## The temperature of the universe and dark matter

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### The temperature of the universe and dark matter

I was doing some thinking and it seems that the figures I've heard for the temperature of the universe and the amount of dark matter are inconsistent. So either I'm misunderstanding something (likely) or I've made a significant deduction (unlikely).

Facts and assumptions I may be wrong about:
1) The average temperature of the universe if 2.73 kelvin
2) Heat = temperature X mass X specific heat capacity of the mass
3) Something like 4.6% of the universe is non dark matter
4) For matter to not be dark it has to be visible. Altering/reflecting light counts, but the majority of visible matter is in stars (or things made thereof).
5) Stars are hot, millions of K.

So if say, 2.73 % of the universe by mass is stars, which average 10^6 K. And letting Cs be the s.p.c. of stars and Co the s.p.c. of the rest of the universe. IF we assume the rest of the universe is absolute zero.

That would mean that Co would be 10,000 times Cs.

Am I missing something?
Last edited by Quizatzhaderac on Tue Aug 19, 2014 6:16 pm UTC, edited 1 time in total.
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### Re: The temperature of the universe and dark matter

IF we assume the rest of the universe is absolute zero.

This is false, due to the uncertainty principle. I think.

I'm not entirely sure what you're getting at here. You're troubled that the specific heat for things-that-aren't-stars is much higher than other substances? In addition, the equation you have for heat only applies to heat transfer--"heat" is the movement of energy.
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### Re: The temperature of the universe and dark matter

Quizatzhaderac wrote:1) The average temperature of the universe is 2.73 kelvin
I don't like your use of "average" with respect to this value.

The spectrum of the cosmic microwave background radiation (which fills otherwise "empty" space) exactly (within miniscule error bars) matches a blackbody radiator with a uniform temperature of 2.725 K. Thus we say the universe itself (empty space with the CMBR, can't get away from it) has a temperature of approx. 2.73 K.

The CMBR is everywhere we look. It is highly uniform. According to the Big-Bang model, it was caused when the universe first became cool enough for stable atoms to form. It wasn't 2.725K back then, much higher. As the universe expanded, things cooled, the radiation dispersed and was redshifted. The CMBR looks very much like a hot gas blown up to the scale of the universe. Planck (a satellite) was launched in 2009 to further study the CMBR, especially the small irregularities/variations/ansiotropies that lie in it, and some other stuff out there. CMBR Planck both co. Wikipedia.

Sir_Elderberry wrote:
IF we assume the rest of the universe is absolute zero.

This is false, due to the uncertainty principle. I think.
It depends of if "the rest of the universe" is whatever mass-energy he didn't include (UP says NO!) or the "background" universe which contains that mass-energy (UP says Huh? I guess, kinda. What?).

BlackSails
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### Re: The temperature of the universe and dark matter

Far less then 2% of the mass of the universe is stars. Most of the mass of the universe is insterstellar plasma.

doogly
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### Re: The temperature of the universe and dark matter

The CMB does not interact thermally with the stuff in the universe. If it did, we wouldn't be able to look at it. Its temperature is thus totally unrelated to dark matter/energy, or to galaxies, or anything else.
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andyisagod
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### Re: The temperature of the universe and dark matter

The temperature of dark matter is unknown since we don't know when it decoupled or its mass. Not everything in the universe is 2.73k for example the neutrino background so using that as some kind of average isn't going to work. The reason that this isn't an average is because the photons have already been decoupled that's why they are interesting they provide a window to what the universe was like back then because since that time they haven't interacted that means they are no longer in thermal equilibrium with the rest of the universe. The process of freeze out is what gives us the different abundances of relic neutrinos, photons dark matter and nuclei and is very interesting physics.

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### Re: The temperature of the universe and dark matter

doogly wrote:The CMB does not interact thermally with the stuff in the universe. If it did, we wouldn't be able to look at it. Its temperature is thus totally unrelated to dark matter/energy, or to galaxies, or anything else.

Thanks, that gets right to heart heart of what I was missing. I had read/heard that 2.73 K was the temperature of the universe, deduced from the CMB. If that's actually the temperate of the universe minus the stuff in the universe that leaves much less to reconcile.

Sir_Elderberry wrote:
IF we assume the rest of the universe is absolute zero.

This is false, due to the uncertainty principle. I think.

I'm not entirely sure what you're getting at here. You're troubled that the specific heat for things-that-aren't-stars is much higher than other substances? In addition, the equation you have for heat only applies to heat transfer--"heat" is the movement of energy.

What I was getting at was that the temperature of the universe derived from observable matter seemed to be much higher than derived from CMB. Of course the rest of the universe can't be absolute zero, but that was a simplification that brought the two points closer.
Once I started doing actual math I realized my understandings could be reconciled with a huge s.p.c differential, but that answer still seemed unsatisfactory.

BlackSails wrote:Far less then 2% of the mass of the universe is stars. Most of the mass of the universe is insterstellar plasma.

So is interstellar plasma categorized as light (non-dark) matter? or was I using a bad figure for the % of universal mass that was light matter (4.6%)?

Thank you for your responses everyone.
Last edited by Quizatzhaderac on Tue Aug 19, 2014 6:18 pm UTC, edited 1 time in total.
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gmalivuk
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### Re: The temperature of the universe and dark matter

Yeah, dust and stuff is still normal matter, so part of that 4.6%. Most of that dust and plasma is not illuminated. Dark matter cannot be illuminated.
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BlackSails
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### Re: The temperature of the universe and dark matter

Dark matter doesnt really mean its dark. It means it doesnt interact very much with normal matter.

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### Re: The temperature of the universe and dark matter

gmalivuk wrote:Yeah, dust and stuff is still normal matter, so part of that 4.6%. Most of that dust and plasma is not illuminated. Dark matter cannot be illuminated.

I thought a small percentage of the non-visible (or unaccounted) universe is down to unilluminated matter. Or was this revised and it's all down to Dark matter? I suppose we can account for things like the interstellar plasma, as although we cannot see where it is, we can use an average.
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gmalivuk
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### Re: The temperature of the universe and dark matter

Yes, a small portion of what we can't see is merely unilluminated normal matter. But even though it's a small portion of what we can't see, there's still a hell of a lot more of it than there are stars.
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Technical Ben
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### Re: The temperature of the universe and dark matter

It will be interesting to see how much is down to normal matter, and how much is down to "exotic" matter. If it's exotic, there's a chance that it could be all around us right now, just not interacting.
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### Re: The temperature of the universe and dark matter

Almost all of it is exotic. And since we live closer to the edge of our galaxy, where the dark matter also likes to live, chances are very good it is zipping through you right now.
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### Re: The temperature of the universe and dark matter

doogly wrote:Almost all of it is exotic. And since we live closer to the edge of our galaxy, where the dark matter ALSO YOU GUYS: likes to live, chances are very good it is zipping through you right now.

We're like 2/3rds of the way out. Hardly on the edge.

Anyhow, in response to OP, part of the problem (though not necessarily the greatest part) is that it gets somewhat tricky when you talk about the "temperature" of empty space. It's not that there's stuff out there kicking around at 2.73K necessarily, it's that if we shoved you out into intergalactic space you'd cool down to around 2.73K. The difference is important, in that "the average temperature of the universe" now has two answers, depending on if you mean the average temperature per unit mass, or the average temperature per unit volume. The second one is more a measure of the average energy content per unit volume than anything, or at least the averag energy content that can be converted into motion when in contact with bayonic (read: normal) matter.

The other reason this is important is, as Sir_Elderberry pointed out, the formua you are using is for heat transfer. And in particular, your number 2 assumption is slightly off. It's heat times temperature DIFFERENCE times s.h.c. So in a theoretical universe that was billions of degrees, but still had stars kicking around for whatever reason, the stars would be recognized as heat SINKS. They would infact be dark spots, not light emmitters. Similarly, if normal interstellar dust is 2.73K, then it can have an absurdly small s.h.c., and still not emit light, simply because there is no temperature difference.

As for the temperature of Dark Matter...we don't know. Dark Matter is matter that only interacts with regular matter through gravity. Since in space the main heat transfer mechanism is EM radiation, and Dark Matter does not give off EM waves, it's temperature is very difficult to define in any meaningful way. If you were to ask "what is the temperature of dark matter" you're really asking "What's the average kinetic energy of dark matter". And That number can be as high or low as you like, it still won't shine, because it doesn't interact with the photon, so it doesn't emit or absorb light.
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doogly
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### Re: The temperature of the universe and dark matter

Eh, close enough.
You can't tell what the temperature is because we aren't sure what it is. But if you have a favorite model of dark energy, like smallest mass supersymmetric partners or axions or what not, you can get its temperature from freeze-out, same as you get CMB temperature.
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andyisagod
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### Re: The temperature of the universe and dark matter

Antimony-120 wrote:As for the temperature of Dark Matter...we don't know. Dark Matter is matter that only interacts with regular matter through gravity. Since in space the main heat transfer mechanism is EM radiation, and Dark Matter does not give off EM waves, it's temperature is very difficult to define in any meaningful way. If you were to ask "what is the temperature of dark matter" you're really asking "What's the average kinetic energy of dark matter". And That number can be as high or low as you like, it still won't shine, because it doesn't interact with the photon, so it doesn't emit or absorb light.

Dark matter has to (well almost has to) have some other interaction than gravity so that it can be produced in the right quantities in the first place. The temperature of dark matter can be fairly well defined its just not in thermal equilibrium with the rest of the universe any more. As doogly said if we knew enough about it and could calculate the temperature of the universe when it underwent freeze out then you can calculate how the temperature has changed since then due to the expansion of the universe.

This might not work if the dark matter has certain properties however. Firstly we normally assume that dark matter is essentially a single particle species but if there is a hidden sector of particles that don't interact strongly with standard model particles but can still interact with themselves the lightest being stable then the temperature of the dark matter is effected by other particles freezing out at different temperatures and decaying. The other assumption is that dark matter was in thermal equilibrium with the rest of the universe in the first place. If its interaction is weak enough it is possible that it didn't undergo freeze-out but is instead produced slowly over a long period of time and this obviously would effect the temperature of the relic dark matter (as well as other things).

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### Re: The temperature of the universe and dark matter

Also Dark Matter != Dark Energy, a lot of the mass of the universe probably isn't from matter.
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