Core Concepts
Image formations near hyperbolic umbilic singularities in strong gravitational lensing offer a unique opportunity to study low-mass substructures in galaxy clusters and can serve as valuable targets for time-delay cosmography.
Stats
For lens ellipticity values ≥0.3, the central maxima image will form sufficiently far from the lens centre (d ≳5′′).
The relative time delay between various pairs of HU characteristic image formation has a typical value of ∼100 days.
Only four to five image formations near HUs have been identified in galaxy clusters.
Around half a dozen additional HU image formations are claimed to be observed in various cluster lenses.
Quotes
"Hyperbolic umbilic (HU) is a point singularity of the gravitational lens equation, giving rise to a ring-shaped image formation made of four highly magnified images, off-centred from the lens centre."
"Like fold/cusp, image formations near HU also satisfy magnification relation (Rhu), i.e., the signed magnification sum of the four images equals zero."
"In addition to satisfying a magnification relation, HU image formations also have an order of magnitude smaller time delays (O (102 days); similar to what we have in galaxy-scale lenses) compared to generic five image formation in cluster lenses."