Absorption by Discrete Intergalactic Clouds: Theory and Some Applications

Using Markoff's method we have derived a general formalism to deal with the absorptions produced by randomly distributed discrete clouds, such as the QSO absorption-line systems. For a power-law H I column density distribution we have calculated the optical depth distribution P(τ) by carrying out the integration of inverse Laplace transform along the steepest descent, and an analytical approximation of P(τ) has also been given. The two important parameters, i.e., the effective optical depth τeff and the count reduction factor ∫c, have been computed for the QSO absorption systems. We then use these results to deal with problems of the attenuation of ionizing background by QSO absorption-line systems, the difficulty of conducting the He II Gun-Peterson test, and the dust grain obscuration of distant quasars. The Lyman-continuum absorption by QSO absorption-line systems not only reduces the intensity of the ionizing field significantly, but also tilts the intrinsic source spectrum to result in a flat background spectrum near VL. With a few reasonable approximations we have derived analytical expressions for JVL (Ζobs) The QSO contribution is calculated to be roughly constant for Ζobs ≥ 2.2 with a value JVL 4 × 10-22 ergs s-1 cm-2 Hz-1 sr-1, if a constant comoving density for QSOs at Ζ ≥ 2.2 is assumed.