What Makes Quadruply Lensed Quasars Quadruple?

Among known strongly lensed quasar systems, ~25% have gravitational potentials sufficiently flat (and sources well aligned) to produce four images rather than two. The projected flattening of the lensing galaxy and tides from neighboring galaxies both contribute potential's quadrupole. Witt's hyperbola Wynne's ellipse permit determination overall quadrupole positions images. position resolves distinct contributions intrinsic ellipticity tidal shear that 31 quadruply quasars systems with statistically significant decompositions, 15 are either reliably ($2\sigma$) or provisionally ($1\sigma$) shear-dominated 11 ellipticity-dominated. For remaining 8, two effects make roughly equal combined cross section (newly derived here) for quadruple lensing. This observational result is at variance ellipticity-dominated forecast Oguri & Marshall (2010).