The Magnification Invariant of Circularly-symmetric Lens Models
  In the context of strong gravitational lensing, the magnification of image is
of crucial importance to constrain various lens models. For several commonly
used quadruple lens models, the magnification invariants, defined as the sum of
the signed magnifications of images, have been analytically derived when the
image multiplicity is a maximum. In this paper, we further study the
magnification of several disk lens models, including (a) exponential disk lens,
(b) Gaussian disk lens, (c) modified Hubble profile lens, and another two of
the popular three-dimensional symmetrical lens model, (d) NFW lens and (e)
Einasto lens. We find that magnification invariant does also exist for each
lens model. Moreover, our results show that magnification invariants can be
significantly changed by the characteristic surface mass density $\kappa_{\rm
c}$.
