Implications of Non-equatorial Relativistic Accretion Flows for Ultra-Fast Inflows in AGNs

TL;DR

This work proposes that ultra-fast inflows (UFIs) in AGNs can be realized as non-equatorial, relativistic GRHD inflows channeled by poloidal magnetic fields in Kerr spacetime. Using stationary, axisymmetric Kerr GRHD in a weak-field limit, the authors derive conical inflow solutions with conserved energy and angular momentum, solve for transonic radial velocity, and compute Fe XXVI Ly$\alpha$ absorption spectra under fixed $N_H$ and $\xi$. The predicted absorption lines shift to the hard X-ray regime ($\sim$4–6.5 keV) due to a combination of gravitational and Doppler redshift, with line strength modulated by a volume filling factor and the gas density profile; results align broadly with several UFI observations. The study highlights the potential of using UFI spectral features to constrain near-horizon inflow dynamics, while noting limitations such as the lack of radiative transfer and the planned extension to GRMHD models for a more complete treatment of magnetized accretion flows.

Abstract

Motivated by a number of X-ray observations of active galactic nuclei (AGNs) that exhibit a potential signature of ultra-fast inflows (UFIs), we consider in this work a scenario that UFIs can be physically identified as weakly-magnetized hydrodynamic accretion flows that is guided and channeled by poloidal magnetic field into low-to-mid latitude above the equatorial disk. In the context of general relativistic hydrodynamics (GRHD) under a weak-field limit in Kerr spacetime, we present a set of preliminary results by numerically calculating the physical property of GRHD flows (e.g. kinematics and density distribution) in an effort to simulate redshifted absorption line spectra. Our model demonstrates that such GRHD accretion off the equatorial plane (i.e. $v \gsim 0.1c$ where $c$ is the speed of light in the vicinity of AGN closer than $\sim 100$ \sw radii) can manifest itself as UFIs in the form of redshifted absorption signature assuming the observed characteristics such as column density of $N_H \sim 10^{23}$ cm$^{-2}$ and ionization parameter of $\log (ξ\rm{[erg~cm~s^{-1}])} \sim 3$ as also seen in recent multi-epoch {\it NuSTAR} observations among other data.

Figures (4)

• Figure 1: Schematic picture of non-equatorial accretion flows guided and channeled by the poloidal magnetic field (purple), which is simplified to be a conical geometry in our calculations so that $u^\theta=0$ for simplicity. Gas is provided from the equatorial disk surface at large distance. Green dashed line denotes line of sight (LoS) angle $\theta_{\rm obs}$. Note that toroidal motion of gas ($u^\phi \ne 0$) is suppressed in this poloidal projection.
• Figure 2: Intrinsic kinematic solution of UFI as a function of distance $r$ for (a) a Schwarzschild BH ($a=0$) with $\ell=2.7$, (b) prograde UFI with $\ell=1.9$ and (c) retrograde UFI with $\ell=-3$ around a Kerr BH ($a=0.99$) with $\theta=60^\circ$ showing $v_{\rm LNRF}^\phi/c$ (dark), $v_{\rm CRF}^r/c$ (green), inflow angular velocity $\Omega$ (cyan), and angular velocity of the inertial frame $\omega$ (i.e. frame-dragging; blue). Superimposed are the normalized number density $n(r)$ (thick red), net redshift $g_{\rm net}$ (dashed magenta) and classical Doppler shift $g_D$ (dashed orange) of UFIs. A sequence of color-coded vertical lines denote a series of sampled radii where we also compute spectra in Figure \ref{['fig:spec']}. Dotted vertical line indicates the sonic radius at $r=r_c \sim 100R_g$.
• Figure 3: Calculated Fe xxvi Ly$\alpha$ absorption line spectra (transmission) for (a) a Schwarzschild BH ($a=0$), (b) prograde UFI and (c) retrograde UFI around a Kerr BH ($a=0.99$) with $\theta=60^\circ$ at various radii corresponding to those (a sequence of color-coded vertical lines) shown in Figure \ref{['fig:accretion']}. We show $\theta_{\rm obs}=60^\circ$ (thick) and $40^\circ$ (thin) for comparison. Shaded region depicts the energy band of the detected UFIs derived from multiple AGN observations. Inset is NuSTAR spectrum of ESP 39607 exhibiting a potential UFI feature (red rectangle) for reference Peca25.
• Figure 4: Calculated maximum line optical depth $\tau_{\rm max}$ (solid) and volume filling factor $b_{\rm vol}$ (dashed) of UFIs as a function of radius $r$ for a Schwarzschild BH (black), prograde UFI (red) and retrograde UFI (blue), corresponding to Figures \ref{['fig:accretion']}-\ref{['fig:spec']}. Here, we assume a constant column $N_H=10^{23}$ cm$^{-2}$ with $\log \xi=3$ in the course of accretion for simplicity.