Intergalactic Lyman-alpha absorption for high redshift quasars (Gunn-Peterson effect)

Question

This is a follow up to a recent question on SE asking about the apparent suppression of radiation shortward of the (red-shifted) Ly-$\alpha$ line of a quasar at redshift $z=6.53$.

The general explanation for this is the Gunn-Peterson effect according to which beyond a certain redshift the universe has not re-ionized yet and thus the hydrogen is neutral throughout and can absorb the Ly-$\alpha$ line at any redshift and not just at redshifts corresponding to the localized clouds of neutral hydrogen (which result in the Ly-$\alpha$ forest (note that the spectra have been scaled back to the quasar reference in that reference)).

Now according to cosmological models it is thought that re-ionization has been completed at a redshift $z=6$, so only quasars with a redshift larger than this show complete absorption of the Ly-$\alpha$ line at wavelengths smaller than its peak wavelength ($9156 \mathring{A}$ in this case). However, if we take for instance the wavelength of $7000 \mathring{A}$ here, hydrogen absorbing locally at $1216 \mathring{A}$ (the Ly-$\alpha$ rest wavelength) must have been at a redshift

$$z_a(7000 \mathring{A})=\frac{7000}{1216} -1 = 4.76$$

($z_a$ should indicate that this is the (wavelength specific) redshift of the Ly-$\alpha$ absorbing hydrogen gas located between us and the quasar , not the redshift of the quasar (which has a fixed value of 6.53 in this case). )

This value of $z_a$ is way beyond the point where re-ionization is thought to have occurred, so hydrogen should not be completely neutral, and thus some of the quasar emission should still reach us at this wavelength. Yet the spectrum shows effectively zero intensity at this and even smaller wavelengths.

How can this paradox be resolved? Did I make some mistake here in my argument?

Answer 1

You're right that it should be possible to see the evolution of the ionization fraction of the intergalactic medium (IGM) in a single, high-redshift quasar spectrum, as you scan through the Lyman $\alpha$ forest toward progressively shorter wavelengths. But even though we usually say that reionization ended at $z\sim6$, residual neutral hydrogen was still able to scatter Ly$\alpha$ photons out of the line of sight for a very long time after.

A reionized Universe may still be opaque to Lyman α

The HI cross section to Ly$\alpha$ scattering is $\sigma=6\times10^{-14}\,\mathrm{cm}^2$, which is rather large compared to most other transitions. So even though the Universe is transparent to most light, Ly$\alpha$ is easily scattered out of the line of sight. In fact you can show that a neutral fraction of as little as $\sim10^{-4}$ is enough to render the IGM optically thick to Ly$\alpha$. In addition to the increased volume of the Universe, the full calculation depends on things like the background photoionization rate and the density field of the IGM (see e.g. this review by Choudhury & Ferrara).

Transmission as a function of redshift

At $z=4.76$, the IGM still only transmits a few tens of percent of the continuum blueward of the Ly$\alpha$ line, as seen in this figure from Songaila (2004) (with my own annotations):

Here the transmission is calculated as ratio between the total measured flux and an unabsorbed quasar template, in the interval 1080 Å to 1185 Å.

Your requested effect is there

Because of this, a spectrum has to have quite long wavelength range in order for the effect that you're looking for to be noticeable. But if you look at several spectra at various redshifts, you will see it. A classic comparison at high redshift is the one by Fan et al. (2006), but I found this figure, from a talk by Ross McLure (again with my own annotations), which shows the effect better (although it's not too good resolution):

Looking at the $z=6.29$ quasar spectrum, you do in fact see that the absorption is a little less at the bluemost wavelengths around 7600–7800 Å than it is just next to the quasar Ly$\alpha$ line around 8600–8700 Å. And for the $z=4.76$ quasar, the absorption also seems just a little larger at ~6800 Å than at ~6000 Å.

Note how in the latter example, the Ly$\beta$ line at $1026\,\mathrm{Å}\times(1+4.76)=5910\,\mathrm{Å}$ is easily seen.