# What did recombination look like?

I recently remembered that someone worked out what the big bang sounded like and that got me thinking...

About 377,000 years after the Big Bang, electrons became bound to nuclei to form neutral atoms. Because of (?) this, the mean free path of photons became effectively infinite, i.e. the universe became transparent to radiation.

What would this have looked like?

More precisely I could ask: did the sky suddenly become dark, or was the amount of radiation basically same after as before?

What would the distribution and timescale have been like? In a perfectly homogeneous universe it would happen at the same rate everywhere. Did the universe have any structure at this point? Would you have been able to see blotches of lighter and darker patches of the sky (assuming you were within one of the more transparent patches), these being proto-shapes of galactic filaments perhaps, or the noisy grit of the CMB? Or would it just be a vague cloud at any scale, and in any part of the spectrum?

• The whole sky would look like the surface of the sun in 360${}^{\circ}$, and gradually redshifting to redder and redder frequencies, until it redshifted out of the visible range. We can still "see" recombination in the sky, only we call it the cosmic microwave background now, because it's been redshifted to microwaves today. – Jerry Schirmer Sep 4 '14 at 15:47
• Hmm, this is more complicated than I initially thought. Presumably there'd be an Olber's paradox type effect so after the area around you had recombined you'd still be illuminated by the light from the shell of plasma at a distance $ct$, where $t$ is the time since recombination. Initially you wouldn't see much difference and the light intensity would only fall as it started getting redshifted due to the expansion of the universe. – John Rennie Sep 4 '14 at 16:26
• The temperature of the universe at recombination was about 4000K. Given that it had a good deal of homogeneity due to inflation, it is reasonable to assume the blackbody curve would be very close to isotropic at 4000K. And that would look fairly red but still bright – Jim Sep 4 '14 at 17:28

The universe about halfway through recombination (it was a long process but at the halfway point, it's flips to being mostly clear), much like the universe today, has a temperature. Today the temperature of the universe is about 2.7K, but at recombination it was around 4000K. This temperature corresponds to the blackbody radiation profile of the universe. Thanks to inflation, this radiation profile is almost perfectly isotropic and almost perfectly fitting to a perfect blackbody curve (He said, perfectly overusing forms of the word "perfect" in this perfect sentence).

At the time of recombination, the universe turned from an opaque mess to clear space. But what did it look like? Today, empty space looks black. If you stare out to the farthest reaches of emptiness, you'll see nothing. The nearly isotropic background radiation produces a temperature profile for a 2.7K curve. Most of the energy of that curve is way outside the range of the visible spectrum, which is why empty space appears black. At recombination, our isotropic radiation profile corresponds to 4000 K and looks something like

I made this plot using Mathematica and you can see that the visible spectrum resides in a significant portion of the emitted radiation. So that means if you were to stare out into the abyss of empty space at the time of recombination, empty space would look like one solid, non-black colour (it's actually an orange colour). It would also be excruciatingly intense. Imagine if everywhere you looked was like looking at the surface of a star (On the bright side, you wouldn't have to worry about vampires any more).

As time goes on and the universe keeps expanding, this background colour will (relatively) soon fade (red-shift) to the black we know so well today.

If you want to see the specific colour that we would perceive at recombination or at any other temperature, go to Wolfram|Alpha and type in "Wien displacement law for [T] K" except replace the [T] with a desired temperature (4000 for our case).

Think that's cool? Then think about this: the original colour of empty space (and if you're an originalist, the true colour) is not black, it's orange. Before this, empty space was hotter, but it was opaque so we can't really talk about the colour of empty space then. And before nucleosynthesis is too short of an amount of time to count. So space is originally orange, it just shifted to black because it expanded. Mind=blown

What the hay, here's the colour we'd perceive empty space looking like:

• As a Dutchman, I approve of this answer :) – Danu Sep 5 '14 at 8:09
• "it was a long process but at the halfway point, it's flips to being mostly clear" -- how quick was the flip? – spraff Sep 5 '14 at 9:44
• @spraff by flip, I mean to say that it turns from mostly ($>50%$) opaque to mostly clear. One would think that the actual time spent at exactly 50% ionized is short, so this flip would be quick. Bu the time the 4000K would be valid for would be on the order of hundreds of years or more. – Jim Sep 6 '14 at 15:43
• Note that Mathematica's blackbody spectrum function is not quite as accurate as one would like. There's a mm.se thread about this somewhere. – Emilio Pisanty Feb 23 '17 at 20:36

did the sky suddenly become dark, or was the amount of radiation basically same after as before? What would the distribution and timescale have been like?

Recombination of hydrogen did not suddenly happen. Instead, to go from 90% of hydrogen being ionized to 10% of hydrogen being ionized, took about 100,000 years, from about 260,000 years after the big bang to 380,000 years after. Helium recombination happened earlier, with doubly ionized helium recombining to single ionized helium about 20,000 years after the big bang, and single ionized helium recombining to neutral helium around 130,000 years after the big bang.

As others have commented, the sky did not suddenly become dark, but would have appeared approximately like a uniform black body of about 3000K at the time of recombination.

Just before recombination, you would see the universe as if in a dense, extremely hot (4000K) fog. It is easy enough to show from Wien's law, that the peak of the blackbody radiation spectrum is in the red part of the spectrum, with relatively little in the blue. The whole universe would look as bright as the surface of an M-dwarf star.

However, the term "fog" is highly misleading. A back of the envelope calculation suggests that if the baryon density today is about $\rho_0 \sim 4\times 10^{-28}$ kg/m$^3$, then at a redshift of $z\sim 1200$ (just prior to recombination), the number density of free electrons (assuming a fully ionised hydrogen gas) is roughly $$n_e = \frac{\rho_0 }{m_u}(1+z)^3= 4\times 10^8\ {\rm m}^{-3}$$

The mean free path of a photon in the plasma is $1/(\sigma n_e) = 4\times 10^{19}$m, where $\sigma$ is the Thomson scattering cross-section. Thus the average photon can travel several thousand light years before being scattered. Thus you would have no problem seeing things in the universe as you can see them now with your naked eye, except that there would be no stars, galaxies or indeed anything to see.

Over the course of the next 100,000 years or so, the recombination occurs and the mean free path exceeds the size of the observable universe. However, every line of sight would lead back to the hot fog at earlier times.

In practical terms, because there is nothing to see and the universe is highly uniform, I do not think you would see any imnediate change at all as the universe changed from being optically thick to optically thin, other than a gradual redshift of what you perceived to be the "sky". If, on the other hand there were other "objects" in the universe besides you (that were not in thermal equilibrium with everything else), then anything further away than 10,000 light years or so would be gradually revealed as recombination proceeded.