Hybrid Black Hole and Disk-Driven Jets: Steady Axisymmetric Ideal MHD Modeling

Abstract

Improved observational precision in relativistic jets has underscored the need for tractable theoretical models. In this study, we construct a semi-analytical hybrid jet model that incorporates both black hole-driven and disk-driven components within the framework of steady, axisymmetric, ideal MHD. We derive a condition that determines the launching sites of cold outflows, introducing a new constraint on the magnetic field configuration threading the accretion disk. Using the Bernoulli equation and critical point analysis, we derive flow solutions along various magnetic field lines. Our hybrid jet model shows that discontinuities in field-line angular velocity lead to clear velocity shear and density jumps at the interface between the two jet components. These features are accompanied by localized enhancements in velocity and density, potentially explaining the observed limb-brightening.

Figures (14)

• Figure 1: Schematic illustration of the jet structure. The BZ process operates along magnetic field lines that thread the black hole horizon, which carry a continuous outward Poynting flux. Along these field lines, plasma inflows occur below the loading zone, while outflows are launched above it. Concurrently, the BP process is realized along magnetic field lines anchored in the accretion disk, which drive outflows via magnetocentrifugal acceleration and magnetic pressure gradients.
• Figure 2: Real roots of the wind equation along a parabolic streamline in a cold MHD jet ($\mu = 1$) in Kerr spacetime with spin $a = 0.9$. The streamline is defined by $r-z = r_+$, where $r_+$ is the event horizon radius. Cylindrical coordinates are given by $x = r \sin{\theta}, z = r \cos{\theta}$. The conserved quantities are $\{\psi, \Omega_F, \eta, E, L\} = \{1.4359 , 0.1287, -0.2002, 0.6156, -0.4044 \}$ for the inflow and $\{ 1.4359, 0.1287, 0.03401, 3.375, 21.0432 \}$ for the outflow. The red solid curve shows the physical solution; gray dashed curves denote unphysical branches.
• Figure 3: Poloidal magnetic field configurations corresponding to Eq. \ref{['BZstream']} are shown for $q = 1$ (left) and $q = 0.5$ (right). Gray dashed lines represent magnetic field lines anchored at various footpoint angles $\theta_+ = n\pi/20$, $n = 1, 2, \dots, 10$; the associated values of $n$ are indicated in the figure. The blue curve denotes the jet launching surface, while red curves indicate the light cylinders.
• Figure 4: A representative BZ flow solution is shown, along a parabolic field line with $q = 1$, $\theta_+ = \pi/2$. In all panels, the gray-shaded region indicates the black hole interior; the black dot-dashed line marks the launching surface; black dashed lines show the light cylinders; the purple line marks the fast magnetosonic point; and orange lines mark the Alfvén points. Top-left: Poloidal velocity $u_p$ for both inflow and outflow (red), Alfvén speed (green), and fast magnetosonic speed (blue). The point labeled FM marks the fast magnetosonic point, while the points labeled A indicate the Alfvén points. Top-right: Plasma number density. Bottom-left: Components of the three-velocity: $v^r$, $v^\theta$, and $v^\phi$ where $v^{i} = u^{i}/u^t$. Bottom-right: Spatial components of the magnetic field.
• Figure 5: A representative BZ flow solution is shown, along a parabolic field line with $x_0 = (r_{\rm ISCO} - 1)\sqrt{20}$ and $b = r_{\rm ISCO} - 1$. We set the spin $a = 0.9$ and terminal Lorentz factor $\gamma_\infty = 3$. The light cylinder is shown as black dashed lines, and the Alfvén surface as an orange line. Top-left: Poloidal velocity $u_p$ for outflow (red), Alfvén speed (green dashed), and FM speed (blue dashed). The point labeled A indicates the outflow Alfvén points. Top-right: Plasma density, which diverges near the launch point. Bottom-left: Components of the three-velocity $v^r$, $v^\theta$, and $v^\phi$. Bottom-right: Magnetic field components $\sqrt{B^r B_r}$, $\sqrt{B^\theta B_\theta}$, and $\sqrt{B^\phi B_\phi}$.