Stochastic Gravitational Lensing and the Nature of Dark Matter Chuck Keeton Rutgers University vitational lens database -- http://cfa-www.harvard.edu/castles with: Arthur Congdon (Rutgers), Greg Dobler (Penn), Scott Gaudi (Harvard), Arlie Petters (Duke), Paul Schechter (MIT)
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Stochastic Gravitational Lensing and the Nature of Dark Matter Chuck Keeton Rutgers University Gravitational lens database -- .
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Stochastic Gravitational Lensingand the Nature of Dark Matter
• Successful in explaining large-scale properties of the universe.– global geometry, distribution of galaxies, cosmic microwave background, …
• Successful in describing many features of galaxies and clusters.– the “missing mass”
• But several challenges (crises?) related to the distribution of dark matter on small scales.
CDM halos are lumpy
Predictions:
• Hierarchical structure formation:small objects form first, then aggregate into larger objects.
• Small objects are dense, so they can maintain their integrity during mergers.
• Large halos contain the remnants of their many progenitors substructure.
• Clump-hunting: How to find them?
cluster of galaxies,~1015 Msun
single galaxy,~1012 Msun
(Moore et al. 1999; also Klypin et al. 1999)
CDM halos are lumpy
Clusters look like this good!
cluster of galaxies,~1015 Msun
single galaxy,~1012 Msun
(Moore et al. 1999; also Klypin et al. 1999)
vs.
CDM halos are lumpycluster of galaxies,~1015 Msun
single galaxy,~1012 Msun
(Moore et al. 1999; also Klypin et al. 1999)
vs.
Galaxies don’t bad?
A Substructure Crisis?
CDM seems to overpredict substructure. What does it mean?
Particle physics• Maybe dark matter isn’t cold and collisionless. (CDM is wrong!)• Maybe it is warm, self-interacting, fuzzy, sticky, …
Astrophysics• We only see clumps if they contain stars and/or gas.• Maybe astrophysical processes suppress star formation in small objects,
so most clumps are invisible.
A Substructure Crisis?
CDM seems to overpredict substructure. What does it mean?
Particle physics• Maybe dark matter isn’t cold and collisionless. (CDM is wrong!)• Maybe it is warm, self-interacting, fuzzy, sticky, …
Astrophysics• We only see clumps if they contain stars and/or gas.• Maybe astrophysical processes suppress star formation in small objects,
so most clumps are invisible.
Need to search for a large population of “invisible” objects!
S
L O
Strong Gravitational Lensing
Lens equation:
The bending is sensitive to all mass, be itluminous or dark, smooth or lumpy.
Point Mass Lens
• Bending angle:
• Lens equation:
• Two images for every source position.
• Source directly behind lens Einstein ring with radius E.
sources
lens
2 images ofeach source
Einsteinring radius
“Of course, there is not much hope of observing this phenomenon directly.”
(Einstein, 1936 Science 84:506)
(MACHO project)
Microlensing!
Data mining: Need to distinguishmicrolensing from variable stars.
Lensing by Galaxies:Hubble Space Telescope Images
“Double”
“Quad”
“Ring”
(Zwicky, 1937 Phys Rev 51:290)
Radio Lenses
10 = 4+4+2
Double
Quad
What is lensing good for?
Strong lensing
• Multiple imaging of some distant source.
• Used to study the dark matter halos of galaxies and clusters of galaxies.
Microlensing
• Temporary brightening of a star in our galaxy.
• Used to probe for dark stellar-mass objects in our own galaxy.
Weak lensing
• Small, correlated distortions in the shapes of distant galaxies.
• Used to study the large-scale distribution of matter in the universe.
Extended Mass Distributions: 2-d Gravity
• Work with 2-d angle vectors on the sky.
• Interpret bending angle as 2-d gravity force gradient of 2-d gravitational potential.
• Extended mass distribution:
• General lens equation:
Fermat’s Principle
• Time delay surface:
• Lens equation:
• Lensed images are critical points of .
– minimum
– saddle
– maximum
Lensing and Catastrophe Theory
• Reinterpet lens equation as a mapping:
• Jacobian:
• The critical points of the mapping are important…
• Observability: image brightness given by
Critical curves:det J = 0
(Two curves.)
Caustics:Image numberchanges by 2
Fold and cusp catastrophes.
1
3/2
5/4
Catastrophes in Lensing
(Bradac et al. 2002)
Substructure complicated catastrophes!
(Schechter & Wambsganss 2002)
Parametric Mass Modeling
Data
• Positions and brightnesses of the images. 3Nimg
• (Maybe a few other observables.) …
Parameters
• Mass and shape of lens galaxy. 3
• Tidal shear field. 2
• Position and brightness of source. 3
• Substructure. ?
Public software -- http://www.physics.rutgers.edu/~keeton/gravlens
Lensing and Substructure
Fact
• In 4-image lenses, the image positions can be fit by smooth lens models.
• The flux ratios cannot.
Interpretation• Flux ratios are perturbed by substructure in the lens potential.
(Mao & Schneider 1998;Metcalf & Madau 2001;
Dalal & Kochanek 2002)
• Recall:
– positions determined by i: itrue i
smooth
– brightnesses determined by ij: ijtrue = ij
smooth + ijsub
Substructure Statistics
• Can always(?) add one or two clumps and get a good model.
• More interesting are clump population statistics. Are they:
– Consistent with known populations of substructure?
(globular clusters, dwarf galaxies, …)
– Consistent with CDM predictions?
– None of the above?
From Lensing to Dark Matter Physics
• Find lenses with flux ratio anomalies.– catastrophe theory
• How do the statistics of anomalies depend on properties of the substructure population?– random critical point theory– marked spatial point processes
• Measure properties of substructure population.– Bayesian inference– small datasets
• Compare with CDM predictions.– testing relations, not just parameters
• How do substructure population statistics depend on physical properties of dark matter?