Gravitational Microlensing by Random Motion of Stars: Analysis of Light Curves

We present a quantitative analysis of the effect of microlensing caused by random motion of individual stars in the galaxy which is lensing a background quasar. We calculate a large number of magnification patterns for positions of the stars slightly offset from one frame to the next, and in this way obtain light curves for fixed quasar and galaxy positions, only due to the change in the relative star positions. These light curves are analyzed to identify micro- lensing events, which are classified according to height, duration, and slope. We find that microlensing events produced by random motion of stars are shorter, steeper, and more frequent than bulk motion events. This difference is caused by the fact that in the case of random motion, caustics can move with arbitrarily high velocity, producing very short events. An accompanying video illustrates these results. For three different values of the surface mass density kappa, it shows time sequences of 1000 magnification patterns for slowly changing lens positions, together with the positions and velocity vectors of the microlensing stars. Short sequences of the video are available as MPEG movie by anonymous ftp at ftp://astro.princeton.edu/jkw/microlensing/moving_stars .