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.
