Gravitational microlensing by the halo of the Andromeda galaxy

It has been shown by Paczy\'nski that gravitational microlensing is a useful method to detect brown dwarfs in the dark halo of our galaxy. At present several experiments are carried out to monitor several million stars in the Large Magellanic Cloud with the aim to find such microlensing events. Here I discuss the possibility to use as targets stars in the Andromeda galaxy. Such an experiment would be sensitive to both the brown dwarfs in our halo and in the one of M31. The optical depth $\tau$ to gravitational microlensing due to brown dwarfs in the halo of M31 turns out to be $\sim 10^{-6}$, which is comparable to the value of $\tau$ for our own halo. I also compute the microlensing rate and the average lensing duration and consider moreover the dependence of $\tau$ on the shape of the halo.