Hα surface brightness (corrected for cosmological surface brightness dimming) versus the logarithm of the [Nii]λ6583/Hα line ratio. The galaxies have been separated into two redshift bins: z < 1.8 (top) and z > 2 (bottom). The lines represent results for photo-ionization modeling (see text for details) for 6 sets of conditions: a range of hydrogen densities, log n_H (cm^-3) = 1 (in green), 2 (blue) and 3 (red), and of column densities, log N_H (cm^-2) = 21 (solid lines) and 20 (dashed lines). The ionization parameters range from log U = −5 to −1 (increasing from left to right along the lines, meaning low ionization parameters have relatively high log [Nii]/Hα and low Hα surface brightnesses). At low ionization parameters the solid and dashed lines for the column densities overlap until the lower column density cloud becomes density bounded, at which point the models reach very low ratios of [Nii]λ6583/Hα (as shown by the sharply dropping dotted lines). For clarity, we only show the log N_H (cm^-2) = 21 and log n_H (cm^-3) = 3 line until log U = −3 and for log N_H (cm^-2) = 21 and log n_H (cm^-3) = 2 until log U = −2.