Next Contents Previous  2.3 The Singular Isothermal Sphere (SIS)
Galaxies and clusters of galaxies that act as gravitational
lenses can be approximated by singular isothermal spheres. It is
then easy to relate an angular scaling parameter xiE, referred
to as the Einstein radius, to the mass inside the corresponding
light cone. The Einstein radius xiE corresponds to the ring
image of a point source aligned exactly on the axis of the lens
(Fig. 7). For a singular isothermal sphere the line of sight
velocity dispersion is constant as well as the gradient of the
projected potential. Therefore, the deviation angle is constant
and xiE can be obtained from the one dimensional velocity
dispersion sigma1D as :  Equation 10 (10) Equation 10   Equation
11 (11) Equation 11  The perfect alignment of the source on the
optical axis of the deflector is quite unlikely, but with a
small misalignment the observer will see two opposite arcs
approximately located at the Einstein radius (Fig. 7).  In fact,
the total mass inside t