Recent observations of galaxy luminosity profiles and dark matter simulations find luminosity and mass distributions characterized by central cusps rather than finite core radii .
We introduce and implement a set of cusped ellipsoidal lens models which include limits similar to the Jaffe , Hernquist , \eta and NFW models and apply them to the gravitational lenses APM 08279+5255 and B 1933+503 .
A successful model of APM 08279+5255 with its central , odd image requires a very shallow cusp , \gamma \mathrel { \raise 1.29 pt \hbox { $ < $ } \mkern - 14.0 mu \lower 2.58 pt \hbox { $ \sim$ } } % 0.4 where \rho \propto r ^ { - \gamma } as r \rightarrow 0 , which is similar to a core rather than the favored 1 \mathrel { \raise 1.29 pt \hbox { $ < $ } \mkern - 14.0 mu \lower 2.58 pt \hbox { $ \sim$ } } % \gamma \mathrel { \raise 1.29 pt \hbox { $ < $ } \mkern - 14.0 mu \lower 2.58 pt \hbox { $ \sim$ } } 2 cusps .
B 1933+503 , by contrast , is well modeled with a steep density cusp , 1.6 \mathrel { \raise 1.29 pt \hbox { $ < $ } \mkern - 14.0 mu \lower 2.58 pt \hbox { $ \sim$ } } % \gamma \mathrel { \raise 1.29 pt \hbox { $ < $ } \mkern - 14.0 mu \lower 2.58 pt \hbox { $ \sim$ } } % 2.0 .