and Cosmology

3. The World of Galaxies
126
Fig. 3.36. Geometry of an “elliptical” lens, whereby it is of little
importance whether the surface mass density Σ is constant
on ellipses (i.e., the mass distribution has elliptical isodensity
contours) or whether an originally spherical mass distribution
is distorted by an external tidal field. On the right-hand side
in both panels, several different source positions in the source
plane are displayed, each corresponding to a different color.
The origin in the source plane is chosen as the intersection
point of the line connecting the center of symmetry in the lens
and the observer with the source plane (see also Fig. 2.22).
Depending on the position of the source, one, three, or five
images may appear in the lens plane (i.e., the observer’s sky);
they are shown on the left-hand side of each panel. The curves
in the lens plane are the critical curves, the location of all
points for which μ →∞. The curves in the source plane (i.e.,
on the right-hand side of each panel) are caustics, obtained
by mapping the critical curves onto the source plane using the
lens equation. Obviously, the number of images of a source
depends on the source location relative to the location of the
caustics. Strongly elongated images of a source occur close
to the critical curves
boosting the image separation to a large value. The lens
system QSO 0957+561 was observed in all wavelength
ranges, from the radio to the X-ray. The two images
of the quasar are very similar at all λ, including the
VLBI structure (Fig. 3.38) – as would be expected since
the lens effect is independent of the wavelength, i.e.,
achromatic.
QSO PG1115+080. In 1980, the so-called triple quasar
was discovered, composed of three optical quasars at
a maximum angular separation of just below 3 ′′ .Component
(A) is significantly brighter than the other two
images (B, C; see Fig. 3.39, left). In high-resolution images
it was found that the brightest image is in fact
a double image: A is split into A1 and A2. The angular
separation of the two roughly equally bright images
is ∼ 0 . ′′ 5, which is considerably smaller than all other
angular separations in this system. The four quasar images
have a redshift of z s = 1.72, and the lens is located
at z d = 0.31. The image configuration is one of those
that are expected for an elliptical lens, see Fig. 3.36.
With the NIR camera NICMOS on-board HST,
not only were the quasar images and the lens galaxy
observed, but also a nearly complete Einstein ring
(Fig. 3.39, right). The source of this ring is the host galaxy
of the quasar (see Sect. 5.4.5) which is substantially
redder than the active galactic nucleus itself.
From the image configuration in such a quadruple
system, the mass of the lens within the images can be
estimated very accurately. The four images of the lens
system trace a circle around the center of the lens galaxy,
the radius of which can be identified with the Einstein
radius of the lens. From this, the mass of the lens within
the Einstein radius follows immediately because the
Einstein radius is obtained from the lens equation (3.56)
by setting β = 0. Therefore, the Einstein radius is the
solution of the equation
θ = α(θ) = m(θ) ,
θ
or
m(θ E ) = 4GM(θ E) D ds
c 2 = θE 2 D d D .
s
This equation is best written as
M(θ E ) = π(D d θ E ) 2 Σ cr , (3.66)
which is readily interpreted: