Images from disk and spherical accretions of Bardeen black hole surrounded by perfect fluid dark matter

TL;DR

The paper addresses how perfect fluid dark matter (PFDM) influences shadows and accretion imagery around a regular Bardeen black hole. It employs null geodesics, photon-sphere analysis, and ray-tracing with both thin-disk and static spherical accretion models, constrained by Event Horizon Telescope (EHT) data. Key findings include a competitive interplay between the PFDM parameter $|\\alpha|$ and the magnetic charge $g$, with SgrA* providing tighter bounds on $\\alpha$ than M87*; PFDM enhances the inner shadow and dims the bright ring, offering observational diagnostics to distinguish PFDM-embedded from classical black holes. The work demonstrates a viable pathway to probe dark matter effects via high-resolution black hole imaging and informs future observational campaigns.

Abstract

In this paper, we investigate the shadow and optical appearance of the Bardeen black hole surrounded by perfect fluid dark matter (PFDM) illuminated by various static accretions. First, we find that as the dark matter parameter $\left|α\right|$ increases, the fundamental characteristic quantities of the black hole, the event horizon $r_h$, the photon sphere radius $r_{ph}$, and the critical impact parameter $b_{ph}$ all increase, while the peak of the effective potential $V_{\text{eff}}$ decreases and shifts toward the direction of increasing $r$. In contrast, the magnetic charge parameter $g$ suppresses $r_h$, $r_{ph}$, and $b_{ph}$, while increases the peak of $V_{\text{eff}}$ and shifts it toward the direction of decreasing $r$. This indicates a competing effect between the dark matter parameter $\left|α\right|$ and the magnetic charge parameter $g$ on the fundamental properties of the black hole. Furthermore, we use the EHT observational data to constrain the dark matter parameters $α$ and find that the constraint range given by the supermassive black hole SgrA* is stricter than that of the black hole M87*. Finally, we investigate black hole images under different accretion models. The results reveal that both dark matter parameters $α$ and accretion models significantly influence the black hole images. For larger dark matter parameters $\left|α\right|$, the inner shadow or central faint illuminating region of the Bardeen black hole surrounded by PFDM is larger, but the bright ring of the image is fainter. This provides a potential method for us to distinguish between classical Bardeen black holes and Bardeen black holes surrounded by PFDM. These preliminary results may provide some clues for future investigations of dark matter using black hole shadows and images.

Figures (8)

• Figure 1: The event horizon $r_h$ and the photon sphere radius $r_{ph}$ as functions of the dark matter parameter $\alpha$ and the magnetic charge parameter $g$ of the Bardeen black hole surrounded by PFDM. Here we set $M=1$.
• Figure 2: The critical impact parameter $b_{ph}$ and the effective potential $V_{\text{eff}}$ as a function of the dark matter parameter $\alpha$ and the magnetic charge parameter $g$ of the Bardeen black hole surrounded by PFDM. Here we set $M=1$.
• Figure 3: Left: the constraints of the coupling parameters $\alpha$ and $g$ by the observational shadow of M87* black hole. The red curve corresponds to the angular diameter $\theta_d=51.06 ~\mu as$. Right: the constraints of the coupling parameters $\alpha$ and $g$ by the observational shadow of SgrA* black hole. The red curve corresponds to the angular diameter $\theta_d=55.7 ~\mu as$.
• Figure 4: Top of (a-h): the number of photon orbits $n$ of the Bardeen black hole surrounded by PFDM as a function of the impact parameter $b$ for different $g$ and $\alpha$ with $M=1$. Bottom of (a-h): a selection of associated photon trajectories in the Euclidean polar coordinates $(r,\phi)$. The black curves, gold curves, and red curves correspond to the direct emissions ($n<3/4$), lensed ring emissions ($3/4<n<5/4$), and photon ring emissions ($n>5/4$), respectively. The black disks and the green dashed curves denote the black holes and photon spheres, respectively.
• Figure 5: The first three transfer functions of a Bardeen black hole surrounded by PFDM with different magnetic charges $g$ and dark matter parameters $\alpha$. They represent the radial coordinates of the first (black), second (gold), and third (red) intersections with the emission. Here, we fix $M=1$.