Weakness of X-rays and Variability in High-redshift AGNs with Super-Eddington Accretion

TL;DR

The paper addresses why JWST-identified high-redshift broad-line AGNs exhibit weak X-rays and minimal UV/optical variability. It develops a disk+warm corona model for super-Eddington accretion, where radiation-driven outflows create moderately thick coronae that upscatter seed disk photons, producing soft X-ray spectra and large X-ray bolometric corrections, while photon trapping suppresses UV/optical variability. The approach yields testable predictions, including an anti-correlation between UV/optical and X-ray variability and redshift-dependent bolometric corrections, and links the observed properties to rapid BH growth in the early universe. The framework aligns with JWST observations and offers a coherent explanation for the X-ray–bright/UV–faint high-z AGN population, with implications for cosmic X-ray background and BH–galaxy co-evolution models.

Abstract

The James Webb Space Telescope (JWST) observations enable the exploration of active galactic nuclei (AGNs) with broad-line emission in the early universe. Despite their clear radiative and morphological signatures of AGNs in rest-frame optical bands, complementary evidence of AGN activity - such as X-ray emission and UV/optical variability - remains rarely detected. The weakness of X-rays and variability in these broad-line emitters challenges the conventional AGN paradigm, indicating that the accretion processes or environments around the central black holes (BHs) differ from those of low-redshift counterparts. In this work, we study the radiation spectra of super-Eddington accretion disks enveloped by high-density coronae. Radiation-driven outflows from the disk transport mass to the poles, resulting in moderately optically-thick, warm coronae formed through effective inverse Comptonization. This mechanism leads to softer X-ray spectra and larger bolometric correction factors for X-rays compared to typical AGNs, while being consistent with those of JWST AGNs and low-redshift super-Eddington accreting AGNs. In this scenario, UV/optical variability is suppressed due to photon trapping within super-Eddington disks, while X-ray emissions remain weak yet exhibit significant relative variability. These characteristics are particularly evident in high-redshift AGNs powered by lower-mass BHs with $\lesssim 10^{7-8}~M_\odot$, which undergo rapid mass accretion following overmassive evolutionary tracks relative to the BH-to-stellar mass correlation in the local universe.

Figures (6)

• Figure 1: X-ray spectral index ($\Gamma$; $F_\nu \propto \nu^{1-\Gamma}$) as a function of Compton $y$-parameter, based on three different studies; Titarchuk_Lyubarskij_1995 (black, our fiducial model), Pozdniakov_1979 (blue), and Beloborodov_1999 (red). Three values of electron temperature in the non-relativistic regime are considered; $\theta_{\rm e}=0.03$ (dotted), $0.1$ (solid), and $0.3$ (dashed). Note that the fitting formula of Pozdniakov_1979 is not applied for $\theta_{\rm e} \mathrel{ \vcenter{\m@th\f@size4 \ialign{$$\cr <\crcr{ } \sim\crcr}}} 0.1$. Alt text: Graphs showing the theory modeled curves from three different studies.
• Figure 2: Broadband SEDs of a $z=4$ AGN with a bolometric luminosity of $L_{\rm bol}=10^{46}~{\rm erg~s}^{-1}$ for different values of the optical depths ($0.1\leq \tau_{\rm es} \leq 10$). The Compton parameter is set to $y=2/3$. The gray curve shows the SED of disk seed photons. For reference, we overlay the upper bound of the stacked AGNs obtained by Chandra observations (black arrows; Maiolino_2024bAkins_2024), and single power-law spectra with indices of $\alpha_{\rm ox}=-1.5$, $-1.75$, and $-2.0$ (dashed lines). Alt text: Graphs showing the results of our SED model and the observational data.
• Figure 3: Broadband SEDs of a $z=4$ AGN powered by a BH with $M_{\rm BH}=10^7~M_\odot$ (left) and $10^8~M_\odot$ (right) accreting at various rates of $0.1\leq \dot{m}_{\rm BH} \leq 10$. Here, $L_{\rm bol}$, $T_{\rm b}$, $T_{\rm seed}$ are calculated consistently for given $M_{\rm BH}$ and $\dot{m}_{\rm BH}$ values. The Compton parameter is set to $y=2/3$, and optical depth is calculated by using Equation (\ref{['eq:tau']}) with $\mathscr{F}_p=0.2$ (solid curves). For sub-Eddington cases ($\dot{m}_{\rm BH}=0.1$ and $0.3$), SEDs with a lower mass-loading factor of $\mathscr{F}_p=0.05$ are presented (dotted curves), corresponding to lower-density coronae consistent with low-redshift AGNs that exhibit X-ray spectral hardness. While the bolometric/UV luminosity increases with $\dot{m}_{\rm BH}$, the X-ray emission is sufficiently weak for $\dot{m}_{\rm BH} \mathrel{ \vcenter{\m@th\f@size4 \ialign{$$\cr >\crcr{ } \sim\crcr}}} 1$ ($M_{\rm BH}=10^7~M_\odot$) and $\dot{m}_{\rm BH} \mathrel{ \vcenter{\m@th\f@size4 \ialign{$$\cr >\crcr{ } \sim\crcr}}} 3$ ($M_{\rm BH}=10^8~M_\odot$), respectively, because of lower electron temperatures (and softer photon index) of the optically-thick corona. Alt text: Graphs showing the results of our SED model and the observational data.
• Figure 4: X-ray bolometric correction in the 2-10 keV band as a function of AGN bolometric luminosity for various BH masses ($10^6 \leq M_{\rm BH}/M_\odot \leq 10^{9}$) and accretion rates ($0.01 \leq \dot{m}_{\rm BH} \leq 10$). The short and long-dashed lines show the bolometric luminosities for $\dot{m}_{\rm BH} =0.1$ and $1.0$. For each BH mass, the Compton parameter is set at $2/3\leq y\leq 1$ (shaded region), where a larger $y$-value results in the higher X-ray luminosity for the same bolometric luminosity. Observation data for various types of AGNs from literatures are overlaid for comparison: JWST-identified broad-line AGNs (orange square; Maiolino_2024b), low-redshift high-$\lambda_{\rm Edd}$ quasars (blue circle; Laurenti_2022), local AGNs including NLSy1 galaxies (red circle; Liu_2021), luminous quasars at $z>6$ (purple circle; Zappacosta_2023), and optical/UV-selected typical quasars at $0<z<7$ (gray circle; Lusso_2020). Alt text: Graphs showing our modeled results and the observational data from the literature.
• Figure 5: Left: The normalized bolometric (blue) and X-ray (orange) luminosities as functions of accretion rate, relative to the Eddington value. The bolometric luminosity of the disk is presented by Watarai_2000 (with a 10% radiative efficiency; our fiducial model). The X-ray luminosity is shown for a BH mass of $M_{\rm BH} =10^7~M_\odot$ with $y=1$ (solid) and $y=2/3$ (dashed). The X-ray Eddington ratio is rescaled by a factor of $10^3$. Right: Variability response defined as $\mathscr{R} \equiv \frac{{\rm d}\log L}{{\rm d} \log \dot{m}_{\rm BH}}$ for both bolometric and X-ray luminosities. In the super-Eddington regime ($\dot{m}_{\rm BH}>1$), the bolometric (UV/optical) luminosity exhibits weak variability due to photon trapping in the dense disk, while the X-ray component shows stronger variability at a given accretion-rate fluctuation. The transition accretion rate depends on the BH spin (the blue dashed curve for a 20% radiative efficiency, corresponding to $a_{\rm BH}\simeq 0.96$). Note that the variability response of X-rays is negative $\mathscr{R}<0$, except at the sub-Eddington regime for $y=1$ (denoted by dotted curve). This results in an anti-correlation between flux variations in the UV/optical and X-ray bands: as the accretion rate increases, UV/optical luminosity rises while X-ray luminosity declines. Alt text: Graphs showing our modeled results.