The surface temperature of the star depends on its mass and on the density of the accreted cloud.
Thus, the relation between the density, the temperature, the flux of light in the atmosphere and the halo depend on these variables. Therefore, the figure provides an explanation of the building of the spectrum, but only orders of magnitudes. The periodicities in the Lyman forest which are precise results are not described in the figure.
The density of hydrogen decreases quickly in the atmosphere of the star (~1000 times faster than on the Earth), then decreases slowly in the accreted cloud.
Close to the star, hydrogen is fully ionised, it does not absorb the light, it is only heated by mechanical processes, so that the temperature decreases fast. With a decrease of temperature, neutral hydrogen and a heating by Lyman absorption appear, so that the decrease of temperature slows down as long as the intensity of the light at the Lyman frequencies is large.
Close to the star, the weak (forbidden) lines are sharp while the other are saturated. If the star is radio-loud, the gas is ionised by the radio energy at the pressures of the discharge pipes, so that there is no redshift, a single frequency for the Lyman lines first in emission, then in absorption. If the star is radio-quiet, the periodicity appears, in emission first, then in absorption: the lines are saturated, with a flat centre corresponding to equilibrium between the temperature of the gas and the temperature of the light (troughs).
When the density of the gas decreases, the de-excitation of the n=2 states of H decreases, so that the redshift increases in comparison with the absorption, the saturations decrease, the lines become sharp.