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Gravitational Lensing

Here is a simple model of Gravitational Lensing. Light emitted from a source bends around intermediate mass usually called the deflector or cluster mass distribution, according to Einstein's Theory of General Relativity. Not all the light emitted from the source reached the observer, only that light which bends through the correct angle.

The amount of deflection caused by huge deflectors, like clusters of galaxies, is at most 10's of arcseconds (that's only radians). So lensing candidates require a great deal of coincidental alignment to start with. But with the huge number of galaxies and clusters of galaxies out there, there are dozens [Surdej & Soucail, 1993] of confirmed examples.

Forward Modeling

Gravitational lensing is easy to "forward model" when you know all about the source and deflector. In the program I'm currently working on, I specify a distribution of masses, like singular isothermal spheres, and then ray-trace the lens. That is, calculate what is seen at each point of the lens, and produce a picture (17.5 Kbyte gif) of the light you would see. The latest version allows the user to interactively move the objects around to try to visually get a good match with observations. I've produced some pretty simulations of strong lensing and also microlensing events. Forward modeling can tell you a lot about the optics of the lens, although it can be kind of hit-and-miss, trial-and-error. You, too, can try some modeling.

Inverse Modeling

If you already know all about the source and the deflector, then really, you're done! The whole point to studying lensing systems is to determine all you can about the distribution of masses that are doing the deflecting, and about the source of the light. This is a classic inverse problem: what distribution of masses can distort the light of a distant source into the picture I see in my telescope? There has been some [Kaiser & Squires, 1993] success with genuine lens inversion through distortion, but it is applicable, at the moment, only to weakly lensing systems. This is a direction I'm hoping to pursue.

The really interesting part about "inverting the lens" is comparing the calculated deflector mass distribution with what you can see. It helps that my supervisor, Greg Fahlman in the Department of Geophysics and Astronomy, does a lot of observing at the Canada France Hawaii Telescope (CFHT). Some of the successfully inverted lenses contain a dark matter component [Fahlman et al, 1994]. These results may provide an estimate of the amount of dark matter there is in the universe, a question that keeps us all awake at night.

Cosmological Applications

Another parameter that may come out of a successfully inverted lens in the Hubble constant which encodes the age and size of the universe. It can be determined, in theory, by measuring two quantities: the angular separation between two images, and the time delay between these images. This time delay is an interesting quantity: Assuming there is some variability in the source, this signal travels down two different geodesics (see the figure below.) There are two contributions to the time delay: the first is the obvious delay due to the difference in path length between the two rays. The second is a General Relativistic effect, the Shapiro time-delay, that causes a change in the rate that clocks tick as they pass through a gravitational field. Because the two rays travel through different parts of the potential well created by the deflector, the clocks carrying the source's signal will emerge out of sync.

Gravitational Lens Gallery

This isn't just a theoretical experiment in General Relativity. Gravitational lenses have been observed since 1979 when Walsh et al. first discovered a multiply imaged quasar in 0957+561. Here are some pictures of interesting gravitational lenses. There are more and more lensing candidates observed, especially now that the Hubble Space Telescope has been fixed.

Sources

  1. Fahlman, G.G., Kaiser, N., Squires, G. & Woods, D. 1994,"Dark matter in ms1224 from the distortions of the background galaxies," Ap. J. 437, 56. [BACK]
  2. Kaiser, N. & Squires, G. 1993, "Mapping the dark matter with weak gravitational lenses," Ap. J. 404, 441. [BACK]
  3. Refsdal, S. 1964, "The gravitational lens effect," M.N.R.A.S. 128, 295.
  4. Schneider, P., Ehlers, J. & Falco, E. 1992, Gravitational Lenses. Springer-Verlag, Berlin.
  5. Surdej, J. & Soucail, G. 1993, "Lists of accepted and proposed gravitational lens systems," in Surdej, J. et al (eds.) Gravitational Lenses in the Universe, 1993, Proceedings of the 31st Liège International Astrophysical Colloquim. [BACK]
  6. Walsh, D. and Carswell, R.F. and Weyman, R.J. 1979, "0957+561 {A},{B}: twin quasistellar objects or gravitational lens?" Nature, 279, 381.

Peter Newbury, e-mail: pnewbury@langara.bc.ca
Last update: 16 February 1996