Gravitational Lensing By a Massive Object in a Dark Matter Halo. I. Critical Curves and Caustics

TL;DR

This paper investigates how a massive object within a dark matter halo affects gravitational lensing, focusing on critical curves and caustics, revealing complex transitions and metamorphoses depending on the object's mass and position.

Contribution

It introduces a simplified model of a point mass in a dark matter halo to systematically analyze critical curves and caustics, identifying new transition phenomena and metamorphoses.

Findings

Existence of a critical mass eliminating the halo's radial critical curve.

Multiple critical-curve transitions depending on the point's position.

Identification of six types of caustic metamorphoses.

Abstract

We study the gravitational lensing properties of a massive object in a dark matter halo, concentrating on the critical curves and caustics of the combined lens. We model the system in the simplest approximation by a point mass embedded in a spherical Navarro$-$Frenk$-$White density profile. The low number of parameters of such a model permits a systematic exploration of its parameter space. We present galleries of critical curves and caustics for different masses and positions of the point in the halo. We demonstrate the existence of a critical mass, above which the gravitational influence of the centrally positioned point is strong enough to eliminate the radial critical curve and caustic of the halo. In the point-mass parameter space we identify the boundaries at which critical-curve transitions and corresponding caustic metamorphoses occur. The number of transitions as a function of position of the point is surprisingly high, ranging from three for higher masses to as many as eight for lower masses. On the caustics we identify the occurrence of six different types of caustic metamorphoses. We illustrate the peculiar properties of the single radial critical curve and caustic appearing in an additional unusual non-local metamorphosis for a critical mass positioned at the halo center. Although we constructed the model primarily to study the lensing influence of individual galaxies in a galaxy cluster, it can also be used to study the lensing by dwarf satellite galaxies in the halo of a host galaxy, as well as (super)massive black holes at a general position in a galactic halo.