Caustics of 1/rⁿbinary gravitational lenses: from galactic haloes to exotic matter

Abstract

Abstract. We investigate the caustic topologies for binary gravitational lenses made up of two objects whose gravitational potential declines as 1/r n . With n < 1 this corresponds to power-law dust distributions like the singular isothermal sphere. The n > 1 regime can be obtained with some violations of the energy conditions, one famous example being the Ellis wormhole. Gravitational lensing provides a natural arena to distinguish and identify such exotic objects in our Universe. We find that there are still three topologies for caustics as in the standard Schwarzschild binary lens, with the main novelty coming from the secondary caustics of the close topology, which become huge at higher n. After drawing caustics by numerical methods, we derive a large amount of analytical formulae in all limits that are useful to provide deeper insight in the mathematics of the problem. Our study is useful to better understand the phenomenology of galaxy lensing in clusters as well as the distinct signatures of exotic matter in complex systems.arXiv:1511.07991v3 [gr-qc]

Caustics in Gravitational Lensing by Mixed Binary Systems

“…On the other side we find that the central caustics have the typical 4-cusps shape and they become smaller as m decreases. Secondary caustics are always triangular but are considerably larger for m > 1, a fact that was already stressed in [58]. Note that for m > 1 triangular caustics move right, while the central caustic is slightly displaced to the left.…”

“…As shown in [58,63], in the range 0 ≤ m < 1 an elliptic umbilic catastrophe exists in the close separation. In an elliptic umbilic, the size of the small oval critical curves goes to zero and then grows up to finite size again.…”

“…In the unequal-strength binary case, in order to keep contact with the previous work, we consider q = 0.1, as in [58], so in terms of the ratio of the Einstein radii, our strength ratio is γ = √ 0.1. We need to multiply s in [58] by a factor q + 1 = √ 1.1, so the transitions between different topologies for n = m = 1 occur as follows: Therefore, in this subsection we have the standard lens on the left with bigger Einstein radius than the lens on the right, for which we vary the potential index m.…”

“…Power-law deflection terms can also be found in gravitational lensing in the presence of plasma [53][54][55][56][57]. Particular attention was posed on the study of caustics of 1/r n binary lenses by Bozza and Melchiorre in [58] and to the investigation of gravitational lensing by exotic lenses with a non-standard form of the equation of state or with a modified gravity theory by Asada [59]. A new method of detecting Ellis wormholes by the use of the images of wormholes surrounded by optically thin dust was investigated by Ohgami and Sakai [35].…”

“…In this work we want to extend the symmetric structure already studied by Bozza and Melchiorre in [58] for 1/r n potentials, in which the two lenses have the same index n, to an asymmetric case in which the lenses have different indexes. This generalization is particularly useful in both scientific contexts described by 1/r n potentials.…”