N. Straumann, Ph. Jetzer, J. Kaplan, Topics on gravitational Lensing, pp. 120, 1998.
ISBN 88-7088-302-7     € 16,00
NAPOLI SERIES ON PHYSICS AND ASTROPHYSICS  1.  

Contents

Forward p.VII

Preface p.IX

Lectures on Gravitational Lensing by Norbert Straumann p.1

Introduction p.3

1:: Basic lensing equations p.5
1.1 Reduction to a problem of ordinary ray optics, effective refraction index. p.5
1.2 Deflection by an arbitrary mass concentration p.7
1.3 The general lens map p.10
1.4 Magnification, critical curves and caustics p.12
1.5 Time delay p.13
1.6 Whitney theorem on generic singularities p.14
1.7 Ciassification of ordinary images, orientation and shape p.16

2 Simple lens models p.21
2.1 Axially symmetric lenses: generalities p.21
2.2 The Schwarzschild lens: microlensing . p.24
2.3 Singular isothermal sphere p.26
2.4 Isothermal sphere with finite core radius p.29
2.5 Lensing experiments p.30
2.6 Extended source .. p.32
2.7 Two point-mass lens p.33

3 Lensing by galaxy clusters p.37
3:1 Strong lensing by clusters p.37
3.2 Mass reconstruction from weak lensing p.40
3.2.1 Relations between plean convergence and reduced shear p.40
3.2.2 Practical difficulties, examples p. 43
3.3 Comparison with results from X-ray observations p. 43

 

4 Extensions to a cosmological context 49
4.1 Lens mapping in cosmology 49
4.2 Hubble constant from time delays 51
4.3 Bounds on the cosmological constant from lensing statistics 54

5 Complex formulation of lensing theory 59
5.1 Complex formulation 59
5.1.1 Mathematical preliminaries 59
5.1.2 The complex lens mapping and its differential . 62
5.2 Applications. 63
5.2.1 Number of images for a regular lens 63
5.2.2 Relations between mean convergence and reduced shear 64
5.2.3 Other useful reconstruction equations 66

Gravitational Microlensing by Philippe Jetzer
Introduction 77
1 Mass of the Milky Way 77
2 Baryonic dark matter candidates 78
3 Present status of microlensing research . 80
3.1 Towards the LMC and the SMC 80
3.2 Towards the galactic centre 81
3.3 Towards the Andromeda galaxy . 82
3.4 Further developments . 82
4 Basics of microlensing 83
4.1 Microlensing probability 83
4.2 Microlensing rate towards the LMC 85
4.3 Microlensing rate towards M31 88
4.4 Microlensing rate towards the galactic bulge . 89
4.5 Most probable mass for a single event 92
4.6 Mass moment method 93
Conclusions 95

Pixel Lensing by Jean Kaplan 101
Introduction. 103
1 Frame subtraction 103
2 Monitoring pixels 104
2.1 The seeing problem 104
2.2 The Analysis 112