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Astron. Astrophys. 320, 8-12 (1997)

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4. A gravitational lens origin for close QSO pairs

Gravitational light deflection can not only lead to the occurrence of multiply imaged QSO and radio galaxies, but it also affects the apparent magnitude of sources when there is a matter concentration in or near the line-of-sight to them. An over-density of matter in the foreground of a source will magnify it. Depending on the steepness of the source counts, this magnification can yield a dramatic biasing effect: Sources which without lensing would be too faint to be included in a flux-limited sample can be boosted above the flux threshold and thus be included in the sample. That is, magnified sources are preferentially included in flux-limited samples. If the source counts are steep, then for every bright source there is a large number of faint sources, from which the magnified sources can be drawn. Hence, this magnification bias is strong for steep counts, and unimportant for flat counts (for a detailed discussion and references on the magnification bias, see Sect. 12.5 of Schneider, Ehlers & Falco 1992).

It can be argued that at least two of the QSO pairs show strong evidence for lensing to be important. This is most obvious in the QSO 1009-025, where the QSO with the larger redshift is multiply imaged. In the spectra of the two QSO images, absorption lines are seen at redshift [FORMULA] and at [FORMULA] i.e., the redshift of the lower-redshift QSO (Hewett et al. 1994). While the available information about this lens system is not sufficient for constructing a detailed lens model, it is likely that the higher-z QSO is magnified by at least 1 mag, as is typical for double images. In AO 0235+164, gravitational lensing has long been suspected, for example to account for the strong variability in the optical and the radio flux, which might find an explanation in terms of microlensing. The long-known companion about [FORMULA] to the south of AO 0235+164A, several candidate galaxies even closer to it (Stickel, Fried & Kühr 1988, Yanny et al. 1989), and the observed 21 cm line absorption (Wolfe, Davis & Briggs 1982) may be indications of potential lenses in this system; in fact, from the image of a galaxy only [FORMULA] away from the BL Lac (Stickel et al. 1988), one may ask why no multiple images are seen in this system (Narayan & Schneider 1990). Also, Iovino & Shaver (1986) have placed upper bounds on the mass of the foreground QSO in the system 1548+114 from the absence of a secondary image of the higher redshift QSO.

One can think of two variants of a lensing scenario: in the first, the lenses are positioned at redshifts lower than both QSOs, i.e., both QSOs are magnified, and in the second, the lens is physically associated with the foreground QSO and magnifying only the background QSO. From the preceding remarks about magnification bias, the former scenario is considered unlikely: in three of the four pairs, the foreground QSO is at [FORMULA] or fainter, i.e., close to or beyond the break in the QSO number counts. At these magnitudes, the magnification bias is very weak and can even lead to a decrease of the local number counts. Hence, in the first scenario one would not expect to obtain an increased number of pairs from lensing. This conclusion may be slightly altered if the Hawkins & Véron (1995) counts are employed, as they do not show a clear turnover towards fainter sources; on the other hand, their bright-end slope is flatter than that assumed here, so that the overall efficientcy of lensing would be reduced with the Hawkins & Véron counts.

Gravitational lensing as an explanation for an increased chance of finding pairs has been invoked by Gott & Gunn (1974) in the context of 1548+115. They picture the foreground QSO as the lens, modelled by a singular isothermal sphere (see also Iovino & Shaver 1986). However, in order to get an appreciable increase of pair probability, the mass associated with the foreground QSO must be quite large. Here we consider a somewhat different picture in which the foreground QSO is physically associated with a larger-scale mass overdensity which acts as the gravitational lens. Hence, the qualitative picture is similar to that empoyed in understanding the large angular scale associations of foreground galaxies with high-redshift QSOs (see, e.g., Bartelmann & Schneider 1994). There is one additional argument in favour of such an interpretation: In two cases (0235+164 and 1548+115) there is evidence for an enhanced number density of galaxies surrounding the QSO which may indicate the existence of an associated (host) cluster. this evidence is supported through spectroscopic observations in the case of 0235+164.

A toy model should illustrate the possible effects of this scenario: Consider a `foreground sky' and a `background sky'; on the latter, the higher-redshift QSOs are randomly distributed, having unlensed source counts of the form [FORMULA], with [FORMULA] (e.g., Hartwick & Schade 1990). Suppose that a fraction f of the `foreground sky' contains matter over-densities which magnify QSOs on the `background sky' by a factor [FORMULA], whereas in the other directions, background sources are (de)magnified by a factor [FORMULA]. Flux conservation (Schneider et al. 1992, Sect. 4.5.1) then requires that [FORMULA]. Futhermore, assume that QSOs in the `foreground' are concentrated towards those directions in which over-densities of matter are present. That is, if [FORMULA] is the mean number density for foreground QSOs, let the number density in the magnifying fraction of the `foreground sky' be [FORMULA], whereas the number density in the rest of the sky is [FORMULA], with [FORMULA]. Using the preceding assumptions, one can then show that in a flux-limited sample of N background QSOs the expected number of foreground QSOs within an angle [FORMULA] is


where the factor


describes the ratio of expected pairs relative to the case that no lensing takes place. In Fig. 1, we have plotted Q as a function of f, for the maximum value of [FORMULA], i.e. all QSOs in the foreground sky are assumed to lie in the over-dense regions.

[FIGURE] Fig. 1. The ratio Q of pairs of foreground-background QSOs in the lensing toy-model described in the text, relative to the case of no lensing present, as a function of the fraction of the sky f in which overdensities of matter leads to magnification of the background QSOs by a factor [FORMULA]. The solid (dotted, dashed) curve corresponds to magnification of half a magnitude (one magnitude, 1.5 magnitudes), and it has been assumed that all foreground QSOs are situated in the overdense regions, [FORMULA]

As can be inferred from the figure, the increase in the expected number of pairs is quite substantial, even for low values of the magnification. For example, if the magnification in [FORMULA] % of the sky is one magnitude [FORMULA], the expected number of pairs increases by a factor of about 3.5. Such an increase would suffice to increase the probability in Eq. (2) to about 18%, and hence the observed number of pairs would not pose an improbable statistical fluctuation. It should be clear that the toy model presented here is not realistic, but it illustrates the basic features of a more realistic lensing scenario. One of the problems encountered in making a realistic model is that the observed number density of QSOs flattens as we go to fainter magnitudes so that while [FORMULA] up to [FORMULA], it becomes [FORMULA] for the range 19.5 to 21.5 (Hartwick and Schade 1990; but see Hawkins & Véron 1995). Another more basic problem is our lack of understanding the relation between matter overdensities and QSOs; if a `biasing factor' were assumed for the QSOs, an analysis similar to that of Bartelmann (1995) could be employed.

To distinguish between a lensing scenario as discussed here and the one employed by Gott & Gunn (1974) one would have to investigate the number of pairs at larger separations. In the case that the QSO acts as a lens on its own, the number of pairs in excess of random would drop quickly beyond separations of a few arcseconds, whereas the other scenario implies lensing effects at larger separations. Unfortunately, no systematic search for (faint) QSOs in the vicinity of bright QSOs has been done, except for the lens surveys which restrict their search radius to a few arcseconds only. The involvement of radio QSOs may be seen as an additional hint for a lensing interpretation: if the foreground QSO is radio loud (as in 1548+115), one can argue from the fact that radio QSOs are supposed to be hosted in ellipticals which prefer a rich environment that the QSO is indeed located in an overdense region. If the background QSO is radio loud (as in 0235+164), the double magnification bias (Borgeest et al. 1991) increases the effective slope of the source counts, making lensing more effective.

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Online publication: July 3, 1998