Cosmological Applications of Gravitational lensing

1
Strong Lensing Constraints on the Properties
of Cluster Galaxies
Liliya L.R. Williams (U Minnesota) Prasenjit Saha
(QMW, U London)
2
Strong Lensing of QSOs and galaxies

• Modeling of galaxies and clusters of galaxies
  that host multiple images
• of background QSOs and galaxies is used to
  obtain
• smooth mass distribution in galaxy cluster
  lenses
• redshift evolution of galaxy properties
• the value of the Hubble constant
• substructure in galaxy cluster lenses

using positions of multiply-imaged QSOs
or galaxies
using positions and relative fluxes of
QSO images (C. Kochanek, N. Dalal, C.
Keeton, B. Metcalf, M. Chiba, and others)
non-parametric or free-form mass modeling
(Williams Saha, this talk)
parametric mass modeling (P. Natarajan
et al., next talk)
3
The effect of substructure in the lens on the
positions of images
with a mass lump added 1 of galaxy mass
smooth elliptical lens
4
Mass Modeling of Systems with multiple images
Model inputs center of the lens
image positions quad QSO gives 8
constraints small obs. uncertainties
time delays between
images at most 3 constraints
flux ratios between images at most 3
constraints affected by tiny substructure Unkno
wns 2D lens mass distribution could be
simple and smooth, . or not
Parametric Mass Modeling lens described
by 5-10 parameters ---
lens mass density
profile slope, scale radius, ellipticity,

position angle, external shear, etc.
Advantages of constraints
from data of model parameters
Disadvantages forcing the lens to
conform to a predefined mass shape
observed
image pos. best fit image pos. gt observational
error
Non-parametric Modeling break up the lens
into 1000 independent mass pixels
lensing data
is used as fixed model constraints
of
constraints from data ltlt of model
parameters
use secondary constraints
Advantages modeling reproduces
observed image positions exactly
can be used
to uncover mass substructure
Disadvantages underconstrained problem even
with secondary constraints
end up with a
multitude of mass models
(use ensemble average
of many models)
Saha Williams (1997) Williams Saha (2000)
5
SDSS J10044112 galaxy cluster with 4 QSO images
Inada et al. (2003) - discovery paper
Oguri et al. (2004) - parametric
modeling z clust 0.68 z QSO 1.734 image sep.
13
!
6
Free-form mass modeling of SDSS J1004

• Fixed model constraints positions of 4 QSO
  images w.r.t. cluster center
• Secondary constraints
• external shear position angle 10 45 deg.
  (Oguri et al. 2004)
• -0.25 lt 2D density slope lt -3.0 (note
  isothermal slope -1)
• density gradient direction constraint
• must point within 8 or 45 deg.
  from radial

PixeLens
A prior
B prior
17.5kpc
Williams Saha (2004)
7
SDSS J1004 finding galaxies in the cluster
Residuals of the reconstructed cluster
mass distribution (i.e. circularly averaged
profile has been subtracted)
blue crosses galaxies NOT used for
modeling red dots QSO images model constraints
B prior
Williams Saha (2004)
in this reconstruction cluster galaxies have
M/L3
8
SDSS J1004 finding galaxies in the cluster
Residuals of the reconstructed cluster
mass distribution (i.e. circularly averaged
profile has been subtracted)
blue crosses galaxies NOT used for
modeling red dots QSO images model constraints
A prior
Williams Saha (2004)
in this reconstruction cluster galaxies have
M/L12
9
SDSS J1004- summary of results

B prior A prior
Density profile slope of cluster
-0.39 -1.25 Mass within
100 kpc, in Msun 5.3 x 1013
3.7 x 1o13 Mass per galaxy, in Msun
3.5 x 1010 1.5 x
1011 Percentage of mass in galaxies
2 9 Average M/L
of galaxies 3
12
compare Mass Sheet
Degeneracy and its non-exact relatives
10
Synthetic Tests
Actual 2D density slope of cluster -1 Actual
of mass in substructure 15
Recovered values -0.77 2.4
-1.08 6
-1.18 9.4
Conclusion recovery of the morphology of
substructure is good, but can be improved
upon Two main problems ? spurious features
? mass
sheet degeneracy
11
HE0230-2130galaxy lens with a superimposed
secondary galaxy
2nd galaxy (substructure)
z gal 0.5 (assumed) z QSO 2.162 image sep.
2 CASTLeS (Kochanek et al.)
12
HE0230-2130galaxy lens with a superimposed
secondary galaxy
Recovered values 2D density slope
-0.51
-1.04 Total mass (Msun)
5.3 x 10 11
4.3
x 10 11 2nd galaxy
7 of total
28 of total
13
HE 0230
14
Conclusions

• Free-form mass modeling of galaxy and cluster
  lenses
• is well suited for the recovery of substructure,
  mass fraction gt 1,
• especially if substructure is dark, or has
  spatially varying M/L ratios.
• In cluster SDSS J1004, galaxies within central
  300 kpc
• compriselt 10 of cluster mass, and have M/L lt15,
  consistent with
• baryonic matter only.
• Uncovering substructure around
  galaxies 2 methods
• ? Flux anomalies method, using parametric
  mass macro-models
• Statistical in nature, sensitive to the
  lower mass substructure,
• Applied to radio (not optical) QSO
  lenses, to minimize effect of microlensing
• ? Free-form method, using image positions
  only
• Produces maps of substructure sensitive
  to higher mass substructure
• Can be applied to QSO lenses detected at
  any wavelength
• The two methods are complementary