Properties of galaxies: constraints from gravitational lensing and dynamics

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NSF Award Abstract - DMS-0104751 Mathematical Sciences: Properties of galaxies: constraints from gravitational lensing and dynamics Abstract DMS-0104751 Hunter The project will follow two complementary two lines of investigation of the large-scale structure of galaxies. The first line is concerned with the gravitational lensing that occurs when a galaxy lies close to the line of sight between us and a much more distant source, such as a quasar. Electromagnetic waves from the distant source are both bent and slowed down as they pass close to the galaxy. As a result, the "gravitational lens" may produce multiple images of that quasar. A number of quasars that are multiply imaged by galaxies are now known. The configuration of those images and their relative magnitudes is determined by the distribution of mass in the intervening galaxy. The principal investigator has developed methods for calculating the lensing properties of elliptical lenses. Applied to observational data, these properties can be used to make deductions about the distribution of mass in the lensing galaxy. He will develop methods that are more powerful and refine them as necessary after testing them on observational data. The second line of investigation is concerned with the dynamics of the stars, which are the major visible components of galaxies. Its ultimate aim is to build dynamical models of galaxies, but two preliminary topics are to be studied first. One is investigation of how central density cusps and central black holes, which are widely believed to be present in many galaxies, influence the orbits of the stars, and to what extent they allow galaxies to be triaxial. The other is to improvement of a procedure for analyzing orbits and computing their fundamental frequencies and orbital densities. The two lines of investigation are complementary because both the orbits of the stars in a galaxy, and the gravitational lensing properties of that galaxy, are influenced by all the matter of the galaxy, whether visible or dark. This project looks at galaxies, the fundamental building blocks of the Universe, from two perspectives. One is that of gravitational lensing and the other is that of the motions of the stars of the galaxies. Light rays are bent when they pass close to a massive object such as a galaxy. Consequently, a galaxy that happens to lie between us and a distant quasar can cause us to see multiple images of that object. This phenomenon is known as gravitational lensing. It is of much current interest because it provides a tool for investigating the combined effects of the visible and dark matter content of a galaxy, since both contribute to the lensing. There are a number of instances of galaxies that produce four images of the same distant quasar. The principal investigator is developing theories for deducing what those image systems, their configurations and their relative strengths, tell us about the arrangement of mass in those galaxies. That arrangement is critical for the structure of the galaxy. Galaxies contain swarms of hundreds of billions of stars. The motions of those stars are governed by the gravitational forces due to all the mass of the galaxy, both visible and dark. Understanding the motion of stars in galaxies will facilitate understanding the large-scale structure of the universe.