Broad Iron Line as a Relativistic Reflection from Warm Corona in AGN

TL;DR

This paper presents a self-consistent model in which a dissipative warm corona lying atop an accretion disk around a supermassive black hole generates highly ionized Fe Kα emission (FeXXV/FeXXVI) that, when subjected to strong gravity, Doppler boosting, and light bending, forms the observed broad iron line around 6.4 keV. The authors combine the photoionization/radiative-transfer code TITAN with relativistic ray-tracing in Kerr spacetime via GYOTO to compute angle- and radius-dependent local spectra and then integrate over the disk to obtain the observed spectrum for a range of black-hole spins $a$, viewing angles $\theta_{\rm obs}$, lamp heights $h$, and energy-dissipation fractions $f_W$ and $f_X$, with inner-disk temperatures reaching $T \sim 10^7-10^8$ K. They find that the broad line is a composite of multiple Fe Kα transitions whose relative contributions vary with spin and inclination, and that the warm corona’s internal heating and external illumination markedly influence the line profile, offering a new diagnostic for warm-corona physics via high-resolution spectroscopy. The work highlights the potential to constrain SMBH spin, disk geometry, and corona properties with current and future X-ray observatories (e.g., XRISM, Athena) by interpreting the relativistically blurred, ionized-iron components rather than assuming a single neutral Fe line origin.

Abstract

We present that the broad feature usually observed in X-ray spectra can be explained by a ray-traced emission from a two-slab system containing a dissipative, warm corona on top of an accretion disk in an AGN. Such an accretion flow is externally illuminated by X-ray radiation from a lamp located above a central SMBH. Thermal lines from highly ionized iron ions (FeXXV and FeXXVI), caused by both internal heating and reflection from the warm corona, can be integrated into an observed broad line profile due to the close vicinity of the SMBH. We investigate the dependence of the broad line profile by varying the SMBH spin parameter, viewing angle, lamp height, and dissipation factor. Our results introduce a new method to probe properties of the warm corona using high-resolution spectroscopic measurements. We use the photoionization code TITAN to compute local ion populations and emission line profiles, and the ray-tracing code GYOTO to include relativistic effects on the outgoing X-ray spectrum. In our models, the temperature of the inner atmosphere covering the disk can reach values of 10^7 - 10^8 K due to internal warm corona dissipation and external illumination, which is adequate for generating the highly ionized iron lines. These lines can undergo significant gravitational redshift near the black hole, leading to a prominent spectral feature centered around 6.4 keV. For all computed models, the relativistic corrections shift highly ionized iron lines to the X-ray region, usually attributed to fluorescent emission from the illuminated skin of an accretion disk. Hence, in the case of a warm corona covering the inner disk regions, the resulting theoretical line profile under strong gravity is a sum of different iron line transitions, and those originating from highly ionized iron contribute the most to the observed total line profile in AGN.

Figures (19)

• Figure 1: A schematic diagram of our model's setup. A hot corona, as in lamp post geometry, is located at height $h$ above the SMBH of mass $M$ and spin $a$. The warm corona, which is radially and vertically stratified, is positioned on top of an accretion disk. The incident flux coming from the hot corona is reprocessed in the warm corona, which is then detected by the observer. The $r_{\rm in}$ and $r_{\rm out}$ are the integration limits for our model. For a give distance $r$ we compute the vertical structure using TITAN with the input parameters depicted in the warm corona panel; $\Gamma$ - photon index, $\xi$ - ionization parameter, $N_{\rm H}$ - column density which is analogous to the optical depth $\tau$, $n_{\rm H}$ - gas number density, $Q$ - internal heating, and $T_{\rm BB}$ - the temperate of black body radiation from the disk.
• Figure 2: Radial distribution of global model parameters that are inputs for TITAN code. The colors represent different spin values given in the top box. The subplots are as follows: top left panel: gas number density [Eq. \ref{['eq:nh_r']}], top middle panel: dissipation flux [Eq. \ref{['eq:D_r']}], top right panel: X-ray flux from a hot corona [Eq. \ref{['eq:FX_r']}], bottom left panel: ionization parameter [Eq. \ref{['eq:xi_r']}], bottom middle panel: internal heating of the warm corona [Eq. \ref{['eq:Q_r']}], and bottom right: accretion disk temperature $T_{\rm BB}$ [Eq. \ref{['eq:T_bb_r']}]. The vertical dashed lines mark the radius at which the output temperature structure from TITAN reaches the maximum, see Fig. \ref{['fig:matter_structure']} and text for details. The computational parameters are described in Sec. \ref{['sec:setup']} and Tab. \ref{['tab:param_space']}, with $M$, $h$, $f_X$, and ${ f_{W}}$ kept constant.
• Figure 3: The temperature dependence on the optical depth for various spin values given in the boxes. The gray gradient of lines represents the matter structure calculated at different radii, with the darkest line at $r_{\rm in}$, and the lightest line at $r_{\rm out}$. The colored lines show the simulation with maximum temperature, which is coherent with the dashed line in Fig. \ref{['fig:mod_params']}. The corresponding radial point where the temperature drop is observed is labeled and marked in green text. The parameters other than spin are chosen to be canonical values from Tab. \ref{['tab:param_space']}. As this is the temperature structure, it is independent of the viewing angle.
• Figure 4: The heating and cooling of the matter structure at equilibrium for spin 0 and mass $10^8 {\rm M_{\odot}}$. The plots depict different points of the radial structure, left: 20.538 $r_{\rm g}$, middle: 21.385 $r_{\rm g}$, right: 22.231 $r_{\rm g}$. The solid lines depict heating and the dashed lines depict cooling.
• Figure 5: The local spectra $\nu F_{\nu}$ versus photon energy $E$, from TITAN code, for different spin values at the $i = 17.6^\circ$. The gray gradient of lines depicts outgoing spectra calculated at different radii, with the darkest line at $r_{\rm in}$, and the lightest line at $r_{\rm out}$. The colored lines show the simulation with maximum temperature, which is coherent with the dashed line in Fig. \ref{['fig:mod_params']} and solid colored lines in Fig. \ref{['fig:matter_structure']}.The parameters other than the spin and the viewing angle are set to be canonical values as depicted in Tab. \ref{['tab:param_space']}. This is the emission spectra, hence the parameter of the angle is chosen from Tab. \ref{['tab:solid_angle']}.