The magnification of stars crossing a caustic. I - Lenses with smooth potentials

The possibility is explored of observing highly magnified images of individual stars within the long arcs that have been observed in rich clusters of galaxies. These images appear when a star crosses a caustic of the cluster's potential. When the cluster mass is distributed smoothly, the maximum magnification reached is typically of the order of 10 to the 7th. The star's image appears suddenly and reaches the maximum magnification in a few hours; then the magnification decreases slowly as the inverse of the square root of the time. This can also occur in the reverse order in time. For typical arcs, stars with bolometric luminosities of around 300 solar luminosities reach a maximum visual apparent magnitude of about 25. If brighter events are detected, the rate of detection is of the order of one every five years, for every arc intersecting a caustic. If the source galaxy is forming stars with a Saltpeter IMF, the probability that a 30-solar-mass star is magnified to a magnitude of 28 at any time is of the order of 20 percent.