R' Ben Metcalf

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Small-scale Structure and Strongly Lensed Quasars
R. Ben Metcalf Max Planck Institute for
Astrophysics UC Irvine (March 24, 2007)
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Outline

• - substructure problem (or prediction)
• constraints on small-scale substructure from the
  
• data
• gravitational lenses from cosmological
• simulations

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Quasar Lensing with Substructure
Small halos are very weak lenses by themselves.
But The effects of small halos on lensing are
greatly enhanced if they are embedded in a
larger strong lens. This makes it possible to
detect even a very small amount of substructure.
perturbation in surface density
change in magnification
host lens magnification
surface density
Magnification is more sensitive to small scale
mass distribution.
host lens galaxy
substructures
QSO
Metcalf Madau, 2001
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PG 1115080
Q22370305
B 1422231
B 2045265
XRJ 0911.40551
H 1413117
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Modeling Gravitational Lenses
The lens models are inevitably degenerate. The
lens is decomposed into normal modes. Using the
image positions and the position of the lens
center, the modes and the space of degenerate
lenses in mode-space can be found through a
system of linear equations. Moving in the
degenerate region of mode-space a model can be
found that is as much like an idealized model of
a galaxy halo as possible. For example the
Most Singular Isothermal Ellipsoidal model (MSIE)
that fits the positions perfectly.
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flux anomalies in radio relative to the MSIE
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classification of 4-image lens configurations
Einstein Cross configuration
fold caustic configuration
long axis cusp caustic configuration
short axis cusp caustic configuration
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Cusp Caustic Lenses
In the case of a cusp caustic the lens
configuration the quantity R (?1 ?2 ?3)/
(?1 ?2 ?3) ? 0 as the source approaches
the cusp for any lens.
XRJ 0911.40551
Observed Cusp Caustic Lenses
The cusp caustic relation is violated in every
known case. Optical IR continuum ratios
could be effected by microlensing by ordinary
stars in the lens galaxies.
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Fold Caustic Lenses
In the case of a fold caustic configuration the
ratio of the close pair of images should be close
to 1.0.
XRJ 0911.40551
Observed Fold Caustic Lenses
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Modeling Gravitational Lenses Measuring
Substructure
Monte Carlo Markov Chain calculations are
preformed where the host substructure lens
model is adjusted randomly to map out the
likelihood function the substructure mass and
number density. The lens is modeled by
decomposing it into normal modes and finding the
degenerate set of models. A smoothness criterion
consistent with observed galaxies is then
imposed. At least 20,000 simulations per lens
for each parameter set (Msub, fsub fraction
of mass in substructure)
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Simulations of Lensing by Substructure
For a finite size source the magnification
is proportional to the size of the image .
For a point source the magnification
can be calculated directly once
the images position is found.

The goal is to solve the lensing equation
source position
sum over substructures
image position
deflection caused by host galaxy
With random distribution of substructures added
to a host lens.
A large dynamical range is required source
sizes from 0.1 to 10 3 pc while the strong
lensing region is 104 pc
mass of lens
1012-13 Msun and the smallest substructures
are 104 Msun or smaller Use an adaptive grid
refinement technique which tracks the image
position as it shrinks the grid region and
increases the number of cells until it has the
required resolution to determine the area of the
image.
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B0712472 m107 Msun
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B2045265 m107 Msun
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PG1115080 m108 Msun
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substructure mass
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CDM Substructure Predictions
Improved resolution has resulted in more
substructure in dark matter halos.
Diemand, Kuhlen Madau (2007) 100 million
particles
dN
Numerical effects could be suppressing
substructure. Baryons could increase it or
destroy more of it.
? M 2
Mass function of substructures
dM
Diemand, Kuhlen Madau 2007
M gt 4x106 Msun 0.3 of surface density at
10 kpc
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Likelihood function for fraction of surface
density in substructure
fraction of surface density in substructure
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Direct simulations of strong lenses
In making the previous constraints the internal
structure of the substructures where modeled
based on extrapolations and analytic
approximations for tidal stripping and
heating. Can cosmological simulations reproduce
the lensing data from first principles? Cosmolo
gical Simulation Deimand, Kauhlen Madau
(2007) The baryons are an essential ingredient
in reproducing a realistic gravitational
lens. Take N-body simulation particle
mass 1.0x105 Msun 108
particles Grow an artificial galaxy inside the
halo to allow the dark matter halo to relax
around it 5.0x1011 Msun Ray
tracing Smooth Particle Lensing (SPL) code with
SPH-like adaptive smoothing and deflection solver
with a 2D tree algorithm Adaptive sampling of
the image plane collaborators Adam Amara ,
J. Deimand, P. Madau, D. Aubert on previous
simulations TJ Cox J. Ostriker
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simulations of gravitational lenses
magnification
RBM, Amara, Diemond Madau
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simulations of gravitational lenses
magnification
radial caustic
Tangential critical curve
RBM, Amara, Diemond Madau
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simulations of gravitational lenses
magnification
Tangential caustic
Radial critical curve
2 kpc
RBM, Amara, Diemond Madau
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2D histograms of Rcusp
90
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Summery
The strong lensing flux ratio anomalies indicate
that small-scales structure makes up between
0.25 and 3 of the surface density at projected
radii of 10 kpc. By the one indicator
studied thus far, substructure in the highest
resolution cosmological simulations are enough
to account for the observed lensing
anomalies. More data is needed and expected.
Future large scale surveys (LSST, PanSTARS,
DUNE, etc.) are expected to find thousands of
multiply imaged quasars and AGN. Follow up
observations in radio and/or mid-IR is needed.
Other methods include strongly lensed radio
jets and comparing magnification ratios from
different emission regions.
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2D histograms of Rcusp
The observed values of Rcusp were clearly not
drawn from the same distribution.
Opening angle of image triplet
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Conclusions
The monochromatic flux ratio anomalies indicate
that small-scales structure makes up between
0.25 and 3 of the surface density at projected
radii of 10 kpc. This is believed to be in
rough agreement with ?CDM. The highest
resolution simulations The indicators of flux
ratio anomalies are robust in simulated
galaxies. More data is needed in the radio or
mid-infrared where the QSO emission region is
too large to be microlensed by stars.
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Simulated Strong Gravitational Lenses
Can N-body and SPH simulations reproduce the
lensing data? The baryons are an essential
ingredient in reproducing a realistic
gravitational lens. We use Moore et al. (1999)s
N-body simulation of a galactic halo.
particle mass 1.68x106 Msun force
resolution is 0.5 kpc 106
particles Implant an artificial galaxy -
both an elliptical and a disk bulge, 50,000
particles Let system relax for 200
Myr collaborators Adam Amara (CEA Saclay),
TJ Cox (Harvard) J. Ostriker
(Princeton/Cambridge)
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Cusp caustic relation as a function source
position
Rcusp (?1 ?2 ?3)/ (?1 ?2 ?3)
In the case of a cusp caustic the lens
configuration, Rcusp ? 0 for a smooth lens.
no smoothing
smoothed at 0.5 kpc
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2D histograms of Rcusp
no smoothing
smoothed at 0.5 kpc
Opening angle of image triplet
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PG1115080 m107 Msun
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Quasar Lensing with Small-Scale Structure
Small halos are very weak lenses by themselves.
But The effects of small halos on lensing are
greatly enhanced if they are embedded in a
larger strong lens. This makes it possible to
detect even a very small amount of substructure.
The magnification is strongly affected near the
critical lines where the primary lens
magnification is large.
perturbation in surface density
change in magnification
critical surface density
host lens magnification
The image magnifications are affected without
substantial changes in the image positions.
Magnification is more sensitive to small scale
mass distribution.
host lens galaxy
QSO
Metcalf Madau, 2001
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Intergalactic Small Scale Structure
It was believed that the halos and galaxies
outside of the primary lens would not contribute
enough to the lensing to account for the observed
magnification anomalies. This conclusion was
based on an analytic cross section type
calculation (Chen, Kravtsov Keeton 2003) where
only one intergalactic halo is included. Numerica
l simulations have shown that in fact
intergalactic dark matter halos could account for
all of the monochromatic magnification ratio
anomalies.
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Importance of Intergalactic Structure
standard deviation in the convergence ( surface
density) of the universe
perturbation to magnification ?? ?2 ??
Mmax 109 , 1010 , 1011 concentration
co M? /(1z) NFW profile
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Importance of Intergalactic Structure
perturbations to the deflection angle
rms deflection perturbation in milliarcseconds
Image separation
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Differences from other lensing work
- Simulate whole lens at once so that the host
lens model and the substructure are accounted for
in a self consistent way. - More general host
lens model than a simple non-Singular Isothermal
Ellipsoid (SIE). - Use only the close pairs of
images. This is more conservative and less
model dependent. - The substructures have NFW
profiles instead of SIS. - Finite sized source
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under abundance of dwarf galaxies in the local
group of galaxies
Moore, et al. 99
results of simulations
observed dwarf galaxies in the local group of
galaxies
circular velocity
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Cusp caustic lens Q1422231 with only
extragalactic substructures
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Cusp caustic lens Q2045265 with only
extragalactic substructures
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caustic structure for several realizations of the
noise
double image region
quadruple image region
swallow tails
second critical curve
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B0712472 m108 Msun
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Likelihood constraints using ALL flux ratios

• 10 of mass in substructure !!
• But
• there is no constraint on the size scale of the
  discrepancies large scale asymmetry in
  galaxy/halo or small scale structure?