2013/05/13 by Zhe Chu, Weipeng Lin, W. P. Lin +1
Decision Sciences · Engineering · Physics and Astronomy · #Advanced Measurement and Metrology Techniques #Atomic physics #Isothermal process #Lens (geology) #Materials science #Optics #Particle Accelerators and Free-Electron Lasers #Physics #Quadrupole #Scientific Measurement and Uncertainty Evaluation #Thermodynamics #astro-ph.CO
paper · pdf · doi:10.1088/2041-8205/770/2/l34
12 pages, 2 figures, accepted for publication in ApJL
arxiv created 2013/05/13 · openalex publication_date 2013/06/06 · arxiv updated 2013/06/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Using an analytical method, we study the singular isothermal quadrupole (SIQ) lens system, which is the simplest lens model that can produce four images. In this case, the radial mass distribution is in accord with the profile of the singular isothermal sphere lens, and the tangential distribution is given by adding a quadrupole on the monopole component. The basic properties of the SIQ lens have been studied in this Letter, including the deflection potential, deflection angle, magnification, critical curve, caustic, pseudo-caustic, and transition locus. Analytical solutions of the image positions and magnifications for the source on axes are derived. We find that naked cusps will appear when the relative intensity k of quadrupole to monopole is larger than 0.6. According to the magnification invariant theory of the SIQ lens, the sum of the signed magnifications of the four images should be equal to unity, as found by Dalal. However, if a source lies in the naked cusp, the summed magnification of the left three images is smaller than the invariant 1. With this simple lens system, we study the situations where a point source infinitely approaches a cusp or a fold. The sum of the magnifications of the cusp image triplet is usually not equal to 0, and it is usually positive for major cusps while negative for minor cusps. Similarly, the sum of magnifications of the fold image pair is usually not equal to 0 either. Nevertheless, the cusp and fold relations are still equal to 0 in that the sum values are divided by infinite absolute magnifications by definition.