Time Delay of Light in the Gravitational lensing of Supermassive Black Holes in Dark Matter Halos

TL;DR

This study investigates how different dark matter halo models affect the time delay of light in gravitational lensing by supermassive black holes, revealing significant enhancements depending on halo properties.

Contribution

It provides a comparative numerical analysis of dark matter effects on light time delay across multiple astrophysical halo models, which was not previously detailed.

Findings

Dark matter halos significantly increase light time delay in gravitational lensing.

The effect is more pronounced with smaller halo scales and larger halo masses.

Different halo models produce varying degrees of time delay enhancement.

Abstract

The dark matter halo has non-negligible effects on the gravitational lensing of supermassive black hole in the galaxy center. Our work presents a study on the time-delay of light in gravitational lensing of black holes enclosed by dark matter halos. To provide a precise description on the distribution of dark matter in galaxies, we choose several famous phenomenological dark matter halo models in astrophysics, including the NFW, Beta, Burkert and Moore models, to carry out the present study. Through numerically calculating the time-delay of light in gravitational lensing, a comparative analysis of the dark matter effects within different halo models has been performed. Assuming typical length scales associated with the galactic gravitational lensing, numerical results indicate that the NFW, Beta, Burkert and Moore dark matter halos can significantly enhance the time delay of light in gravitational lenisng of central supermassive black holes. The enhancing effect becomes more pronounced with a small dark matter halo scale and an increasing dark matter halo mass. Keywords: Black Hole; Gravitational Lensing; Time Delay; Dark Matter Halo