# Harvard Astronomy 201b

## ARTICLE: On the Density of Neutral Hydrogen in Intergalactic Space

In Journal Club, Journal Club 2011 on April 21, 2011 at 2:07 pm

### Read the (classic) paper by Gunn & Peterson (1965).

Summary by Ragnhild Lunnan & Aaron Meisner.

The starting point of the Gunn & Peterson analysis is the discovery of the quasar 3C 9, which at a redshift of 2 has the Ly-α line redshifted  into the visible spectrum. The main idea can be summarized by a few sentences from the introduction:

“Consider, however, the fate of photons emitted to the blue of Ly-α. As we move away from the source along the line of sight, the source becomes redshifted to observers locally at rest in the expansion, and for one such observer, the frequency of any such photon coincides with the rest frequency of Ly-α in his frame and can be scattered by neutral hydrogen in his vicinity.”

Derivation of the Gunn-Peterson Trough

To calculate this effect is a relatively straightforward exercise in radiative transfer (and cosmology). Start with a standard metric: $ds^2 = dt^2 - a(t)^2(du^2 + u^2 d\gamma^2)$

The probability of scattering a photon in a proper length interval $dl = a(t) du$ is given by $dp = n(t)\sigma(\nu_s) dl$, where n(t) is the number density of neutral hydrogen at time t, and $\sigma(\nu_s)$ is the cross-section for the Ly-α transition. $\nu_s$ is the redshift at which the photon is being scattered, i.e. $\nu_s = \nu \times (1+z)$, where $z$ is less than the redshift $z_0$ of the quasar. Plugging in $\sigma(\nu) = \frac{\pi e^2}{m c} f g(\nu - \nu_a)$, together with an expression for dl/dz from the cosmology, the total optical depth can be found by integrating over redshift. This again yields a relation between the optical depth and the number density of (neutral) hydrogen.

(While the 1965 cosmological model used in the paper is outdated, the structure of the argument remains the same. The $q_0 = 1/2$ model in the paper corresponds to a cosmology where $\Omega = \Omega_m = 1$.)

Interpretation: Hydrogen must be ionized!

Gunn & Peterson point out, however, that given the modest suppression of flux bluewards of Ly-α in the spectrum of 3C-9, the inferred density of neutral hydrogen is extremely small. This lack of a “Gunn-Peterson trough” (as the effect later became known as) is reconciled as follows:

“We are thus led to the conclusion that either the present cosmological ideas about the density are grossly incorrect, and that space is very nearly empty, or that the matter exists in some other form. […] It is possible that [the assumption that intergalactic space is filled with hydrogen gas] is still valid but that essentially all of the hydrogen is ionized; this conclusion can be defended if we are allowed to make the intergalactic hydrogen temperature high enough.”

The authors further argue that collisional ionization is too inefficient and so unlikely to be the culprit, but radiative ionization can do the job provided that the temperature of the IGM is high enough.

Constraints on the Epoch of Reionization

Finally, it is pointed out that ionized hydrogen will lead to non-negligible optical depth due to Thomson scattering, for very distant objects. The measurement of the Thomson optical depth in the CMB, in fact, places constraints on the mean redshift of reionization.

More directly, though, observations of the (lack of) Gunn-Peterson troughs in quasars place lower limits on the end of reionization: if no trough is observed at z=6, for example, reionization must have been essentially complete at that redshift.

(The first claim of a detected Gunn-Peterson trough was made by Becker et al. in 2001, for a quasar at z ~ 6.2.)

1. […] Astrobite, and our classmates Ragnhild Lunnan and Aaron Meisner have a great writeup of the original paper by Gunn & Peterson in 1965 that first identified this effect and speculated on its cosmological […]

2. […] Astrobite, and our classmates Ragnhild Lunnan and Aaron Meisner have a great writeup of the original paper by Gunn & Peterson in 1965 that first identified this effect and speculated on its cosmological […]