Gravitational lensing by the supermassive black hole in the center of M31

We examine the possibility of observing gravitational lensing in the weak deflection regime by the supermassive black hole in the center of the galaxy M31. This black hole is significantly more massive than the black hole in the center of our Galaxy, qualifying itself as a more effective lens. However, it is also more distant, and the candidate stellar sources appear consequently fainter. We separately consider as potential sources stars belonging to the bulge, to the disk, and to the triple nucleus formed by P1 + P2 and by the recently discovered inner cluster P3. We calculate the number of simultaneously lensed stars at a given time as a function of the threshold magnitude required for the secondary image. For observations in the K band we find 1.4 expected stars having secondary images brighter than K = 24 and 182 brighter than K = 30. For observations in the V band we expect 1.3 secondary images brighter than V = 27 and 271 brighter than V = 33. The bulge stars have the highest chance of being lensed by the supermassive black hole, whereas the disk and the composite nucleus stars contribute 10% each. The typical angular separation of the secondary images from the black hole range from 1 mas to 0.1''. For each population we also show the distribution of the lensed sources as a function of their distance and absolute magnitude, the expected angular positions and velocities of the generated secondary images, and the rate and the typical duration of the lensing events.