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) * * Observer Lens (mass M) True Source Position Image 1 Image 2 * DdDd D ds DsDs
ANITA workshop. Jan 2003 Notes E depends on –Mass contained within images –Angular diameter distances (D ds, D d, D s ) which in turn depend on cosmology (H 0, m, ) for extragalactic lensing Galactic scale: Cosmological Narayan & Bartelmann lecture notes are an excellent starting point (astro-ph/ )
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, 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 )
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 ≤ z lens ≤ 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” Q
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.
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 H 0 –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 2003 The “Amoeba” (downhill simplex method) Modelling - QSOs parameters Source (x,y) Galaxy model Solve lens Equation for image positions Model image 22 Data New parameters
ANITA workshop. Jan 2003 Modelling – resolved images Data Entropy Model Image Source Source Project Reverse Project SourceAdjustment Too many parameters. Aargh!
ANITA workshop. Jan 2003 Example ” Data Model Image Reconstructed 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: 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