Past exam of the mathematics course of the University of Cambridge / 2009 / iii / Paper 66 / 3 / i / Solution

The Lyman-alpha forest is the collection of absorption lines blueward of a distant quasar's own Lyman-alpha line. Foreground neutral hydrogen removes photons at rest wavelength ${\lambda }_{\alpha }\simeq 1215.67$ angstroms, observed at $\lambda =(1+z){\lambda }_{\alpha }$ because of cosmological redshift. Gas at many different foreground redshifts therefore produces many lines. The weak forest traces diffuse, mostly ionized intergalactic medium, rather than a population of fully neutral clouds; much stronger, self-shielded absorbers are a separate regime. Madau's account of quasar absorption systems distinguishes these column-density regimes.