Keck NGAO Science:
Strong Gravitational Lensing
Phil Marshall and Tommaso Treu
September 2007
Outline
• Examples of strong lensing science:
➔ The dark and stellar mass of elliptical galaxies out
to, and beyond z = 1
➔ CDM substructure: imaging the mass
➔ Super-resolving high redshift galaxies – and their
velocity fields
• “Kinematic lensing” - what a well-resolved
multiply-imaged velocity field can do for you
• Why can we not do this now?
• Why will we need NGAO in the future?
• What will we need NGAO to provide?
The masses of elliptical galaxies
• SEDs – and K-band photometry in particular – gives
stellar mass
• Gravitational lensing measures total mass, independent of
dynamical assumptions
• Combining the two gives the dark matter fraction, and a
way of calibrating the masses of larger samples of nonlens galaxies
Measuring mass (profiles) with
strong lensing requires high resolution
imaging
The combination of gravitational
lensing with stellar dynamics is
extremely powerful
CDM substructure: imaging the mass
• Extended sources give giant arcs and Einstein rings
• The multiple nature of the images allows source structure to
be separated from lensing effect
• Small scale perturbing masses can be imaged via this effect
(eg Koopmans et al 2005)
108 Mo dark perturber is
detectable – with HST
ACS resolution imaging
K-band imaging gives:
•smoother lens and source
surface brightness
•stellar mass of CDM
satellites
Super-resolving high-redshift velocity fields
• Gravitational lenses typically provide an order of
magnitude magnification – independent of the lens mass
• Fainter, smaller, lower mass galaxies are made much more
visible – observe with an IFU
eg Swinbank et al 2006:
Galaxy-scale lenses are
more easily modelled (as
the source size is large
compared to the lens mass
fluctuations – and they are
MUCH more numerous.
Select your own cosmic
telescope!
Outline
• Strong lensing science:
➔ The dark and stellar mass of elliptical galaxies out
to, and beyond z = 1
➔ CDM substructure: imaging the mass
➔ Super-resolving high redshift galaxies – and their
velocity fields
• “Kinematic lensing” - what a well-resolved
multiply-imaged velocity field can do for you
• Why can we not do this now?
• Why will we need NGAO in the future?
• What will we need NGAO to provide?
Kinematic-lensing
• Traditional lensing exploits preservation of surface
brightness to construct a model of the potential of the
lens and the surface brightness of the source (e.g.
yesterday’s talk)
• Kinematic lensing exploits lensing achromaticity to:
– Improve the model of the lens potential
– Reconstruct and super-resolve the velocity field of a
magnified source
• It can be done with the emission lines of
background source - and therefore simplifies lens
subtraction
• Lens galaxy dynamics come for free – but ignore
this for now...
Lens System Modeling
Use parametric forms:
;m
SB SP
v SP
z
Lens mass
;s
;u
Source surface brightness
Source line of sight velocity
'Simplest' Example:
SIE lens mass:
Source surface brightness:
Source velocity profile: Vmax,
,
M,
r_0,
b/a,
r_e
i
Predict OSIRIS data cube,
optimise misfit between this and real data
PA,
i,
x,
PA,
y
x,
13 parameters
y,
Model source plane
plane
Model image
Model image plane
data
Simulated
Can we do it now, at Keck?
Sample: SLACS
Example. I: velocity field
Test KLens on a SLACS lens:
• Using the ACS image, model the lens using surface
brightness only.
• Add 'reasonable' velocity field parameters and generate
synthetic OSIRIS image and velocity data.
• Reconstruct the source and estimate error on parameters.
• Unlensed
• Unlensed w/ LGSAO
• Lensed
• Lensed w/ LGSAO
• Assuming: 9500s exptime; line flux 5e-16 cgs; Z-band;
Strehl 0.2
OSIRIS
OSIRIS+lensing
OSIRIS+LGSAO
OSIRIS+LGSAO+lensing
Source rotation velocity: 130-170 km/s
OSIRIS
OSIRIS+LGSAO
160
140
OSIRIS+lensing
0.04
0.08
OSIRIS+LGSAO+lensing
Velocity scale radius: 0.04 - 0.08 arcsec
Example. II: lens model
Simulated lens from SLACS:
● Using the ACS image, model the lens using surface
brightness only.
● Add 'reasonable' velocity field parameters and generate
synthetic OSIRIS image and velocity data.
● Reconstruct the lens parameters for
● LGSAO+OSIRIS emission line imaging
● LGSAO+OSIRIS emission lines imaging + velocity
field
● Assuming: 10800s exptime; line flux 5e-16 cgs; Z-band;
Strehl 0.15
Vmax
Clean lens
subtraction!


Does it work in practice?
We don’t know yet...
• Half night allocated June 2006:
• partially cloudy. 1.5 hours in three
pointings (effectively 1800s) in Z-band.
No detection
• One night allocated September 2006:
• completely lost to wavefront sensor
failure
• With current technology is hard!
• 2007: system more stable, targets
improved: Richard (Caltech) has data...
Improvements wish list:
• Higher redshift targets. In Z, OSIRIS field of view is too
small, need mosaicing with loss of time:
• Much better at longer wavelengths. 3.2”x6.4” or
4.8”x6.4” is larger than lens (typically <3”). Dither on
targets. Larger field is more efficient
• Brighter targets:
• With full SLACS (88 vs 23 last year) or SL2S we can
find even brighter emission lines
• Higher Strehl ratios:
reduce exposure times and thus make it practical to
collect sizeable samples.
(Beginning to sound like NGAO)
KLens: Summary
• AO + integral field spectroscopy +
kinematic lensing =
– Virgo-like resolution at cosmological distances
– Velocity fields/masses (Tully Fisher..)
– Improved mass models
• Source/lens decomposition in emission line image
• Currently hard with SLACS sample and
present capabilities/time allocations. Things
will improve with ongoing lens surveys
• With NGAO this will work very well!
Outline
• Strong lensing science:
➔ The dark and stellar mass of elliptical galaxies out
to, and beyond z = 1
➔ CDM substructure: imaging the mass
➔ Super-resolving high redshift galaxies – and their
velocity fields
• “Kinematic lensing” - what a well-resolved
multiply-imaged velocity field can do for you
• Why can we not do this now?
• Why will we need NGAO in the future?
• What will we need NGAO to provide?
Feeder surveys
Current samples (eg based on SDSS) are limited to z~0.2
and contain ~100 systems
In the NGAO era, the lens sample will be an order of
magnitude larger, and extend to higher redshift (z>1) –
interesting subsamples can be selected and exploited
SL2S (2005-) ongoing imaging survey based on CFHTLS,
finding ~100 new lenses at z~0.5-1.0
DES (2009-2014) will find a few hundred lenses
PanSTARRS-1 (2008-2012) will find ~few 1000 lenses
SDSS-III (2010?) ~ SLACS x 10 at higher z?
LSST (2014-2024?) would find ~10,000 lenses
SNAP (2019-2021?) would find ~20,000 lenses
Dune (2019-2021?) would find ~few 100,000 lenses
Ground vs. Space – what can JWST do?
NGAO out-performs HST:
We expect JWST
to have resolution
no better than HST
bluer than 2 microns
- but background is lower
Detailed simulations will
show up the differences.
NGAO has planned
multi-object capability...
Multiplexing over a 3' field of regard
Lenses are rare – but a Multiplex IFU:
•would speed up observation (simultaneous background
monitoring)
•and allow piggy-backing on the high-z program (their
targets are more common)
•and enable cluster lensing science (larger collecting area
cosmic telescopes – but that's a whole other talk!)
Summary: NGAO requirements
As for the high-z galaxy program,
(eg high strehl imaging, sufficient spectral resolution to measure velocities
to 20km/s, low background, large fraction of sky accessible etc etc)
but with a few additions:
•> 4” IFU field of view (lenses magnify galaxies, such
that ~all systems are 2-3” in diameter)
•bluer filters broaden the range of accessible redshifts,
and help in SED analysis of lensed sources
•z, Y bands also enable lens galaxy absorption line
dynamical mass estimates at z~1
Extra slides
Strong Lensing Basics. I:
• Strong lensing can be seen
as a mapping from the
source plane (what would be
seen without a lens) to the
image plane (what is
actually seen)
• The transformation is the so
called lens-equation:
• =+()
For azimuthal symmetry
Strong Lensing Basics. II:
• Deflection angle  is
gradient of gravitational
potential: lensing
measures mass.
• Lensing preserves
surface brightness:
magnification is given
by the Jacobian of the
transformation
For azimuthal symmetry
Strong Lensing Basics. III:
caustics critical
lines
0047-281
Koopmans & Treu 2003
Curves where the transformation is singular are called caustics and
critical lines. They correspond to infinite magnification. Sources get
SL2S
• Ground based selected
candidates (from CFHT-LS)
• AO-NIRC2 to confirm and
exploit scientifically
(hopefully in 2007B)
• Lens redshift z~0.7
• Source redshift z~1.4 (Ha in
H band!)
Generating 'Ideal' Image Plane
Pixellate image plane: {i}
For each , use lens equation to calculate .
Map conserved quantities:
SB
IP
IP
vz
i
SP
;m, s
i
SB
; m, u
i
vz
i
SP
i
;m ; s
; m ;u
Lens Equation > 
SB, vz <- Source model <-
(i
)
Constructing 2
Need to compare:
observed image plane with model source plane
Recall lens equation:
;m
“Forward”:
Given true position, , find observed position(s), .
*Difficult!
“Backward”:
Given observed position, , find true position, .
*Easy!
... but it is not straightforward to map pixellated data
onto source plane.
Creating 'Model' Image Plane
Convolve surface brightness with instrumental PSF.
Using exposure time, zero point, convert SB to counts.
N
model
i
;m, s
Perform weighted convolution for line of sight velocity.
Ignore points for which no velocity measurement is
possible.
model
vz
i
; m ,u
Finding Best Parameters
Finally, compute 2 for given parameters:
2
Nobs
m, s ,u
i
i
Nmodel
2
N
;m, s
i
i
2
vobs
z
i
vmodel
z
2
vz
;m,u
i
i
Minimize 2 over all free parameters.
This can be challenging since minimizing over many parameters.
(Recall, simple example has 13 parameters!)
Broyden-Fletcher-Goldfarb-Shanno method is efficient:
Gives set of best parameters:
{m , s ,u}
Also gives approximate covariance matrix at minimum.
2
MCMC Basics
Markov Chain Monte Carlo (MCMC) allows us to sample points
from an arbitrary probability distribution, P.
Given a probability distribution P(a) that we can evaluate for any a, create a 'chain' of
points using the following rules:
1.
From ai draw a new poisition a' from a proposal distribution, Q(a',a).
2.
If P' > Pi :
If P' < Pi :
ai+1=a'
ai+1=a'
with probability P'/Pi, otherwise ai+1=ai.
Results in {ai} sampled from true probability distribution, P.
Independent of starting point, a0, and proposal distribution, Q.
Need multiple chains to test for convergence:
variation within each chain = variation between chains
Efficient MCMC
MCMC is useful when dealing with parameter spaces with
many dimensions.
Likely that some parameters are degenerate.
(e.g. Vmax and r_0)
Sampling with fixed step sizes
along parameter axes is
inefficient.
Instead, can use steps given
by diagonalizing
covariance matrix.
The kinematics of Einstein Rings
Tommaso Treu, Phil Marshall and Laura Melling (UCSB)
Properties of lens mapping:
• Non-linear
• Preserves surface brightness
• Independent of frequency
(ACHROMATIC)
• Magnifies sources
SLACS: examples
See www.slacs.org and Bolton et al. 2006, 2007
Why do we care?
•
Lensing measure masses:
–
•
Exploiting lensing achromaticity improves knowledge of
gravitational potential of deflector
Lensing magnifies, hence “gravitational telescopes”:
–
The internal structure of distant galaxies can be study with a typical
factor of 10 improvement in sensitivity and spatial resolution