Unifying the X-ray coronae and ultra-fast outflows: a PBI-enhanced outflow-based corona model for the inner accretion disc

Abstract

The fact that luminous X-ray coronae and Ultra-Fast Outflows (UFOs) are both inferred to originate from the innermost regions of active galactic nuclei (AGNs) suggests a deep physical connection between them. However, standard magnetic buoyancy models struggle to transport sufficient energy through the radiation-pressure-dominated inner disc to sustain both the phenomena, creating a theoretical energy deficit. In this work, we propose an outflow-based model with energy transport enhanced by the Photon Bubble Instability (PBI) in the inner region. By coupling this enhanced energy supply with the MHD turbulence-driven mass-loading mechanism appropriate for weakly magnetized standard discs, we solve the dynamical and thermodynamic structure of the corona. We find that the model can successfully launch high speed winds matching observed UFO kinematics provided the mechanical acceleration efficiency is high ($f_{\rm acc}\gtrsim 0.5$). Furthermore, the model naturally reproduces the observed spectral evolution found in AGN coronae: as the accretion rate increases, the corona becomes optically thicker and cooler and produces a softer spectrum. Our results support an extended slab-like coronal geometry and suggest that UFOs and X-ray coronae in the inner discs are manifestations of the same magnetic activity.

Figures (7)

• Figure 1: Radial distribution of the coronal energy fraction $f$ for different viscosity and magnetic buoyancy prescriptions. The BH mass $m$ in the left and right panels are 10 and $10^{7}$, respectively. The dimensionless accretion rate is $\dot{m}= 0.1$. The red lines represent the standard $\alpha$ prescription $\tau_{r\phi}= \alpha P_{\rm tot}$, while the blue lines represent the modified $\alpha$ prescription $\tau_{r\phi}= \alpha \sqrt{P_{\rm gas}P_{\rm tot}}$. The solid lines represent the situation where PBI is taken into account in the radiation-pressure-dominated region, while the dashed lines do not consider PBI. The vertical gray line indicates the position where the $P_{\rm gas}=P_{\rm rad}$.
• Figure 2: Radial distribution of the inferred upper limit on wind mass loading for different viscosity and magnetic buoyancy prescriptions. The BH mass is $m_{\rm BH}=10^{7}$. The meanings of different line styles (red/blue and solid/dashed) are the same as those in the Fig. \ref{['fig:f-R']}. The bold green line represents the empirical mass-loading profile of the wind implied by the combined UFO+WA sample of T13. The vertical gray line indicates the position where the $P_{\rm gas}=P_{\rm rad}$.
• Figure 3: Radial distribution of the cumulative outflow rate for different values of $\alpha_{\rm w}$ and $\dot{m}_{\rm in}$. The standard $\alpha$ prescription and PBI mechanism are included. In the upper panel, $\alpha_{\rm w}$ is fixed to $0.01$, from bottom to top the curves correspond to $\dot{m}_{\rm in}=0.02, 0.2$ and $2$, respectively. In the lower panel, $\dot{m}_{\rm in}$ is fixed to $0.2$, from bottom to top the curves correspond to $\alpha_{\rm w}=0.001, 0.01$ and $0.1$, respectively. The red and purple points are the UFO samples of T13 and G15, respectively.
• Figure 4: Radial profiles of the outflow velocity at the top of the corona derived from our model. The solid coloured curves, from bottom to top, correspond to mechanical efficiencies of $f_{\rm acc}= 0.1, 0.5,$ and $0.9$, respectively. The dashed line indicates the local Keplerian velocity, $v_{\rm K}= \sqrt{GM/R}$. The red and purple points are the UFO samples of T13 and G15, respectively.
• Figure 5: Radial structure of the corona for different mechanical efficiencies $f_{\rm acc}$. The upper panel shows the profiles of ion temperature $T_{\rm i}$ (dash-dotted curves) and electron temperature $T_{\rm e}$ (solid curves) and the scales in K and keV units are all marked in the figure. The lower panel shows the profiles of the vertical Thomson optical depth $\tau_{\rm c}$ of the corona (solid curves) and the resulting energy spectral index $\alpha_{\rm spec}$ (dash-dotted curves).