3.3 Critical surface mass density3 Basics of Gravitational Lensing3.1 Lens equation

3.2 Einstein radius

For a point lens of mass M, the deflection angle is given by Equation (4Popup Equation). Plugging into Equation (6Popup Equation) and using the relation tex2html_wrap_inline2229 (cf. Figure  3), one obtains:

equation149

For the special case in which the source lies exactly behind the lens (tex2html_wrap_inline2231), due to the symmetry a ring-like image occurs whose angular radius is called Einstein radius tex2html_wrap_inline2233 :

equation157

The Einstein radius defines the angular scale for a lens situation. For a massive galaxy with a mass of tex2html_wrap_inline2235 at a redshift of tex2html_wrap_inline2237 and a source at redshift tex2html_wrap_inline2239, (we used here tex2html_wrap_inline2241 as the value of the Hubble constant and an Einstein-deSitter universe), the Einstein radius is

  equation172

(note that for cosmological distances in general tex2html_wrap_inline2243 !). For a galactic microlensing scenario in which stars in the disk of the Milky Way act as lenses for bulge stars close to the center of the Milky Way, the scale defined by the Einstein radius is

equation181

An application and some illustrations of the point lens case can be found in Section  4.7 on galactic microlensing.



3.3 Critical surface mass density3 Basics of Gravitational Lensing3.1 Lens equation

image Gravitational Lensing in Astronomy
Joachim Wambsganss
http://www.livingreviews.org/lrr-1998-12
© Max-Planck-Gesellschaft. ISSN 1433-8351
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