Annu. Rev. Astron. Astrophys. 1992. 30: 311-358
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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 Msmsun, 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 ~ (xi c / Dd thetaE)2, where xi 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 Msmsun (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 gtapprox 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 Sigma > Sigmacr (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 2thetaE, which is then converted to the velocity dispersion sigma 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 sigma range from ~ 200-500 km s-1. It is believed that in some cases, especially where the derived sigma 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 Msmsun (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.

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