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

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 the 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 nonlocal metamorphosis for a critical mass positioned at the halo center. Although we construct 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.

Gravitational lensing effects of supermassive black holes in cluster environments

“…We find that the kappa profile, following the density profile presented in Fig. 1 , reaches ∼0.1 after 0.02 arcsec -extremely similar to the lensing behaviour produced by the analytical point mass profile used by Karamazov et al ( 2021 ) and Karamazov & He yro vsk y ( 2022 ). We remind the reader that the convergence for a point mass is zero everywhere except at its location.…”

“…As noted by Karamazov & He yro vsk y ( 2022 ), the inclusion of a point-like mass at the centre of the cluster BCG potential can strongly affect the resulting lensing configurations. Karamazov et al ( 2021 ) distinguish two regimes where formally the ratio of the convergence produced by the BCG to that of the SMBH exceeds 10 −4 , when a single NFW profile is used to model the BCG and a point-like source the SMBH. Our empirical, observationally based approach does not make such distinctions of regimes based on the convergence, and instead we focus on the ratio of measured quantities -the mass ratio between different contributors to the o v erall mass budget.…”

New Light on Dark Extended Lenses with the Roman Space Telescope

“…At points where the slope of v(u) becomes infinite, the magnification diverges. This feature is known as a caustic (see, e.g., Hurtado et al 2014;Karamazov et al 2021 for a discussion of their presence in the lightcurves of spherical extended lenses). If these caustic features can be resolved, their location and shape contain information about the underlying mass profile, providing a unique opportunity to uncover the microphysical nature of the lens.…”