  We study microlensing of the faint images that form close to the centers of
strong gravitational lens galaxies. These central images, which have finally
begun to yield to observations, naturally appear in dense stellar fields and
may be particularly sensitive to fine granularity in the mass distribution. The
microlensing magnification maps for overfocussed (i.e., demagnified) images
differ strikingly from those for magnified images. In particular, the familiar
"fold" and "cusp" features of maps for magnified images are only present for
certain values of the fraction, f, of the surface mass density contained in
stars. For central images, the dispersion in microlensing magnifications is
generally larger than for normal (minimum and saddle) images, especially when
the source is comparable to or larger than the stellar Einstein radius. The
dispersion depends in a complicated way on f; this behaviour may hold the key
to using microlensing as a probe of the relative densities of stars and dark
matter in the cores of distant galaxies. Quantitatively, we predict that the
central image C in PMN J1632-0033 has a magnification dispersion of 0.6
magnitudes for Rsrc/Rein <~ 1, or 0.3 mag for Rsrc/Rein = 10. For comparison,
the dispersions are 0.5-0.6 mag for image B and 0.05-0.1 mag for image A, if
Rsrc/Rein <~ 1; and just 0.1 mag for B and 0.008 mag for A if Rsrc/Rein = 10.
(The dispersions can be extrapolated to larger sources sizes as sigma \propto
Rsrc^{-1}.) Thus, central images are more susceptible than other lensed images
to microlensing and hence good probes for measuring source sizes.

Astrophysics