Effects of dark matter on shadows and rings of Brane-World black holes illuminated by various accretions

In this study, by taking the accretions into account, the observed shadows and rings cast by the Brane-World black hole were numerically investigated when the observer was located at the cosmological horizon. The results showed that the radius r(p) of the photon sphere increased with the cosmological parameter alpha and dark matter parameter beta, while the impact parameter b(p) decreased with alpha and increased with beta. For thin disk accretion, the total observed intensity is mainly composed of direct emission. Simultaneously, the lensing ring and photon ring have only small and negligible contributions, respectively. We also found that shadows and rings exhibit different and exciting features when the disk is located at different positions. For static and infalling spherical accretions, it is evident that the size of shadows is always the same for both accretions. This implies that shadows are only related to space-time geometry in this case. The luminosity of the shadow and photon sphere is closely associated with the Doppler effect and the emissivity per unit volume j(v(e)). In addition, the influence of dark matter and cosmological constant on the observed intensity of shadows and rings is carefully emphasized throughout this paper. Finally, we obtained the burring images of shadows and rings using the nominal resolution of the event horizon telescope. We also studied the upper limits of the X-clod dark matter parameter beta using the data of the shadow of M87.

Automated summary

In this study, the effects of cosmological acceleration and dark matter on the shadows and rings cast by the Brane-World black hole were numerically investigated. The results showed that the radius and impact parameter of the photon sphere were influenced by the cosmological and dark matter parameters. The observed intensity from thin disk accretion was mainly contributed by direct emission, with the lensing ring and photon ring having negligible contributions. Different features of shadows and rings were observed for disks located at different positions.