Modelling Complex Gravitational Microlensing Events

Abstract

This thesis outlines the theory underlying gravitational lensing, describes in some detail software developed by the author to model microlensing events for extracting physical parameters from observed light curves, and then presents an independent analysis of five binary lens events using the modelling software. Chapter 1 provides a general introduction to the subject and places it in an historical context. It concludes with a brief description of the current microlensing survey and monitoring groups; the New Zealand / Japan MOA collaboration in particular. Chapter 2 reviews gravitational lensing theory in a quite general way, starting with a key result from Einstein's general relativity concerning the deflected paths of light rays in gravitational fields. As a backdrop for this theory and to provide more completeness, appendices A and B provide a study of exactly how much tensor analysis (appendix A) and physics (appendix B) is required at a minimum level in order to arrive at the starting point of chapter 2: the amount of deflection of a light ray by a massive object. Chapter 3 provides an overview and presents some theory about the various aspects concerning microlensing observations and microlensing modelling. The emphasis is on modelling binary lensing events, since this is where both the beauty and complexity of microlensing events really comes alive. Also in this chapter, an overall description is given of the algorithms used in the developed and implemented modelling software. The underlying method used for determining the impact of intervening massive objects affecting the paths of photons travelling from the source star to the observer is the inverse ray tracing method. Two slightly different methods are used to generate lensing event light curves with this method, and they are discussed in this chapter. The methods used to search the X2 hyperspace for a best fit to the data include the use of the Markov Chain Monte Carlo method. Supporting material for this latter method is also provided in appendix C. Parts of Chapter 6 provide more details on the modeling software implementation, and demonstrates the performance of the software Detailed modelling of three recent microlensing events together with one historic event is presented in chapters 4 to 7. These events are all those from which the four confirmed. microlensing planets to date have been discovered. The recent planetary event OGLE-2005-BLG-390 is discussed in detail in chapter 4. This event was published as a Nature article in, January this year (2006) and included some modelling work using the software presented in this thesis. The most likely modelling conclusion is that the binary lens consists of a low mass star and a planet about 5 times the mass of the Earth. Chapter 4 looks at this conclusion in detail and examines two alternative models. Three other planetary lensing events .are covered in chapters 5, 6 and 7. To complete the specific modelling work, the binary lensing event MOA-2002-BLG-42 is discussed in chapter 8. With largely unbroken degeneracy involving the mass ratio and the binary separation, a surprising results is that in the best-fitting models the background star has the closest approach to the much lighter binary component, while the higher mass component is at large distance. The lowest X2 is reached for models in planet regime, although the event time scale does not favour such models. Continued modelling of this event still suggests further work, including the use of detailed limb darkening models. Chapter 9 provides a summary with closing remarks.