Parameter degeneracy in models of the quadruple lens system Q2237+0305

The geometry of the quadruple lens system Q2237+0305 is modeled with a simple astigmatic lens: a power-law mass distribution: m \propto r^\beta with an external shear \gamma. The image positions can be reproduced with an accuracy better than 0.01 arcsec for any 0.0 < \beta < 1.85 and the corresponding value of \gamma = 0.1385 - 0.0689 \beta. This is a factor of about 4 more precise than what can be achieved by the best constant M/L lens models. The image intensity ratios and the time delay ratios are almost constant along our one parameter family of models, but the total magnification varies from 8 to > 1000, and the maximum time delay (between leading image B and trailing image C) for H_0 of 75 km/sec/Mpc varies from more than 20 hours to about 1.5 hours, while \beta increases from 0.0 to 1.85.Comment: 15 pages uuencoded compressed postscript text plus 4 postscript figures; MPI Astrophysik report MPA-821; to appear in Astronomical Journa

Detectability of extrasolar moons as gravitational microlenses

We evaluate gravitational lensing as a technique for the detection of extrasolar moons. Since 2004 gravitational microlensing has been successfully applied as a detection method for extrasolar planets. In principle, the method is sensitive to masses as low as an Earth mass or even a fraction of it. Hence it seems natural to investigate the microlensing effects of moons around extrasolar planets. We explore the simplest conceivable triple lens system, containing one star, one planet and one moon. From a microlensing point of view, this system can be modelled as a particular triple with hierarchical mass ratios very different from unity. Since the moon orbits the planet, the planet-moon separation will be small compared to the distance between planet and star. Such a configuration can lead to a complex interference of caustics. We present detectability and detection limits by comparing triple-lens light curves to best-fit binary light curves as caused by a double-lens system consisting of host star and planet -- without moon. We simulate magnification patterns covering a range of mass and separation values using the inverse ray shooting technique. These patterns are processed by analysing a large number of light curves and fitting a binary case to each of them. A chi-squared criterion is used to quantify the detectability of the moon in a number of selected triple-lens scenarios. The results of our simulations indicate that it is feasible to discover extrasolar moons via gravitational microlensing through frequent and highly precise monitoring of anomalous Galactic microlensing events with dwarf source stars.Comment: 14 pages, 11 figures. Updated to A&A published version: updated references, 1 additional illustration (Fig. 10), further analogies to solar system and extended discussio

Discovering Galactic Planets by Gravitational Microlensing: Magnification Patterns and Light Curves

The current searches for microlensing events towards the galactic bulge can be used to detect planets around the lensing stars. Their effect is a short-term modulation on the smooth lightcurve produced by the main lensing star. Current and planned experiments should be sensitive enough to discover planets ranging from Jupiter mass down to Earth mass. For a successful detection of planets, it is necessary to accurately and frequently monitor a microlensing event photometrically, once it has been "triggered". We present a large variety of two-dimensional magnification distributions for systems consisting of an ordinary star and a planetary companion. We cover planet/star mass ratios from $m_{pl}/M_* = 10^{-5}$ to $10^{-3}$. These limits correspond roughly to $M_{Earth}$ and $M_{Jup}$, for a typical lens mass of $M_* = 0.3 M_{\odot}$. We explore a range of star-planet distances, with particular emphasis on the case of "resonant lensing", a situation in which the planet is located at or very near the Einstein ring of the lensing star. We show a wide selection of light curves - one dimensional cuts through the magnification patterns - to illustrate the broad range of possible light curve perturbations caused by planets. The strongest effects are to be expected for caustic crossings. But even tracks passing outside the caustics can have considerable effects on the light curves. The easiest detectable (projected) distance range for the planets is between about 0.6 and 1.6 Einstein radii. Planets in this distance range produce caustics inside the Einstein ring of the star. For a lensing star with a mass of about $0.3 M_{\odot}$ at a distance of 6 kpc and a source at 8 kpc, this corresponds to physical distances between star and planet of about 1 to 3 AU.Comment: 8 pages Latex plus 10 Figures (partly in GIF/JPEG format due to size constraints). High quality Postscript figures can be obtained electronically at the URL: http://www.aip.de:8080/~jkw/planet_figures.html . Hardcopies of figures can be obtained on request. To appear in MNRAS (Jan.1, 1997, Volume 284, pp.172-188

Gravitational Microlensing

This review forms the microlensing part of the 33rd Saas-Fee Advanced Course "Gravitational Lensing: Strong, Weak & Micro'', which was held in April 2003 in Les Diablerets. It contains an introduction to the lensing effects of single and binary stars and it summarizes the state-of-the-art of microlensing observations and prospects at the time of the meeting. Stellar microlensing as well as quasar microlensing are covered.Comment: 93 pages, 51 figures; to appear (April 2006) in: Kochanek, C.S., Schneider, P., Wambsganss, J.: "Gravitational Lensing: Strong, Weak & Micro", Proceedings of the 33rd Saas-Fee Advanced Course; G. Meylan, P. Jetzer, P. North, eds. (Springer-Verlag, Heidelberg); pp. 45

Gravitational lensing: numerical simulations with a hierarchical tree code

AbstractThe mathematical formulation of gravitational lensing — the lens equation — is a very simple mapping R2→R2, between the lens (or sky) plane and the source plane. This approximation assumes that all the deflecting matter is in one plane. In this case the deflection angle α is just the sum over all mass elements in the lens plane. For certain problems — like the determination of the magnification of sources over a large number of source positions (up to 1010) for very many lenses (up to 106) — straightforward techniques for the determination of the deflection angle are far too slow. We implemented an algorithm that includes a two-dimensional tree-code plus a multipole expansion in order to make such microlensing simulations “inexpensive”. Subsequently we modified this algorithm such that it could be applied to a three-dimensional mass distribution that fills the universe (approximated by many lens planes), in order to determine the imaging properties of cosmological lens simulations. Here we describe the techniques and the numerical methods, and we mention a few astrophysical results obtained with these methods