The Net Advance of Physics: The Nature of Dark Matter, by Kim Griest -- Section 7B.

Microlensing

Microlensing has arrived as a powerful new tool for exploring

the structure of our Galaxy. However, from the dark matter point of

view, I'd like to note that the current experiments may have the

capability to give a definitive answer to the question of whether the

dark matter in our Galaxy is baryonic. The microlensing searches

are probably sensitive to any objects in the range

, just the range in which such objects are

theoretically allowed to exist. Objects made purely of H and He with

masses less than are expected to evaporate due to

the microwave background in less than a Hubble time, while objects

with masses greater than would have disrupted known

globular clusters.

The idea of microlensing rests upon Einstein's observation that if a

massive object lies directly on the line-of-sight to a much more

distant star, the light from the star will be lensed and form a ring

around the lens. This ``Einstein ring" sets the scale for all the

microlensing searches, and in the lens plane, the radius of that ring

is given by

where and are the solar radius and mass, m is the Macho

mass, L is the distance to the star being monitored, and x is the

distance to the Macho divided by L.

In fact, it is extremely unlikely for a Macho to pass precisely on the

line-of-sight, but if there is a near miss, two images of the star

appear separated by a small angle. For masses in the stellar range

and distances of galactic scale this angle is too small to be resolved,

but the light from both images add and the star appears to brighten.

The amount of brightening can be large, since it is roughly inversely

proportional to the minimum impact parameter . Since the

Macho, Earth, and source star are all in relative motion, the star

appears to brighten, reaches a peak brightness, and then fades back

to its usual magnitude. The brightening as a function of time is

called the ``lightcurve" and is given by

where A is the magnification, is dimensionless impact

parameter, is the time of peak amplification, is the

duration of the microlensing event, is the transverse speed of the

Macho relative to the line-of-sight, and is value of u when

. Thus the signature for a microlensing event is a

time-symmetric brightening of a star occurring as a Macho passes

close to the line-of-sight. When a microlensing event is detected,

one fits the lightcurve and extracts , , and . The primary

physical information comes from , which contains the Macho

velocity, and through the Macho mass and distance.

Unfortunately, one cannot uniquely find all three pieces of

information from the measurement of . However, statistically, one

can use information about the halo density and velocity

distribution, along with the distribution of measured event

durations to gain information about the Macho masses. Using a

standard model of the dark halo, Machos of jupiter mass ( )

typically last 3 days, while brown dwarf mass Machos ( )

cause events which last about a month [35, 49].

In order to perform the experiment, a large number of stars must be

followed, since, assuming a halo made entirely of Machos, the

probability of any Macho crossing in front of a star is about .

Thus many millions of stars must be monitored in order to see a

handful of microlensing events. In addition, if one wants to see

microlensing from objects in the dark halo, the monitored stars

must be far enough away so that there is a lot of halo material

between us and the stars. Therefore, the best stars to monitor are

those in the Large and Small Magellanic Clouds (LMC and SMC),

at distances of 50 kpc and 60 kpc respectively, and also stars in the

galactic bulge, at 8 kpc.

There are several experimental groups that have undertaken the

search for microlensing in the LMC and galactic bulge and have

returned results. The EROS collaboration has reported 3 events

towards the LMC [33], the OGLE group has reported about 15

events towards the bulge [34], and the DUO collaboration has about

a dozen preliminary events towards the bulge [36]. Our

collaboration has seen about 5 events towards the LMC [32, 37, 38],

and about 60 events towards the bulge [39, 40, 41]. We are also

monitoring the SMC, but have yet to analyze that data. In what

follows I will concentrate on MACHO collaboration data.

BIBLIOGRAPHY