Annu. Rev. Astron. Astrophys. 1994. 32: 531-590
Copyright © 1994 by . All rights reserved

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7.1. Macrolensing Constraints on Compact Objects

If one has a population of compact objects with mass M and density parameter Omegac, then the probability P of one of them image-doubling a source at redshift z approx 1 and the separation between the images theta are given by

Equation 7.1        (7.1)

(Press & Gunn 1973). One can therefore use upper limits on the frequency of macrolensing for different image separations to constrain Omegac as a function of M. Although optical searches, VLA, and the Hubble Space Telescope (HST) can only constrain objects down to 1010 Msun (corresponding to a resolution of 0.1 arcsec), speckle cameras (with a resolution of 10-2 arcsec) can get down to 108 Msun, while VLBI and VLBA (with resolutions of 1 and 0.1 milliarcsec) can search for objects as small as 106 Msun and 104 Msun. The best strategy is to look for dim images near bright objects (Nemiroff & Bistolas 1990), which requires a large dynamic range, but one can also look for circular distortions and gravity rings (Saslaw et al 1985, Turner et al 1990). The usual approach is to derive the "detection volume," defined as the volume between the source and observer within which the lens would need to lie in order to produce an observable effect (Nemiroff 1989, Kassiola et al 1991). Limits are then obtained by adding the detection volume for each source and comparing this to the volume per source expected for a given OmegaC.

There have been several optical and radio surveys to search for multiply-imaged quasars (Hewitt et al 1989, Bahcall et al 1992b). In particular, Hewitt (1986) used VLA observations to infer OmegaC(1011-1013 Msun) < 0.4, Nemiroff (1991b) used optical QSO data from Crampton et al (1989) to infer OmegaC(M > 109.9 Msun) < 1 and OmegaC(M > 1010.3 Msun) < 0.25, and Surdej et al (1993) used data on 469 highly luminous quasars (including HST observations) to infer OmegaC(1010-1012 Msun) < 0.02. To probe smaller scales, one must use high resolution radio sources: Kassiola et al (1991) have used lack of lensing in 40 VLBI objects to infer OmegaC(107-109 Msun) < 0.4, while a study by Patnaik et al (1992) of 200 flat spectrum radio sources may lead to a limit OmegaC(106-109 Msun) < 0.01 (Henstock et al 1993). (Flat spectrum sources are dominated by a single core and are therefore more likely to be lensed: this limit assumes that no sources are identified and is not included in Figure 5.)

Future observations could strengthen these constraints considerably: Speckle interferometry could push OmegaC(108-1010 Msun) down to 0.01, while VLBA could push OmegaC(105-108 Msun) down to 0.001 (Surdej et al 1993). These two limits are shown as broken lines in Figure 5. Another interesting possibility is to search for lensing distortions in radio jets (Kronberg et al 1991): this would permit the detection of objects with mass around 106 Msun since the Einstein radius for such objects is of order milliarcsecs and therefore comparable to the characteristic jet scale. Of course, jets may be intrinsically kinky but Wambsganss & Paczynski (1992) have pointed out that this poses no problem if one uses VLBI and VLBA maps of the jets in image-doubled quasars because only one of the images would then be kinked. Their numerical simulations show that the effects of supermassive black holes would be numerous and obvious. Lenses between 0.3 and 3 × 106 Msun would certainly be noticeable for a dynamic range of 100:1 and may have already been excluded (Heflin et al 1991, Garrett et al 1994).

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