ANITA workshop. Jan 2003 Gravitational lensing and the VO Randall Wayth

ANITA workshop. Jan 2003

Gravitational lensing and the VO

Randall Wayth


Outline

• Lensing basics

• Observable effects of lensing and parameters

• Possible simulations

• Lens modelling

• Lensing and the VO


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


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


Magnification

• Lensing conserves surface brightness

• Magnification is generated by– Multiple images of the

source– Increasing the size of the

images


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


Microlensing example

• Bulge microlensing event

(from MACHO page www.macho.mcmaster.ca)


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


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


Examples…

3.3”

Q2237+0305 0047-2808


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


Caustic network movie

Courtesy Liliya L. R. Williams. http://www.astro.umn.edu/~llrw/


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


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.


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


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


Modelling – resolved images

DataDataEntropyEntropy

Model ImageModel Image

SourceSourceProjectProject

Reverse ProjectReverse Project

SourceSource

AdjustmentAdjustment

Too many parameters.

Aargh!


Example...

0.42”

Data Model ImageReconstructed

Source


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)


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!

http://cfa-www.harvard.edu/castles/


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


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?)


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

Documents

ANITA workshop. Jan 2003 Gravitational lensing and the VO Randall Wayth