2017MNRAS.464.1137B

Incorporating the time-dependent second-order perturbation theory for the Lyman scattering cross-section, we investigate the intergalactic absorption profiles of extremely high column density systems near the end of cosmic reionization. Assuming a representative set of the redshift distribution of neutral hydrogen, we quantitatively examined the impact of inhomogeneous density on the intrinsic absorption profiles. The cumulative absorption by neutral patches in the line of sight mainly affects the far off-centre region of the red damping wing, but the effect is not significant. The shape of the line centre can be modified by the near-zone distribution due to high opacities of the near-resonance scattering. On the other hand, the HWHM (half width at half-maximum) as an effective line width is relatively less sensitive to the local inhomogeneity. Specifically, when the two local damping wings of Lyα and Lyβ are close in spectra of the strongly damped systems, accurate profiles of both lines are required. In the case of N_ H  I_ 10²¹ cm^–2, the two-level approximation is marginally applicable for the damping wing fit within 5 - 7 per cent errors. However, as the local column density reaches N_ H  I_∼10^22.3 cm^–2, this classical approximation yields a relative error of a 10 per cent overestimation in the red wing and a 20 per cent underestimation in the blue wing of Lyα. If severe extinction by the Lyα forests is carefully subtracted, the intrinsic absorption profile will provide a better constraint on the local ionized states. For practical applications, an analytic fitting function for the Lyβ scattering is derived.