Annu. Rev. Astron. Astrophys. 1992. 30:
311-358 Copyright © 1992 by . All
rights reserved |

*microlensing*, in contrast to the effect of
the smooth mass distribution which is referred to as *macrolensing*.

^{*}/ _{cr}, where ^{*} is the total
stellar surface density, and is independent of the masses of the
individual stars. When << 1,
the faint microimages associated with
individual stars are unimportant except on the rare occasions when a
star crosses within a few _{E} of the line of sight. When this
happens the source will brighten and fade on a timescale given by

where *V* is the velocity of the star relative to the source-earth
line and *D'* is given by Equation 7.
In contrast to the optical depth, *t*_{var} does depend on
the mass of the microlens
(Kayser *et
al.* 1986,
Kayser & Refsdal
1989,
Kayser 1992).

*et
al.* 1989,
Wambsganss 1990,
Witt 1990).
The backgound shear from the
largescale mass distribution of the lens makes the network
anisotropic and the variability will be sensitive to the direction of
transverse motion relative to the shear
(Wambsganss 1990,
Wambsganss *et
al.* 1990a).
Frequent, large amplitude image variation is possible in this regime
(Paczynski 1986a,
Nemiroff 1986,
Schneider &
Weiss 1987,
Witt 1990).
If there is a smooth, supercritical background
density, then dramatic demagnifications are also expected when the
ray associated with the brightest microimage intercepts a star. The
net effect will be to conserve flux so that the mean magnification is
the same as if the mass in the stars had been smoothed out
(Peacock 1986).
Since fold caustics dominate at the highest magnification, the
asymptotic probability for large magnification by more than *µ*
scales as *µ*^{-2}
(Section 3.3,
Vietri &
Ostriker 1983,
Nityananda &
Ostriker 1984,
Blandford &
Narayan 1986),
with a normalization that can be computed exactly
(Schneider 1987c).
Numerical simulations show
a significant excess in the crosssection (over and above the
analytical normalization of the *µ*^{-2} law) at moderate
magnifications
(Rauch *et
al.* 1991).

^{-2}
again but the relative fluctuations, for fixed
source size, are found to increase
(Deguchi &
Watson 1988).
In this limit the angular profile of the macroimage consists of a Gaussian
core and a power law tail ^{-4}
(Katz *et
al.* 1986).

*et
al.* (1989) and
Corrigan *et
al.* (1991)
have reported variability
in the images of Q2237+031. Since the optical depth for microlensing
in this case is ~ 0.5, the
variations have been plausibly
interpreted as being the result of microlensing.
Schild & Smith
(1991)
appear to have measured variability due to microlensing in
Q0957+561.