Cluster Strong LensingCluster Strong Lensing

Neal Dalal

IAS

Cluster Strong LensingCluster Strong Lensing

• Images of background galaxies strongly distorted by potential of foreground massive cluster

• Typically 2-3 images merged together into “giant arcs”

• Canonical giant arcs have l/w > 10

• Usually azimuthally oriented but radial arcs are also observed

Lensing surveysLensing surveys

Survey Redshifts Area (deg2) Depth Observed

EMSS 0.15 < z < 0.6 ~ 360 V < 22 8

LCDCS 0.5 < z < 0.7 69 R < 21.5 2

RCS z < 0.6

z > 0.6

90

90

R < 24

R < 24

0

4

Comparison of Previous Arc Surveys

Ongoing and future surveys (e.g. SDSS, MACS, RCS-2, CFHTLS, DES) increase area and number of detected arcs by many orders of magnitude!

SDSS ArcsSDSS ArcsSDSS ArcsSDSS Arcs

What good are arcs for What good are arcs for cosmology?cosmology?

What good are arcs for What good are arcs for cosmology?cosmology?

1. Study properties of clusters

• Calibrate mass-observable relations

• Measure DM properties (e.g. radial profile, triaxiality, etc.)

2. Cosmological parameters

• Statistics

• Geometrical measure

modelling of individual systemsmodelling of individual systems

Abell 1689 (Broadhurst et al. 2004)

By fitting 100’s of lensed images, can reconstruct non-parametric mass model

Strong lens selectionStrong lens selection

Strong lensing can give a precise determination of cluster mass profile. But which clusters are selected with a lens-selected sample?

Related: which cluster properties are important in determining lensing cross-section?

Ray Tracing SimulationsRay Tracing Simulations

• Ran 10243 cosmological N-body simulation in 320 h-1 Mpc box

• Compute surface density and ray-trace from source plane to image plane (~14000 ray-traces for zl=0.4, zs=1)

Lens Plane

Massive Cluster

• Identify massive cluster halos, measure structural properties (e.g. ~900 clusters at z=0.4)

Shallow density cusps imply:– SL cross section is a steep function of mass and concentration – Extreme sensitivity to fluctuations caused by substructure and halo triaxiality– Large spread in cross sections as a function of viewing angle and among clusters of

similar mass

Strong Lensing by CDM HalosStrong Lensing by CDM HalosStrong Lensing by CDM HalosStrong Lensing by CDM Halos

For NFW:

rcrit exponentially sensitive to small variations in

20”

rs rvirhi

/cr

it

Analog HalosAnalog HalosSpherical

No Substructure

Simulated

Triaxial

Analog HalosAnalog Halos

Hennawi et al. (2005) in prep

• Replace each halo with analog halo. Ray trace and compare number of arcs to original simulated clusters

• Substructure identified by FOF algorithm with b = 0.05

• Triaxiality boosts cross sections by factor 4-25 compared to spherical

• Analytical models under predict arc abundance by– up to 50 for spherical models

– up to 2 for triaxial models

• Halo Triaxiality much more important than projections of substructure onto small radii

Source plane: zs = 2.0; Lens Plane: zd = 0.41

N(>

) N

um

ber

of

Arc

s

10” 15” 20” 25” 30”

Real/No Subs 1.06 1.10 1.13 1.18 1.24

Real/Triaxial 1.31 1.40 1.53 1.74 2.04

Real/Spherical 4.76 5.09 6.43 11.2 51.7

Biases in Lensing Selected SamplesBiases in Lensing Selected SamplesWith a sample of well studied lensing clusters we can measure distributions of cluster properties. However lenses are biased with respect to . . . .

Mass Concentration

OrientationSubstructure

Mvir c/c(M)

Msub

M1/2 = 4.5 1014 [c/c(M)]1/2 = 1.18

[Msub]1/2 = 0.045

[Msub]1/2 = 0.041

|cos|

|cos|1/2 = 0.50|cos|1/2 = 0.67

q2 lower third q2 middle third q2 upper third

2-D vs. 3-D quantities2-D vs. 3-D quantitiesWe measure 2-D profile and infer 3-D parameters. Because of triaxiality and projection bias, our 3-D inferences are biased.

Can this explain the oddly high concentrations seen in detailed analyses of many lensing clusters (e.g. A1689, CL0024, RCS0224)?

Note cvir¼ 14

Broadhurst et al. (2004)

2-D vs. 3-D quantities2-D vs. 3-D quantities

Note that concentrations of 15-20 are very unlikely

How important are mergers?How important are mergers?

It has been claimed that mergers can enhance lensing cross section by 10£. Is this true?

most massive substructurevirial mass

mass in substructurevirial mass

Line-of-sight projectionsLine-of-sight projections

Multi-plane Single plane

Large-scale structure can significantly affect shear-selected cluster samples (Hennawi & Spergel 2005). Is this also the case for strong-lens selected clusters (e.g. Wambsganss et al. 2004)?

Giant Arc AbundanceGiant Arc AbundanceGiant Arc AbundanceGiant Arc Abundance

Survey Redshifts Area (deg2) Depth Observed Predicted

EMSS 0.15 < z < 0.6 ~ 360 V < 22 8 8.2

LCDCS 0.5 < z < 0.7 69 R < 21.5 2 1.2

RCS z < 0.6

z > 0.6

90

90

R < 24

R < 24

0

4

2

1

Dalal, Holder, & Hennawi (2004) based on GIF simulations

Comparison of Arc Surveys to Ray Trace Predictions

• EMSS: 8 of 38 clusters with LX > 2 1044 ergs/s show giant arcs.

• Extrapolating gives ~ 900 over full sky.

• Ray tracing sims + HDF galaxy counts predicts ~ 1000

• NO GIANT ARC PROBLEM!

– Previous claim of order of magnitude discrepancy incorrectly extrapolated EMSS and used lower source density

N(>

r) N

um

ber

of

Arc

s

r [arcsecs]

Solid: EMSS Dashed: Simulations

ConclusionsConclusions

• Cluster lensing is a powerful probe of the distribution of dark matter on ~ 100 kpc/h scales

• Shallow density cusps of CDM clusters imply SL cross sections are extremely sensitive to ellipticity/triaxiality of dark matter halos

• Abundance of giant arcs behind low-z clusters agrees with prediction for LCDM. Hint of an excess for high-z clusters (Gladders/RCS)

• Search for clusters lenses in SDSS Gpc3 volume will yield > 200 new giant arcs and ~ 8 new wide separation multiply image quasars

modelling of individual systems

modelling of individual systems

MS 2137-23 (Gavazzi et al. 2003)

Even with just 1 or 2 arcs, it is stillpossible to derive interesting interesting constraints with highresolution imaging!

3)1(/1 rrDM inner slope

Dalal & Keeton (2004)

1.093.0

Modelling individual systemsWith ground-based imaging, it is harder to match up images, making modeling more difficult. But systems with multiple arcs can still be useful:

Example 1: tangential arcs roughly measure enclosed mass : so can we use multiple arcs to measure M(r) and hence radial slope?

error in M(r)is O(e)

dashed: 30% ellipticity

solid: 15% ellipticity

RCS 0224-0002 (Gladders et al. 2002)super-concentrated (c

vir~15)?

15% ellipticity30% ellipticity

isothermalflat

nR

example 2: combining tangential & radial arcsfor spherical lenses: the ratio of radial critical line totangential critical line gives slope.

However, this is strongly affected by ellipticity

Cluster Lenses in the SDSSCluster Lenses in the SDSS

• SDSS quasar samples– Spectro: 50,000 quasars -- 4000 deg2

– Photo: 400,000 quasars -- 7000 deg2

• Search for companions around quasars with similar colors

• Follow up spectroscopy (ARC 3.5m) required because of fiber collisions

SDSS 2.5m ARC 3.5m

Jim Gunn

Multiply Imaged Quasars Giant Arcs

Apache Point Observatory

UH 2.2m

• SDSS cluster sample– Richness selected clusters out to

z < 0.6 -- 7000 deg2 or ~ Gpc3

– Photo-z’s good to within dz = 0.02• Deep imaging (g < 26) of richest clusters

on 4m class imagers• Arc redshifts from Magellan and MMT• HST imaging of lenses discovered?

WIYN 3.5m

SDSS ArcsSDSS Arcs

Extreme example of minoraxis cusp? Or instead, is BCG off-center?

Lin et al. (2005) in preparation

Counter Image? • Brightest arc (g ~ 22 ) = 11”

• Discovered by visual inspection of SDSS southern coadd data (r < 24)

• Magellan spectroscopy– BCG galaxy @ z = 0.65

– Arc A @ z = 1.14

• Preliminary models prefer the BCG to be off center?

WIYN gri composite - seeing ~ 0.6”

30”

SDSS ArcsSDSS Arcs

A

B30”

WIYN g + i composite - seeing ~ 1.2”

• Arcs at = 35” and = 12”

• Abell cluster @ z = 0.28. LX = 8.7 1044 (NORAS)

• Models prefer high ellipticities (q < 0.5) for inner slopes typical of CDM halos (n ~ 0.5)

Hennawi et al. (2005) in preparation

N(>

r) N

um

ber

of

Arc

sr [arcsecs]

Cosmology with Cluster LensesCosmology with Cluster Lenses Why is Cluster Strong Lensing interesting for Cosmology?

– Natural Gravitational Telescopes magnify high-z galaxies

– Measure Cosmological Parameters??

– Constrain distribution of dark matter in clusters on small scales where density is highest

For a giant arc with ~ 20”

YES: For wide separation arcs, all cluster lensing observables canbe predicted ab initio

NO: Need to simulate effects of cooling and star formation on dark matter. Ask A. Kravtsov?

Strong Lensing StatisticsStrong Lensing Statistics

Detailed Modeling of Individual Lenses– Measure structural parameters of cluster (concentration, ellipticity/triaxiality, inner

slope) for each cluster lens. Compare to analogous distributions in N-body simulations

Abundance– Count the number of lensed arcs (QSOs?) per deg2 as a function of angular separation and compare to

prediction from N-body sims

CONS

• Arcs identified by eye. Selection function very difficult to quantify (QSOs?)

• Uncertainty in cluster mass scale creeps in unless entire survey area is deeply imaged

PROS

• Simplest ‘one-point’ statistic

• Requires ground based imaging of most massive clusters

PROS• Isolates parameters of halos breaking

‘degeneracies’ which could produce the same abundance

• Does not require knowledge of selection function of arcs

CONS

• Requires multiple arcs. Imaging from space required to obtain tight constraints

• Even with multiple arcs degeneracies between model parameters complicates comparison to simulations