Anisotropic Radiation in Super-Eddington Active Galactic Nuclei: The Responsivity of Broad-Line Regions to Continuum Variability

abstract · abstract

Anisotropic ionizing radiation is a natural theoretical expectation for super-Eddington accretion in active galactic nuclei (AGNs), implying that the ionizing flux incident on the broad-line region (BLR) clouds differs from that measured along the observer's line of sight. Reverberation mapping studies have revealed systematically shortened time lags of the broad H$β$ emission line relative to continuum variations in super-Eddington AGNs, a phenomenon that can be naturally interpreted as a consequence of anisotropic ionizing continuum radiation. To further investigate this anisotropy, we perform a systematic analysis of the H$β$ line responsivity, defined as the ratio of the variability amplitude of H$β$ to that of the driving continuum, for both sub- and super-Eddington AGNs. By combining the effective responsivities measured relative to the driving continuum, after correcting for the continuum--emission-line delay, with photoionization calculations, we infer the ionizing radiation field received by their BLRs. We find that, in super-Eddington AGNs, the ionizing flux inferred from the H$β$ responsivity differs significantly from that observed along the line of sight, whereas the two are in closer agreement in sub-Eddington AGNs. These results provide compelling evidence for strong anisotropy of the incident ionizing radiation in super-Eddington AGNs. We conclude by discussing the broader implications of this anisotropy, including its potential relevance to the "little red dots" recently discovered by the James Webb Space Telescope.

S2.SS2.SSS4: II.2.4 Measurement of Responsivity / block 1 · html

For objects with multiple RM campaigns, we first measured η \eta from each campaign independently and then combined the results using a weighted average. Because some light curves suffer from relatively low signal-to-noise ratios or sparse temporal sampling, the corresponding η \eta estimates can carry large uncertainties. To ensure robust measurements, we retained only those campaigns with a Pearson correlation coefficient of r ≥ 0.6 r\geq 0.6 and a detection significance of η / η err ≥ 1 \eta/\eta_{\rm err}\geq 1 , discarding those that do not satisfy these criteria. We have verified that adopting slightly more or less stringent thresholds does not affect the conclusions of this work. Our final sample comprises 128 AGNs with a total of 175 light curves.

S3.SS4.SSS1: III.4.1 Correlations Between Φ H iso \Phi_{\mathrm{H}}^{\mathrm{iso}} , Φ H ion \Phi_{\mathrm{H}}^{\mathrm{ion}} , and Accretion Rate / block 1 · html

We can measure the Φ H ion \Phi_{\mathrm{H}}^{\mathrm{ion}} of each individual object from its responsivity based on the CLOUDY responsivity result under the single-cloud approximation. In this approximation, the BLR is represented by a single cloud characterized by a specific incident ionizing photon flux, gas density, and responsivity. Figure 4 illustrates two examples of Φ H ion \Phi_{\mathrm{H}}^{\mathrm{ion}} measurements for individual objects, assuming solar metallicity and the SED from [ 76 ] . Examples corresponding to a metallicity of 5 ​ Z ⊙ 5Z_{\odot} and the SED of [ 33 ] are presented in Appendix A . The regions shaded with white dots and surrounded with black lines are the parameter space of n H n_{\mathrm{H}} and Φ H \Phi_{\mathrm{H}} where the responsivity is within the specific value derived from the RM light curves (Section II.2.4 ). The left panel is a sub-Eddington object (Mrk 1148, see D.-W. Bao et al. 7 ) whereas the right panel is a super-Eddington one (SDSS J101000, see P. Du et al. 29 ). For comparison, the Φ H iso \Phi_{\mathrm{H}}^{\mathrm{iso}} obtained from their luminosities and BLR radii (Section III.2.1 ) are shown overlaid with blue and red dashed lines, with the shaded regions in both panels indicating their measurement uncertainties. From Figure 4 , it is clear that the ranges of Φ H iso \Phi_{\mathrm{H}}^{\mathrm{iso}} and Φ H ion \Phi_{\mathrm{H}}^{\mathrm{ion}} are more similar (with significant overlap) in the sub-Eddington AGN while Φ H iso \Phi_{\mathrm{H}}^{\mathrm{iso}} substantially exceed Φ H ion \Phi_{\mathrm{H}}^{\mathrm{ion}} in super-Eddington AGN.

S4: IV Discussion / block 1 · html

Figure 10: Cartoons illustrating the BLRs illuminated by accretion disks in sub- and super-Eddington AGNs. The blue clouds represent the BLR clouds that respond to continuum variability. In the top panel, for sub-Eddington AGNs with geometrically thin accretion disks, the ionizing photon flux received by the clouds, Φ H ion \Phi_{\mathrm{H}}^{\mathrm{ion}} , is comparable to, or only slightly weaker than, the flux inferred under the isotropic assumption, Φ H iso \Phi_{\mathrm{H}}^{\mathrm{iso}} . In the bottom panel, for super-Eddington AGNs, the inner regions of slim disks are geometrically thick, producing anisotropic ionizing radiation such that Φ H ion ≪ Φ H iso \Phi_{\mathrm{H}}^{\mathrm{ion}}\ll\Phi_{\mathrm{H}}^{\mathrm{iso}} for clouds near the equatorial plane, resulting in a smaller effective response radius. The panels are schematic and not to scale.

S5: V Conclusion / block 1 · html

In this work, we systematically investigate the responsivity of broad H β \beta emission lines based on the light curves of RM objects, aiming to reveal how the strength of radiation anisotropy in the accretion disk depends on AGN properties. The main results are summarized as follows:

S5: V Conclusion / block 1 · html

We found that the responsivity of H β \beta to continuum variability is statistically anti-correlated with SMBH mass and positively correlated with accretion rate and the strength of iron emission.

S5: V Conclusion / block 1 · html

From CLOUDY photoionization calculations, we determined that the responsivity of BLR clouds is more sensitive to the incident ionizing photon flux Φ H \Phi_{\mathrm{H}} than to the local gas density n H n_{\mathrm{H}} of the clouds. By comparing the ionizing photons ( Φ H ion \Phi_{\mathrm{H}}^{\mathrm{ion}} ) received by the BLR clouds–derived from responsivity based on CLOUDY calculations–with those ( Φ H iso \Phi_{\mathrm{H}}^{\mathrm{iso}} ) inferred from the observer’s line of sight under the isotropic assumption, we can investigate radiation anisotropy in different AGNs.

S5: V Conclusion / block 1 · html

Φ H ion \Phi_{\mathrm{H}}^{\mathrm{ion}} is more similar to Φ H iso \Phi_{\mathrm{H}}^{\mathrm{iso}} in sub-Eddington AGNs, while a greater discrepancy is observed in super-Eddington AGNs. The difference Δ ​ log ⁡ Φ H \Delta\log\Phi_{\mathrm{H}} shows the most significant correlation with accretion rate, indicating a higher degree of radiation anisotropy in super-Eddington AGNs compared to sub-Eddington ones. This provides observational support for the self-shadowing effect expected from slim-disk accretion.

S5: V Conclusion / block 1 · html

As discussed in Section IV.6 , compact objects or stellar-mass black holes within accretion disks, acting as additional energy sources, may further puff up the disks and enhance their radiation anisotropy, in addition to the self-shadowing effect. Therefore, we will consider the contribution of these additional energy sources in the super-Eddington regime in future work.

S3.SS1: III.1 Correlations with SMBH Mass, Accretion Rate, and Fe ii Strength / block 1 · html

where G G is the gravitational constant, Δ ​ V \Delta V is the line width (which may be taken as either the FWHM or the line dispersion), and f BLR f_{\mathrm{BLR}} is a factor that accounts for the geometry and kinematics of the BLR [ 85 , 45 , 48 , 109 , 112 , e.g.,] . The value of the f BLR f_{\mathrm{BLR}} factor can be calibrated using the M ∙ M_{\bullet} – σ bul \sigma_{\rm bul} , M ∙ M_{\bullet} – L bul L_{\rm bul} , or M ∙ M_{\bullet} – M bul M_{\rm bul} relations in inactive galaxies, where σ bul \sigma_{\rm bul} , L bul L_{\rm bul} , and M bul M_{\rm bul} represent the stellar velocity dispersion, luminosity, and mass of the galaxy bulge, respectively [ 85 , 45 , 48 , 109 , 112 , e.g.,] . Alternatively, the f BLR f_{\mathrm{BLR}} factor can be directly obtained through dynamical modeling of the BLR for individual AGNs [ 86 , 67 , e.g.,] . The derived value of f BLR f_{\mathrm{BLR}} is close to unity if Δ ​ V \Delta V is the FWHM, or approximately 5 if Δ ​ V \Delta V is the line dispersion (see the aforementioned references). For simplicity, we adopt f BLR = 1 f_{\mathrm{BLR}}=1 to estimate the SMBH mass, while acknowledging the possible scatter of approximately 0.3–0.5 dex in its value for individual objects and its potential dependence on AGN properties (see more details in, e.g., S. Yang et al. 112 ).

S3: 3 Extreme H α \alpha EWs: blue SEDs vs. covering factor / block 1 · html

Figure 3 displays the resulting broad H α \alpha EW probability density functions (PDFs), computed assuming random observer orientations weighted by the random-orientation distribution p ⁡ ( i ) = sin ⁡ i p(i)=\sin i . The shaded region indicates the full range of EWs observed in the high- z z sample of Maiolino et al. (2025) ( 200 ≲ EW ≲ 1200 200\lesssim{\rm EW}\lesssim 1200 Å). While the observed histogram is a population statistic that also reflects intrinsic scatter in black hole mass, accretion rate, and BLR gas properties, our model curves isolate the variance due to orientation alone and are therefore narrower. Nevertheless, the shift of the probability-weighted peak EW with ionization parameter provides a useful handle on the overall scaling needed to reproduce typical line strengths. In the most edge-on tail of the orientation distribution, the model predicts very large EWs because the observed optical continuum decreases approximately geometrically, ∝ cos ⁡ i \propto\cos i , while the broad-line luminosity is assumed to be isotropic. In practice, once the direct nuclear continuum becomes extremely faint – in our models this occurs at i ≳ 85 ∘ i\gtrsim 85^{\circ} – the observed rest-optical continuum will not continue to dim indefinitely. A low-level continuum floor from host starlight and/or scattered AGN light is expected to dominate over the highly foreshortened direct disk emission at these inclinations, effectively truncating the high-EW tail. We therefore impose a conservative cap EW ⁡ ( H ​ α ) ≤ 2000 {\rm EW}(\mathrm{H}\alpha)\leq 2000 Å when constructing the PDFs. This cap affects only the extreme edge-on tail and does not alter the probability-weighted median used to calibrate C BLR C_{\rm BLR} .

S3: 3 Extreme H α \alpha EWs: blue SEDs vs. covering factor / block 1 · html

Our results contrast with Yan et al. (2025) , who argue that the observed broad H α \alpha strengths require near-unity covering factors and therefore invoke an enshrouded geometry with nearly 4 ​ π 4\pi coverage by dense gas ( n H = 10 8 n_{\rm H}=10^{8} – 10 10 ​ cm − 3 10^{10}\,{\rm cm^{-3}} ). In our super-Eddington models, large Balmer EWs can be produced with modest C BLR C_{\rm BLR} because the BLR-illuminating continuum has a higher ionizing-to-optical photon budget than standard quasar composites, and the inclination dependence is driven by anisotropic continuum dilution at fixed line emission. For more face-on sightlines, the observer sees the boosted funnel continuum, whereas the BLR does not intercept a proportionally larger ionizing flux, so the lines are diluted and the EWs fall to values typical of Type 1 AGNs. Thus, the most extreme LRD H α \alpha EWs require high inclinations, not unusually large covering factors.

S8.SS3: 8.3 Insights into the X-ray weakness of JWST -selected AGN / block 1 · html

However, one of the most puzzling observational results obtained by combining data from JWST and from X-ray missions, such as Chandra , is the lack of hard X-ray emission in most JWST -selected AGN ( Yue et al., 2024 ; Maiolino et al., 2024a ; Ananna et al., 2024 ; Kokubo & Harikane, 2024 ; Lambrides et al., 2024 ; Lyu et al., 2024 ) . For example, as shown by Maiolino et al. (2024a) , compared to quasars selected in the UV/optical at low redshift, JWST -selected AGN at z ≳ 4 z\gtrsim 4 with similar bolometric luminosities, no matter whether they are Type 1 or Type 2, are 1-2 orders of magnitude weaker in their X-ray luminosities. Similarly, Lambrides et al. (2024) found that the broad-line AGN selected by JWST must have their α ox \alpha_{\rm ox} offset from the lower redshift broad-line AGN at similar UV luminosities by more than 0.6 dex.

S9: 9 Conclusions / block 1 · html

The narrow component of H β \beta is extremely narrow, unresolved (conservatively, σ < 47 \sigma<47 km ​ s − 1 \rm km~s^{-1} ). This, together with the compact size of the galaxy, was used to set an tight, conservative upper limit on the dynamical mass of M dyn < 4 × 10 8 ​ M ⊙ M_{\rm dyn}<4\times 10^{8}~M_{\odot} , which is one order of magnitude lower than the stellar mass of the galaxy inferred when assuming that the Balmer break and optical continuum are of stellar origin ( 4 × 10 9 ​ M ⊙ 4\times 10^{9}~M_{\odot} ). Our finding indicates that the stellar light cannot contribute more than 10% (very conservatively) to the Balmer break and to the optical continuum.

S4.SS2: IV.2 H α \alpha Variability / block 1 · html

Our sample-wide intrinsic rms variability estimates σ 0 , lc \sigma_{0,\rm lc} agree with the low-amplitude variability seen in Fig. 8 . The LRDs exhibit 4.02% H α \alpha variability on rest-frame ∼ \sim months, with consistent results seen for both the cool LRDs and more typical “hot” LRDs. However, considering that the H α \alpha flux estimates likely have underestimated uncertainty from systematics, this represents an upper limit of variability in LRDs. Only one of our cool LRDs (NX7607) exhibits tentative variability ( ∼ \sim 30%), although the impact of systematics complicates its significance. We discuss this further in Section V.2 .

S6: VI Conclusion / block 1 · html

Our LRDs and BLAGNs display intrinsic rms H α \alpha flux variability of 4.02% and 6.16% on rest-frame timescales ≲ \lesssim 100 days, though there are a population of JWST BLAGNs that are substantially more variable in H α \alpha flux. We consider these variability constraints upper limits given potential residual systematics in the flux measurements.

S4: IV Summary and Discussion / block 1 · html

Figure 5: The existence of direct sight-lines from the accretion indicates a covering fraction < 1 <1 of the broad-line gas.

S4: IV Summary and Discussion / block 1 · html

In summary, we find a statistically significant flux increase of at least > 1.65 >1.65 for all strongly detected emission lines, and note a > 10 ​ σ >10\sigma differences between the broad H ​ α \mathrm{H}{\alpha} flux and [O iii ] λ ​ λ ​ 4960 , 5008 \lambda\lambda 4960,5008 between the epochs. These results imply several important constraints on the nature of this source:

A3.SS2: C.2 DCE and photoionization simulations / block 2 · html

emission, which represents the intrinsic continuum irradiating the BLR clouds, and the diffuse emission, arising from photoionised gas within the BLR. These results correspond to a single-cloud photoionisation model with n H = 10 12 ​ cm − 3 n_{\text{H}}=10^{12}\,\mathrm{cm^{-3}} , column density of 10 23 ​ cm − 2 10^{23}\,\mathrm{cm^{-2}} , solar metallicity, and a fixed distance of 162 light-days. A constant covering fraction of 20% is assumed, and no additional kinematic broadening is applied beyond CLOUDY’s default spectral binning of 1 Å. The sum of all components, including transmitted, reflected, and diffuse contributions, is shown alongside the observed total emission, derived from our photometric light curves. There is a good qualitative agreement between the observed and modelled emissions. The bottom panel in Fig. 8 shows the fractional contribution of the DCE, as a function of wavelength. The black circles represent the effective DCE fractions integrated over the photometric filter bands used in this study. The DCE contribution is approximately 2.3% at 4858 ​ Å 4858\,\text{\AA} , 3.9% at 5315 ​ Å 5315\,\text{\AA} , 8.3% at 6043 ​ Å 6043\,\text{\AA} , and 26.3% at 7705 ​ Å 7705\,\text{\AA} . These values indicate that the DCE contribution is small at shorter wavelengths but increases significantly toward longer wavelengths.

S3.SS2: 3.2 Modelling the accretion disc response / block 1 · html

This scaling relationship is particularly significant as it establishes a direct link between the accretion disc size, which can be measured efficiently over a six-month photometric monitoring campaign, and the BLR size. By coupling this result with single-epoch CIV line velocity dispersion measurements, the black hole mass can be estimated without the need for decades-long spectroscopic monitoring of the BLR. This breakthrough highlights the potential for accretion disc size measurements to serve as a faster and more efficient proxy for BLR-based black hole mass determinations, particularly for high-redshift quasars, where monitoring timescales are otherwise prohibitive. However, to determine whether this scaling factor of ∼ 125 − 150 \sim 125\ -150 is universal across different quasars, it will be essential to monitor a larger sample of sources at high redshifts. Such an effort will allow us to test the robustness of this relationship and explore any dependencies on black hole mass, accretion rate, or quasar properties. Future time-domain surveys and high-cadence monitoring campaigns will be crucial in addressing this question and solidifying the role of accretion disc measurements in black hole mass estimation.

S1: I Introduction / block 1 · html

Where applicable, we adopt the best-fit cosmological parameters from the WMAP 9 yr results: H 0 = 69.32 H_{0}=69.32 km ​ s − 1 ​ Mpc − 1 {\rm km\,s^{-1}\,Mpc^{-1}} , Ω M = 0.2865 \Omega_{M}=0.2865 , and Ω Λ = 0.7135 \Omega_{\Lambda}=0.7135 [ 55 ] , and the stellar initial mass function from G. Chabrier [23] .

S7.SS4: VII.4 Intrinsic Spectra of LRDs Hidden within a Dense Hydrogen Cloud / block 1 · html

Moving beyond typical AGNs, our analysis suggests three possible interpretations for the nature of LRDs, driven by requiring consistency with the observed He ii EWs and the red optical continuua. We organize the discussion of these scenarios to follow the sequence of results presented in Section VI.5 .

S5.SS3.SSS3: V.3.3 Mrk 268 / block 1 · html

To investigate this effect on Mrk 268, we calculated the SF data from the ZTF light curve after subtracting the host component assuming its contribution of 50% of the minimum flux of the original light curve data. As a result, while the derived SF values increase, it does not show a clear dependence on time separation as in the original SF data. This result indicates that even when considering host contamination, the ZTF light curve of Mrk 268 does not show a significant flux variation due to the AGN.

S6.SS1.SSS1: VI.1.1 MCG -3-34-64 / block 1 · html

As a result, we obtained the intrinsic broad H α \alpha luminosity of MCG -3-34-64 as log ⁡ ( L bH ​ α , int . / erg ​ s − 1 ) = 41.82 \log(L_{\mathrm{bH\alpha,int.}}\mathrm{/erg\ s^{-1}})=41.82 with a typical uncertainty of 0.4 dex [ 171 ] . As a result, L bH ​ α , obs . L_{\mathrm{bH\alpha,obs.}} is consistent with L bH ​ α , int . L_{\mathrm{bH\alpha,int.}} within the uncertainty. In other words, the ratio of L bH ​ α , obs . L_{\mathrm{bH\alpha,obs.}} to L bH ​ α , int . L_{\mathrm{bH\alpha,int.}} of MCG -3-34-64 is significantly larger than predicted from the scattering model. We note that, while we do not account for stellar absorption of the H α \alpha line in our spectral fitting, its effect is thought to be negligible because the typical equivalent width (EW) of stellar absorption [ 127 , 25 , E ​ W ∼ EW\sim a few Å, e.g.] is much smaller than that of the fitted broad H α \alpha component of MCG -3-34-64 ( E ​ W ∼ 300 EW\sim 300 Å).

S2.SS3: II.3 Emergent SED and the Balmer break / block 1 · html

The observed monochromatic luminosity for a given inclination i i is obtained by integrating the emergent intensity over the visible surfaces of the near and far (relative to the observer) sides of the disk (see Appendix B ). The resulting SED for an SMBH with M BH = 10 7 ​ M ⊙ M_{\mathrm{BH}}=10^{7}M_{\odot} and m ˙ = 1000 \dot{m}=1000 is shown in Figure 4 . The spectrum is well-approximated by a blackbody with T eff = 6000 T_{\mathrm{eff}}=6000 K, and the Balmer break is clearly visible in high-inclination cases with i ≳ 60 ∘ i\gtrsim 60^{\circ} . This is due to severe geometric obscuration of the inner disk at large angles. The high-temperature UV emission is blocked by the “puffed-up” disk, making the Balmer break from the cooler outer radii more visible.

S2.SS4: II.4 The broad emission lines / block 1 · html

If the BLR clouds follow a disk-like Keplerian velocity field, a high inclination angle will naturally correspond to a large line-of-sight velocity, resulting in broader lines. Our model therefore predicts a positive correlation between Balmer break strength and the full width at half maximum (FWHM) of the BELs, as tentatively observed by [ 82 ] . Consequently, single-epoch black hole mass estimators calibrated on low-inclination type-1 AGNs may introduce an inclination-dependent bias when applied to LRDs. Assuming a mean inclination of 30 ∘ 30^{\circ} for type-1 AGNs and 75 ∘ 75^{\circ} for LRDs, the inclination effect induces an overestimation factor of ( sin ⁡ 30 ∘ / sin ⁡ 75 ∘ ) 2 ≈ 3.7 (\sin 30^{\circ}/\sin 75^{\circ})^{2}\approx 3.7 . For LRDs with Balmer breaks, the rest-frame 5100 ​ A ̊ 5100\ \mathring{\mathrm{A}} luminosity may be a useful empirical proxy for black hole mass.