<p>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 <span class="math-container">$\alpha$</span> forest toward progressively shorter wavelengths. But even though we usually say that reionization ended at <span class="math-container">$z\sim6$</span>, residual neutral hydrogen was still able to scatter Ly<span class="math-container">$\alpha$</span> photons out of the line of sight for a very long time after.</p>
<h4>A reionized Universe may still be opaque to Lyman α</h4>
<p>The HI cross section to Ly<span class="math-container">$\alpha$</span> scattering is <span class="math-container">$\sigma=6\times10^{-14}\,\mathrm{cm}^2$</span>, which is rather large compared to most other transitions. So even though the Universe is transparent to <em>most</em> light, Ly<span class="math-container">$\alpha$</span> is easily scattered out of the line of sight. In fact you can show that a neutral fraction of as little as <span class="math-container">$\sim10^{-4}$</span> is enough to render the IGM optically thick to Ly<span class="math-container">$\alpha$</span>. 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 <a href="https://ui.adsabs.harvard.edu/abs/2006astro.ph..3149C" rel="nofollow noreferrer">Choudhury &amp; Ferrara</a>).</p>
<h4>Transmission as a function of redshift</h4>
<p>At <span class="math-container">$z=4.76$</span>, the IGM still only transmits a few tens of percent of the continuum blueward of the Ly<span class="math-container">$\alpha$</span> line, as seen in this figure from <a href="https://ui.adsabs.harvard.edu/abs/2004AJ....127.2598S" rel="nofollow noreferrer">Songaila (2004)</a> (with my own annotations):</p>
<p><a href="https://i.sstatic.net/8giLt.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/8giLt.png" alt="Tigm" /></a></p>
<p>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.</p>
<h4>Your requested effect is there</h4>
<p>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 <a href="https://ui.adsabs.harvard.edu/abs/2006AJ....132..117F" rel="nofollow noreferrer">Fan et al. (2006)</a>, but I found this figure, from <a href="https://blackholeswithrevelations.wordpress.com/2013/09/19/stfcastro-lyman-alpha-forest/" rel="nofollow noreferrer">a talk by Ross McLure</a> (again with my own annotations), which shows the effect better (although it's not too good resolution):</p>
<p>Looking at the <span class="math-container">$z=6.29$</span> 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<span class="math-container">$\alpha$</span> line around 8600–8700 Å. And for the <span class="math-container">$z=4.76$</span> quasar, the absorption also seems just a little larger at ~6800 Å than at ~6000 Å.</p>
<p>Note how in the latter example, the Ly<span class="math-container">$\beta$</span> line at <span class="math-container">$1026\,\mathrm{Å}\times(1+4.76)=5910\,\mathrm{Å}$</span> is easily seen.</p>
<p><a href="https://i.sstatic.net/qmuHC.jpg" rel="nofollow noreferrer"><img src="https://i.sstatic.net/qmuHC.jpg" alt="QSOs" /></a></p>

CC BY-SA 4.0
2022-02-07T19:07:10.573Z
Yes, the value of z=4.76 in this plot is a strange coincidence, but in this case it is the quasar redshift, whereas in my consideration it is the redshift of the hydrogen gas that would produce the absorption at 7000 A for the z=6.53 quasar. You can see though that the maximum peak amplitudes in the spectra are virtually constant both with z and wavelength, only the gaps are getting bigger with increasing z. So based on your very plot, one should expect some signal also at 7000 A for the z=6.53 quasar (which corresponds to hydrogen at z=4.76). Btw, your Ly$\beta$ figure should be 5910 A.
Thomas
CC BY-SA 4.0
2022-02-08T12:10:00.543Z
@Thomas Yes, I understand. I think though that I can in fact convince myself there your z = 6.53 _does_ show more signal around 7000 Å than around 8500 Å. The problem is that your spectrum is quite noisy, so it's not easy to see. Anyway, thanks for catching my typo.
pela
CC BY-SA 4.0
2022-02-08T18:52:12.460Z
Yes, the spectrum for z=6.53 is quite noisy, but the noise is practically symmetrical around zero, which means that it is just that, noise. There is no systematic continuum intensity anymore at all, even not any obvious Ly$\beta$ emission (which should be at 7726 A). Note also that the differences in your highlighted regions for the z=4.76 and z=6.29 spectra are quite evidently due to Ly$\beta$ emission, not different continuum absorption. Do you know where to get the data for these kind of high z-spectra from? I would be interested in trying to analyze them in more detail in this respect.
Thomas
CC BY-SA 4.0
2022-02-09T09:47:24.087Z
By "less absorption" I don't mean the amplitude of the continuum, but the density of absorption lines, so it's not the Lyβ line (which in the z=6.29 spectrum is outside the range). Your spectrum is indeed _practically_ symmetric around zero, but I don't think it is exactly zero at the blue end. You could try smoothing it, but I can't seem to find the data of that spectrum. But you can find other spectra e.g. [here](http://rafelski.com/data/DLA/hizesi) or [here](https://aanda.org/articles/aa/full_html/2018/08/aa32737-18/aa32737-18.html) (hi-z) or [here](https://data.sdss.org/sas/dr14) (lo-z).
pela
CC BY-SA 4.0
2022-02-10T08:18:04.147Z
I was thinking of the data in numerical form, so that I can do my own processing of it. Are there any publicly accessible, or would I have to contact the authors of the relevant papers? There have been quite a few systematic studies how the absorption changes with quasar redshift, but I have not found any how it changes within a given spectrum.
Thomas
CC BY-SA 4.0
2022-02-10T09:45:53.723Z
@Thomas You should be able to download the data from the links I gave above, but yes, contacting the author is also an option, most astronomers are happy to share their data.
pela
CC BY-SA 4.0
2022-02-07T08:00:40.667Z
2022-02-08T12:10:30.513Z
2022-02-08T12:10:30.513Z
pela
<p>This is a follow up to a <a href="https://astronomy.stackexchange.com/questions/48188/how-to-interpret-this-spectrum-of-the-new-desi-quasar-at-z-6-53-what-causes/48191?noredirect=1#comment105174_48191">recent question on SE</a> asking about the apparent suppression of radiation shortward of the (red-shifted) Ly-<span class="math-container">$\alpha$</span> line of a quasar at redshift <span class="math-container">$z=6.53$</span>.
<a href="https://i.sstatic.net/xHUWA.jpg" rel="nofollow noreferrer"><img src="https://i.sstatic.net/xHUWA.jpg" alt="enter image description here" /></a></p>
<p>The general explanation for this is the <a href="https://en.wikipedia.org/wiki/Gunn%E2%80%93Peterson_trough" rel="nofollow noreferrer">Gunn-Peterson effect</a> 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-<span class="math-container">$\alpha$</span> line at any redshift and not just at redshifts corresponding to the localized clouds of neutral hydrogen (which result in the <a href="https://astro.ucla.edu/%7Ewright/Lyman-alpha-forest.html" rel="nofollow noreferrer">Ly-<span class="math-container">$\alpha$</span> forest</a> (note that the spectra have been scaled back to the quasar reference in that reference)).</p>
<p>Now according to cosmological models it is thought that re-ionization has been completed at a redshift <span class="math-container">$z=6$</span>, so only quasars with a redshift larger than this show complete absorption of the Ly-<span class="math-container">$\alpha$</span> line at wavelengths smaller than its peak wavelength (<span class="math-container">$9156 \mathring{A}$</span> in this case). However, if we take for instance the wavelength of <span class="math-container">$7000 \mathring{A}$</span> here, hydrogen absorbing locally at <span class="math-container">$1216 \mathring{A}$</span> (the Ly-<span class="math-container">$\alpha$</span> rest wavelength) must have been at a redshift</p>
<p><span class="math-container">$$z_a(7000 \mathring{A})=\frac{7000}{1216} -1 = 4.76$$</span></p>
<p>(<span class="math-container">$z_a$</span> should indicate that this is the (wavelength specific) redshift of the Ly-<span class="math-container">$\alpha$</span> 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). )</p>
<p>This value of <span class="math-container">$z_a$</span> 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.</p>
<p>How can this paradox be resolved? Did I make some mistake here in my argument?</p>

CC BY-SA 4.0
2022-02-06T20:10:47.917Z
What spectrum? The only spectrum shown is a quasar at $z=6.53$.
ProfRob
CC BY-SA 4.0
2022-02-06T20:43:32.273Z
@ProfRob No radiation of the quasar with a wavelength less than 9156 A is present in the shown spectrum. It is 'absorbed' by Ly-$\alpha$ scattering on its way to us that is at smaller redshifts than 6.53. The radiation at 7000 A for instance is absorbed at z=4.76, but re-ionization would have happened by then quite a while ago, so the spectrum should look more like a Ly-$\alpha$ forest in this frequency region, not have zero intensity.
Thomas
CC BY-SA 4.0
2022-02-06T21:34:37.053Z
Ok, I understand.
ProfRob
CC BY-SA 4.0
2022-02-07T08:52:08.997Z
Hi Thomas, I just saw your edit. Just to make clear, I realize that the redshift "4.76" is just a random example (although chosen to be far from the redshift of the quasar). In my answer, the fact that one of the quasars in my example has z = 4.76 is a pure coincidence. I'm still referring to the differences in regions of the forest at various redshifts blueward of the quasar Lyα emission.
pela
<cosmology><redshift><quasars><intergalactic-space>
Intergalactic Lyman-alpha absorption for high redshift quasars (Gunn-Peterson effect)
Thomas
# Intergalactic Lyman-alpha absorption for high redshift quasars (Gunn-Peterson effect)

(Asked by: username_0 on 2022-02-06)

This is a follow up to a [recent question on SE](https://astronomy.stackexchange.com/questions/48188/how-to-interpret-this-spectrum-of-the-new-desi-quasar-at-z-6-53-what-causes/48191?noredirect=1#comment105174_48191) asking about the apparent suppression of radiation shortward of the (red-shifted) Ly-$\alpha$ line of a quasar at redshift $z=6.53$.
[![enter image description here](https://i.sstatic.net/xHUWA.jpg)](https://i.sstatic.net/xHUWA.jpg)

The general explanation for this is the [Gunn-Peterson effect](https://en.wikipedia.org/wiki/Gunn%E2%80%93Peterson_trough) 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](https://astro.ucla.edu/%7Ewright/Lyman-alpha-forest.html) (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?

**Tags:** cosmology, redshift, quasars, intergalactic-space
> **Comments:**
> **username_1**: What spectrum? The only spectrum shown is a quasar at $z=6.53$.  
> **username_0**: @ProfRob No radiation of the quasar with a wavelength less than 9156 A is present in the shown spectrum. It is 'absorbed' by Ly-$\alpha$ scattering on its way to us that is at smaller redshifts than 6.53. The radiation at 7000 A for instance is absorbed at z=4.76, but re-ionization would have happened by then quite a while ago, so the spectrum should look more like a Ly-$\alpha$ forest in this frequency region, not have zero intensity.  
> **username_1**: Ok, I understand.  
> **username_2**: Hi Thomas, I just saw your edit. Just to make clear, I realize that the redshift "4.76" is just a random example (although chosen to be far from the redshift of the quasar). In my answer, the fact that one of the quasars in my example has z = 4.76 is a pure coincidence. I'm still referring to the differences in regions of the forest at various redshifts blueward of the quasar Lyα emission.  

---

## 1 answers

### Answer by username_2 on 2022-02-07. Score: 2

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](https://ui.adsabs.harvard.edu/abs/2006astro.ph..3149C)).

#### 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)](https://ui.adsabs.harvard.edu/abs/2004AJ....127.2598S) (with my own annotations):

[![Tigm](https://i.sstatic.net/8giLt.png)](https://i.sstatic.net/8giLt.png)

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)](https://ui.adsabs.harvard.edu/abs/2006AJ....132..117F), but I found this figure, from [a talk by Ross McLure](https://blackholeswithrevelations.wordpress.com/2013/09/19/stfcastro-lyman-alpha-forest/) (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.

[![QSOs](https://i.sstatic.net/qmuHC.jpg)](https://i.sstatic.net/qmuHC.jpg)

> **Comments:**
> **username_0**: Yes, the value of z=4.76 in this plot is a strange coincidence, but in this case it is the quasar redshift, whereas in my consideration it is the redshift of the hydrogen gas that would produce the absorption at 7000 A for the z=6.53 quasar. You can see though that the maximum peak amplitudes in the spectra are virtually constant both with z and wavelength, only the gaps are getting bigger with increasing z. So based on your very plot, one should expect some signal also at 7000 A for the z=6.53 quasar (which corresponds to hydrogen at z=4.76). Btw, your Ly$\beta$ figure should be 5910 A.  
> **username_2**: @Thomas Yes, I understand. I think though that I can in fact convince myself there your z = 6.53 _does_ show more signal around 7000 Å than around 8500 Å. The problem is that your spectrum is quite noisy, so it's not easy to see. Anyway, thanks for catching my typo.  
> **username_0**: Yes, the spectrum for z=6.53 is quite noisy, but the noise is practically symmetrical around zero, which means that it is just that, noise. There is no systematic continuum intensity anymore at all, even not any obvious Ly$\beta$ emission (which should be at 7726 A). Note also that the differences in your highlighted regions for the z=4.76 and z=6.29 spectra are quite evidently due to Ly$\beta$ emission, not different continuum absorption. Do you know where to get the data for these kind of high z-spectra from? I would be interested in trying to analyze them in more detail in this respect.  
> **username_2**: By "less absorption" I don't mean the amplitude of the continuum, but the density of absorption lines, so it's not the Lyβ line (which in the z=6.29 spectrum is outside the range). Your spectrum is indeed _practically_ symmetric around zero, but I don't think it is exactly zero at the blue end. You could try smoothing it, but I can't seem to find the data of that spectrum. But you can find other spectra e.g. [here](http://rafelski.com/data/DLA/hizesi) or [here](https://aanda.org/articles/aa/full_html/2018/08/aa32737-18/aa32737-18.html) (hi-z) or [here](https://data.sdss.org/sas/dr14) (lo-z).  
> **username_0**: I was thinking of the data in numerical form, so that I can do my own processing of it. Are there any publicly accessible, or would I have to contact the authors of the relevant papers? There have been quite a few systematic studies how the absorption changes with quasar redshift, but I have not found any how it changes within a given spectrum.  
> **username_2**: @Thomas You should be able to download the data from the links I gave above, but yes, contacting the author is also an option, most astronomers are happy to share their data.  

---

