Tutorial & Examples

by Ian Boyle and Chuck Keeton

30 Aug 2005


INTRODUCTION

This tutorial provides step by step instructions for four basic lensing calculations as an introduction to the gravlens software as well as one section that covers additional commands. Each example is presented in two parts: the analytical solution and the solution as found using gravlens. This tutorial assumes familiarity with basic lens theory.
For quantitative examples, the following values are assumed:

G = 6.67 x 10-8 dyne cm g-2
c = 3 x 1010 cm/s 
M  =  1012Msolar = 1.99 x 1045 g
Ds = 2000 Mpc = 2 x 109 pc = 6.67 x 1027 cm
Dl  = 1000 Mpc = 109 pc = 3.09 x 1027 cm
Dls = 1000 Mpc = 109 pc = 3.09 x 1027 cm

Dls = Ds - Dl *
* Not the case for cosmological distances in general

This tutorial progressively builds on the material presented so each section assumes an understanding of the material explained in the previous sections.  The following index lists the gravlens material reviewed in each part of the tutorial:

SECTION I.   Point Mass Lens
SECTION II.   Singular Isothermal Sphere Lens Without Shear
SECTION III.   Singular Isothermal Sphere Lens With Shear (At Origin)
SECTION IV.   Singular Isothermal Sphere Lens Without Shear
SECTION V.   Additional Commands


SECTION I >