The Fate of Transonic Shocks around Black Holes and their Future Astrophysical Implications

TL;DR

The paper addresses how transonic shocks form and persist in low-angular-momentum accretion onto Kerr black holes and what this implies for corona formation and jet launching. It employs high-resolution 2D GRHD and GRMHD simulations across a range of spins $a_{ m k}$, energies ${\cal E}_0$, angular momenta $\lambda_0$, and magnetizations to map global shocks between sonic points, with shocks characterized by a Mach number ${\cal M}=1$ at the transition. Key findings include the existence of global shocks for tuned $(\lambda_0,{\cal E}_0)$ in hydro and weakly magnetized flows, spin-dependent jet properties (prograde spin yields hotter post-shock regions and faster jets, retrograde yields weaker ones), and the suppression of shocks by strong magnetization, giving rise to magnetically dominated jets. These results suggest a framework for shock-driven coronae and jet launching in systems like Sgr A$^*$ and BH-XRBs, while highlighting limitations of 2D, non-radiative modeling and the need for future 3D GRMHD studies with radiative transfer for direct observational comparisons.

Abstract

Theoretical models have long predicted the existence of shocks in multi-transonic accretion flows onto a black hole, yet their fate under realistic general relativistic simulations has not been fully tested. In this study, we present results from high-resolution two-dimensional general relativistic hydrodynamic (GRHD) and general relativistic magnetohydrodynamic (GRMHD) simulations of low-angular-momentum accretion flows onto Kerr black holes, focusing on the formation of shocks in transonic accretion flow. We demonstrate that for specific combinations of energy and angular momentum, global shock solutions naturally emerge between multiple sonic points. These shocks are sustained in both corotating and counter-rotating cases, and their locations depend on specific energy, angular momentum, and the spin of the black hole which is in good agreement with analytical solutions. In magnetized flows, weak magnetic fields preserve the shock structure, whereas strong fields suppress it, enhancing turbulence and driving powerful, magnetically dominated jets/outflows. The strength and structure of the outflow also depend on a black hole spin and magnetization, with higher black hole spin parameters leading to faster jets. Shock solutions are found only in super-Alfvénic regions, where kinetic forces dominate. Our findings provide important insights into the physics of hot corona formation and jet launching in low-angular-momentum accretion systems such as Sgr~A$^*$ (weak jet/outflow) and X-ray binaries.

Figures (14)

• Figure 1: Vertically integrated mass flux ($\int_0^\pi \sqrt{-g}\rho u^r d\theta$ in an arbitrary unit, considering $u^r>0$ as inflow) for the targeted time range ($t=20000-30000\,t_g$) for different simulation models marked on the figure. The dashed vertical line corresponds to $r=700\,r_g$.
• Figure 2: (a) The time and vertically averaged radial Mach number (${\cal M}$) profiles for different pairs of $(\lambda_0, {\cal E}_0)$. (b) Vertically averaged radial Mach number (${\cal M}$) profiles at different simulation times for $(\lambda_0=3.4,{\cal E}_0=1.001$). The horizontal dotted line corresponds to Mach number ${\cal M}=1$. The thick dotted lines in panel (b) correspond to the semi-analytical solutions for the given parameters.
• Figure 3: The time-average logarithmic ( upper panels) normalized density ($\log_{\rm 10}(\rho/\rho_{\rm max})$) and ( lower panels) Mach number ($\log_{\rm 10}{\cal M}$) distribution on the poloidal plane for different values of $(\lambda_0, {\cal E}_0)$. The gray lines in the upper panels correspond to the velocity streamlines, and the white lines in the lower panels correspond to the sonic surface ${\cal M}=1$.
• Figure 4: The time-average logarithmic ( upper panels) normalized density ($\log_{\rm 10}(\rho/\rho_{\rm max})$), ( middle panels) Mach number ($\log_{\rm 10}{\cal M}$), and ( lower panels) logarithmic Lorentz factor ($\log_{\rm 10}(\gamma -1)$) distribution on the poloidal plane for different values of Kerr parameters with properly chosen $(\lambda_0, {\cal E}_0=1.001)$. The gray lines in the upper panels correspond to the velocity streamlines, the white lines in the middle panels correspond to the sonic surface ${\cal M}=1$, and the white lines in the lower panels correspond to the outflow surface $\sqrt{-g}\rho u^r=0$.
• Figure 5: Time evolution of the mass accretion rate through the relativistic jet and non-relativistic wind for different simulation models with different Kerr parameters. See text for more details.