ANITA workshop. Jan 2003 Gravitational lensing and the VO Randall Wayth.
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Transcript of ANITA workshop. Jan 2003 Gravitational lensing and the VO Randall Wayth.
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ANITA workshop. Jan 2003
Gravitational lensing and the VO
Randall Wayth
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ANITA workshop. Jan 2003
Outline
• Lensing basics
• Observable effects of lensing and parameters
• Possible simulations
• Lens modelling
• Lensing and the VO
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ANITA workshop. Jan 2003
Lensing Basics
• When source/lens/observer lie on a line, a “ring” image is formed with radius
• This is the “Einstein radius” (E) which sets the characteristic angular scale in
lensing (even for non symmetric cases)
2
4
c
GM
*
*
Observer
Lens (mass M)
TrueSource Position
Image 1
Image 2 *Dd
Dds
Ds
21
2
)(4
sd
dsEE DD
D
c
GM
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ANITA workshop. Jan 2003
Notes• E depends on
– Mass contained within images
– Angular diameter distances (Dds, Dd, Ds) which in turn depend on cosmology (H0, m, ) for extragalactic lensing
• Galactic scale:
• Cosmological• Narayan & Bartelmann lecture notes are an excellent
starting point (astro-ph/9606001)
21
2
)(4
sd
dsEE DD
D
c
GM
2121
10)9.0(
kpc
D
M
MmasE
2121
1110)"9.0(
Gpc
D
M
ME
s
dsd
D
DDD
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ANITA workshop. Jan 2003
Magnification
• Lensing conserves surface brightness
• Magnification is generated by– Multiple images of the
source– Increasing the size of the
images
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ANITA workshop. Jan 2003
Microlensing light curves
• Due to motions of source/lens/observer, a source moves through a field of high magnification producing a characteristic light curve with time scale,
v
kms
D
D
kpc
D
M
Myr
v
Dt
s
dsd
Ed
121
21
21
0
200
10214.0
Distance from point of closest approach
Magnification
∆X=0.1
∆X=0.2
∆X=0.5
∆X=1.0
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ANITA workshop. Jan 2003
Microlensing example
• Bulge microlensing event
(from MACHO page www.macho.mcmaster.ca)
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ANITA workshop. Jan 2003
Observable effects of Galactic lensing
• Microlensing– Light curve magnifications & time scales.– Simple 1-peak cases are easy (with
mass/distance/velocity degeneracies)
– Hard cases for binary lens/caustic crossing events (asymmetric, multiple peaks, many degeneracies)
• Event rates depend on optical depth of sources and lenses and lens mass function
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ANITA workshop. Jan 2003
Observable effects of cosmological scale lensing (galaxy lenses)
• Multiple (observable) images of background sources (galaxy, QSO, radio lobe)
• Image separations (Einstein radius) depends on galaxy mass and distances (typically 0.1 ≤ zlens ≤ 1.0)
• Image magnifications depend on galaxy mass profile
• Image statistics depend on galaxy mass function and cosmology
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ANITA workshop. Jan 2003
Examples…
3.3”
Q2237+0305 0047-2808
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ANITA workshop. Jan 2003
Galaxy lens observables (continued)
• Lensed QSOs can also have microlensing happening on each image (depending on optical depth of point masses in the vicinity of the images)
• Clusters also form giant arcs and many arclets from weak lensing
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ANITA workshop. Jan 2003
Caustic network movie
Courtesy Liliya L. R. Williams. http://www.astro.umn.edu/~llrw/
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ANITA workshop. Jan 2003
Theoretical applications of galaxy lensing - Simulations
• Statistical properties of galaxy lenses– Focus on galaxy mass profile, mass
substructure (image location, brightness)– Focus on cosmology– Focus on evolution
• Weak lensing properties of “aggregate” haloes from many individual galaxies
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ANITA workshop. Jan 2003
Microlensing in multiply imaged QSOs
• Microlensing depends on– Galaxy transverse motion– Stellar proper motions– Microlens mass function– QSO continuum region size
• During a high magnification event (HME) the colour changes of the image yield (more) info about the source.
• Predicting the HMEs is important• See Stu Wyithe’s work over the last few years.
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ANITA workshop. Jan 2003
Modelling galaxy lenses
• Motivations:– Location & brightness of images depends on
total mass within images and mass profile in the region of the images
– Time delays (for lensed QSOs) depend on mass profile and H0
– For resolved images, the source can be accurately reconstructed
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ANITA workshop. Jan 2003
Modelling (continued)
• Use parameterised models for mass• Find range of parameters which can fit image• Models can be:
– Simple (e.g. an isothermal sphere)– complex (e.g. bulge + disc + halo)
• QSO lenses provide ~10 constraints (if you believe flux ratios)
• Resolved images potentially provide much more (recall- surface brightness is conserved)
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ANITA workshop. Jan 2003The “Amoeba”(downhill simplex method)
Modelling - QSOs
parameters
Source (x,y)Galaxy model
Solve lensEquation for imagepositions
Modelimage
2
Data
Newparameters
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ANITA workshop. Jan 2003
Modelling – resolved images
DataDataEntropyEntropy
Model ImageModel Image
SourceSourceProjectProject
Reverse ProjectReverse Project
SourceSource
AdjustmentAdjustment
Too many parameters.
Aargh!
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ANITA workshop. Jan 2003
Example...
0.42”
Data Model ImageReconstructed
Source
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ANITA workshop. Jan 2003
Issues…
• For QSO lenses– solve lens equation for location of images (relatively
easy)– fixed number of parameters used for source
• For resolved lenses:– must create a “mapping” between source and image
which preserves brightness to project the source into an image
– How many parameters are used in the source as it is reconstructed?
– Do we enforce other constraints on the source? (positivity etc)
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ANITA workshop. Jan 2003
Lensing and the VO…
• Availability of (public) software is #1 hurdle• Several algorithms published, but code is
not available. Chuck Keeton’s “gravlens” package is the good exception (available from Castles site: http://cfa-www.harvard.edu/castles/)
• There are few incentives for people to make their code public
• There are opportunities for distributed computing in lens modelling!
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ANITA workshop. Jan 2003
Why is making code public a good thing?
• Correctness. Others will do a much better job of testing the code than the author
• Non-duplication of work. Prevent the wheel being re-invented
• Enhancements. Keen collaborators/users can make improvements to the code
• Reuse. Others can still do good science if you are doing something else
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ANITA workshop. Jan 2003
How do we create incentives for people to make codes public?
• Supervisors: design PhD projects with the VO in mind.– How can this work fit in with existing/planned
work in the VO?– Create the expectation that the code will
become public from the beginning
• $$: allocate some money for making codes VO friendly (postdocs?)
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ANITA workshop. Jan 2003
Conclusions
• More publicly available lensing code would be good
• Lens modelling/simulations lend themselves to a distributed (grid) computing environment
• Issues for making codes public are similar to general software engineering issues
• Design your PhD projects with the VO in mind