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Stony Brook University
Graduate Seminar Fall 2007
David Keitel
Gravitational Lensing
p. 2/24
Gravitational Lensing
What is it?
• deflection of light by massive objects...
• ... or large scale mass distributions
• an important test of General Relativity
• a powerful tool for all fields of astronomy
p. 3/24
Overview
• Basic mechanism
• Lensing by the sun
• Strong Lensing
• Weak Lensing
• Cosmic Shear
• Microlensing
• Results, current and future projects
Gravitational Lensing
[SHA]
p. 4/24
Gravitational Lensing – Basic mechanism
How does lensing work?
• light travels along geodesics of space-time
• large masses distort space-time
• multiple images with different positions on the sky
• distortions and magnifications may occur
p. 5/24
Gravitational Lensing – Basic mechanism
[SCH]
p. 6/24
Gravitational Lensing – Basic mechanism
• multiple solutions � multiple images
• beams of a light bundle will be deflected
differentially
• this gives distortion and, via Jacobian,
magnification:
p. 7/24
Gravitational Lensing – Basic mechanism
• lines in lens plane with detA=0: critical curves
• mappings of these in source plane: caustics
• highest magnifications occur near caustics
• image number changes by 2 on caustics
p. 8/24
Gravitational Lensing – Basic mechanism
Caustics Critical curves
[AHK]
p. 9/24
Gravitational Lensing – Basic mechanism
Einstein rings
[NBL]
• sources on axis are imaged into a ring
• Einstein angle:
• star-star lensing:
~ 1 mas
• galaxy-galaxy lensing:
~ 1 as[BOL]
p. 10/24
Gravitational Lensing – Basic mechanism
Mass models
• deflection angle depends on surface mass density
• a priori unknown
• models solved analytically or numerically
• results compared to observations, parameters tuned
p. 11/24
Gravitational Lensing – Lensing by the sun
First observation
• 1919: solar eclipse
• deflection of stars near
solar rim confirmed Einstein
[WC1]
p. 12/24
Gravitational Lensing – Lensing by the sun
Albert
EinsteinArthur Stanley
Eddington
A fun anecdote:
Einstein 1911:
Einstein 1915:
[NPO] [WC2]
p. 13/24
Gravitational Lensing – Strong Lensing
Strong Lensing
• High mass needed: big galaxies, galaxy clusters
• multiple images common, Einstein rings possible
• sources on cluster caustics are imaged into
giant luminous arcs
• arc radius yields Einstein angle and thus,
with model, cluster mass
p. 14/24
Gravitational Lensing – Strong Lensing
QSO 0957+561,
„twin quasar“
[YOU] [HAR]
Multiple quasar
images and
host galaxy
Einstein ring
[IMP]
p. 15/24
Gravitational Lensing – Strong Lensing
Abell 2218
[FRU]
p. 16/24
Gravitational Lensing – Weak Lensing
Weak Lensing
• Clusters also lens background sources far from caustics
• no strong effects, but shape distortions
• arclets or at least increased ellipticity
• statistical analysis can yield cluster mass
Gravitational Lensing – Weak Lensing
Abell 1689
[BEN]
p. 17/24
p. 18/24
Gravitational Lensing – Cosmic Shear
Cosmic Shear
• deflection not only by concentrated masses
• large scale structure has statistical influence
• measured by ellipticity distribution of large fields
• structure formation, cosmological parameters
p. 19/24
Gravitational Lensing - Microlensing
Microlensing
• lenses too small for image distortions may still
show up by magnification effect
• source moving behind lens gives characteristic light curve
• low probability, monitoring of large field required
• statistics give information about galactic structure
• surveys towards LMC estimate number of MACHOs
Gravitational Lensing - Microlensing
first microlensing
event towards LMC
[ALC]p. 20/24
p. 21/24
Gravitational Lensing – Results and projects
• predictions of General Relativity proven
• cluster and galaxy masses reconstructed
• tons of indications for dark matter
• major MACHO contribution to dark matter ruled out
• extrasolar planets found
• models of structure formation checked
• independent values of Hubble constant
and cosmological parameters
Results so far
p. 22/24
Gravitational Lensing – Results and projects
• extrasolar planet searches
• cosmological parameters from cluster lensing
• weak lensing search for filaments between clusters
• wide field surveys
• James Webb Space Telescope will enhance weak lensing
+ cosmic shear � dark energy, compare to Planck CMB
Current and future projects
p. 23/24
Gravitational Lensing
References
• [SHA]: K. Sharon, E. Ofek, ACS, HST, NASA / ESA (2006)
• [SCH]: P. Schneider - Gravitational Lensing, Lecture Notes (2007)
• [AHK]: H. Asada, T. Hamana, M. Kasai - A&A 397, 825-829 (2003)
• [NBL]: R. Narayan, M. Bartelmann - Lectures on Gravitational Lensing (2007)
• [BOL]: A. Bolton, ACS, HAST, NASA / ESA (2005)
• [WC1]: commons.wikimedia.org/wiki/Image:1919_eclipse_positive.jpg
• [NPO]: nobelprize.org/nobel_prizes/physics/laureates/1921/index.html
• [WC2]: commons.wikimedia.org/wiki/Image:Eddington_2.jpeg
• [YOU]: P. Young et al. - ApJ 244, 736 (1981)
• [HAR]: M. Harvanek et al. - AJ 114, 2240 (1997)
• [FRU]: A. Fruchter (STScI) et al., WFPC2, HST, NASA (2000)
• [BEN]: N. Benitez (JHU) et al., ACS, HST, NASA (2002)
• [ALC]: C. Alcock et al. - Nature 365 621 (1993)
• [MCN]: M. Markevitch et al., D. Clowe et al., NASA/STScI (2004)
• [JFN]: M.J. Jee, H. Ford, ACS, HST, NASA / ESA (2004)
Gravitational Lensing
Any Questions?
„bullet cluster“
„dark matter ring“
[JFN]
[MCN]
Gravitational Lensing - Appendix
Gravitational Lensing - Appendix
• PLANET collaboration since 1995
• About 500 events a year
• 170 planets identified so far
Search for exoplanets
References:
• planet.iap.fr
• Dominik et al., proceedings of the XIXth IAP colloquium, Aps. Conf. Ser. (2004)
• Beaulieu et al., Nature 439, 437 (2006) - arXiv:astro-ph/0601563v1
Gravitational Lensing - Appendix
Cosmological parameters
Gravitational Lensing - Appendix
Reference: Spergel et al., ApJ (2007) - arXiv:astro-ph/0603449v2
Gravitational Lensing - Appendix
CLASS, Chae et. al 2002:
Soucail et al. 2004:
Allen et al. 2004:
Voevodkin & Vikhlinin 2004:
Some values from Lensing:
Hubble Key project:
Hubble constant:
From strong
lensing on
clusters
(Freedman et al. 2001)
for different galaxy lens models (Schneider 2007)
Lensing: