Dark matter effect on the weak deflection angle by black holes at the center of Milky Way and M87 galaxies

TL;DR

This study examines how dark matter influences the weak gravitational lensing angle near black holes at galactic centers, comparing three dark matter profiles and suggesting potential for dark matter detection through lensing effects.

Contribution

It introduces a detailed analysis of dark matter effects on weak deflection angles using the Gauss-Bonnet theorem and compares different dark matter profiles with observational data.

Findings

Dark matter causes measurable variations in the weak deflection angle.

The Universal Rotation Curve profile is easiest to detect via lensing.

Dark matter effects are most prominent near the core radius.

Abstract

In this paper, we investigated the effect of dark matter on the weak deflection angle by black holes at the galactic center. We consider three known dark matter density profiles such as the Cold Dark Matter (CDM), Scalar Field Dark Matter (SFDM), and the Universal Rotation Curve (URC) from the Burkert profile. To achieve this goal, we used how the positional angles are measured by Ishihara et al. method based on Gauss-Bonnet theorem (GBT) on the optical metric. With the help of the non-asymptotic form of the GBT, the longitudinal angle difference is also calculated. First, we find the emergence of apparent divergent terms on the said profiles, which indicates that the spacetime describing the black hole-dark matter combination is non-asymptotic. We showed that these apparent divergent terms vanish when the distance of the source and receiver are astronomically distant from the black hole. Using the current observational data in the Milky Way and M87 galaxies, we find interesting behaviors of how the weak deflection angle varies with the impact parameter, which gives us some hint on how dark matter interacts with the null particles for each dark matter density profile. We conclude that since these deviations are evident near the dark matter core radius, the weak deflection angle offers a better alternative for dark matter detection than using the deviation from the black hole shadow. With the DM profiles explored in this study, we find that SFDM is the most difficult to detect, while the easiest is the URC profile. With the dark matter profiles explored in this study, we find that the variation of the values for weak deflection angle strongly depends on the dark matter mass on a particular profile.