Physics 250: Weak Lensing

MW 2:10-3:30pm in Physics 525
CRN: 59613
Credits: 3
Instructor: David Wittman
High-redshift cluster of galaxies discovered
through its gravitational effects alone.

Objective: Gravitational lensing is the most direct method of observing dark matter, and it is "weak" for all but the densest lines of sight in the universe (~1 gm cm-2). We will get familiar with the methods of this new and rapidly developing field, and look at the results with an eye to the larger context of observational cosmology. If time permits, at the end of the quarter we may take a look at strong lensing as well.

Reading: You will save money because there is no textbook for this exciting new subject! Instead we will read accessible review articles and look at some recent papers with the latest developments in the field. There is a bibliography at the bottom of this page.

Format: This will be a small class and highly interactive. Some class time will be devoted to cooperative group problem-solving. Reading assignments must be done before class so that you are ready to discuss them in class. Homework assignments may include researching open-ended questions and presenting the results to the class.

Project: We will write the (currently nonexistent) Wikipedia article on weak lensing. Students are responsible for dividing the work and managing the project, subject to my review. Details will be announced soon. Because Wikipedia is at a somewhat lower level than a graduate course, each student will also make a more detailed presentation on his/her topic in the last week of class.

Grading: 60% homework and 40% project (including final presentation). There will be no exams.


  • Fundamentals of lensing
    • Monday March 31: Class logistics and fun stuff: how to explain lensing to non-experts. Ray-tracing vs wavefront points of view.

    • Reading for next time:
      • Narayan and Bartelmann review. This review is quite old, but it remains the best short introduction to the basics. Read through section 3 for Wednesday. You can skim the parts which talk about "current results" because they are not so current anymore, and also sections 3.4 and later, which concentrate on strong lensing. Give more attention to the basics. Note: the astro-ph version has the figures at the end. This review is also a chapter in the book Formation of Structure in the Universe, which contains the figures inline.
      • History of lensing: Section 1.1 of Schneider, Ehlers and Falco. For fun: article about the publication of Einstein's 1936 paper.

    • Wednesday April 2: discussion of basic lensing ideas and equations. Additional (cosmology) background not in the Narayan and Bartelmann review.

    • Reading for next time: the remainder of the Narayan and Bartelmann review. Again, give more attention to the basics than to "current results."

    • Monday April 7: Continued discussion of the Narayan and Bartelmann treatment of basic lensing equations, leading to the weak lensing approximation. For next time: no additional reading. Catch up if you are behind!

    • Wednesday April 9: Conclude discussion of Narayan and Bartelmann, leading into weak lensing by clusters and large-scale structure, which is mostly an afterthought in that review. For next time: do Homework 1!
  • Observables and data analysis
    • Monday April 14: Overview of data processing/analysis required for weak lensing work. For next time: read KSB. We may not get to it Wednesday, but you will need to be slightly ahead on your reading, as the following reading assignment is massive!
    • Wednesday April 16: HW1 due. Discuss HW (see me if you need another copy of the handwritten solutions). Finish overview of observational/data issues. For next time: finish reading KSB paper, start on Bernstein and Jarvis 2002.
    • Monday April 21: Discussion of KSB methods. For next time: finish reading BJ02.
    • Wednesday April 23: BJ02 discussion. For next time: read STeP papers: Heymans et al and Massey et al
    • Monday April 28: Discuss STeP papers. For next time: read Miller et al on Bayesian shape measurement and skim the GREAT08 Handbook. And, of course, do Homework 2.
    • Wednesday April 30: Homework 2 due. (Solutions here.) Data analysis wrapup: discuss Miller et al and GREAT08. Jim Bosch presentation on shapelets and his research project.
  • Applications
      Reading due May 5: Diaferio et al 2008 for a review of clusters in general. Also take a look at Biviano 2000 and Bahcall 1996. I have extensive comments on them in the bibliography below. The main point here is to get familiar with the resources available concerning clusters should you need them, as it will be impossible to read them both through (as I did to decide on the required reading!). For lensing by clusters, read section 3 of Mellier 1999 (but skipping 3.3 if you wish) and section 2 of Wittman 2002.

    • Monday May 5: Clusters of galaxies. Hand out Homework 3 (due May 12): grab the data by following this link.
    • Wednesday May 7: Clusters continued: lensing/X-ray/optical relations.
    • Monday May 12: HW3 due. Cluster wrap-up: shear selection. Reading due for next time: the first two sections of Limousin et al 2007 will serve as a good intro to galaxy-galaxy lensing.
    • Wednesday May 14: Galaxy-galaxy lensing. Presentations by Ami Choi and Dave Lagatutta. For next time: do Homework 4 (download and, and read sections 3-5 of Hoekstra & Jain 2008 (other sections are not required, but you may find them useful).
    • Monday May 19: Class rescheduled to Friday, May 30
    • Wednesday May 21: HW4 due. Cosmic shear part 1.
    • Monday May 26: Memorial Day Holiday
    • Wednesday May 28: Cosmic shear part 2.
  • Other topics
    • Friday May 30: (Note Friday meeting: make-up class for May 19. Meet in Room 416 at the usual time!) Weak lensing surveys.
    • Monday June 2: Presentation of projects.
    • Wednesday June 4: Finish presentation of projects. Course evaluation.



Gravitational Lenses, by Schneider, Ehlers, and Falco. There is almost nothing about weak lensing in this book, but it remains almost the only book-length introduction to lensing. On reserve in the library.

Gravitational Lensing:An Astrophysical Tool This little book is a set of five review papers as of 2003. Not held by the library, but you can get links to the chapters on ADS. Note: The chapters titled Quasar Lensing and Gravitational Optics Studies of Dark Matter Halos could be better titled Strong Lensing/Intro to Lensing and Galaxy-Galaxy Lensing respectively.

Gravitational Lensing: Strong, Weak and Micro: Saas-Fee Advanced Course 33 On reserve in the library.

Extragalactic Astronomy and Cosmology: An Introduction This will be a good reference for students who do not come from an astronomy background. For any topic in this huge field, you can get a brief summary at the level of an advanced undergraduate from this book. On reserve in the library.

This book has a chapter on lensing by Bartelmann, but I have not seen it.

Review Articles:

Narayan and Bartelmann 1996. This review is quite old, but it remains the best short introduction to the basics (of all lensing, not just weak).

Mellier 1999: Probing the Universe with Weak Lensing. A good all-around review, if a bit dated.

Bartelmann and Schneider 2001 All about weak lensing, heavy on the theory.

Wittman 2002 All about weak lensing, heavy on the observational aspects.

Making Measurements:

KSB: the seminal paper.

Bernstein and Jarvis 2002: representative of newer approaches.

Heymans et al (STEP 1): comparison of blind analyses by different groups.

Massey et al (STEP 2): blind analyses of more detailed simulations.

Miller et al: new method, Bayesian shape measurement.

GREAT08 Handbook: blind analysis challenge to the larger statistics community.

Clusters of Galaxies

Background reading about clusters in general

Online review by Biviano (2000): This is an extensive historical review of clusters as astrophysical laboratories. The HTML version pointed to here allows you to jump around easily. If you'd like a printable version, it is also available on the preprint archive. The history is fascinating at times (e.g., Zwicky's obituary in 1974 did not even mention his discovery of dark matter because it was not widely accepted at the time), but the review is too historical at times, if you are simply trying to learn about clusters. It also does not zoom out to include clusters as probes of cosmology. Still, I would recommend reading Section 4 at least.

1996 review by N. Bahcall: This review is older, but is straightforward physics without the historical development. It does discuss clusters as part of cosmology, but overall it reads a bit like a laundry list of cluster results, without much engaging discussion. Still, a good resource for quickly looking up anything to do with clusters.

Diaferio et al 2008: I settled on this as the required reading because it gives a lot of physical and cosmological context, is up to date, and is not too long. Its shortcoming is that it is not very long. By covering a lot of ground, it skips lightly over many areas. For instance, it has just one paragraph about lensing.

Additional papers mentioned in class: Hoekstra 2007 (lensing/X-ray relations); Kaiser & Squires 1993, Squires & Kaiser 1996, and Starck et al 2005 (making maps); Wittman et al 2006, Gavazzi & Soucail 2007, and others listed in my slides (shear selection).

Galaxy-galaxy lensing

Limousin et al 2007 contains, in the first two sections, a nice summary of the field. Consult references therein if you wish to dig deeper.

Cosmic shear

Hoekstra & Jain 2008: good up-to-date summary. Focuses on cosmic shear in sections 3-5, but you may find other sections useful as well.


Handy "cheat sheets":

Keeton's catalog of mass profiles.

Hogg's summary of distance measures in cosmology. For a deeper understanding, consult a cosmology textbook such as Peebles or Dodelson.