= Neutral-hydrogen column-density distribution
{title2=$f(N,z)=\partial^2\mathcal N/(\partial N\,\partial z)$}
The neutral-hydrogen column-density distribution counts <Lyman-alpha absorption> systems per unit <column density> and <redshift>. A count in logarithmic column bins is $N\ln(10)f(N,z)$. At low forest columns an approximate power law $f\propto N^{-\beta}$ with $\beta$ near $1.5$ is useful, but the slope and normalization depend on column range and epoch. <Lyman limit systems> are optically thick at the hydrogen photoionization edge; <damped Lyman-alpha systems> have strong radiative damping wings. A distribution per <absorption distance> instead removes the geometrical path factor.
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