  The optical depth to microlensing toward M31 due to known stars in the disk
of M31 itself is $\tau\sim 2\times 10^{-7}e^{-r/d}$ where $d$ is the disk scale
length and $r$ is the distance along the major axis. Thus, there can be
significant lensing toward the M31 disk even if M31 contains no dark compact
objects. The optical depth has a strong dependence on azimuthal angle: at fixed
radius $\tau\propto[1+ (h/d)\tan i\cos\phi]^{-2}$ where $h$ is the scale height
of the disk, $i=75^\circ$ is the inclination of M31, and $\phi$ is the
azimuthal angle relative to the near minor axis. By measuring the optical depth
as a function of radial and azimuthal position, it is possible to estimate $h$
and $d$ for the mass of the M31 disk, and so determine whether the disk light
traces disk mass. Ground-based observations in $0.\hskip-2pt''5$ seeing of 0.8
$\rm deg^2$ once per week could yield $\sim 3$ events per year. With an
ambitious space-based project, it would be possible to to observe $\sim 80$
events per year. If lensing events were dominated by the M31 spheroid rather
than the disk, the event rate would be higher and the spheroid's parameters
could be measured. The pattern of optical depths differs substantially for a
disk and a spheroid.

Astrophysics