anita workshop. jan 2003 gravitational lensing and the vo randall wayth
TRANSCRIPT
ANITA workshop. Jan 2003
Gravitational lensing and the VO
Randall Wayth
ANITA workshop. Jan 2003
Outline
• Lensing basics
• Observable effects of lensing and parameters
• Possible simulations
• Lens modelling
• Lensing and the VO
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
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
ANITA workshop. Jan 2003
Magnification
• Lensing conserves surface brightness
• Magnification is generated by– Multiple images of the
source– Increasing the size of the
images
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
ANITA workshop. Jan 2003
Microlensing example
• Bulge microlensing event
(from MACHO page www.macho.mcmaster.ca)
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
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
ANITA workshop. Jan 2003
Examples…
3.3”
Q2237+0305 0047-2808
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
ANITA workshop. Jan 2003
Caustic network movie
Courtesy Liliya L. R. Williams. http://www.astro.umn.edu/~llrw/
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
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.
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
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)
ANITA workshop. Jan 2003The “Amoeba”(downhill simplex method)
Modelling - QSOs
parameters
Source (x,y)Galaxy model
Solve lensEquation for imagepositions
Modelimage
2
Data
Newparameters
ANITA workshop. Jan 2003
Modelling – resolved images
DataDataEntropyEntropy
Model ImageModel Image
SourceSourceProjectProject
Reverse ProjectReverse Project
SourceSource
AdjustmentAdjustment
Too many parameters.
Aargh!
ANITA workshop. Jan 2003
Example...
0.42”
Data Model ImageReconstructed
Source
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)
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!
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
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?)
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