  < 7’’)
?
 ~ 1-3” for a lens galaxy
 ~ 10-50” for a cluster of galaxies
Cf ESO seminar Bernard Fort November 24
Does it exist cosmic strings lenses?
SNAP
Joint 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
JWST: Le successeur de Hubble dans l’Infrarouge
• Un miroir de 6,6 m
• Lancement en 2011 mission
de 5 à 10 ans
INSTRUMENT MIRI
Spectro-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