An updated analytic model for attenuation by the intergalactic medium

We present an updated version of the so-called Madau model for the attenuation by the intergalactic neutral hydrogen against the radiation from distant objects. First, we derive a distribution function of the intergalactic absorbers from the latest observational statistics of the Ly$\alpha$ forest, Lyman limit systems, and damped Ly$\alpha$ systems. The distribution function excellently reproduces the observed redshift evolutions of the Ly$\alpha$ depression and of the mean-free-path of the Lyman continuum simultaneously. Then, we derive a set of the analytic functions which describe the mean intergalactic attenuation curve for objects at $z>0.5$. The new model predicts less (or more) Ly$\alpha$ attenuation for $z\simeq3$--5 ($z>6$) sources through usual broad-band filters relative to the original Madau model. This may cause a systematic difference in the photometric redshift estimates, which is, however, still as small as about 0.05. Finally, we find a more than 0.5 mag overestimation of the Lyman continuum attenuation in the original Madau model at $z>3$, which causes a significant overcorrection against direct observations of the Lyman continuum of galaxies.