Extended Data Fig. 7: Photoionization models for inflow/outflow and the transmitted spectral energy distributions.

a, The ionization structure of a primordial model with n_H = 10⁷ cm⁻³ and U = 10^0.5 that is directly illuminated by the central continuum source of the quasar. If integrated from the illuminated surface, the model with \({N}_{{\rm{c}}{\rm{o}}{\rm{l}}}({{\rm{H}}}_{n=2}^{0})\) and \({N}_{{\rm{col}}}\left({{\rm{He}}}^{0}{2}^{3}{\rm{S}}\right)\) values that are comparable to the measurements predicts \({N}_{{\rm{col}}}\left({{\rm{C}}}_{{\rm{ground}}}^{3+}\right)\) values of more than 10¹⁹ cm⁻², far from the estimated \({N}_{{\rm{col}}}\left({{\rm{C}}}_{{\rm{ground}}}^{3+}\right)\) in the redshifted broad absorption line. An alternative solution is that the inflow in fact corresponds to the grey area, which is gas behind the C³⁺ region (the light green area, where C³⁺ and other high-ionization ions dominate). In such a picture, the outflow is suggested to play an equivalent role to the C³⁺ region in this panel in eliminating high-energy ionizing photons. b, Plot of the ionization structure for an outflow with n_H = 10^9.5 cm⁻³ and U = 10^0.5. The requirement for transmitted radiation (which should have the same spectral energy distribution as the incident radiation on inflow) could constrain the thickness of outflow model. The outer surface of this model (red dashed line) coincides highly with the extension of the C³⁺ region. However, N_col(He⁰2³S), measured using the blueshifted He i* λ10,830, defines a thinner outflow gas (blue dashed line) if we assume that the local covering factor, C_f, is wavelength independent. c, The transmitted spectral energy distributions through the spectral-energy-distribution-constrained outflow and the N_col(He⁰2³S)-defined outflow are plotted. The former (red) naturally coincides with the incident spectral energy distribution for the inflow model, while the latter (blue) shows considerable excess in soft X-ray, which would result in a much larger \({N}_{{\rm{col}}}\left({{\rm{C}}}_{{\rm{ground}}}^{3+}\right)\) in the inflow than the measurement. d, Transmitted spectral energy distributions through a N_col(He⁰2³S)-defined outflow model with n_H = 10^9.5 cm⁻³, U = 10^0.5 and different metallicities. The spectral-energy distribution depends sensitively on the metallicity. As the metallicity increases from 1Z_ʘ to 10Z_ʘ, the transmitted spectral energy distribution seems to match the incident spectral energy distribution required by the inflow model, suggesting that a metal-rich outflow model could explain the measurement in both the redshifted and the blueshifted broad-absorption-line systems.