Studying the Lyman α optical depth fluctuations at z ∼ 5.5 using fast semi-numerical methods

Abstract

We present a computationally efficient and fast semi-numerical technique for\nsimulating the Lyman-$\\alpha$ (Ly$\\alpha$) absorption optical depth in presence\nof neutral hydrogen "islands" left over from reionization at redshifts $5\n\\lesssim z \\lesssim 6$. The main inputs to the analysis are (i) a\nsemi-numerical photon-conserving model of ionized regions during reionization\n(named SCRIPT) along with a prescription for simulating the shadowing by\nneutral islands and (ii) the fluctuating Gunn-Peterson approximation to model\nthe Ly$\\alpha$ absorption. Our model is then used for simulating the\nlarge-scale fluctuations in the effective optical depth as observed along sight\nlines towards high$-z$ quasars. Our model is fully described by five\nparameters. By setting two of them to default values and varying the other\nthree, we obtain the constraints on reionization history at $5 \\lesssim z\n\\lesssim 6$ as allowed by the data. We confirm that reionization is \\emph{not}\ncomplete before $z \\sim 5.6$ at $\\gtrsim 2\\sigma$ confidence, with the exact\nconfidence limits depending on how the non-detections of the flux in the data\nare treated. We also confirm that the completion of reionization can be as late\nas $z \\sim 5.2$. With further improvements in the model and with more sight\nlines at $z \\sim 6$, we can take advantage of the computational efficiency of\nour analysis to obtain more stringent constraints on the ionization fraction at\nthe tail-end of reionization.\n