What is main radiative mechanism in Gunn-Peterson effect? I'm having a hard time understanding the Gunn-Peterson effect and the Ly-alpha line and I've written a couple of questions below. 

The trough we see in the spectra of quasars is the Gunn-Peterson trough, right? Does this trough have to start from the Ly-alpha line?

If neutral hydrogen along the line of sight to the distant quasar is few, do we expect the Ly-alpha forest to be sparse?

What is the main radiative mechanism in the Gunn-Peterson effect?
The Gunn-Peterson trough is a feature in the spectrum of a (background) source near the Lyman $\alpha$ line, caused by a high density of intervening, neutral hydrogen (HI).

The background source may be a quasar, but could also be e.g. a gamma-ray burst or just a regular galaxy with a strong Ly$\alpha$ line.

Absorption vs. scattering

The cross section of hydrogen for Ly$\alpha$ photons is quite large, so the mean free path of the photons is very small. Because Ly$\alpha$ excites hydrogen to the first excited level, the electron can only fall back to the ground state again, emitted another Ly$\alpha$ photon, in another direction. Hence, hydrogen doens't absorb Ly$\alpha$ photons, but rather scatters them.

Inside the (host) galaxy, the HI density is so large that Ly$\alpha$ is all the time scattered both into and out of the LOS. However, when the photons escape the galaxy and enters the circum- and intergalactic medium (IGM), the density decreases. Along the LOS to the galaxy, a photon hitting a hydrogen atom is "lost", and no new photons are added to the observed flux, so effectively, it becomes an absorption process rather than a scattering process.

The figure below (from Laursen 2010) illustrates this phenomenon: the three photons are initially emitted in random directions, but end up traveling toward the observer on the right. On their way through the IGM, two of them are scattered out of the line of sight (LOS), and the probability of a photon from another galaxy being scattered into the LOS is negligible.



Reionization

In the early days of the (post-recombination) Universe, hydrogen was mainly neutral, but as star formation emerged, these stars started to reionize the IGM. This process started already at $z\simeq15$–$20$, when the Universe was ~200 million years old , but until $z\simeq6$, when the Universe was ~a billion years old, there was still so much HI left that Ly$\alpha$ photons scatter all the time in the IGM.

Blue wavelengths are eventually redshifted to Lyman $\alpha$

Now when light leaves a galaxy, it gets redshifted due to the expansion of the Universe. That means that after a while, light blueward of the Ly$\alpha$ line is redshifted to become Ly$\alpha$, and may hence scatter. As the spectrum travels through the IGM, it redshifts continuously, so that every wavelength of the "original" Ly$\alpha$ line eventually becomes Ly$\alpha$.

If the HI density in the IGM is high enough, that means that everything blueward of the Ly$\alpha$ line is wiped out. This is the Gunn-Peterson trough. If the density is low, but with some neutral clouds dispersed, then an absorption line occurs exactly at the wavelength that, at the location of the cloud, happens to have been redshifted to Ly$\alpha$. When there are many such clouds around, you'll gets lots of absorption lines, forming the so-called Lyman $\alpha$ forest. The fewer the amount of such clouds, the more sparse the forest will be.

The Gunn-Peterson trough doesn't have to start at Ly$\alpha$, but since this is the strongest transition, it is most distinct here. But you will often see a corresponding absorption at Ly$\beta$ (and even Ly$\delta$ and Ly$\gamma$, as well as the stronger metal lines like MgII and CIV). This is visible in the figure below (from Becker et al. 2015)



You see that immediately blueward of Ly$\alpha$, everything is wiped. As you go along the spectrum toward the blue, that part corresponds to later and later epochs, because is takes longer time to redshift that part into Ly$\alpha$. Hence, eventually the Universe becomes less and less neutral, and the absorption is no longer complete.