An updated analytic model for the 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. 
Akio K. Inoue (1), Ikkoh Shimizu (2), Ikuru Iwata (3), Masayuki Tanaka   (4) ((1) Osaka Sangyo University, (2) The Universit...
astro-ph.CO