Sustainable Development Goals
Abstract/Objectives
We perform axisymmetric, 2D magnetohydrodynamic simulations to investigate accretion flows around spinning active galactic nuclei. To mimic the space-time geometry of spinning black holes, we consider effective Kerr potential, and the mass of the black holes is 108 MȮ. We initialize the accretion disc with a magnetized torus by adopting the toroidal component of the magnetic vector potential. The initial magnetic field strength is set by using the plasma beta parameter (β0). We observe self-consistent turbulence generated by magneto rotational instability (MRI) in the disc. The MRI turbulence transports angular momentum in the disc, resulting in an angular momentum distribution that approaches a Keplerian distribution. We investigate the effect of the magnetic field on the dynamics of the torus and associated mass outflow from the disc around a maximally spinning black hole (ak = 0.99). For the purpose of our analysis, we investigate the magnetic state of our simulation model. The model β0 = 10 indicates the behaviour similar to the 'magnetically arrested disc' state, and all the other low magnetic model remains in the SANE state. We observe that mass outflow rates are significantly enhanced with the increased magnetic field in the disc. We find a positive correlation between the magnetic field and mass outflow rates. We also investigate the effect of black hole spin on the magnetized torus evolution. However, we have not found any significant effect of black hole spin on mass outflows in our model. Finally, we discuss the possible astrophysical applications of our simulation results. © 2023 The Author(s). Published by Oxford University Press on behalf of Royal Astronomical Society.
Results/Contributions

For singularly perturbed linear differential equations constrained by boundary conditions, it is challenging to determine their exact solutions, and the effectiveness of the maximum principle cannot be guaranteed. Therefore, accurately identifying boundary asymptotics has become an important challenge. To address this challenge, we have developed a rigorous asymptotic method aimed at recovering boundary data and enhancing the accuracy and reliability of the solutions. The core of this method lies in transforming 'non-local' boundary conditions into 'local' boundary conditions, thereby simplifying the complexity of the problem. Through 'logarithmic' estimates, we obtained refined boundary asymptotics under singular perturbation parameters, which aids in a deeper understanding of the system's long-term behavior. Additionally, for the non-homogeneous case, we revealed a diverse range of asymptotic behaviors, including uniform boundedness and asymptotic blow-up, which are significant for predicting and controlling the system's dynamic evolution. Numerical simulations and validations further support the corresponding theoretical results, confirming the effectiveness and accuracy of our method. Considering sustainability, our approach not only aids in understanding and predicting various phenomena arising in the natural sciences and engineering, such as climate models and ecosystem dynamics, but can also be applied to optimize resource allocation, improve energy efficiency, and develop more resilient infrastructure.

Keywords
Singular perturbationIntegral boundary conditionNonlocal boundary effect
Contact Information
李俊璋老師
lee2@mx.nthu.edu.tw