J. F. L. Simmons

Microlensing of extended stellar sources

Abstract We investigate the feasibility of reconstructing the radial intensity profile of extended stellar sources by inverting their microlensed light curves. Using a simple, linear, limb darkening law as an illustration, we show that the intensity profile can be accurately determined, at least over the outer part of the stellar disc, with realistic light curve sampling and photometric errors. The principal requirement is that the impact parameter of the lens be less than or equal to the stellar radius. Thus, the analysis of microlensing events provides a powerful method for testing stellar atmosphere models.

The classical Kepler problem and geodesic motion on spaces of constant curvature

In this paper we clarify and generalize previous work by Moser and Belbruno concerning the link between the motions in the classical Kepler problem and geodesic motion on spaces of constant curvature. Both problems can be formulated as Hamiltonian systems and the phase flow in each system is characterized by the value of the corresponding Hamiltonian and one other parameter (the mass parameter in the Kepler problem and the curvature parameter in the geodesic motion problem). Using a canonical transformation the Hamiltonian vector field for the geodesic motion problem is transformed into one which is proportional to that for the Kepler problem. Within this framework the energy of the Kepler problem is equal to (minus) the curvature parameter of the constant curvature space and the mass parameter is given by the value of the Hamiltonian for the geodesic motion problem. We work with the corresponding family of evolution spaces and present a unified treatment which is valid for all values of energy continuous...

The use of light polarization in weak-lensing inversions

The measurement of the integrated optical polarization of weakly gravitationally lensed galaxies can provide considerable constraints on lens models. The method outlined depends on fact that the orientation of the direction of optical polarization is not affected by weak gravitational lensing. The angle between the semi-major axis of the imaged galaxy and the direction of integrated optical polarization thus informs one of the distortion produced by the gravitational lensing. Although the method depends on the polarimetric measurement of faint galaxies, large telescopes and improved techniques should make such measurements possible in the near future.

The polarisation signatures of microlensing

Abstract It has already been shown that microlensing can give rise to a non-zero variable polarisation signal. Here we use realistic simulations to demonstrate the additional information that can be gained from polarimetric observations of lensing events.

Variable polarisation and luminosity for microlensing of extended stellar sources

Microlensing of extended stellar sources in the LMC and Galaxy by low mass lenses can produce variable polarisation. The characteristics of the polarisation and flux profiles can provide considerable information about the lens geometry, and help determine the importance of such low mass objects as a dark matter component.

Inversion of polarimetric data from eclipsing binaries

We describe a method for determining the limb polarization and limb darkening of stars in eclipsing binary systems, by inverting photometric and polarimetric light curves. Because of the ill-conditioning of the problem, we use the Backus-Gilbert method to control the resolution and stability of the recovered solution, and to make quantita- tive estimates of the maximum accuracy possible. Using this method we conrm that the limb polarization can in- deed be recovered, and demonstrate this with simulated data, thus determining the level of observational accuracy required to achieve a given accuracy of reconstruction. This allows us to set out an optimal observational strat- egy, and to critcally assess the claimed detection of limb polarization in the Algol system. The use of polarization in stars has been proposed as a diagnostic tool in microlensing surveys by Simmons et al. (1995), and we discuss the extension of this work to the case of microlensing of extended sources.