Extended Source Effects in Substructure Lensing

We investigate the extended source size effects on gravitational lensing inwhich a lens consists of a smooth potential and small mass clumps(``substructure lensing''). We first consider a lens model that consists of aclump modeled as a singular isothermal sphere (SIS) and a primary lens modeledas an external background shear and convergence. For this simple model, wederive analytic formulae for (de)magnification of circularly symmetric top-hatsources with three types of parity for their lensed images, namely, positive,negative, and doubly negative parities. Provided that the source size issufficiently larger than the Einstein radius of the SIS, we find that in thepositive (doubly negative) parity case, an extended source is always magnified(demagnified) in comparison with the unperturbed macrolens system, whereas inthe negative parity case, the (de)magnification effect, which depends on thesign of convergence minus unity is weaker than those in other parities. It isshown that a measurement of the distortion pattern in a multiply lensed imageenables us to break the degeneracy between the lensing effects of clump massand those of clump distance if lensing parameters of the relevant macrolensmodel are determined from the position and flux of multiple images. We alsoshow that an actual density profile of a clump can be directly measured byanalyzing the ``fine structure'' in a multiply lensed image within the Einsteinradius of the clump.Comment: 32 pages, 15 EPS files. Accepted version for publication in ApJ. A new subsection "Mean (de) magnification for a point soure" is added. A number of typos in the original version are correcte