ITP talk

1
Lensing Substructure
Neal Dalal Institute for Advanced Study

• Outline
• Flux anomalies in GL systems
• a. what are they?
• b. evidence for substructure?
• 2. Comparison with CDM predictions
• 3. Future directions

Columbus Lensing 2005
2
Strong galaxy lensing

• Deflection of light by foreground galaxy causes
  multiple imaging of background source

Q2237030
Simple mass models (e.g. isothermal ellipsoids)
can account for image positions, but usually FAIL
to explain image fluxes in quad lenses! More
complex models (e.g. boxy or disky) also fail to
fit image fluxes. These so-called flux
anomalies are nearly ubiquitous among quads.
3
Flux anomalies - examples

• fluxes of close images obey asymptotic
  relationships for smooth mass models (e.g.
  Schneider et al. 1992)

cusp relation fA fC ¼ fB
fold relation fA ¼ fB
B2045265 (Fassnacht et al. 1999)
B1555375 (Marlow et al. 1999)
and plenty more examples
4
Universality relations
For a smooth potential, close pairs of images
should have nearly equal fluxes
for folds, nearby images should have same fluxes
within
image splitting local scale length
similarly for cusps, middle image should have
flux equaling the sum of the two nearby images
Note universality relations depend on geometric
optics, not gravity!
5
CDM Substructure

• CDM models predict much more substructure than is
  seen in luminous satellites (Klypin et al. 1999,
  Moore et al. 1999).
• This satellite excess has been viewed as a
  problem for CDM, leading to warm dark matter,
  etc., or may indicate that feedback processes
  suppress star formation in low mass halos

substructure affects magnification properties of
lens galaxy
Bradac et al. (2002)
can CDM satellites explain GL flux anomalies?
6
laundry list of possible causes

• propagation effects (e.g. scintillation,
  absorption)
• variability
• wrong smooth model for galaxy
• stellar microlensing
• aliens tricking us
• massive (gt106 M) substructure

7
Properties of (radio) flux anomalies

• Little dependence on frequency

data taken from CLASS papers

• Long-lasting
• parity dependence

8
Properties of (radio) flux anomalies

• Little dependence on frequency
• Long-lasting Koopmans et al. (2003)

• Long-lasting
• parity dependence

9
Properties of (radio) flux anomalies

• Little dependence on frequency
• Long-lasting
• parity dependence

Parity orientation (or handedness) of lensed
image relative to source.
for regular quad geometry, parities alternate
around ring of images.
minimum
saddle
10
Properties of (radio) flux anomalies

• Little dependence on frequency
• Long-lasting
• parity dependence

B1555375
-


-

-

-
B2045265
11
What does this tell us?

• parity dependence frequency independence ? must
  be gravity

12
What does this tell us?

• parity dependence frequency independence ? must
  be gravity
• must be able to place perturbations anywhere
  along Einstein ring

13
What does this tell us?

• parity dependence frequency independence ? must
  be gravity
• must be able to place perturbations anywhere
  along Einstein ring
• since close images are affected differently, the
  fluctuations have significant small-scale power
• (but not smaller than source size!)

e.g. cos(4q) perturbations
14
What does this tell us?

• parity dependence frequency independence ? must
  be gravity
• must be able to place perturbations anywhere
  along Einstein ring
• since close images are affected differently, the
  fluctuations have significant small-scale power
• lots of demagnified saddles and few demagnified
  minima ? 1-pt. function of dk is asymmetric
  symmetric distribution wont distinguish from

a160.05
and mass clumps
15
laundry list of possible causes

• propagation effects (e.g. scintillation,
  absorption)
• variability
• wrong smooth model for galaxy
• stellar microlensing
• aliens tricking us
• massive (gt106 M) substructure

16
Substructure lensing

• naturally explains frequency independence
  (equivalence principle)
• long variation timescale millennia
• predicts observed parity dependence for both
  microlensing (Schechter Wambsganss 2002) and
  subhalo lensing (KD03, Bradac et al 2004)

17
How Much Substructure?

• approximate Bayesian analysis finds 2 of
  surface density in substructure best fits data

for bsat2.5 mas, Msat2 107 M
This is much more substructure than is present in
the light ? must be DM substructure (both
subhalos in lens and low-mass projected
halos, e.g. Chen et al. 2003, Metcalf 2004)
18
What next?

• Satellite-subhalo connection several lenses have
  luminous satellites falling near the images. In
  these cases, we can measure satellite masses!
  Can test if luminous satellites really do sit in
  extremely massive subhalos.
• we also want to measure the mass scale of dark
  subhalos. There have been two ideas for how to
  do this
• Astrometric effects Besides perturbing image
  fluxes, substructure should also perturb image
  positions (at the 1-10 mas level) and image
  morphologies. Again, these effects are easiest
  to see for fold and cusp images.
• Spectroscopic lensing (Metcalf Moustakas 2003).
  Use the different source sizes for the continuum
  emitting region, BLR, NLR, mid-IR torus, etc., to
  differentiate between microlensing (which affects
  only sources smaller than mas) and substructure
  lensing.

CL00241654
19
Satellite-subhalo connection
Finding copious DM substructure still does not
explain dearth of Local Group dwarfs. Some ideas
are

• form few galaxies in low-mass halos (e.g.
  photoionization squelching)

20
Satellite-subhalo connection
Finding copious DM substructure still does not
explain dearth of Local Group dwarfs. Some ideas
are

• form few galaxies in low-mass halos (e.g.
  photoionization squelching)
• galaxies form only in high-mass halos, which
  become low mass via dynamical processes (e.g.
  stripping)

21
Satellite-subhalo connection
Finding copious DM substructure still does not
explain dearth of Local Group dwarfs. Some ideas
are

• form few galaxies in low-mass halos (e.g.
  photoionization squelching)
• galaxies form only in high-mass halos, which
  become low mass via dynamical processes (e.g.
  stripping)
• galaxies are in high-mass halos, they just look
  low-mass

22
Satellite-subhalo connection
Several lenses have luminous satellites falling
near the images. In these cases, we can measure
satellite masses! Can test if luminous
satellites really do sit in extremely massive
subhalos.
Object X in MG04140534
MG2016112
like LMC at z1
87 lt s lt 101 at 95 confidence
81 lt s lt 102 at 95 confidence
23
What next?

• Satellite-subhalo connection several lenses have
  luminous satellites falling near the images. In
  these cases, we can measure satellite masses!
  Can test if luminous satellites really do sit in
  extremely massive subhalos.
• we also want to measure the mass scale of dark
  subhalos. There have been two ideas for how to
  do this
• Astrometric effects Besides perturbing image
  fluxes, substructure should also perturb image
  positions (at the 1-10 mas level) and image
  morphologies. Again, these effects are easiest
  to see for fold and cusp images.
• Spectroscopic lensing (Metcalf Moustakas 2003).
  Use the different source sizes for the continuum
  emitting region, BLR, NLR, mid-IR torus, etc., to
  differentiate between microlensing (which affects
  only sources smaller than mas) and substructure
  lensing.

CL00241654
24
Astrometric signals from substructure?
B0128437, Biggs et al. 2004
5 GHz VLBA
1 GHz EVN
25
Simple test for substructure

• If potential is smooth, then a single matrix
  x1/x2 relates image 1 to image 2.

x2
x1
For J0414, we can find simple matrices relating
image A1 to the other images (worst case is A1
? A2, which gives 3 mas residuals).
For J2016, no single matrix relates the two fold
images!
MG J2016112
26
Focus on folds
In general, 22 matrix x1/x2 has 4 degrees of
freedom. But for a fold pair, the behavior is
more restricted. To leading order (in a certain
coordinate frame)
where a/y1/2, b/y0, c/y1 for vertical distance y
to the caustic. This has only 2 deg. of freedom,
can constrain with single vector! ? Measure
deviations from this both for smooth models, and
those with substructure.
For random jets of size 5 mas on source plane,
results are
27
What next?

• Satellite-subhalo connection several lenses have
  luminous satellites falling near the images. In
  these cases, we can measure satellite masses!
  Can test if luminous satellites really do sit in
  extremely massive subhalos.
• we also want to measure the mass scale of dark
  subhalos. There have been two ideas for how to
  do this
• Astrometric effects Besides perturbing image
  fluxes, substructure should also perturb image
  positions (at the 1-10 mas level) and image
  morphologies. Again, these effects are easiest
  to see for fold and cusp images.
• Spectroscopic lensing (Metcalf Moustakas 2003).
  Use the different source sizes for the continuum
  emitting region, BLR, NLR, mid-IR torus, etc., to
  differentiate between microlensing (which affects
  only sources smaller than mas) and substructure
  lensing.

CL00241654
28
for Q22370305, Metcalf et al (2004) find flux
ratios in continuum ¹ BLR ¹ NLR ¹
mid-IRradio See also Morgan et al. (2004) for
HE 0435-1223 See also Chibas talk on this!
29
Summary

• Flux anomalies in lenses provide compelling
  evidence for low mass substructure in the
  projected density at lens galaxies, at a level
  fsub¼ 2
• Lenses can also measure masses of luminous
  satellites at a variety of redshifts z0.3-1, and
  constrain HOD for dwarf galaxies in lowest mass
  halos
• Astrometric perturbations are detectable (and may
  have been detected!) but stay tuned for talk by
  J. Chen
• Flux ratios in lines / mid-IR can detect
  substructure in radio-quiet lenses, constrain
  perturber mass-scale.
• see talk by M. Chiba

30
The End
31
Astrometric signals from substructure?
Local astrometric perturbations can produce kinks
in jet images not seen in counter-images
32
Astrometric signals from substructure?
Local astrometric perturbations can produce kinks
in jet images not seen in counter-images But
anisotropic magnification can do the same thing!
33
Astrometric signals from substructure?
Breaking of mirror symmetry for folds (and
similarly for cusps)
In MG0414, note how the p,q,r,s spacings are
different in counter-images
34
Mirror symmetry
looks like astrometric anomaly!
35
Mirror symmetry
For a regular mirror, symmetric and
anti-symmetric directions are orthogonal
symmetric
antisymmetric
For a fold, symmetric and anti-symmetric
directions are NOT orthogonal

• So how to detect astrometric signals of
  substructure?
• modeling of global lens data (as with flux
  anomalies)
• any purely local signal?

36
wrong macro model?

• Flux anomalies are measured relative to a simple
  mass model isothermal ellipsoid external
  shear. What if this is the wrong model for
  galaxy could this explain apparent anomalies?
• different radial profile from isothermal?
• doesnt work since all 4 images are at similar
  radii
• different angular profiles (e.g. unmodeled
  boxiness or diskiness)
• typical levels in elliptical galaxies (Rest et
  al. 2001) or simulated CDM halos (Burkert Naab
  2003) are a4 0.02, insufficient to affect
  fluxes
• in 3 of 6 anomalous lenses, extended source
  structure allows direct measurement ! a4 0.02
  
• allowing as free parameter in fit, only in 1
  system can anomaly be explained, using a4
  0.09 none of the rest can be fixed
• Flux anomalies generated by multipoles
• have incorrect parity dependence

37
Radio microlensing

• typical microlens Einstein radius
• source sizes unresolved, but lower limit set by
  Compton catastrophe (e.g. Kellermann
  Pauliny-Toth 1969)
• such large source sizes make microlensing
  unimportant
• one possible escape - relativistic beaming can
  enhance apparent brightness temperature by
  Doppler factor D g, thereby reducing minimum
  source size by D-1/2 (Koopmans de Bruyn 2000)
• superluminal motion ? short variability
  timescale?can average away effect in year
• frequency dependence roughly sm /hmi / n

38
Radio microlensing

• However sources must be 2 orders of magnitude
  below Compton limit for microlensing to give
  asymmetry between saddles and minima!

This requires Doppler factors of order D 104
! (recall area of beaming cone g-2)
39
minimum source sizes
40
Procedure

• First fit data to smooth macro model for lens
  (SIE shear) residuals give smooth c0210-100
  for Ndof2-4
• Assume satellite density fsatS and mass scale b,
  and generate random satellite perturbers as
  tidally truncated SISs. Throw them down randomly
  near the lens images.
• Add these perturbations to smooth models
  predictions for positions fluxes. Reoptimize
  macro model using linear perturbation theory, get
  new c2 P(c2) exp(-c2/2)
• 4. Repeat for 105 Monte Carlo trials, average to
  get ltP(c2)gt. This is the probability of
  generating observed data given fsat and b
  P(data fsat, b) ltP(c2)gt
• 5. Bayes P( fsat, b data) P(data) P( fsat,
  b) P(data fsat, b)

want this constant prior
compute this
NB it is important to reoptimize macro model
for each substructure realization. Example 3
observables, macro model can adjust 2 of them
41
radio flux anomalies
Lens discrepancy B0128437 none (modeling
uncertainty?) B0712472 20 B1422231 20 B155
5375 50 B1608656 none B1933503 50 B2045
265 50 MG04140534 20 PG1115080 30