5.2 External Galaxies
5.2.1 CORES The high surface density
associated with the cores of galaxies,
coupled with the expectation that most of this density is due to
stars, implies that images of a background source that happen to be
superimposed on the central region of a foreground galaxy are likely
to display microlensing effects. Q2237+031, with four images less
than 1 kpc from the center of a z = 0.039 galaxy, was recognized soon
after its discovery to be an excellent candidate
(Kayser et
al. 1986,
Schneider et
al. 1988,
Kayser & Refsdal
1989).
Indeed, an apparent microlensing event was seen in 1988
(Irwin et
al. 1989),
when image A
brightened by a fraction of a magnitude within a time of order a
month. Other events have since been seen in image A and in the
other images
(Corrigan et
al. 1991).
Detailed numerical simulations
(Wambsganss
et al. 1990a,
b,
Witt et
al. 1993)
indicate that the observed
variations are similar to those expected with a normal stellar mass
distribution in the lens, with a mass cutoff ~ 0.1 M,
and a transverse velocity < 1000 km s-1. This is a
unique instance where the dynamical mass of a cosmologically distant
star has been measured.
Gravitational lensing can also provide information on the overall mass
distribution of the lens. In Q2237+031, the positions and relative
magnifications of the four images are well-reproduced by a mass
distribution assumed to follow the light
(Schneider et
al. 1988).
The derived mass-to-blue light ratio is ~ 10, which is consistent
with Population II stars. It appears that the core of this galaxy
does not contain a significant amount of dark matter.
Further information on the mass distribution in the cores of lensing
galaxies comes from observed upper limits on the strength of the
central/odd image. The magnification of this image is expected to be
~ ( c
/ Dd E)2, where c is the
core radius of the mass distribution. The fact that no central
image has been seen in any example of lensing so far suggests that the
core radii of the lenses are no more than a few hundred parsecs
(Narayan et
al. 1984,
Narayan &
Wallington 1992a),
or that the centers
of the lenses have compact masses of ~ 1010 M (Narasimha
et al. 1986). This is consistent with directly measured core radii of
nearby galaxies
(Lauer et
al. 1991).
However, a contrary indication is
obtained from a number of BL Lac objects that apparently lie behind
the cores of low redshift galaxies
(Stickel et
al. 1988a,
b,
1989).
None of these sources is multiply-imaged, which sets a lower limit 2 kpc to the core radii
of the galaxies
(Narayan &
Schneider 1990).
Discussions of the mass distribution in the core become complicated
when the additional magnification due to microlensing is included.
This is because the optical depth for microlensing is usually large,
and so the expected distribution of image intensities is likely to be
strongly modified
(Section 3.5). Moreover, if
> cr (which is
almost always the case for the central image), the primary image can
sometimes be ``swallowed'' by a star
(Section 3.5), leading to a highly
demagnified image
(Chang & Refsdal
1984,
Subramanian
et al. 1985,
Paczynski 1986a).
Microlensing at large optical depth can also occasionally give
extremely large magnifications. It has been suggested that several
apparent low redshift BL Lacs are in fact faint high redshift OVVs
that have been microlensed by stars in a foreground galaxy in such a
way that the continuum is highly brightened while the line-emitting
regions are not
(Ostriker &
Vietri 1985,
1986,
1990).
The rapid variability of these objects may also be attributed to
microlensing
(Nottale 1986,
1988,
Schneider &
Weiss 1987).
Magnification bias is used to explain
the intrinsically unlikely alignment of the OVV with the galaxy.
However, BL Lacs (including those claimed to be lensed) have distinct
radio properties, and the radio emission is unlikely to be microlensed
since it is thought to come from a region at least as large as the
broad-line emitting region
(Gear 1991).
Also, if the microlensing is due to a normal star, then the bright phase
will only last a couple of years, whereas several of the BL Lacs have
been known for nearly 20 years
(Kayser 1992).
5.2.2 HALOS Direct estimates of the masses of
gravitational lenses may be obtained
in most cases of multiple lensing provided the redshifts of the lens
and the source are measured. At the crudest level, the angular
separation of the images gives an estimate of 2E, which is
then converted to the velocity dispersion of the lens (Equation
8) or the mass enclosed within the image cylinder (Equation
4, but this is not always reliable, cf
Nemiroff 1988a).
Estimated values of
range from ~ 200-500 km s-1. It is believed that in some
cases, especially where the
derived turns out to be
large, e.g. Q0957+561, there is a
significant contribution to the lensing from a galaxy cluster
surrounding the primary lens. An upper limit to the mass of a quasar
can be obtained whenever another quasar with a higher redshift happens
to lie in nearly the same direction and not show any evidence of
multiple-imaging (e.g. the quasar pairs Q1548+115, Q1038+528,
Gott & Gunn 1974,
Dyer & Roeder
1982).
Detailed models provide a better estimate of the mass of a lens, and also
help determine the ``shape'' of the projected mass density. Such models
are available for the multiply-imaged quasars, Q0957+561
(Falco et
al. 1991a),
Q1115+080
(Narasimha et
al. 1982),
Q2016+112
(Narasimha et
al. 1987),
Q0142-100
(Surdej et
al. 1988), and
Q1413+117
(Kayser et
al. 1990).
It appears that the solutions are not unique
since differently parametrized models are comparably successful in
fitting the observations
(Kochanek 1991a),
though the various
parametrizations do tend to be qualitatively similar to one another in certain
essential features of the mass distribution. The radio ring sources
have arguably the best-constrained mass models because of the larger
number of observational constraints provided by the resolved images
(Kochanek et
al. 1989).
However, there could be an undetermined
normalization if the redshift of either the lens or the source is not
known (as in MG1131+0456). The mass enclosed within the ring in
MG1654+1346, where both the lens and the source have
been observed, is
estimated to be 9 ± 0.4 x 1010h-1
M
(Langston et
al. 1990)
and the mass-to-blue light ratio is 16h solar units
(Burke 1992).
Usually, the derived mass of a gravitational lens is the sum of the
mass in the galaxy and that in a surrounding cluster (if any).
Interestingly, if the time delay between two of the images is
measured, then the mass of the galaxy alone (enclosed between the
images) may be estimated, independently of the cluster
(Borgeest 1986,
Narayan 1991).
This is possible whenever the cluster can be
approximated as a quadratic lens.
Several attempts have been made to check whether the observed numbers
of multiply-imaged quasars, and the distribution of image separations,
apparent magnitudes, etc. are consistent with the number density and
masses/velocity dispersions of galaxy-like mass condensations in the
universe
(Hacyan 1982,
Tyson 1983,
Turner et
al. 1984,
Dyer 1984,
Hinshaw & Krauss
1987,
Kochanek &
Blandford 1987,
Narayan & White
1988,
Wu 1989,
Kochanek 1991b,
Fukugita &
Turner 1991,
Mao 1991,
Narayan &
Wallington 1992a).
The probability that a given quasar will
be multiply-imaged in some particular image configuration can be
written as the product of factors describing respectively the assumed
mass distribution of the lens, the cosmography of the world model, the
effects of magnification bias (which depends upon the quasar
luminosity function), an angular resolution factor (to model the
difficulty of discovering small angular separation pairs), and some
allowance for other selection effects (e.g. large magnitude-difference
image pairs are hard to find). In the modeling, it is found that the
introduction of a core radius enhances the mean image separation but
reduces the overall cross section for lensing. Also, in comparing the
relative incidence of doubly- and quadruply-imaged quasars, it is
essential to consider nonspherical lenses. Overall, it appears from
such studies that the observations are consistent with the hypothesis
that most of the lensing of quasars is done by galaxies. Some
additional deflection due to galaxy groups, clusters and other
large-scale mass distribution is needed to explain a minority of the
cases with large image separations
(Turner et
al. 1984,
Anderson &
Alcock 1986,
Katz & Paczynski
1987,
Narayan & White
1988,
Jaroszynski 1991).
The existence of lens candidates with no detected lensing galaxy down
to deep limits (Section 2.1) does
leave open the possibility that the
universe may contain galaxy-sized condensations made entirely of dark
matter. Since lensing galaxies have been seen in roughly half the
known cases of lensing, the number density of such dark mass
concentrations is probably no larger than that of real galaxies.
However, if the dark lenses have large core radii and subcritical
central surface densities, then they will produce multiple imaging only
when two or more lenses happen to line up toward a distant quasar
(Subramanian
et al. 1987).
In that case their number density could be substantially larger.
Multiply-imaged quasars probe only the mass distribution interior to
the images, typically the inner regions of lens galaxies. Although
lines-of-sight through outer galaxy halos do not lead to
multiple-imaging, there can nevertheless be measurable distortions in
the images of background optical and radio galaxies
(Blandford &
Jaroszynski 1981,
Noonan 1983,
Saslaw et
al. 1985,
Kochanek &
Lawrence 1990,
Kronberg et
al. 1991).
Tyson et
al. (1984)
have set observational limits on the tangential elongation induced in
background galaxies by the lensing action of foreground galaxies. The
data are generally consistent with galaxy masses derived from rotation
curves assuming extended halos
(Kovner &
Milgrom 1987).
Several intriguing claims have been made that background sources,
particularly quasars, BL Lacs and radio galaxies, preferentially occur
behind foreground galaxies
(Arp 1981,
1982;
Sulentic 1981;
Tyson 1986;
Stocke et
al. 1987;
Webster et
al. 1988a;
Fugmann 1988,
1989,
1990;
Hammer & Le
Fevre 1990).
Some of these claims appear to be
statistically significant. A plausible explanation of the phenomenon
is that the sources are magnified by the lensing action of the
galaxies and so, because of magnification bias, these sources are
found preferentially in the vicinity of the lenses
(Canizares 1981,
Hammer & Nottale
1986a).
There are two opposing effects at work
here. For a magnification µ, the observed number density of a
given population of sources actually goes down by a factor µ
because the sky is locally ``stretched'' by the magnification.
However, this effect is compensated by the fact that sources that are
fainter by up to a factor of µ will be brought into a
flux-limited
sample as a result of the brightening. If the logarithmic cumulative
counts have a slope steeper than 0.4 per magnitude, then the net
observed number density will increase
(Narayan 1989,
Kovner 1989b,
Schneider 1989).
Counts of optical quasars are steeper than this
limit at the bright end, but shallower at faint magnitudes, with the
break occurring at B ~ 19
(Boyle et
al. 1988).
Thus, bright
quasars, at least, should display preferential association with
foreground galaxies. However, the magnitude of the effect is not
expected to be large
(Vietri &
Ostriker 1983,
Zuiderwijk 1985,
Narayan 1989,
Kovner 1989b,
Schneider 1989,
Hogan et
al. 1989,
Schneider 1992),
particuarly for quasars close to the break magnitude,
and this may be in strong conflict with a substantial overdensity seen
in one sample
(Magain et
al. 1992).
The recent suggestion of a possible double magnification bias
(Borgeest et
al. 1991)
in a sample that is flux-limited in two independent
wavelength bands, e.g. optical and radio, merits further investigation.
One question yet to be settled is whether quasar-galaxy associations
are primarily due to macrolensing by the overall mass distribution of
the galaxy or whether microlensing by individual stars in the
galactic halo is also important. An argument for the latter is the
fact that the preferential association appears to be strongest for
compact sources such as optical and X-ray quasars and BL Lacs (and
possibly compact flat spectrum radio sources, though the case for
microlensing here is weaker). Also, theoretical arguments indicate
that magnification bias is stronger when macro and microlensing are
considered together than with the former alone
(Vietri &
Ostriker 1983,
Nityananda &
Ostriker 1984,
Ostriker &
Vietri 1986,
Schneider 1986,
1987a,
b,
Bartelmann &
Schneider 1991,
Nemiroff 1991).
However, it has been claimed that 3C radio sources, most of which are
quite extended, have foreground galaxies in their vicinity unusually
often
(Hammer & Le
Fevre 1990).
This cannot be due to microlensing.
Also, a natural way to reconcile the rarity of the gravitational
lensing phenomenon (the probability of a given source being multiply
imaged is ~ 10-4 - 10-3) with the fact that
1830-211, one of the brightest radio sources known, is lensed into an
Einstein ring, is to invoke magnification bias. Again, since the source is
well-resolved, microlensing cannot be important.
Microlensing in a galaxy halo would be directly confirmed if the
associated time variability in a background quasar is ever detected
(Chang & Refsdal
1979,
1984,
Gott 1981,
Young 1981,
Subramanian
et al. 1985).
Such variability would reveal the mass of the microlens and
provide information on the stellar content of the lens.
Schild & Smith
(1991)
have obtained fairly convincing evidence for microlensing in Q0957+561. A few other claims of variability have
been made
(Borgeest et
al. 1992a,
b,
Altieri & Giraud
1992),
but none are unambiguous.