Duration of the original CMB radiation

[LexLuther]

The radiation we see today as the CMBR - was this originally released as a pulse or was it continuous for some length of time ?

 

[marcus]

Good question! Released over a period of time as the hot gas was exanding and cooling.

Let me go fetch a figure for the Hubble expansion rate back then. Distances were expanding more rapidly so the gas would have cooled correspondingly rapidly---a time window.

If the gas filling space is too hot (>>3000 kelvin) then it is effectively opaque, light can't travel very far without getting scattered, so we don;t see it

But if the gas is too cold (<<3000 kelvin) then it doesn't glow and make light. So a time window.

To get a handle on things back at year 380,000 (redshift z=1100) google
"cosmological calculator 2010" and get Jorrie's calculator, put in 1100.
It is also the "cosmocalc.htm" link in my signature.
Let's see what happens when you put in z = 1100 and get the Hubble expansion rate from back then.

You know the Hubble expansion rate today is 71 km/s per Megaparsec of distance. The bigger the distance, the faster it is growing.

but back then the calculator says a Megaparsec distance was growing at a much more rapid rate
1.5 million km/s.

 

[cepheid]

The radiation we see today as the CMBR - was this originally released as a pulse or was it continuous for some length of time ?

It's unclear what you mean by the question, so I will just say a few things, and if you still do not understand whatever it is you are trying to understand, then let me know.

At times around 380,000 years after the big bang (and earlier) the universe was a hot dense plasma, a soup of charged particles at a temperature of about 3000 K (or higher, the farther you go back in time). In addition to charged particles (matter) this "gas" also consisted of a bunch of photons, because anything with a temperature above absolute zero emits electromagnetic radiation. Everything was in thermal equilibrium with everything else (including the photons with the matter) and as a result, the photons at the time had a nearly perfect blackbody thermal emission spectrum corresponding to an equilibrium temperature of 3000 K (The blackbody spectrum now corresponds to a blackbody radiation temperature of ~3 K, because the expansion of the universe has caused those photons to redshift by a factor 1000).

In any case, this "primordial" plasma was essentially opaque, because photons had a very high probability of interacting with free electrons by a mechanism known as Thompson scattering. Because of this, the mean free path of photons was very small. They couldn't get very far in any direction before undergoing a "collision" or "scattering" event with an electron, and being sent of in some other direction entirely. So, if you had been there at this time in the early universe, you wouldn't have been able to see very far in any given direction, because really distant photons could never reach you directly. The only ones that would reach you directly would be the ones that were last scattered in your direction approximately the distance of a mean free path away from you before entering your eye. This is directly analogous to being in a thick fog.

At around 380,000 years after the big bang, the universe had expanded and cooled sufficiently that free electrons and protons could combine together to form stable hydrogen atoms for the very first time. Prior to this, the temperature was high enough, that there were enough energetic photons present, that a hydrogen atom would tend to be re-ionized as soon as it formed. As the universe cooled and the blackbody spectrum of the photons shifted to lower frequencies (and energies), there were no longer enough of the really energetic photons to keep all the gas ionized, and neutral atomic hydrogen was able to form and to persist. This event is known as "recombination", which is a bit of misnomer, because the combination of protons and electrons into atoms was happening for the very first time.

Without any more free electrons, there was no longer any Thomson scattering. In other words, photons could now travel through space in straight lines completely unimpeded by charged matter. They began freely streaming through space in all directions. The universe essentially went from being "opaque" to being "transparent." Everything I've said up to now has been leading up to this point: the photons in question were everywhere, because this "primordial plasma" pervaded the entire universe. So in some sense, asking what the "duration" of the "emission" of the CMB photons was doesn't make sense, because the CMB photons exist now, everywhere, and this has always been the case. In that sense, the whole universe is "bathed" in a 3 kelvin "gas" of photons left over from this era in which the universe was much hotter and denser than it is now.

But, you may protest, when I look out into the universe, I don't see CMB at all distances away from Earth i.e. throughout the entire 3D volume of the observable universe. I only see CMB emission coming from a 2D surface at nearly at the outer edge of that volume. Why is that? The answer is because recombination occurred a very short time after the big bang (compared to the present age of the universe) which means that those photons began free-streaming nearly 13.7 billion years ago. So, the CMB photons that are arriving at Earth NOW are the ones that began their journey at a sufficiently far enough distance that they are only just getting here now. In other words, we see CMB coming from a surface representing the distance away from us for which emitted photons had a light travel time of 13.7 billion years in order to get here. In contrast, CMB photons that began freely streaming from the part of the universe where the Andromeda galaxy is now, would have reached the part of the universe where Earth is now a LONG LONG time ago, and would have long since gone past us. So we don't see CMB photons coming from closer distances, where the light travel time for photons to get here would have been much shorter.

This surface of emission is also called the last scattering surface, because it is the set of all points from which the photons that are arriving now were scattered for the very last time before beginning to stream freely (and heading directly towards us). Because the universe was opaque at epochs earlier than recombination, we cannot see any photons coming from distances farther than the last scattering surface. The CMB is therefore the oldest light that we can see.

So, in light of what I've just said about the last scattering surface, another interpretation of your question might be, "were all CMB photons 'last scattered' at exactly the same time, which would mean they are all coming to us from exactly the same distance, or did some get last scattered later than others?" The answer is that not all CMB photons were last scattered at exactly the same time. Some began free streaming slightly earlier than others. This means that some CMB photons have a larger redshift than others. The ones that "last scattered' earlier came from a slightly farther distance, so in that sense, when we see them, we are seeing "farther back" into the primordial plasma than we are when we see the CMB photons that scattered slightly later, and hence originated slightly closer to us. In this sense, the last scattering surface is perhaps more aptly described as a last scattering layer (think of it as a thin spherical shell from within which the current CMB photons that we are seeing originated). It's not a big effect by any means. One reference I have states that (for a typical cosmological model) the average redshift of the CMB is 1090, but the distribution of redshifts for the CMB photons that we see now can vary anywhere between 983 and 1178. So that's a redshift interval of 195. Using the handy dandy cosmological calculator that marcus mentioned above, we see that these redshifts correspond to the age of the universe being 329,000 years old (z = 1183), 377,000 years old (z = 1090), and 449,000 years old (z = 983).

So, for the CMB photons that we are seeing now, there is very narrow window of time within which they were "emitted" (or began their journey here unimpeded), and hence a very narrow window of distances from which they originated.


This explanation went on a lot longer than I intended. I hope that at the very least, the stuff in boldface gets at what you were trying to find out.