Unveiling BLR Structure in AGN with High Resolution X-Ray Spectra: An Analytic Approach to Wind Emission Line Profiles

TL;DR

The paper tackles the challenge of interpreting the Fe-Kα complex in AGN by disentangling multiple emission regions and introducing an analytic wind model for BLR-scale material. It presents xwind, an analytic framework that parameterizes wind geometry, velocity, and density, computes a self-consistent Fe-Kα emissivity from a simple photoionization prescription, and converts this into an observed line profile including Doppler and gravitational effects. Applied to XRISM observations of NGC 4151, the model is combined with a three-component spectral decomposition (torus reflection, BLR wind, and inner disc emission), yielding physically plausible launch radii, a low wind mass-outflow rate, and a self-consistent Fe-Kα equivalent width. The results demonstrate that BLR-scale winds can produce the observed smooth, moderately broadened Fe-Kα profiles, and the publicly released xwind code enables rapid, physically grounded fits to high-resolution X-ray spectra from XRISM and future missions. Overall, the work advances a practical, physically motivated method to probe BLR winds in AGN and paves the way for systematic studies across the AGN population.

Abstract

XRISM has provided an unprecedented view of the emission and absorption lines in the X-ray. Notably, early results showed significant complexity to the Fe-K$α$ line profile in AGN, with clear contributions from at least three emitting structures: an inner disc, intermediary broad line region (BLR) scale material, and an outer torus. This poses a new challenge for the modelling of the emission lines, as while fast sophisticated models exist for disc line-profiles, large scale-height material is typically much more complex. In this paper we aim to address this gap, by building a fully analytic model for the emission line profiles from a wind, aimed towards BLR scale material, motivated on previous reverberation studies suggesting a wind on the inner edge of the BLR. Our approach gives a physically motivated, yet computationally fast, model for the intermediary component to the Fe-K$α$ complex seen in the XRISM data. We demonstrate our model on the XRISM observations of NGC 4151 from the performance verification phase, showing that it gives a good description of the data, with physically reasonable parameters for BLR scale material. We also show that our model naturally gives the smooth line profile seen in the data, due to the large spatial extent of a wind. Finally, we make our model code public to the community, and name it xwind.

Figures (10)

• Figure 1: Left: Definition of our model geometry. The wind is launched between $r_{\rm{in}}$ and $r_{\rm{out}}$, at an angle defined by the distance of the focus below the origin, $d_f$. The covering fraction $f_{\rm{cov}}$ defines the maximum radial extent of the wind $r_{\rm{max}}$ (in spherical polar coordinates), giving a spherical boundary condition. Right: Example of our calculation grid (at significantly lower resolution for clarity). We split the wind into cells of $\cos(\theta)$ with width $d\cos(\theta)$ in the range $\cos(\theta) \in [0, f_{\rm{cov}}]$, and radius $r$ with width $d\log(r)$. The grid in $r$ extends from the inner streamline to either the outer streamline (defined from $r_{\rm{out}}$) or $r_{\rm{max}}$, depending on whichever is smallest. Our wind cells are illustrated as the dark shaded regions. Throughout this paper we will evaluate the wind emission and density at the centre of each cell $\theta_i$ and $r_j$. For completeness, this also defines the length travelled along the streamline $l_{ij}$ at each cell.
• Figure 2: Wind density profile (left column) and corresponding emissivity profile (middle column) for a range of outflow velocities (increasing from top to bottom, value given in top left corner of each row). The right column shows the column-density profile for varying lines-of-sight through the winds. These have all been calculated for a wind launched between $r_{\rm{in}} = 1000$ and $r_{\rm{out}} = 3000$, with $d_{f} = r_{\rm{in}}\sqrt{3}$ and $f_{\rm{cov}} = 0.9$. The mass outflow rate has been set to $\dot{m} = 0.1$, for a $10^8\,M_{\odot}$ black hole (where the mass is required to obtain physical units). The velocity profile has been given a scale length of $r_v = 500$ and exponent $\beta = 1$, and the initial density profile (at the base) has $\kappa = -1$, weighting the outflow towards smaller radii. As expected, when the outflow velocity increases, the overall density also reduces. In general, the emissivity is weighted more strongly towards the base of the wind, where the density is highest (hence stronger absorption/fluorescence). For low velocity (high density), the emission will be strongly weighted to the inner edge of the wind, as now the absorption is sufficiently strong that the internal wind regions do not see significant illumination. Our highest velocity examples are chosen for demonstrative purposes rather than an attempt at a realistic BLR wind.
• Figure 3: Example emission line profiles and their evolution with varying wind parameters. These have all been re-normalised to have the same total flux, and have all been calculated for an observed inclination of $45$ deg. Each panel shows the effect of varying an individual parameter, given in the top left corner of each panel. When not being varied, parameters are fixed at: $\dot{m}_w = 10^{-2}$, $r_{\rm{in}} = 700$, $r_{\rm{out}} = 3r_{\rm{in}}$, $d_f = \sqrt{3} r_{\rm{in}}$, $f_{\rm{cov}} = 0.6$, $v_{\infty} = 10^{-3}$, $r_v = 100$, $\beta = 1$, $\kappa=-1$. These are all viewed at an observers inclination of $i=45$ deg. The parameter choices for $d_f$ are chosen such that they correspond to wind opening angles on the inner edge of $\alpha_{\rm{min}} = 60^{o}, 45^{o}, 30^{o}, 20^{o},$ and $10^{o}$ (see Fig. \ref{['fig:geom_definition']} for a definition of the opening angle).
• Figure 4: Left: Colour-plot showing the equivalent width of the Fe-K$\alpha$ emission line for varying $\dot{m}_w$ and $v_{\infty}$. The darker the shade of green, the larger the equivalent width. The vertical/horizontal solid/dashed lines correspond to the slices used to extract the curves of growth on the right as a function of $\dot{m}_w$/$v_{\infty}$ Right: Curves of growth as a function of $\dot{m}_w$ (left panel) and $v_{\infty}$ (right panel). As $\dot{m}_w$ increases, so does the equivalent with, until eventually the line saturates due to the wind going optically thick. Conversely, increasing $v_{\infty}$ will reduce the equivalent width, as this reduces the overall density of the wind (see Fig. \ref{['fig:dens_and_emiss']}) leading to a lower degree of absorption and thus fewer photons available to re-emit as Fe-K$\alpha$.
• Figure 5: Best fit broad-band continuum, using combined XRISM-xtend (black crosses) and NuSTAR (orange/grey crosses for FPMA/B respectively). The solid red line shows the total spectral model, with the dotted/dashed lines showing the individual components. These are: the scattered continuum (dotted blue), reflection spectrum (dashed magenta), and the primary continuum (dashed-dotted blue). The plotted NuSTAR data have been corrected by a cross-calibration constant used to account for instrumental differences between XRISM-xtend and NuSTAR. The data have been re-binned slightly for clarity.