tokens: effect of photoionization feedback may be further reduced for realistic accretion disc spectra, compared to the case of the single power-law spectrum usually assumed in most works (Takeo et al. 2019 ). As mentioned in Section 3 , for accretion rates satisfying the DPT condition, photon trapping due to electron scattering is also naturally realized. In the case of DPT, radiation feedback at radii larger than the dust sublimation radius is effectively suppressed, while the entire accretion disc radiation may be efficiently trapped. Under such extreme trapping conditions, most of the infalling matter may be accreted (Volonteri et al. 2015 ). Since the accretion rate leading to DPT is much larger than the Eddington rate, it should be associated with super-Eddington accretion and a rapid build-up of the BH mass. For instance, adopting the DPT accretion rate as the minimal value, the enhancement factor could be of a few orders of magnitude compared to the Eddington-limited value. It is known that photon trapping also modifies the emergent spectral energy distribution. Higher energy photons originating in the inner accretion flow are more efficiently trapped than lower energy photons produced from the outer regions. As a result, the peak frequency of the spectral energy distribution shifts towards lower energies, and the active galactic nucleus (AGN) spectrum becomes softer with increasing accretion rate (Ohsuga, Mineshige Watarai 2003 ). In the case of DPT, the whole disc radiation can be efficiently trapped, and the overall luminosity output may be considerably reduced, leading to faint AGNs. This may not be the case for photon trapping due to electron scattering, where only the inner parts of the accretion disc remain trapped (unless the accretion rate is extremely high). Since UV/optical photons are trapped within the dusty accretion flow, the central AGN will be obscured. In this context, X-ray photons would be even more readily trapped than UV/optical photons, and thus super-Eddington accretion will be likely obscured at both X-ray and UV/optical wavelengths (Wyithe Loeb 2012 ). In our picture, DPT accretion is indeed associated with significant obscuration, with large column densities expected at early times. Cosmological hydrodynamic simulations also suggest heavy obscuration on different physical scales around the growing BHs in the early Universe (Trebitsch, Volonteri Dubois 2019 ; Ni et al. 2020 ). Assuming a standard radiative efficiency of ε ∼ 0.1, it has been estimated that the obscured fraction at z > 7 could be of the order of (Davies, Hennawi Eilers 2019 ). In fact, much of the early growth of massive BHs could be obscured, and a large number of such obscured quasars may be missed in current optical surveys (Hickox Alexander 2018 ; Inayoshi et al. 2020 , and references therein). On the other hand, obscuration by dusty gas may cause higher energy photons to be reprocessed into lower energy photons, leading to an increase in the
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