PRINCIPLES AND APPLICATIONS OF GRAVITATIONAL …Gravitational Lens Models •! Assume a singular...
Transcript of PRINCIPLES AND APPLICATIONS OF GRAVITATIONAL …Gravitational Lens Models •! Assume a singular...
PRINCIPLES AND APPLICATIONS OF
GRAVITATIONAL LENSING
Georges Meylan
Laboratoire d’Astrophysique
Ecole Polytechnique Fédérale de Lausanne
http://lastro.epfl.ch
Cours de Cosmologie observationnelle Master 2010-2011 EPFL 18 May 2011
1 April 2011 : gravitational lensing effect by a black hole of 1 mJ
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 ve at the surface
of a spherical mass M of radius r :
!
ve
=2 GM
r
Schwarzschild radius
deflection angle (Newton)
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 (1920)
The Sun : first gravitational lens
rv
GM
rv
GM
22
2
2tan =!= "
"
kmM
M
c
GMR
sol
S95.2
2
2!"
r
R
rc
GMS
24
2==!
The phenomenon of gravitational lensing
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 0957+561 Walsh, Carswell, Weymann, 1979, Nature, 279, 381
The disruptive action of the lensing galaxy splits
the single image of the quasar into two or more componants
QSO A image
QSO B image
QSO
ionmagnificat=!
!=
s
i
d
dµ
QSO 0957+561: first gravitational
lens at cosmological distance
•! HST/WFPC2
•! "(A,B) = 6.1"
•! VA = VB # 17.1
•! z(source)=1.41
•! VG=19.1
•! z(lens)=0.36
•! "(A,B) = 6.1"
•! VA = VB # 17.1
•! z(source)=1.41
Image A
Image B
Walsh, Carswell, Weymann
1979, Nature, 279, 381 CIV 1549 Å CIII] 1909 Å MgII 2798 Å
QSO 0957+561: first gravitational
lens at cosmological distance
All pairs of quasars observed in the
Universe do not always proceed
from the effect of a gravitational lens
PKS 1145-071: first tight pair of quasars
Djorgovski & Meylan, 1987, ApJ, 321, L17
A
B
z = 1.345
PKS 1145-071: first tight pair of quasars
Djorgovski & Meylan, 1987, ApJ, 321, L17
Radio image from VLA
IA/IB = 2.7 in V
IA/IB > 104 in radio
"(A,B) = 4.2"
PHL 1222: second tight pair of quasars
Meylan & Djorgovski (1994)
QSO A
QSO B
KECK U KECK V
"(A,B) = 4.2" z ! 1.91
PHL 1222: second tight pair of quasars
Meylan & Djorgovski (1991) "(A,B) = 4.2" z ! 1.91
LBQS 1429-008
•! Discovered by Hewett et al. (1989), two QSO components (A and B), proposed as a gravitational lens; z = 2.076
•! Suggested as a binary QSO by Kochanek et al. (1999), Mortlock et al. (1999), and Faure et al. (2003) –! No obvious lensing galaxy
–! Difficult to model as a lens
–! Faure et al. find no weak lensing distortion in the field
•! deep Keck and VLT images reveal additional components, one of which (C) is a QSO at the same redshift
CASTLES HST image
A
B
C
Hewett et al.
QQQ 1429-008 : first tight triplet of quasars
Djorgovski et al. (2007) "(A,B) = 4.2" z = 2.076
1
A
B
C 4
3
8
2
9
5 arcsec
I band (Keck)
1
A
B
C 4
3
8
2 9
5 arcsec
D?
K band (Keck + VLT)
Keck Spectra of the QSO Components
Absorbers: za1 = 1.512 (A,B), za2 = 1.662 (A), za3 = 1.837 (B,C)
$obs (Å)
%
%
%
%
% a1
a1
a1
a1
a1 a2
a1
a3
a3 a3 a3 a3
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 L2: image A is an unresolved blend, "& < 0.05”
•! Both scenarios fail: –! L1: best reduced '2 = 1941 (!), image D is the brightest, images B
and C about equal, positions off by ~ 0.5”
–! L2: best reduced '2 = 74, image A is ~ 1.2” displaced
•! Conclude that the lensing hypothesis is unlikely
What about the lensing galaxy? Our “best” lensing model L2 predicts a massive and
luminous lens galaxy, which is not seen, even if placed
in an optimal position:
Putative
lens
Putative
lens
A B
C
Observed L2: z lens = 0.5 L2: z lens = 1.4
K lens > 24 mag K lens = 18.5 mag K lens = 17.1 mag
Flux Ratios of the QSO Spectra
Spectrum Differences •! Component C has a bluer UV continuum, but redder optical to
IR colors:
•! 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:
"VAB = 280 ± 160 km/s, "VBC = 100 ± 400 km/s
•! While the optical and IR flux ratio is A/B = 25 ± 3, but in X-rays
it is A/B = 5.3 ± 1.8 (from ChaMP; Kim et al. 2006)
A B C
(R-K) 2.49 ± 0.03 2.27 ± 0.03 3.23 ± 0.21
(J-K) 1.13 ± 0.03 0.85 ± 0.03 1.87 ± 0.13
(Due to a
contamination by the host
galaxy?)
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)
1
A
B
C
4
3
8
2
9
D?
R band (VLT)
MCS deconvolution
3 arcsec Disturbed host galaxy?
QQQ 1429-008 : first tight triplet of quasars
Djorgovski et al. (2007) "(A,B) = 4.2" z = 2.076
QQQ 1429-008 : first tight triplet of quasars
Djorgovski et al. (2007) "(A,B) = 4.2" z = 2.076
Conclusion about LBQS 1429-008
•! 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/0701155
3 directions: - to the lens
- to the source
- to the image
3 angles: - ! " #
3 plans: - of the source $
- of the image %
- of the observer
3 distances: - Ds Dd Dds
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 :
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 :
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 + ( , ).
SRbbc
MGdz
c
242
22==!"=
#$!"
%
!
Theoretical bases
i
ii
iii
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 Dd , Ds and Dds are
defined in such a way that the relation is true
in the space-time of GR : such distances are
called “angular-diameter distances”.
(in general)
with
dssdDDD !"
22
0
0
0 )1)(1(
))(1(2),(
ji
jiji
i
j
jizz
GGGG
H
czzD
++!
""!"==
#
$
2/1
0 )1(iizG !+=
Einstein radius in the case of a lens with axial symmetry
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 :
Einstein radius
!
!
" =!
# $! % (!
# ) & "(#) = # $Dds
DdDs
4GM(#)
c2#
!
"E
=4GM("
E)
c2
Dds
DdDs
#
$ %
&
' (
1/ 2
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:
A galaxy as a lens (Zwicky’s optimism)
of masse M # 10 11 M! at D # 1 Gpc:
2/12/1
109000.0
!
""#
$%%&
'""#
$%%&
'((=
Kpc
D
M
M
sol
E)
2/12/1
11110
9.0
!
""#
$%%&
'""#
$%%&
'((=
Gpc
D
M
M
sol
E)
B1938+666
HST-NICMOS
zsource = ??
zlentille = 0.881
King et al. 1998, MNRAS, 295, L41
Full Einstein ring
in the IR
(diameter # 1")
MG 0414+0534
HST-WFPC2 B
A2
A1 C
G diameter # 2.12"
zsource = 2.64
zlentille = 0.96
Courbin et al. 1999
HST-ACS image of RXJ 1131-1231!
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!
Sluse et al. (2006)!
Abell 2218 HST WFPC2 zamas = 0.175 zsources ~ 0.7-5.6
Kneib et al., 1996, ApJ, 471, 643 -amas = 1370 ± 140 km s-1
235 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
•! MICRO: one single image of the source, with
only its luminosity strongly perturbed
QSO 2237+0305: La Croix d’Einstein
HST-WFPC2
"(A,B)=1.7"
zsource = 1.69
zlentille = 0.04 A
B C
D
galaxie . macro lentille
étoiles . micro lentilles
QSO 2237+0305: La Croix d’Einstein
Adam et al., 1989, A&A, 208, L15
z = 1.69
slight complication from microlensing
QSO 2237+0305: 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 = 1.69.
Moyen très direct de mesurer la taille d’un QSO dans le visible
C B
D A
microlensing events
Einstein Cross ESO-VLT June 2006
Usefulness of gravitational lenses via microlensing
•! 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
•! 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, con-
fined by their own mean gravitational potential, with
spherical symmetry :
equation of state
thermal equilibrium
hydrostatic equilibrium 2
2
)(
r
drrMGg
dp
kTm
m
Tkp
v
=
=
=
!
"
!
A galaxy acting as a lens: Isothermal sphere with central singularity (SIS)
A simple solution : SIS
surface density
deflection angle
Multiple images only if the source verifies : " < #E
Solutions of the lens equation : #± = " ± #E
2
2 1
2)(
rGr
v
!
"# =
!
"!
1
2)(
2
G
v=#
2
12
2
)220(4.14
!""==
kmsc
vv##
$%!
A galaxy acting as a lens: Isothermal sphere with central core (CIS)
A simple solution : CIS
surface density
22
2 1
2)(
c
v
rrGr
+=
!
"#
22
2 1
2)(
c
v
rG +=!
"
#"
sc
dsdv
Dr
DD
cD
2
2
4!
"#
0
2
0
00
11
!
!"!
#++= D
defines the number of images
lens equation
A galaxy acting as a lens: Isothermal sphere with central core (CIS)
0
2/12
000 /]1)1[( !!!" #+#= D
multiple
images
if D > 2
critical lines and
positions of the images
(lens plane)
caustics and
position of the source
(source plane)
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 inver-
ted, 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
d"S
= det(#!
$
#!
% )
&1
Adet
1=µ
d'I+
d'I- d'S
QSO HE 1104-1805 ESO-MPI 2.2-m IRAC J Courbin et al., 1998, ApJ, 330, 57 "(A,B)=3.19" zsource = 2.32 zlens = 0.73
Observations 0.7" After deconvolution 0.3"
The deconvolution provides an essential step
•
•
• • • •
•
• • •
•
• • •
•
•
•
•
critical lines caustics
HE1104-1805
H1413+117
PG1115+080
B1422+231
The local
properties of
the application
source plane – lens plane are described
by its jacobian
matrix :
A . &" /&#
The locus
of a point
where A cannot be
locally
inverted,
zero jacobian:
critical lines
and caustics.
movie
The Hubble constant and
the age of the Universe
http://cfa-www.harvard.edu/~huchra
Evolution of the Hubble constant Ho with time !
http://cfa-www.harvard.edu/~huchra
Evolution of the Hubble constant H0 with time !
Efstathiou, 2003: H0 between 37 and 72
WMAP data do not independantly constrain H0
(Spergel et al. 2003, 2006)
Data from WMAP Spergel et al. 2003
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
Time delay between two different
light paths with different lengths
* *
*
*
Intrinsic QSO light variations * time delay "/
obs
Time delay the travel time of a photon (Refsdal 1964, 1966)
•! The geometric term tgeom represents the time delay induced by the longer light path followed by the deflected photons.
•! The gravitational term tgrav 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 "/ * H0
!
t(!
" ) =(1+ zd )
c
DdDs
Dds
1
2
!
" #!
$ ( )2
#%(!
" )&
' ( )
* + = tgeom + tgrav
Measure of the time delay in radio
QSO 0957+561 Haarsma et al., 1997, ApJ, 479, 102
Visible: "/ = 417 ± 3 days
H0 via QSO 0957+561
model: redshifts, positions, magnitudes, mass profile
Observations:
-v (lens) = 279 ± 12 km s-1
"/BA = 417 ± 3 days
!
H0 = 67 ± 8 km s-1 Mpc-1
Falco et al. 1997, ApJ, 484, 70
!
H0
= 98"11+12 # v
330km s"1
$
% &
'
( )
2
1.1yr
*+BA
$
% &
'
( ) km s
"1Mpc
"1
H0 via photometric monitoring for QSO RX 0911+05
•! 17
Burud et al., 2003
"/AB = 146 days
H0 = 74 ± 9 km s-1 Mpc-1
H0 via photometric monitoring for QSO RX 0911+05
•! 17
"/AB = 146 days
H0 = 74 ± 9 km s-1 Mpc-1
Burud et al., 2003
intrinsic luminosity fluctuations
! time delay measurement
! Hubble constant determination
!
age of the Universe
The Hubble constant from quasar time delays!
10 gravitational lenses * H0 = 61 ± 7 km s-1 Mpc-1
H0 = 72 ± 8 km s-1 Mpc-1
H0 = 61 ± 7 km s-1 Mpc-1
Goal: production of 20 time delays over the next few years
COSMOGRAIL COSmological MOnitoring of GRAvItational Lenses
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
COSMOGRAIL
COSmological Monitoring GRAvitatIonal Lenses
currently, 22 quasars observed as frequently as possible
Observations
La Palma Spain
Paranal La
Silla Cerro
Tololo Chili
Maidanak
Ouzbekistan Keck
Gemini
Hawaii
Himalayan
Chandra
Telescope India
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 !
Eigenbrod et al. 2006b, A&A 451, 759!
1.5 arcsec!
COSMOGRAIL : gravitational lens and time delay!
SDSS J1650+4251!
Image A!
Image B!
Vuissoz et al. 2006a, A&A, submitted, see astro-ph/0606317
Image A!
Image B!
Vuissoz et al. 2007, A&A, 464, 845!H0 = 52 ± 4 km s-1 Mpc-1
COSMOGRAIL : gravitational lens and time delay!
SDSS J1650+4251!QSO RXJ 1131-123
Claeskens et al. 2006 A&A 451 865!
Sluse et al. 2006 A&A 449 539
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!
VLT spectroscopy:!
- lens redshift!
- chromatic microlensing!
HST-ACS image of RXJ 1131-1231 (Sluse et al. 2006)!
HE 0435-1223
Lens with 4 images, zs = 1.69, zl = 0.45, separation = 2.6”
one clear Einstein ring connecting all four images
about 10 galaxies within 40”
HST IR images NIC 2
HE 0435-1223 5 seasons with Euler+Mercator+Maidanak (01/04-02/08) 1pt / 5j
+ measurements 2 seasons from SMARTS (Kochanek et al. 2006) HE 0435-1223
5 seasons with Euler+Mercator+Maidanak (01/04-02/08) 1pt / 5j
+ measurements 2 seasons from SMARTS (Kochanek et al. 2006)
Status in 2010 : The Hubble constant from quasar time delays!
18 time delays * H0 = 63.4 ± 8.4 km s-1 Mpc-1
HST KP : H0 = 74.2 ± 3.6 km s-1 Mpc-1
Lensing : H0 = 63.4 ± 8.4 km s-1 Mpc-1
Conclusions
•! Time delays are not so cheap :
- 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
•! H0 0 63.4 ± 8.4 km s-1 Mpc-1
•! If lenses are on average isothermal, then H0 0 72 ± 6 km s-1 Mpc-1
~ 15 more time delays in hand,
however, slow careful interpretation
“You may delay, but time will not.”
Benjamin Franklin
1706 - 1790
Convergence and shear
The local properties of the application source plane ! lens plane are described by its jacobian matrix: A . &" /&#
With the convergence 1 and the shear 2 :
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 2 and orientation 3.
!!"
#$$%
&
''!!"
#$$%
&'=
((
(()*
2cos2sin
2sin2cos
10
01)1(A
*
Field of deformation
of background galaxies
without deformation with deformation
Abell 1689 HST ACS (2003)
zamas = 0.182
(a= 1848 ± 166 km s-1
Deep HST image
tint = 13.2 hours
Abell 1689 HST ACS
Abell 1689 HST ACS
Abell 1689 HST ACS (2003)
zamas = 0.182
(a= 1848 ± 166 km s-1
Deep HST image
tint = 13.2 heures
Thousands of mirages in this image !!!
z = 3.04
z = 3.04
Shear 2
as a function of
the convergence 1
weak lensing see lectures by P. Schneider
Seitz & Schneider,
1997, A&A, 318, 687
Reconstruction of the mass distribution
via the gravitational distortions
image colombi IAP
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 2007
Based on Cosmos data
Sarah Bridle Great08
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
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 H0
- 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