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

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