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.
It is widely recognized that the known populations of stars account
for only a fraction of the mass in the halo of the Galaxy
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 M are allowed (cf
All of the above, except comets, can be potentially detected through their
gravitational lensing action on background sources
and especially Paczynski 1986d).
The Einstein radius of a stellar lens of mass M in the halo is
E (M / M)1/2
(D / 10 kpc)-1/2 mas
(cf Equation 4) and the critical surface density is cr = 3 x
104 (D'/ 10 kpc)-1 g cm-2 (cf
Equation 7). Any compact background source that has an angular size
< E and whose
line-of-sight happens to be within ~ E of the lens, will
be strongly lensed and will appear to vary with
a timescale tvar ~ 0.2(M / M)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
Mao & Paczynski
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
is 0.1 g
cm-2 ~ 10-6 cr.
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
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
Gould & Loeb 1992).
Several attempts are underway to put this idea
into practice, using photographic methods and CCD arrays at existing
and with dedicated telescopes and detectors built specifically for
(Alcock et al. 1992).
However, even under optimistic
scenarios, for example a halo bound by objects with masses
~ 3 x 10-3 M , 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
106 M , say primordial black holes, which produce distortions
on angular scales
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
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
(Krauss & Small
This could, in principle, be used to measure the mass of the deflecting star.