and Cosmology

3. The World of Galaxies
130
An even more precise determination of the mass was
obtained for the lens galaxy of the Einstein ring in
the system MG 1654+13 (Fig. 3.43). The dependence
on the other cosmological parameters is comparatively
weak, especially at low redshifts of the source and the
lens. Most lens galaxies are early-type galaxies (ellipticals),
and from the determination of their mass
it can be concluded that ellipticals also contain dark
matter.
Fig. 3.41. Spectra of the four images of the quasar 2237+0305,
observed with the CFHT. As is clearly visible, the spectral
properties of these four images are very similar; this is the
final proof that we are dealing with a lens system here. Measuring
the individual spectra of these four very closely spaced
sources is extremely difficult and can only be performed under
optimum observing conditions
3.8.4 Applications of the Lens Effect
Mass Determination. As mentioned previously, the
mass within a system of multiple images can be determined
directly, sometimes very precisely. Since the
length-scale in the lens plane (at given angular scale)
and Σ cr depend on H 0 , these mass estimates scale
with H 0 . For instance, for QSO 2237+0305, a mass
within 0 . ′′ 9of(1.08 ± 0.02)h −1 × 10 10 M ⊙ is derived.
Environmental Effects. Detailed lens models show
that the light deflection of most gravitational lenses
is affected by an external tidal field. This is due to
the fact that lens galaxies are often members of galaxy
groups which contribute to the light deflection as
well. In some cases the members of the group have
been identified. Mass properties of the corresponding
group can be derived from the strength of this external
influence.
Determination of the Hubble Constant. The light
travel times along the different paths (according to the
multiple images) are not the same. On the one hand
the paths have different geometrical lengths, and on the
other hand the light rays traverse different depths of the
gravitational potential of the lens, resulting in a (general
relativistic) time dilation effect. The difference in
the light travel times Δt is measurable because luminosity
variations of the source are observed at different
times in the individual images. Δt can be measured
from this difference in arrival time, called the time
delay.
Fig. 3.42. The radio source 1938+666 is
seen to be multiply imaged (contours in the
right-hand figure); here, the radio source
consists of two components, one of which is
imaged four-fold, the other two-fold. A NIR
image taken with the NICMOS camera onboard
the HST (left-hand figure, also shown
on the right in gray-scale) shows the lens
galaxy in the center of an Einstein ring that
originates from the stellar light of the host
galaxy of the active galactic nucleus