1 / 24

Gravitational lensing and the VO

Gravitational lensing and the VO. Randall Wayth. Outline. Lensing basics Observable effects of lensing and parameters Possible simulations Lens modelling Lensing and the VO. Image 1. *. a. q. True Source Position. x. *. Observer. Lens (mass M). Image 2. *. D ds. D d. D s.

genera
Download Presentation

Gravitational lensing and the VO

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

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

  2. Outline • Lensing basics • Observable effects of lensing and parameters • Possible simulations • Lens modelling • Lensing and the VO ANITA workshop. Jan 2003

  3. Image 1 * a q True Source Position x * Observer Lens (mass M) Image 2 * Dds Dd Ds Lensing Basics • When source/lens/observer lie on a line, a “ring” image is formed with radius • This is the “Einstein radius” (qE) which sets the characteristic angular scale in lensing (even for non symmetric cases) ANITA workshop. Jan 2003

  4. Notes • qE depends on • Mass contained within images • Angular diameter distances (Dds, Dd, Ds) which in turn depend on cosmology (H0, Wm, WL) for extragalactic lensing • Galactic scale: • Cosmological • Narayan & Bartelmann lecture notes are an excellent starting point (astro-ph/9606001) ANITA workshop. Jan 2003

  5. Magnification • Lensing conserves surface brightness • Magnification is generated by • Multiple images of the source • Increasing the size of the images ANITA workshop. Jan 2003

  6. 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, ∆X=0.1 ∆X=0.2 ∆X=0.5 ∆X=1.0 Magnification ANITA workshop. Jan 2003 Distance from point of closest approach

  7. Microlensing example • Bulge microlensing event (from MACHO page www.macho.mcmaster.ca) ANITA workshop. Jan 2003

  8. 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

  9. 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

  10. Examples… 3.3” Q2237+0305 0047-2808 ANITA workshop. Jan 2003

  11. 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

  12. Caustic network movie Courtesy Liliya L. R. Williams. http://www.astro.umn.edu/~llrw/ ANITA workshop. Jan 2003

  13. 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

  14. 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

  15. 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

  16. 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

  17. parameters Source (x,y) Galaxy model Solve lens Equation for image positions Model image New parameters c2 Data The “Amoeba” (downhill simplex method) Modelling - QSOs ANITA workshop. Jan 2003

  18. Entropy Source Adjustment Reverse Project Too many parameters. Aargh! Modelling – resolved images Project Source Model Image Data c2 c2 ANITA workshop. Jan 2003

  19. Example... 0.42” Reconstructed Source Data Model Image ANITA workshop. Jan 2003

  20. 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

  21. 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

  22. 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

  23. 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

  24. 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 ANITA workshop. Jan 2003

More Related