Time-dependent behaviour of Lyman α photon transfer in a high-redshift optically thick medium

Using the Monte Carlo simulation method, we investigate the time-dependent behaviour of Lyα photon transfer in an optically thick medium of the concordance ΛCDM universe. At high redshifts, the Lyα photon escaping from the optically thick medium has a time-scale as long as the age of the luminous object, or even comparable to the age of the Universe. In this case, time-independent or stationary solutions of the Lyα photon transfer with resonant scattering will overlook important features of the escaped Lyα photons in physical and frequency spaces. More importantly, the expansion of the Universe means that the time-independent solutions of the Lyα photon transfer might not exist. We show that time-dependent solutions are sometimes essential for understanding Lyα emission and absorption at high redshifts. For Lyα photons from sources at redshift 1 +z= 10, which are surrounded by the neutral hydrogen intergalactic medium (IGM) of the ΛCDM universe, the escape coefficient is found to be always less, or much less, than one, regardless of the age or lifetime of the sources. In such an environment, we also find that even when the Lyα photon luminosity of the sources is stable, the mean surface brightness gradually increases in the first 10⁶ yr, and then decreases with a power law of time. However, it never approaches a stable, time-independent state. That is, all 1 +z= 10 sources in a neutral Hubble expanding IGM with Lyα luminosity L have their maximum of mean surface brightness ∼10^-21(L/10⁴³ erg s^-1) erg s^-1 cm^-2 arcsec^-2 at the age of about 10⁶ yr. We also address the time-dependent effects on the red damping wing profile.