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Observables Flux ratios Multiwavelength Milli-images Grav. imaging Time delays Recap Theory Framework Local Long-range Local vs. total Total Complementarity Outlook A “Multimessenger” Approach to Substructure Lensing Chuck Keeton July 22, 2009
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A ``Multimessenger'' Approach to Substructure Lensingkiss.caltech.edu/workshops/dark_matter/presentations/keeton.pdf · I optical emission lines (Moustakas & Metcalf 2003, Metcalf

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Page 1: A ``Multimessenger'' Approach to Substructure Lensingkiss.caltech.edu/workshops/dark_matter/presentations/keeton.pdf · I optical emission lines (Moustakas & Metcalf 2003, Metcalf

Observables

Flux ratios

Multiwavelength

Milli-images

Grav. imaging

Time delays

Recap

Theory

Framework

Local

Long-range

Local vs. total

Total

Complementarity

Outlook

A “Multimessenger” Approach toSubstructure Lensing

Chuck Keeton

July 22, 2009

Page 2: A ``Multimessenger'' Approach to Substructure Lensingkiss.caltech.edu/workshops/dark_matter/presentations/keeton.pdf · I optical emission lines (Moustakas & Metcalf 2003, Metcalf

Observables

Flux ratios

Multiwavelength

Milli-images

Grav. imaging

Time delays

Recap

Theory

Framework

Local

Long-range

Local vs. total

Total

Complementarity

Outlook

Substructure lensing

Past.

I Mao & Schneider 1998: connect flux ratios and substructure

I Metcalf & Madau 2001, Chiba 2002: propose to test CDM

I Dalal & Kochanek 2002: constrain substructure mass fraction

Present/future.

I New observables.

I Can we learn more about substructure?

I Is there really a population of clumps?

I Can we constrain its: mass function? spatial distribution?redshift evolution?

I What does it reveal about dark matter?

Page 3: A ``Multimessenger'' Approach to Substructure Lensingkiss.caltech.edu/workshops/dark_matter/presentations/keeton.pdf · I optical emission lines (Moustakas & Metcalf 2003, Metcalf

Observables

Flux ratios

Multiwavelength

Milli-images

Grav. imaging

Time delays

Recap

Theory

Framework

Local

Long-range

Local vs. total

Total

Complementarity

Outlook

Flux ratio anomalies

without clump with clump

Flux ratio anomalies are hard to miss, and hard to misinterpret.(CRK, Gaudi & Petters 2003, 2005; Congdon & CRK 2005; Yoo et al. 2005, 2006)

Page 4: A ``Multimessenger'' Approach to Substructure Lensingkiss.caltech.edu/workshops/dark_matter/presentations/keeton.pdf · I optical emission lines (Moustakas & Metcalf 2003, Metcalf

Observables

Flux ratios

Multiwavelength

Milli-images

Grav. imaging

Time delays

Recap

Theory

Framework

Local

Long-range

Local vs. total

Total

Complementarity

Outlook

B1555+375

Marlow et al. (1999)

Smooth models generically predict A−B ≈ 0. (CRK, Gaudi & Petters 2005)

Page 5: A ``Multimessenger'' Approach to Substructure Lensingkiss.caltech.edu/workshops/dark_matter/presentations/keeton.pdf · I optical emission lines (Moustakas & Metcalf 2003, Metcalf

Observables

Flux ratios

Multiwavelength

Milli-images

Grav. imaging

Time delays

Recap

Theory

Framework

Local

Long-range

Local vs. total

Total

Complementarity

Outlook

B2045+265

Fassnacht et al. (1999)

Smooth models predict A−B + C ≈ 0. (CRK, Gaudi & Petters 2003)

Page 6: A ``Multimessenger'' Approach to Substructure Lensingkiss.caltech.edu/workshops/dark_matter/presentations/keeton.pdf · I optical emission lines (Moustakas & Metcalf 2003, Metcalf

Observables

Flux ratios

Multiwavelength

Milli-images

Grav. imaging

Time delays

Recap

Theory

Framework

Local

Long-range

Local vs. total

Total

Complementarity

Outlook

Flux ratios and substructure

Dalal & Kochanek (2002): constrain substructure mass fraction

0.001 0.01 0.1 1

Single-wavelength flux ratios reveal∫m

dN

dmdm

but say little about dN/dm itself.

Page 7: A ``Multimessenger'' Approach to Substructure Lensingkiss.caltech.edu/workshops/dark_matter/presentations/keeton.pdf · I optical emission lines (Moustakas & Metcalf 2003, Metcalf

Observables

Flux ratios

Multiwavelength

Milli-images

Grav. imaging

Time delays

Recap

Theory

Framework

Local

Long-range

Local vs. total

Total

Complementarity

Outlook

Finite source effects

Flux perturbation depends on size of subhalo relative to size ofsource. (Dobler & CRK 2006)

-2

-1

0

1

2

-2 -1 0 1 2

a = 1.2

-2

-1

0

1

2

-2 -1 0 1 2

a = 1.2

-2

-1

0

1

2

-2 -1 0 1 2

a = 1.2

-6

-4

-2

0

2

4

6

-6 -4 -2 0 2 4 6

a = 1.2

-6

-4

-2

0

2

4

6

-6 -4 -2 0 2 4 6

a = 1.2

-6

-4

-2

0

2

4

6

-6 -4 -2 0 2 4 6

a = 1.2

-6

-4

-2

0

2

4

6

-6 -4 -2 0 2 4 6

a = 1.2

Page 8: A ``Multimessenger'' Approach to Substructure Lensingkiss.caltech.edu/workshops/dark_matter/presentations/keeton.pdf · I optical emission lines (Moustakas & Metcalf 2003, Metcalf

Observables

Flux ratios

Multiwavelength

Milli-images

Grav. imaging

Time delays

Recap

Theory

Framework

Local

Long-range

Local vs. total

Total

Complementarity

Outlook

Finite source effects

Flux perturbation depends on size of subhalo relative to size ofsource. (Dobler & CRK 2006)

-2

-1

0

1

2

-2 -1 0 1 2

a = 0.8

-2

-1

0

1

2

-2 -1 0 1 2

a = 0.8

-2

-1

0

1

2

-2 -1 0 1 2

a = 0.8

-6

-4

-2

0

2

4

6

-6 -4 -2 0 2 4 6

a = 0.8

-6

-4

-2

0

2

4

6

-6 -4 -2 0 2 4 6

a = 0.8

-6

-4

-2

0

2

4

6

-6 -4 -2 0 2 4 6

a = 0.8

-6

-4

-2

0

2

4

6

-6 -4 -2 0 2 4 6

a = 0.8

Page 9: A ``Multimessenger'' Approach to Substructure Lensingkiss.caltech.edu/workshops/dark_matter/presentations/keeton.pdf · I optical emission lines (Moustakas & Metcalf 2003, Metcalf

Observables

Flux ratios

Multiwavelength

Milli-images

Grav. imaging

Time delays

Recap

Theory

Framework

Local

Long-range

Local vs. total

Total

Complementarity

Outlook

Finite source effects

Flux perturbation depends on size of subhalo relative to size ofsource. (Dobler & CRK 2006)

-2

-1

0

1

2

-2 -1 0 1 2

a = 0.4

-2

-1

0

1

2

-2 -1 0 1 2

a = 0.4

-2

-1

0

1

2

-2 -1 0 1 2

a = 0.4

-6

-4

-2

0

2

4

6

-6 -4 -2 0 2 4 6

a = 0.4

-6

-4

-2

0

2

4

6

-6 -4 -2 0 2 4 6

a = 0.4

-6

-4

-2

0

2

4

6

-6 -4 -2 0 2 4 6

a = 0.4

-6

-4

-2

0

2

4

6

-6 -4 -2 0 2 4 6

a = 0.4

Page 10: A ``Multimessenger'' Approach to Substructure Lensingkiss.caltech.edu/workshops/dark_matter/presentations/keeton.pdf · I optical emission lines (Moustakas & Metcalf 2003, Metcalf

Observables

Flux ratios

Multiwavelength

Milli-images

Grav. imaging

Time delays

Recap

Theory

Framework

Local

Long-range

Local vs. total

Total

Complementarity

Outlook

Finite source effects

Flux perturbation depends on size of subhalo relative to size ofsource. (Dobler & CRK 2006)

-2

-1

0

1

2

-2 -1 0 1 2

a = 0.2

-2

-1

0

1

2

-2 -1 0 1 2

a = 0.2

-2

-1

0

1

2

-2 -1 0 1 2

a = 0.2

-6

-4

-2

0

2

4

6

-6 -4 -2 0 2 4 6

a = 0.2

-6

-4

-2

0

2

4

6

-6 -4 -2 0 2 4 6

a = 0.2

-6

-4

-2

0

2

4

6

-6 -4 -2 0 2 4 6

a = 0.2

-6

-4

-2

0

2

4

6

-6 -4 -2 0 2 4 6

a = 0.2

Page 11: A ``Multimessenger'' Approach to Substructure Lensingkiss.caltech.edu/workshops/dark_matter/presentations/keeton.pdf · I optical emission lines (Moustakas & Metcalf 2003, Metcalf

Observables

Flux ratios

Multiwavelength

Milli-images

Grav. imaging

Time delays

Recap

Theory

Framework

Local

Long-range

Local vs. total

Total

Complementarity

Outlook

Finite source effects(Dobler & CRK 2006)

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

-2 -1.5 -1 -0.5 0 0.5 1 1.5 2-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

-2 -1.5 -1 -0.5 0 0.5 1 1.5 2-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

-2 -1.5 -1 -0.5 0 0.5 1 1.5 2 1

1.5

2

2.5

3

3.5

4

4.5

5

5.5

6

6.5

0.001 0.01 0.1 1 10

1

1.2

1.4

1.6

1.8

2

2.2

2.4

2.6

0.001 0.01 0.1 1 10 1.1

1.2

1.3

1.4

1.5

1.6

1.7

1.8

1.9

2

2.1

0.001 0.01 0.1 1 10

Page 12: A ``Multimessenger'' Approach to Substructure Lensingkiss.caltech.edu/workshops/dark_matter/presentations/keeton.pdf · I optical emission lines (Moustakas & Metcalf 2003, Metcalf

Observables

Flux ratios

Multiwavelength

Milli-images

Grav. imaging

Time delays

Recap

Theory

Framework

Local

Long-range

Local vs. total

Total

Complementarity

Outlook

Multiwavelength flux ratios

Heuristically, each wavelength probes substructure above somemass threshold:

δµ(λ) ∼∫ mhi

m(Rsrc(λ))

mdN

dmdm

Plus, useful “resonance” if Rein(m) ≈ Rsrc.

Many possibilities:

I radio

I mid-IR (Chiba et al. 2005, Poindexter et al. 2007, Minezaki et al. 2009, Fadely & CRK)

I optical emission lines (Moustakas & Metcalf 2003, Metcalf et al. 2004, CRK et al. 2006, Sluse et

al. 2007, Sugai et al. 2007, Eigenbrod et al. 2008)

I optical continuum

I X-ray (Blackburne et al. 2006, Pooley et al. 2006, 2007, 2009, Kochanek et al. 2007, Morgan et al. 2008,

Chartas et al. 2009, Dai et al. 2009)

Page 13: A ``Multimessenger'' Approach to Substructure Lensingkiss.caltech.edu/workshops/dark_matter/presentations/keeton.pdf · I optical emission lines (Moustakas & Metcalf 2003, Metcalf

Observables

Flux ratios

Multiwavelength

Milli-images

Grav. imaging

Time delays

Recap

Theory

Framework

Local

Long-range

Local vs. total

Total

Complementarity

Outlook

Mass “threshold”

Band corresponds to range of redshifts in current sample.

1 100 104 106 108M HMsunL

1017

1018

1019

1020

1021

Rein HcmL

Page 14: A ``Multimessenger'' Approach to Substructure Lensingkiss.caltech.edu/workshops/dark_matter/presentations/keeton.pdf · I optical emission lines (Moustakas & Metcalf 2003, Metcalf

Observables

Flux ratios

Multiwavelength

Milli-images

Grav. imaging

Time delays

Recap

Theory

Framework

Local

Long-range

Local vs. total

Total

Complementarity

Outlook

Milli-imagesMG 2016+112, Koopmans et al. (2002)

Center at RA 20 19 18.04171 DEC 11 27 11.3350

BOTH: 2016+112 IPOL 4984.990 MHZ 2016R3U804K.ICLN02.2PLot file version 2 created 01-NOV-2000 16:54:49

Grey scale flux range= 0.000 6.000 MilliJY/BEAMCont peak flux = 6.6350E-03 JY/BEAM Levs = 1.410E-04 * (-3, 3, 5, 10, 20)

Mill

iAR

C S

EC

MilliARC SEC100 50 0 -50 -100

50

40

30

20

10

0

-10

-20

-30

Center at RA 20 19 18.18469 DEC 11 27 14.5700

BOTH: 2016+112 IPOL 4984.990 MHZ 2016R3U804K.ICLN.2PLot file version 1 created 01-NOV-2000 17:02:38

Grey scale flux range= 0.000 6.000 MilliJY/BEAMCont peak flux = 6.0946E-03 JY/BEAM Levs = 1.410E-04 * (-3, 3, 5, 10, 20)

Mill

iAR

C S

EC

MilliARC SEC30 20 10 0 -10 -20 -30 -40

30

20

10

0

-10

-20

-30

-40

Center at RA 20 19 17.97967 DEC 11 27 13.0600

BOTH: 2016+112 IPOL 4984.990 MHZ 2016R3U804K.ICLN01.2PLot file version 1 created 01-NOV-2000 17:01:09

Grey scale flux range= 0.000 6.000 MilliJY/BEAMCont peak flux = 5.9581E-03 JY/BEAM Levs = 1.410E-04 * (-3, 3, 5, 10, 20)

Mill

iAR

C S

EC

MilliARC SEC40 30 20 10 0 -10 -20 -30

30

20

10

0

-10

-20

-30

-40

B2B1

C2

C13C12C11

A1A2

Page 15: A ``Multimessenger'' Approach to Substructure Lensingkiss.caltech.edu/workshops/dark_matter/presentations/keeton.pdf · I optical emission lines (Moustakas & Metcalf 2003, Metcalf

Observables

Flux ratios

Multiwavelength

Milli-images

Grav. imaging

Time delays

Recap

Theory

Framework

Local

Long-range

Local vs. total

Total

Complementarity

Outlook

Milli-imagesB0128+437, Biggs et al. (2004)

Page 16: A ``Multimessenger'' Approach to Substructure Lensingkiss.caltech.edu/workshops/dark_matter/presentations/keeton.pdf · I optical emission lines (Moustakas & Metcalf 2003, Metcalf

Observables

Flux ratios

Multiwavelength

Milli-images

Grav. imaging

Time delays

Recap

Theory

Framework

Local

Long-range

Local vs. total

Total

Complementarity

Outlook

Milli-imagesMG J0414+0534, Trotter et al. (2000)

Mill

iAR

C S

EC

MilliARC SEC200 150 100 50

500

480

460

440

420

400

380

360

340

320

Mill

iAR

C S

EC

MilliARC SEC-500 -550 -600 -650

2000

1950

1900

1850

Mill

iAR

C S

EC

MilliARC SEC100 50 0 -50 -100

100

50

0

-50

-100

Mill

iAR

C S

EC

MilliARC SEC-1850 -1900 -1950 -2000

400

350

300

250

200

p

q

s

r

s

r

qp

r

sp

q

sr

q

p

A2

A1

B

C

Page 17: A ``Multimessenger'' Approach to Substructure Lensingkiss.caltech.edu/workshops/dark_matter/presentations/keeton.pdf · I optical emission lines (Moustakas & Metcalf 2003, Metcalf

Observables

Flux ratios

Multiwavelength

Milli-images

Grav. imaging

Time delays

Recap

Theory

Framework

Local

Long-range

Local vs. total

Total

Complementarity

Outlook

Gravitational imaging

Vegetti & Koopmans (2009ab): clumps & 108M� visibly perturbEinstein ring images (a la SLACS)

(my illustration)

Page 18: A ``Multimessenger'' Approach to Substructure Lensingkiss.caltech.edu/workshops/dark_matter/presentations/keeton.pdf · I optical emission lines (Moustakas & Metcalf 2003, Metcalf

Observables

Flux ratios

Multiwavelength

Milli-images

Grav. imaging

Time delays

Recap

Theory

Framework

Local

Long-range

Local vs. total

Total

Complementarity

Outlook

Time delay millilensing

(CRK & Moustakas 2009)

Page 19: A ``Multimessenger'' Approach to Substructure Lensingkiss.caltech.edu/workshops/dark_matter/presentations/keeton.pdf · I optical emission lines (Moustakas & Metcalf 2003, Metcalf

Observables

Flux ratios

Multiwavelength

Milli-images

Grav. imaging

Time delays

Recap

Theory

Framework

Local

Long-range

Local vs. total

Total

Complementarity

Outlook

Time delay millilensing

(CRK & Moustakas 2009)

Page 20: A ``Multimessenger'' Approach to Substructure Lensingkiss.caltech.edu/workshops/dark_matter/presentations/keeton.pdf · I optical emission lines (Moustakas & Metcalf 2003, Metcalf

Observables

Flux ratios

Multiwavelength

Milli-images

Grav. imaging

Time delays

Recap

Theory

Framework

Local

Long-range

Local vs. total

Total

Complementarity

Outlook

Time delay millilensing

(CRK & Moustakas 2009)

Page 21: A ``Multimessenger'' Approach to Substructure Lensingkiss.caltech.edu/workshops/dark_matter/presentations/keeton.pdf · I optical emission lines (Moustakas & Metcalf 2003, Metcalf

Observables

Flux ratios

Multiwavelength

Milli-images

Grav. imaging

Time delays

Recap

Theory

Framework

Local

Long-range

Local vs. total

Total

Complementarity

Outlook

Time delay millilensing

(CRK & Moustakas 2009)

Page 22: A ``Multimessenger'' Approach to Substructure Lensingkiss.caltech.edu/workshops/dark_matter/presentations/keeton.pdf · I optical emission lines (Moustakas & Metcalf 2003, Metcalf

Observables

Flux ratios

Multiwavelength

Milli-images

Grav. imaging

Time delays

Recap

Theory

Framework

Local

Long-range

Local vs. total

Total

Complementarity

Outlook

Time delay millilensing

(CRK & Moustakas 2009)

Page 23: A ``Multimessenger'' Approach to Substructure Lensingkiss.caltech.edu/workshops/dark_matter/presentations/keeton.pdf · I optical emission lines (Moustakas & Metcalf 2003, Metcalf

Observables

Flux ratios

Multiwavelength

Milli-images

Grav. imaging

Time delays

Recap

Theory

Framework

Local

Long-range

Local vs. total

Total

Complementarity

Outlook

Random time delays

Page 24: A ``Multimessenger'' Approach to Substructure Lensingkiss.caltech.edu/workshops/dark_matter/presentations/keeton.pdf · I optical emission lines (Moustakas & Metcalf 2003, Metcalf

Observables

Flux ratios

Multiwavelength

Milli-images

Grav. imaging

Time delays

Recap

Theory

Framework

Local

Long-range

Local vs. total

Total

Complementarity

Outlook

Scalings

σt ∝

(fs

⟨m2⟩

〈m〉

)1/2

Page 25: A ``Multimessenger'' Approach to Substructure Lensingkiss.caltech.edu/workshops/dark_matter/presentations/keeton.pdf · I optical emission lines (Moustakas & Metcalf 2003, Metcalf

Observables

Flux ratios

Multiwavelength

Milli-images

Grav. imaging

Time delays

Recap

Theory

Framework

Local

Long-range

Local vs. total

Total

Complementarity

Outlook

RX J1131−1231Morgan et al. (2006): M2 (2.2± 1.6 d) M1 (9.6± 2.0 d) S1.

Smooth models predict M1 leads M2.

Page 26: A ``Multimessenger'' Approach to Substructure Lensingkiss.caltech.edu/workshops/dark_matter/presentations/keeton.pdf · I optical emission lines (Moustakas & Metcalf 2003, Metcalf

Observables

Flux ratios

Multiwavelength

Milli-images

Grav. imaging

Time delays

Recap

Theory

Framework

Local

Long-range

Local vs. total

Total

Complementarity

Outlook

RX J1131−1231Morgan et al. (2006): M2 (2.2± 1.6 d) M1 (9.6± 2.0 d) S1.

But substructure can reverse that ordering. (CRK & Moustakas 2009)

Page 27: A ``Multimessenger'' Approach to Substructure Lensingkiss.caltech.edu/workshops/dark_matter/presentations/keeton.pdf · I optical emission lines (Moustakas & Metcalf 2003, Metcalf

Observables

Flux ratios

Multiwavelength

Milli-images

Grav. imaging

Time delays

Recap

Theory

Framework

Local

Long-range

Local vs. total

Total

Complementarity

Outlook

Summary of observables

I radio flux ratios

I multiwavelength flux ratios

I milli-images

I gravitational imaging

I time delays

I . . . ?

They probe different aspects of the subhalo population . . .but how, exactly?

Page 28: A ``Multimessenger'' Approach to Substructure Lensingkiss.caltech.edu/workshops/dark_matter/presentations/keeton.pdf · I optical emission lines (Moustakas & Metcalf 2003, Metcalf

Observables

Flux ratios

Multiwavelength

Milli-images

Grav. imaging

Time delays

Recap

Theory

Framework

Local

Long-range

Local vs. total

Total

Complementarity

Outlook

Lensing with stochastic substructure

Can we develop a general theory of substructure lensing?

1. Improve substructure modeling:I fasterI richer — broader substructure modelsI better — understanding of systematic uncertainties

2. Develop general insights:I how is information about substructure encoded in lensing

observables?I what are the “reduced observables” we can/should aim to

measure?

Page 29: A ``Multimessenger'' Approach to Substructure Lensingkiss.caltech.edu/workshops/dark_matter/presentations/keeton.pdf · I optical emission lines (Moustakas & Metcalf 2003, Metcalf

Observables

Flux ratios

Multiwavelength

Milli-images

Grav. imaging

Time delays

Recap

Theory

Framework

Local

Long-range

Local vs. total

Total

Complementarity

Outlook

Framework

Lensing potential from 2-d Poisson equation:

∇2φ = 2κ = 2Σ

Σcrit

Time delay:

τ(x;u) =1 + zlc

DlDs

Dls

[12|x− u|2 − φ(x)

]Fermat’s principle ∇xτ = 0 gives lens equation:

u = x−α(x) where α(x) = ∇φ(x)

Distortions/magnifications:

M =(∂u

∂x

)−1

=[

1− φxx −φxy−φxy 1− φyy

]−1

Page 30: A ``Multimessenger'' Approach to Substructure Lensingkiss.caltech.edu/workshops/dark_matter/presentations/keeton.pdf · I optical emission lines (Moustakas & Metcalf 2003, Metcalf

Observables

Flux ratios

Multiwavelength

Milli-images

Grav. imaging

Time delays

Recap

Theory

Framework

Local

Long-range

Local vs. total

Total

Complementarity

Outlook

Characterizing substructure effects

Can express observables in terms of

potential φ

deflection αx =∂φ

∂x

αy =∂φ

∂y

convergence κ =12

(∂2φ

∂x2+∂2φ

∂y2

)shear γc =

12

(∂2φ

∂x2− ∂2φ

∂y2

)γs =

∂2φ

∂x∂y

Formally, we need to know the (joint) probability distribution ofΦ = {φ, αx, αy, κ, γc, γs} at all image positions.

Page 31: A ``Multimessenger'' Approach to Substructure Lensingkiss.caltech.edu/workshops/dark_matter/presentations/keeton.pdf · I optical emission lines (Moustakas & Metcalf 2003, Metcalf

Observables

Flux ratios

Multiwavelength

Milli-images

Grav. imaging

Time delays

Recap

Theory

Framework

Local

Long-range

Local vs. total

Total

Complementarity

Outlook

Deflection

αx =∂φ

∂xαy =

∂φ

∂y

Page 32: A ``Multimessenger'' Approach to Substructure Lensingkiss.caltech.edu/workshops/dark_matter/presentations/keeton.pdf · I optical emission lines (Moustakas & Metcalf 2003, Metcalf

Observables

Flux ratios

Multiwavelength

Milli-images

Grav. imaging

Time delays

Recap

Theory

Framework

Local

Long-range

Local vs. total

Total

Complementarity

Outlook

Convergence

κ =12

(∂2φ

∂x2+∂2φ

∂y2

)

Page 33: A ``Multimessenger'' Approach to Substructure Lensingkiss.caltech.edu/workshops/dark_matter/presentations/keeton.pdf · I optical emission lines (Moustakas & Metcalf 2003, Metcalf

Observables

Flux ratios

Multiwavelength

Milli-images

Grav. imaging

Time delays

Recap

Theory

Framework

Local

Long-range

Local vs. total

Total

Complementarity

Outlook

Shear

γc =12

(∂2φ

∂x2− ∂2φ

∂y2

)γs =

∂2φ

∂x∂y

Page 34: A ``Multimessenger'' Approach to Substructure Lensingkiss.caltech.edu/workshops/dark_matter/presentations/keeton.pdf · I optical emission lines (Moustakas & Metcalf 2003, Metcalf

Observables

Flux ratios

Multiwavelength

Milli-images

Grav. imaging

Time delays

Recap

Theory

Framework

Local

Long-range

Local vs. total

Total

Complementarity

Outlook

Use polar coordinates (ri, θi) centered on an image:

φ =∑i

mi

πln ri[

αxαy

]= −

∑i

mi

πri

[cos θisin θi

][γcγs

]= −

∑i

mi

πr2i

[cos 2θisin 2θi

](Small corrections for any clump that overlaps line of sight.)

Can we just use the Central Limit Theorem?

No: variances diverge.

Trouble caused by clump(s) closest to image. If we can handlethose, we can use CLT on the bulk of the remaining population.

Page 35: A ``Multimessenger'' Approach to Substructure Lensingkiss.caltech.edu/workshops/dark_matter/presentations/keeton.pdf · I optical emission lines (Moustakas & Metcalf 2003, Metcalf

Observables

Flux ratios

Multiwavelength

Milli-images

Grav. imaging

Time delays

Recap

Theory

Framework

Local

Long-range

Local vs. total

Total

Complementarity

Outlook

Use polar coordinates (ri, θi) centered on an image:

φ =∑i

mi

πln ri[

αxαy

]= −

∑i

mi

πri

[cos θisin θi

][γcγs

]= −

∑i

mi

πr2i

[cos 2θisin 2θi

](Small corrections for any clump that overlaps line of sight.)

Can we just use the Central Limit Theorem?No: variances diverge.

Trouble caused by clump(s) closest to image. If we can handlethose, we can use CLT on the bulk of the remaining population.

Page 36: A ``Multimessenger'' Approach to Substructure Lensingkiss.caltech.edu/workshops/dark_matter/presentations/keeton.pdf · I optical emission lines (Moustakas & Metcalf 2003, Metcalf

Observables

Flux ratios

Multiwavelength

Milli-images

Grav. imaging

Time delays

Recap

Theory

Framework

Local

Long-range

Local vs. total

Total

Complementarity

Outlook

Local analysis: Uniform spatial distribution

Goal: find probability distributions for most extreme shear,deflection, and potential.

Work through uniform case analytically for illustration.

px(x) =κs

N 〈m〉

(Over some large but finite area such that∫px(x) d2x = 1.)

Polar coordinates (ri, θi) centered on an image. Shear strength:

γi =mi

πr2i

What is the probability distribution for the largest shear?

Page 37: A ``Multimessenger'' Approach to Substructure Lensingkiss.caltech.edu/workshops/dark_matter/presentations/keeton.pdf · I optical emission lines (Moustakas & Metcalf 2003, Metcalf

Observables

Flux ratios

Multiwavelength

Milli-images

Grav. imaging

Time delays

Recap

Theory

Framework

Local

Long-range

Local vs. total

Total

Complementarity

Outlook

Probability that the shear from clump i is bigger than γ:

Pi(>γ) =∫miπr2i

px(xi) pm(mi) d2xi dmi

=1

N 〈m〉

∫dm pm(m)

∫dθ

∫ ( mπγ )1/2

0

dr r κs

=1

N 〈m〉

∫dm pm(m)× 2π × 1

2

(m

πγ

)κs

=κsNγ

Probability that all shears are smaller than γ:

Pall(<γ) =(

1− κsNγ

)N→ exp

(−κsγ

)for N →∞

This is the cumulative probability distribution for γmax.

Page 38: A ``Multimessenger'' Approach to Substructure Lensingkiss.caltech.edu/workshops/dark_matter/presentations/keeton.pdf · I optical emission lines (Moustakas & Metcalf 2003, Metcalf

Observables

Flux ratios

Multiwavelength

Milli-images

Grav. imaging

Time delays

Recap

Theory

Framework

Local

Long-range

Local vs. total

Total

Complementarity

Outlook

Deflection strength:

αi =mi

πri

What is the probability distribution for the largest deflection?

Probability that the deflection from clump i is bigger than α:

Pi(>α) =∫miπri

px(xi) pm(mi) d2xi dmi

=1

N 〈m〉

∫dm pm(m)

∫dθ

∫ mπα

0

dr r κs

=κs

Nπα2

⟨m2⟩

〈m〉

Probability that all deflections are smaller than α:

Pall(<α) =

(1− κs

Nπα2

⟨m2⟩

〈m〉

)N→ exp

(− κsπα2

⟨m2⟩

〈m〉

)

Page 39: A ``Multimessenger'' Approach to Substructure Lensingkiss.caltech.edu/workshops/dark_matter/presentations/keeton.pdf · I optical emission lines (Moustakas & Metcalf 2003, Metcalf

Observables

Flux ratios

Multiwavelength

Milli-images

Grav. imaging

Time delays

Recap

Theory

Framework

Local

Long-range

Local vs. total

Total

Complementarity

Outlook

Local analysis: Power law spatial dist’n

Substructure population: κs ∝ rη−2 with 0 < η ≤ 2.

Taylor series expansions for large local shear/deflection:

P (<γ) = 1− κs,img

γ

+κs,img

γ2

[κs,img

2−⟨m2⟩

〈m〉(η − 2)2

8πr2img

]+O

(γ−3

)P (<α) = 1−

⟨m2⟩

〈m〉κs,img

πα2

+κs,img

2π2α4

[⟨m2⟩2

〈m〉2κs,img −

⟨m4⟩

〈m〉(η − 2)2

4πr2img

]+O

(α−6

)

Page 40: A ``Multimessenger'' Approach to Substructure Lensingkiss.caltech.edu/workshops/dark_matter/presentations/keeton.pdf · I optical emission lines (Moustakas & Metcalf 2003, Metcalf

Observables

Flux ratios

Multiwavelength

Milli-images

Grav. imaging

Time delays

Recap

Theory

Framework

Local

Long-range

Local vs. total

Total

Complementarity

Outlook

Mass function: Local shear

κs ∝ r−1 and dN/dm ∝ m−1.9.

Fix meff =⟨m2⟩/ 〈m〉. Vary q = mhi/mlo = 1, 10, 100, 1000.

Theory.

0

0.2

0.4

0.6

0.8

1

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18

PD

F

shear

Page 41: A ``Multimessenger'' Approach to Substructure Lensingkiss.caltech.edu/workshops/dark_matter/presentations/keeton.pdf · I optical emission lines (Moustakas & Metcalf 2003, Metcalf

Observables

Flux ratios

Multiwavelength

Milli-images

Grav. imaging

Time delays

Recap

Theory

Framework

Local

Long-range

Local vs. total

Total

Complementarity

Outlook

Mass function: Local shear

κs ∝ r−1 and dN/dm ∝ m−1.9.

Fix 〈m〉. Vary q = mhi/mlo = 1, 10, 100, 1000.

0

0.2

0.4

0.6

0.8

1

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18

PD

F

shear

Page 42: A ``Multimessenger'' Approach to Substructure Lensingkiss.caltech.edu/workshops/dark_matter/presentations/keeton.pdf · I optical emission lines (Moustakas & Metcalf 2003, Metcalf

Observables

Flux ratios

Multiwavelength

Milli-images

Grav. imaging

Time delays

Recap

Theory

Framework

Local

Long-range

Local vs. total

Total

Complementarity

Outlook

Mass function: Local deflection

κs ∝ r−1 and dN/dm ∝ m−1.9.

Fix meff =⟨m2⟩/ 〈m〉. Vary q = mhi/mlo = 1, 10, 100, 1000.

Theory.

0

0.2

0.4

0.6

0.8

1

0 0.005 0.01 0.015 0.02 0.025

PD

F

deflection (arcsec)

Page 43: A ``Multimessenger'' Approach to Substructure Lensingkiss.caltech.edu/workshops/dark_matter/presentations/keeton.pdf · I optical emission lines (Moustakas & Metcalf 2003, Metcalf

Observables

Flux ratios

Multiwavelength

Milli-images

Grav. imaging

Time delays

Recap

Theory

Framework

Local

Long-range

Local vs. total

Total

Complementarity

Outlook

Mass function: Local deflection

κs ∝ r−1 and dN/dm ∝ m−1.9.

Fix 〈m〉. Vary q = mhi/mlo = 1, 10, 100, 1000.

0

0.2

0.4

0.6

0.8

1

0 0.005 0.01 0.015 0.02 0.025

PD

F

deflection (arcsec)

Page 44: A ``Multimessenger'' Approach to Substructure Lensingkiss.caltech.edu/workshops/dark_matter/presentations/keeton.pdf · I optical emission lines (Moustakas & Metcalf 2003, Metcalf

Observables

Flux ratios

Multiwavelength

Milli-images

Grav. imaging

Time delays

Recap

Theory

Framework

Local

Long-range

Local vs. total

Total

Complementarity

Outlook

Mass function: Local potential

κs ∝ r−1 and dN/dm ∝ m−1.9.

Fix meff =⟨m2⟩/ 〈m〉. Vary q = mhi/mlo = 1, 10, 100, 1000.

0

0.2

0.4

0.6

0.8

1

-0.006 -0.005 -0.004 -0.003 -0.002 -0.001 0 0.001 0.002

PD

F

potential (arcsec^2)

Page 45: A ``Multimessenger'' Approach to Substructure Lensingkiss.caltech.edu/workshops/dark_matter/presentations/keeton.pdf · I optical emission lines (Moustakas & Metcalf 2003, Metcalf

Observables

Flux ratios

Multiwavelength

Milli-images

Grav. imaging

Time delays

Recap

Theory

Framework

Local

Long-range

Local vs. total

Total

Complementarity

Outlook

Spatial distribution: Local shear

κs ∝ rη−2 and dN/dm ∝ m−1.9 with q = 100.Isothermal (η = 1), steeper (η = 0.5), and shallower (η = 1.5).

0

0.2

0.4

0.6

0.8

1

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18

PD

F

shear

Page 46: A ``Multimessenger'' Approach to Substructure Lensingkiss.caltech.edu/workshops/dark_matter/presentations/keeton.pdf · I optical emission lines (Moustakas & Metcalf 2003, Metcalf

Observables

Flux ratios

Multiwavelength

Milli-images

Grav. imaging

Time delays

Recap

Theory

Framework

Local

Long-range

Local vs. total

Total

Complementarity

Outlook

Spatial distribution: Local deflection

κs ∝ rη−2 and dN/dm ∝ m−1.9 with q = 100.Isothermal (η = 1), steeper (η = 0.5), and shallower (η = 1.5).

0

0.2

0.4

0.6

0.8

1

0 0.005 0.01 0.015 0.02 0.025

PD

F

deflection (arcsec)

Page 47: A ``Multimessenger'' Approach to Substructure Lensingkiss.caltech.edu/workshops/dark_matter/presentations/keeton.pdf · I optical emission lines (Moustakas & Metcalf 2003, Metcalf

Observables

Flux ratios

Multiwavelength

Milli-images

Grav. imaging

Time delays

Recap

Theory

Framework

Local

Long-range

Local vs. total

Total

Complementarity

Outlook

Spatial distribution: Local potential

κs ∝ rη−2 and dN/dm ∝ m−1.9 with q = 100.Isothermal (η = 1), steeper (η = 0.5), and shallower (η = 1.5).

0

0.2

0.4

0.6

0.8

1

-0.006 -0.005 -0.004 -0.003 -0.002 -0.001 0 0.001 0.002

PD

F

potential (arcsec^2)

Page 48: A ``Multimessenger'' Approach to Substructure Lensingkiss.caltech.edu/workshops/dark_matter/presentations/keeton.pdf · I optical emission lines (Moustakas & Metcalf 2003, Metcalf

Observables

Flux ratios

Multiwavelength

Milli-images

Grav. imaging

Time delays

Recap

Theory

Framework

Local

Long-range

Local vs. total

Total

Complementarity

Outlook

Long-range analysis

Can use Central Limit Theorem ⇒ need to know variance.

Illustrate with deflection:

αx =∑i

αxi

Variance:

var(αx) =⟨α2x

⟩− 〈αx〉2

=∑i

∑j

〈αxiαxj〉 −

(∑i

〈αxi〉

)2

=∑i

⟨α2xi

⟩+∑i

∑j 6=i

〈αxi〉 〈αxj〉 −(N 〈αxi〉

)2

= N⟨α2xi

⟩−N 〈αxi〉2

Page 49: A ``Multimessenger'' Approach to Substructure Lensingkiss.caltech.edu/workshops/dark_matter/presentations/keeton.pdf · I optical emission lines (Moustakas & Metcalf 2003, Metcalf

Observables

Flux ratios

Multiwavelength

Milli-images

Grav. imaging

Time delays

Recap

Theory

Framework

Local

Long-range

Local vs. total

Total

Complementarity

Outlook

〈αxi〉 =1

N 〈m〉

∫dmi pm(mi)

∫d2xi κs(xi)

mi cos θiπri⟨

α2xi

⟩=

1N 〈m〉

∫dmi pm(mi)

∫d2xi κs(xi)

(mi cos θπri

)2

Note

N 〈αxi〉2 ∼ O(

1N

)Thus

var(αx) ≈ N⟨α2xi

⟩=

⟨m2⟩

〈m〉

∫d2xi κs(xi)

(cos θπri

)2

Similar analysis for all quantities.

Page 50: A ``Multimessenger'' Approach to Substructure Lensingkiss.caltech.edu/workshops/dark_matter/presentations/keeton.pdf · I optical emission lines (Moustakas & Metcalf 2003, Metcalf

Observables

Flux ratios

Multiwavelength

Milli-images

Grav. imaging

Time delays

Recap

Theory

Framework

Local

Long-range

Local vs. total

Total

Complementarity

Outlook

Local vs. total: Shear

κs ∝ r−1 and dN/dm ∝ m−1.9 with q = 100.

0

0.2

0.4

0.6

0.8

1

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18

PD

F

shear

Page 51: A ``Multimessenger'' Approach to Substructure Lensingkiss.caltech.edu/workshops/dark_matter/presentations/keeton.pdf · I optical emission lines (Moustakas & Metcalf 2003, Metcalf

Observables

Flux ratios

Multiwavelength

Milli-images

Grav. imaging

Time delays

Recap

Theory

Framework

Local

Long-range

Local vs. total

Total

Complementarity

Outlook

Local vs. total: Deflection

κs ∝ r−1 and dN/dm ∝ m−1.9 with q = 100.

0

0.2

0.4

0.6

0.8

1

0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.045

PD

F

deflection (arcsec)

Page 52: A ``Multimessenger'' Approach to Substructure Lensingkiss.caltech.edu/workshops/dark_matter/presentations/keeton.pdf · I optical emission lines (Moustakas & Metcalf 2003, Metcalf

Observables

Flux ratios

Multiwavelength

Milli-images

Grav. imaging

Time delays

Recap

Theory

Framework

Local

Long-range

Local vs. total

Total

Complementarity

Outlook

Local vs. total: Potential

κs ∝ r−1 and dN/dm ∝ m−1.9 with q = 100.

0

0.2

0.4

0.6

0.8

1

-0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5

PD

F

potential (arcsec^2)

Page 53: A ``Multimessenger'' Approach to Substructure Lensingkiss.caltech.edu/workshops/dark_matter/presentations/keeton.pdf · I optical emission lines (Moustakas & Metcalf 2003, Metcalf

Observables

Flux ratios

Multiwavelength

Milli-images

Grav. imaging

Time delays

Recap

Theory

Framework

Local

Long-range

Local vs. total

Total

Complementarity

Outlook

Mass function: Total shear

κs ∝ r−1 and dN/dm ∝ m−1.9.

Fix meff =⟨m2⟩/ 〈m〉. Vary q = mhi/mlo = 1, 10, 100, 1000.

0

0.2

0.4

0.6

0.8

1

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18

PD

F

shear

Page 54: A ``Multimessenger'' Approach to Substructure Lensingkiss.caltech.edu/workshops/dark_matter/presentations/keeton.pdf · I optical emission lines (Moustakas & Metcalf 2003, Metcalf

Observables

Flux ratios

Multiwavelength

Milli-images

Grav. imaging

Time delays

Recap

Theory

Framework

Local

Long-range

Local vs. total

Total

Complementarity

Outlook

Mass function: Total deflection

κs ∝ r−1 and dN/dm ∝ m−1.9.

Fix meff =⟨m2⟩/ 〈m〉. Vary q = mhi/mlo = 1, 10, 100, 1000.

0

0.2

0.4

0.6

0.8

1

0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.045

PD

F

deflection (arcsec)

Page 55: A ``Multimessenger'' Approach to Substructure Lensingkiss.caltech.edu/workshops/dark_matter/presentations/keeton.pdf · I optical emission lines (Moustakas & Metcalf 2003, Metcalf

Observables

Flux ratios

Multiwavelength

Milli-images

Grav. imaging

Time delays

Recap

Theory

Framework

Local

Long-range

Local vs. total

Total

Complementarity

Outlook

Mass function: Total potential

κs ∝ r−1 and dN/dm ∝ m−1.9.

Fix meff =⟨m2⟩/ 〈m〉. Vary q = mhi/mlo = 1, 10, 100, 1000.

0

0.2

0.4

0.6

0.8

1

-0.015 -0.01 -0.005 0 0.005 0.01 0.015 0.02

PD

F

potential (arcsec^2)

Page 56: A ``Multimessenger'' Approach to Substructure Lensingkiss.caltech.edu/workshops/dark_matter/presentations/keeton.pdf · I optical emission lines (Moustakas & Metcalf 2003, Metcalf

Observables

Flux ratios

Multiwavelength

Milli-images

Grav. imaging

Time delays

Recap

Theory

Framework

Local

Long-range

Local vs. total

Total

Complementarity

Outlook

Spatial distribution: Total shear

κs ∝ rη−2 and dN/dm ∝ m−1.9 with q = 100.Isothermal (η = 1), steeper (η = 0.5), and shallower (η = 1.5).

0

0.2

0.4

0.6

0.8

1

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18

PD

F

shear

Page 57: A ``Multimessenger'' Approach to Substructure Lensingkiss.caltech.edu/workshops/dark_matter/presentations/keeton.pdf · I optical emission lines (Moustakas & Metcalf 2003, Metcalf

Observables

Flux ratios

Multiwavelength

Milli-images

Grav. imaging

Time delays

Recap

Theory

Framework

Local

Long-range

Local vs. total

Total

Complementarity

Outlook

Spatial distribution: Total deflection

κs ∝ rη−2 and dN/dm ∝ m−1.9 with q = 100.Isothermal (η = 1), steeper (η = 0.5), and shallower (η = 1.5).

0

0.2

0.4

0.6

0.8

1

0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.045

PD

F

deflection (arcsec)

Page 58: A ``Multimessenger'' Approach to Substructure Lensingkiss.caltech.edu/workshops/dark_matter/presentations/keeton.pdf · I optical emission lines (Moustakas & Metcalf 2003, Metcalf

Observables

Flux ratios

Multiwavelength

Milli-images

Grav. imaging

Time delays

Recap

Theory

Framework

Local

Long-range

Local vs. total

Total

Complementarity

Outlook

Spatial distribution: Total potential

κs ∝ rη−2 and dN/dm ∝ m−1.9 with q = 100.Isothermal (η = 1), steeper (η = 0.5), and shallower (η = 1.5).

0

0.2

0.4

0.6

0.8

1

-0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5

PD

F

potential (arcsec^2)

Page 59: A ``Multimessenger'' Approach to Substructure Lensingkiss.caltech.edu/workshops/dark_matter/presentations/keeton.pdf · I optical emission lines (Moustakas & Metcalf 2003, Metcalf

Observables

Flux ratios

Multiwavelength

Milli-images

Grav. imaging

Time delays

Recap

Theory

Framework

Local

Long-range

Local vs. total

Total

Complementarity

Outlook

Lensing Complementarity

Einstein radius, Rein ∝ m1/2. Scaled distance, r̂ = r/Rein.

observable mnemonic mass scale spatial scale

magnifications δµ ∼ 1/r̂2∫m dN

dm dm quasi-local

positions δx ∼ Rein/r̂⟨m2⟩/ 〈m〉 intermediate

time delays δt ∼ R2ein ln r̂

⟨m2⟩/ 〈m〉 long-range

Different observables contain different information about theclump population.

Page 60: A ``Multimessenger'' Approach to Substructure Lensingkiss.caltech.edu/workshops/dark_matter/presentations/keeton.pdf · I optical emission lines (Moustakas & Metcalf 2003, Metcalf

Observables

Flux ratios

Multiwavelength

Milli-images

Grav. imaging

Time delays

Recap

Theory

Framework

Local

Long-range

Local vs. total

Total

Complementarity

Outlook

Outlook

what how reduced observables

mass function combine∫m (dN/dm) dm

observables and⟨m2⟩/ 〈m〉

low-mass cutoff multiwavelength∫m (dN/dm) dm for

(e.g., WDM) flux ratios different thresholds

spatial time delays something likedistribution

∫r−n κs(x) d2x

Page 61: A ``Multimessenger'' Approach to Substructure Lensingkiss.caltech.edu/workshops/dark_matter/presentations/keeton.pdf · I optical emission lines (Moustakas & Metcalf 2003, Metcalf

Observables

Flux ratios

Multiwavelength

Milli-images

Grav. imaging

Time delays

Recap

Theory

Framework

Local

Long-range

Local vs. total

Total

Complementarity

Outlook

Outlook

Radio quads.

I radio loud: 9 — 3 currently have milli-images

I radio quiet: &20 — doable with EVLA and e-MERLIN?(N. Jackson, O. Wucknitz)

Multiwavelength (optical/IR).

I Others: 4 quads + 1 double published

I Fadely: 1 quad + 5 doubles now, 2 quads + 8 doubles soon

Quad time delays. (Congdon et al. ApJ submitted)

I 7 known currently; more and better measurements to come. . .

I 1 with clear evidence for substructure

I 4 with “anomalies”

Gravitational imaging: &100 SLACS lenses. (S. Vegetti et al.)

Page 62: A ``Multimessenger'' Approach to Substructure Lensingkiss.caltech.edu/workshops/dark_matter/presentations/keeton.pdf · I optical emission lines (Moustakas & Metcalf 2003, Metcalf

Observables

Flux ratios

Multiwavelength

Milli-images

Grav. imaging

Time delays

Recap

Theory

Framework

Local

Long-range

Local vs. total

Total

Complementarity

Outlook

Outlook

Wide-field time-domain surveys will yield thousands of new lenses:Pan-STARRS, DES, LSST, SKA, . . .

Dream:

I Clean sample of ∼100 quads.

I Radio/mid-IR photometry: multiwavelength flux ratios.

I Radio interferometry: milli-images.

I Optical/near-IR monitoring: precise time delays.(Also microlensing and AGN structure.)

The Observatory for Multi-Epoch Gravitational lens Astrophysics(OMEGA)! (L. Moustakas et al.)

Page 63: A ``Multimessenger'' Approach to Substructure Lensingkiss.caltech.edu/workshops/dark_matter/presentations/keeton.pdf · I optical emission lines (Moustakas & Metcalf 2003, Metcalf

Observables

Flux ratios

Multiwavelength

Milli-images

Grav. imaging

Time delays

Recap

Theory

Framework

Local

Long-range

Local vs. total

Total

Complementarity

Outlook

Outlook

Wide-field time-domain surveys will yield thousands of new lenses:Pan-STARRS, DES, LSST, SKA, . . .

Dream:

I Clean sample of ∼100 quads.

I Radio/mid-IR photometry: multiwavelength flux ratios.

I Radio interferometry: milli-images.

I Optical/near-IR monitoring: precise time delays.(Also microlensing and AGN structure.)

The Observatory for Multi-Epoch Gravitational lens Astrophysics(OMEGA)! (L. Moustakas et al.)