Shadow and thin accretion disk around Ayón-Beato-García black hole coupled with cloud of strings

TL;DR

This work examines the shadow and thin accretion disk around a regular Ayón-Beato-García black hole coupled to a cloud of strings in a nonlinear electrodynamics framework. By solving equatorial null geodesics and analyzing photon-sphere structure, the authors connect the shadow diameter via $d_{sh}=2 b_c$ to the model parameters, classifying photon trajectories into direct, lensing, and photon-ring regimes. They derive joint observational constraints on the CS parameter $a$ and NLED charge $g$ using EHT data for M87$^*$ and Sgr A$^*$, demonstrating that the shadow grows with $a$ and shrinks with $g$, and provide concrete bounds (e.g., for $g=0.5M$, $0.006<a<0.158$; for Sgr A$^*$, $a\leq0.061M$ at $g=0.5M$). The accompanying thin-disk analysis, based on Page–Thorne formalism, shows how $F(r)$ and $T(r)$ respond oppositely to changes in $a$ and $g$, and uses transfer-function imaging to predict observed flux patterns, revealing that disk emission features remain largely insensitive to $(a,g)$ while shadow morphologies evolve. Overall, the study delivers novel, joint astrophysical constraints on ABG-NLED-CS parameters and highlights the potential of horizon-scale imaging to test nonstandard gravity and matter near black holes.

Abstract

In this paper, we investigate the shadow and thin accretion disk around Ayón-Beato-García (ABG) black hole (BH) coupled with a cloud of strings (CS), characterized by the nonlinear electrodynamics (NLED) parameter $g$, and the CS parameter $a$. By comparing shadow diameters with Event Horizon Telescope (EHT) observations of M87$^{*}$ and Sgr A$^*$, we have established constraints on the BH parameters $g$ and $a$. Additionally, we analyze the BH shadow, lensing ring, and photon ring features for the ABG BH coupled with CS. Our results indicate that the shadow radius increases monotonically with the CS parameter $a$, while it decreases with increasing $g$. Finally, the study explores the physical properties and observational signatures of thin accretion disks around ABG BH with CS. The results show that an increase in parameter $g$ leads to a hotter and more luminous disk, while an increase in parameter $a$ results in a cooler and less luminous disk.

Figures (15)

• Figure 1: Regions of black hole horizon existence in the $(a, g/M)$ parameter space.
• Figure 2: Shadow diameter $d_{sh} = 2b_{c}$ as a function of the parameters $(a, g/M)$. The red and black curves represent the M87$^*$ shadow diameter at $d_{sh} = 9.5$ and $d_{sh} = 12.5$, respectively. The region between these curves corresponds to the 1$\sigma$ bound for the M87$^*$ shadow measurement, highlighting the parameter space in which the theoretical model is consistent with observational data (left panel). For Sgr A$^*$, the yellow line denotes $d_{sh} = 9.1$, and the green curve represents $d_{sh} = 10.44$. The shaded region indicates the 1$\sigma$ confidence interval of the observed shadow diameter, highlighting the range of parameters that are consistent with the measured Sgr A$^{*}$ shadow (right panel).
• Figure 3: The behavior of photon trajectories around an ABG BH coupled with a CS as a function of the impact parameter $b$. The upper panel displays the total number of orbits $(n = \phi/2\pi)$, classifying trajectories into three categories based on $n$: direct emission $(n<3/4)$ depicted in black, lensed trajectories $(3/4 < n < 5/4)$ shown in orange, and photon ring trajectories $(n > 5/4)$ colored in red. In the lower panel, selected photon paths are visualized using Euclidean polar coordinates $(r, \phi)$. The impact parameter spacing is adjusted to $1/10$, $1/100$, and $1/1000$ for direct emissions, lensed paths, and photon rings, respectively. Three scenarios are analyzed: setting $g=0.6,a=0.02$ in the first column; $g=0.6,a=0.05$ in the second column; and $g=0.6,a=0.08$ in the third column.
• Figure 4: The first three transfer functions for BHs corresponding to different values of $\alpha$ and $g$. From left to right, the panels represent the cases with $(g=0.6,a=0.02)$, $(g=0.6,a=0.05)$, and $(g=0.6,a=0.08)$, respectively. These curves correspond to the radial positions of the first (black), second (orange), and third (red) intersections between the light rays and the emission disk.
• Figure 5: Observational appearance of a geometrically and optically thin disk with different emission profiles near an ABG BH coupled with a CS. The left column shows the emission profiles $I^{\text{em}}(r)$ for various cases. The middle column displays the corresponding observed intensities $I^{\text{obs}}$ as functions of the impact parameter $b$, for the ABG BH coupled with a CS, with results shown for $a = 0.02$ (blue), $a = 0.05$ (green), and $a = 0.08$ (red). The right column presents the density plots of the observed intensity $I^{\text{obs}}(b)$ for the case $a = 0.02$. The parameter $g$ is fixed at $0.6$.