and Cosmology

3.9 Population Synthesis
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Fig. 3.44. Lens geometry in two universes with different Hubble
constant. All observables are dimensionless – angular
separations, flux ratios, redshifts – except for the difference in
the light travel time. This is larger in the universe at the bottom
than in the one at the top; hence, Δt ∝ H0 −1 . If the time
delay Δt can be measured, and if one has a good model for
the mass distribution of the lens, then the Hubble constant can
be derived from measuring Δt
Fig. 3.43. The quasar MG1654+13 shows, in addition to the
compact radio core (Q), two radio lobes; the northern lobe is
denoted by C, whereas the southern lobe is imaged into a ring.
An optical image is displayed in gray-scales, showing not
only the quasar at Q (z s = 1.72) but also a massive foreground
galaxy at z d = 0.25 that is responsible for the lensing of the
lobe into an Einstein ring. The mass of this galaxy within the
ring can be derived with a precision of ∼ 1%
It is easy to see that Δt depends on the Hubble constant,
or in other words, on the size of the Universe. If
a universe is twice the size of our own, Δt would be
twice as large as well – see Fig. 3.44. Thus if the mass
distribution of the lens can be modeled sufficiently well,
by modeling the geometry of the image configuration,
then the Hubble constant can be derived from measuring
the difference in the light travel time. To date, Δt has
been measured in about 10 lens systems (see Fig. 3.45
for an example). Based on “plausible” lens models we
can derive values for the Hubble constant that are compatible
with other measurements (see Sect. 3.6), but
which tend towards slightly smaller values of H 0 than
that determined from the HST Key Project (3.36). The
main difficulty here is that the mass distribution in lens
galaxies cannot unambiguously be derived from the
positions of the multiple images. Therefore, these determinations
of H 0 are currently not considered to be
precision measurements. On the other hand, we can
draw interesting conclusions about the radial mass profile
of lens galaxies from Δt if we assume H 0 is known.
In Sect. 6.3.4 we will discuss the value of H 0 determinations
from lens time delays in a slightly different
context.
The ISM in Lens Galaxies. Since the same source is
seen along different sight lines passing through the lens
galaxy, the comparison of the colors and spectra of the
individual images provides information on reddening
and on dust extinction in the ISM of the lens galaxy.
From such investigations it was shown that the extinction
in ellipticals is in fact very low, as is to be expected
from the small amount of interstellar medium they contain,
whereas the extinction is considerably higher for
spirals. These analyses also enable us to study the relation
between extinction and reddening, and from this
to search for deviations from the Galactic reddening
law (2.21). In fact, the constant of proportionality R V is
different in other galaxies, indicating a different composition
of the dust, e.g., with respect to the chemical composition
and to the size distribution of the dust grains.