Annu. Rev. Astron. Astrophys. 1992. 30: 311-358
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5. DARK MATTER

Gravitational lensing provides a powerful diagnostic to probe the distribution of matter in the universe, particularly dark matter, over a wide range of scales. In the following sections we discuss some of the possibilities, starting with dark matter in the Milky Way and working outward to the largest scales in the universe.

5.1 Our Galaxy

It is widely recognized that the known populations of stars account for only a fraction of the mass in the halo of the Galaxy (Gilmore et al. 1990). It has been suggested that the rest of the mass may consist of one or more varieties of dark compact objects, e.g. ``comets,'' ``asteroids,'' ``Jupiters,'' brown dwarfs, cool white dwarfs, neutron stars, black holes; in the case of black holes, masses of up to 106 Msmsun are allowed (cf Ostriker 1992). All of the above, except comets, can be potentially detected through their gravitational lensing action on background sources (Liebes 1964, Bontz 1979, and especially Paczynski 1986d).

The Einstein radius of a stellar lens of mass M in the halo is thetaE appeq (M / Msmsun)1/2 (D / 10 kpc)-1/2 mas (cf Equation 4) and the critical surface density is Sigmacr = 3 x 104 (D'/ 10 kpc)-1 g cm-2 (cf Equation 7). Any compact background source that has an angular size < thetaE and whose line-of-sight happens to be within ~ thetaE of the lens, will be strongly lensed and will appear to vary with a timescale tvar ~ 0.2(M / Msmsun)1/2 (D' / 10 kpc)1/2 (V / 200 km s-1)-1 yr (cf Equation 12). The source will brighten considerably and then fade to its original flux with a symmetric and achromatic light curve that is precisely calculable in the case of an isolated lens and a point source. Therefore, unless either sources or lenses occur predominantly in compact binaries (Griest 1991, Mao & Paczynski 1991), the signature of microlensing events should be distinguishable from intrinsic variability of the source. However, reliable discrimination will be possible only with a high signal-to-noise ratio and frequent sampling of the light curve.

The mean surface density of the Galaxy at the solar radius (Gilmore et al. 1990) is ltapprox 0.1 g cm-2 ~ 10-6 Sigmacr. Therefore, even if the entire mass of the Galaxy is in compact objects, one will still have to observe ~ 106 sources in order to find one that is microlensed. This could be achieved by monitoring the stars in the LMC or other nearby galaxies, or in the bulge of the Milky Way, on a nightly basis for a few years (Paczynski 1986d, 1991, Griest et al. 1991). With sufficiently closely spaced observations (several measurements per night) it may be possible to distinguish microlensing from intrinsic source variability, and even, in principle, to detect signatures of double stars and planets (Mao & Paczynski 1991, Gould & Loeb 1992). Several attempts are underway to put this idea into practice, using photographic methods and CCD arrays at existing telescopes (Milstajn 1990, Vidal-Madjar 1991, Paczynski 1992) and with dedicated telescopes and detectors built specifically for this purpose (Alcock et al. 1992). However, even under optimistic scenarios, for example a halo bound by objects with masses ~ 3 x 10-3 Msmsun , only ~ 15 events are predicted per year.

Compact dark objects in the Milky Way may also be found through lens-induced distortions in the images of background sources. This technique is suitable for objects of mass 105 Msmsun ltapprox M ltapprox 106 Msmsun , say primordial black holes, which produce distortions on angular scales gtapprox 0.1". A background optical continuum source such as the Andromeda Galaxy, the Galactic Center, or an extended radio source like Centaurus A has to be imaged with high dynamic range and subarcsecond resolution, and one then looks for characteristic lensing patterns such as Einstein rings and arcs (Turner et al. 1990). At least 1 square degree of sky must be imaged in order to have a reasonable chance of success.

Yet another proposal is that compact lenses in the Galaxy may cause variable time delays that may be detected, e.g. in the signal from a radio pulsar (Krauss & Small 1991). This could, in principle, be used to measure the mass of the deflecting star.

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