Constraints on the inner mass profiles of lensing galaxies from missing odd images

Most gravitational lens systems consist of two or four observable images. The absence of detectable odd images allows us to place a lower limit on the power-law slope of the inner mass profile of lensing galaxies. Using a sample of six two-image radio-loud lens systems and assuming a singular power-law surface density (Sigma proportional to r(-beta)) for the inner several kiloparsecs of the mass distribution, we find that there is less than a 10% probability that the data are consistent with profile slopes beta < 0.80. Furthermore, individual mass modeling yields <beta> > 0.85 for B0739+366 and beta > 0.91 for B1030+074. Modeling central black holes as additional point masses changes the constraints in these systems to beta > 0.84 and beta > 0.83, respectively. The inner mass profiles of lensing galaxies are therefore not much shallower than isothermal.