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

We study the possibility 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 potential of the cluster. When the mass of the cluster is distributed smoothly (i. e. , in the absence of microlensing), the maximum magnification reached is typically of the order of 10⁷^. The star 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 L~300 Lₛun_ reach a maximum visual apparent magnitude of ~ 25. If all brighter events are detected, the rate of detection is of order one every five years, for every arc intersecting a caustic. Events produced by brighter stars are easier to detect, since even though they occur more rarely, the magnified star can be seen for a much longer time, for a constant flux threshold for detection. If the source galaxy is forming stars with a Salpeter IMF, the probability that a 30 Mₛun_ star (with L=10⁵^ Lₛun_) is magnified to a magnitude mV_ = 28 at any time is of order 20%. However, such a star could only be detected in the presence of time variability of its magnitude, either intrinsic to the star or produced by microlensing. The nature of these magnification events can be very much affected by microlensing. The observation of the phenomenon could provide a probe of the objects producing microlensing, either in the dark matter or in intracluster stars.