Modelling the Sgr A* Black Hole Immersed in a Dark Matter Spike

TL;DR

This study models the impact of a dark matter spike on the spacetime around Sgr A* and assesses the detectability of such effects through astronomical observations, finding the effects are weak and unlikely to be observed soon.

Contribution

It develops a spacetime metric for a black hole with a dark matter spike and evaluates observational signatures, extending previous models to include realistic dark matter densities.

Findings

Dark matter spike effects on the black hole shadow are weak for realistic densities.

Significant effects only occur at very high dark matter densities (~10^{-19}-10^{-20} g/cm^3).

Current observational techniques are unlikely to detect these effects in the near future.

Abstract

In this paper, we investigate the effects of a dark matter (DM) spike on the neighborhood of Sgr A*, the black hole (BH) in the center of the Milky Way galaxy. Our main goal is to investigate whether current and future astronomical observations of Sgr A* could detect the presence of such a DM spike. At first, we construct the spacetime metric around a static and spherically symmetric BH with a DM spike, and later this solution is generalized for a rotating BH using the Newman-Janis-Azreg A\"{i}nou algorithm. For the static BH metric, we use the data of the S2 star orbiting the Sgr A* to determine and analyze the constraints on the two free parameters characterizing the density and the innermost boundary of the DM halo surrounding the BH. Furthermore, by making use of the available observational data for the DM spike density $\rho_\text{sp}$ and the DM spike radius $R_\text{sp}$ in the Milky Way galaxy, we consider a geometrically-thick accretion disk model around the Sgr A* BH and demonstrate that the effect of DM distribution on the shadow radius and the image of the BH is considerably weak for realistic DM densities, becoming significant only when the DM density is of the order $\rho_\text{sp} \sim (10^{-19}-10^{-20})$ g/cm$^3$ near the BH. We further analyze the possibility of observing this effect with radio interferometry, simulating observations with an EHT--like array, and find that it is unlikely to be detectable in the near future.