2002/07/29 by Sun Hong Rhie, Rhie, Sun Hong
Earth and Planetary Sciences · Physics and Astronomy · #Adaptive optics and wavefront sensing #Astrophysics (astro-ph) #FOS: Physical sciences #Geophysics and Gravity Measurements #Stellar, planetary, and galactic studies #astro-ph
paper · pdf · doi:10.48550/arxiv.astro-ph/0207612
13 pages + 5 figures
arxiv created 2002/07/29 · openalex publication_date 2002/07/29 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Criticality in graviational microlensing is an everyday issue because that is what generates microlensing signals which may be of photon-challenged compact objects such as black holes or planetary systems ET calls home. The criticality of these quasi-analytic lenses is intrinsically quadratic, and the critical curve behaves as a mirror generating two mirror images along the image line (parallel +/- E-) at the same distances from the critical curve in the opposite sides. At the (pre)cusps where the caustic curve "reflects" and develops cusps, however, "would-be" two pairs of quadratic images "superpose" to produce three mirror images because of the degenerate criticality. The critical curve behaves as a parabolic mirror, and the image inside the parabola is indeed a superposed image having the sum of the magnifications of the other two that are outside the parabola. All three images lie on a parabolic image curve shaped by a property (nabla J) of the (pre)cusp, and two distances of the system determine the position of the image curve and positions of the three images on the image curve. The triplet images satisfy sum J-1 = 0, and the function sum J-1 is discontinuous at a caustic crossing where a pair of quadratic images disappear into a critical point. The reflection symmetry of the image curve is a manifestation of the symmetry of the cusp which is also respected by a trio of parabolic curves that are tangnet at the (pre)cusp and define the image domains. The symmetry is guaranteed when J+- vanishes or can be ignored, and the cusps on the lens axis of the binary lenses are strongly symmetric having J+- = 0 because of the global reflection symmetry of the binary lenses. "E+/--algebra" is laid out for users' convenience.