A Space & astronomy forum. SpaceBanter.com

Go Back   Home » SpaceBanter.com forum » Astronomy and Astrophysics » Research
Site Map Home Authors List Search Today's Posts Mark Forums Read Web Partners

CMB temperature at different ages



 
 
Thread Tools Display Modes
  #1  
Old November 21st 05, 08:08 PM posted to sci.astro.research
external usenet poster
 
Posts: n/a
Default CMB temperature at different ages

A discussion elsewhere lead me to wonder what the temperature
of the CMB was at about the time that Jupiter was forming. (I was
wondering how the different background temperature would affect the
rate at which the initial gravitational infall energy was radiated.)
I'd guess that the temperature is declining exponentially, so I
should be able to work out an expression from the decomposition
temperature of hydrogen (ca. 5,000 K ? ), the present age of the
universe (13.7 Gyr) and the present CMB temperature (3.7 K). But it
would only be a guess.
Does anyone have an expression that would give the CMB's
temperature as a function of time - either time after the hydrogen
recombination/ big bang, or back from the present day? Doesn't have to
be too accurate - give or take a factor of two would be fine.

--
Aidan Karley,
Aberdeen, Scotland,
Location: +57d10' , -02d09' (sub-tropical Aberdeen), 0.021233
Written at Mon, 21 Nov 2005 18:05 GMT
  #2  
Old November 21st 05, 11:29 PM posted to sci.astro.research
external usenet poster
 
Posts: n/a
Default CMB temperature at different ages

Aidan Karley .group wrote:
A discussion elsewhere lead me to wonder what the temperature
of the CMB was at about the time that Jupiter was forming. (I was
wondering how the different background temperature would affect the
rate at which the initial gravitational infall energy was radiated.)
I'd guess that the temperature is declining exponentially, so I
should be able to work out an expression from the decomposition
temperature of hydrogen (ca. 5,000 K ? ), the present age of the
universe (13.7 Gyr) and the present CMB temperature (3.7 K). But it
would only be a guess.
Does anyone have an expression that would give the CMB's
temperature as a function of time - either time after the hydrogen
recombination/ big bang, or back from the present day? Doesn't have to
be too accurate - give or take a factor of two would be fine.


At the epoch from which we now see radiation at redshfift z, the
CMB had temperature 2.73(1+z). The time-z mapping depends on
the cosmological parameters, and doesn't necessarily have
a nice closed form. Ned Wright's calculator at
http://www.astro.ucla.edu/~wright/CosmoCalc.html
will deliver lookback times (which is what you need) for
various z and cosmologies. For the popular WMAP "consensus"
values, 4.6 Gyr back corresponds to z=0.44, for a CMB temperature
of 3.9 K.

Bill Keel
  #3  
Old November 21st 05, 11:30 PM posted to sci.astro.research
external usenet poster
 
Posts: n/a
Default CMB temperature at different ages

In article , Aidan Karley
.group writes:

A discussion elsewhere lead me to wonder what the temperature
of the CMB was at about the time that Jupiter was forming. (I was
wondering how the different background temperature would affect the
rate at which the initial gravitational infall energy was radiated.)
I'd guess that the temperature is declining exponentially,


Why? Exponential decline of temperature is associated with flow of heat
from a warmer to a cooler body (IIRC this is known as "Newton's law of
cooling"), which is not the case here.

so I
should be able to work out an expression from the decomposition
temperature of hydrogen (ca. 5,000 K ? ), the present age of the
universe (13.7 Gyr) and the present CMB temperature (3.7 K). But it
would only be a guess.


What is the relation between the decomposition temperature of hydrogen
and the formation of Jupiter? Jupiter didn't form as soon as hydrogen
could exist.

Does anyone have an expression that would give the CMB's
temperature as a function of time - either time after the hydrogen
recombination/ big bang, or back from the present day? Doesn't have to
be too accurate - give or take a factor of two would be fine.


The temperature is inversely proportional to the scale factor. Thus, if
the universe doubles in size, the temperature is half of what it was.
If you know the epoch at which Jupiter was being formed, you can then
work out the increase in the scale factor since then, and from that can
easily calculate the temperature.

The difficult part is the increase of scale factor with time. This
depends on the cosmological parameters. However, they are relatively
well known.

Ned Wright's cosmology calculator might be interesting to look at.

For some theory on how the temperature of the CMB evolves, see the first
part of chapter 8 of Berry's COSMOLOGY AND GRAVITATION.

Interestingly, since spectra are influenced by the ambient temperature,
one can actually OBSERVE what the temperature was at high redshift,
rather than just calculating it.

The present temperature is approximately 2.7, not 3.7.

Very roughly, Jupiter formed when the universe was about 2/3 of its
present age. Since then, the rate of expansion has, on average, been
roughly linear (to a first approximation). So, roughly, 4 K.
  #4  
Old November 22nd 05, 10:54 AM posted to sci.astro.research
external usenet poster
 
Posts: n/a
Default CMB temperature at different ages

In article , Phillip
Helbig---remove CLOTHES to reply wrote:
I'd guess that the temperature is declining exponentially,


Why?

It was a guess. I Am Not A Physicist.

What is the relation between the decomposition temperature of hydrogen
and the formation of Jupiter? Jupiter didn't form as soon as hydrogen
could exist.

It was to give one fixed point for getting the equation of the
(guessed) exponential. Present-day being the other fixed point. Age of the
planets/ Solar system/ Sol being the variable. Out pops the CMB
temperature as (present temperature)*(1+z), moving the problem to getting
a "z" value. (Thanks to others, William & Steve, for that.)

The temperature is inversely proportional to the scale factor. Thus, if
the universe doubles in size,

That's what was making me aware that I was guessing with an
exponential - doubles in linear dimension, in volume, in 4-d hypervolume?
IANAP, as above.

The difficult part is the increase of scale factor with time.

As Mrs Beaton put it a century or so ago, "first catch your
rabbit".

Ned Wright's cosmology calculator might be interesting to look at.

Reading the FAQ in another window just now.

Anyway, CMB temperature around 3.9 K when Jupiter was formed, so to
answer my original speculation, there's not going to be a lot of
difference in the cooling curve of Jupiter when compared to a simple model
of a blob of matter sitting in a constant-temperature universe. Which is
what I'd expected. But it's nice to be able to put numbers to it.

--
Aidan Karley,
Aberdeen, Scotland,
Location: +57d10' , -02d09' (sub-tropical Aberdeen), 0.021233
Written at Tue, 22 Nov 2005 03:55 GMT
  #5  
Old November 23rd 05, 10:29 AM posted to sci.astro.research
external usenet poster
 
Posts: n/a
Default CMB temperature at different ages

In article , Aidan Karley
.group writes:

The temperature is inversely proportional to the scale factor. Thus, if
the universe doubles in size,

That's what was making me aware that I was guessing with an
exponential - doubles in linear dimension, in volume, in 4-d hypervolume?
IANAP, as above.


Here, linear dimension.
 




Thread Tools
Display Modes

Posting Rules
You may not post new threads
You may not post replies
You may not post attachments
You may not edit your posts

vB code is On
Smilies are On
[IMG] code is On
HTML code is Off
Forum Jump

Similar Threads
Thread Thread Starter Forum Replies Last Post
The Apollo Hoax FAQ (is not spam) :-) Nathan Jones UK Astronomy 8 August 1st 04 09:08 PM
Apollo Buzz alDredge Misc 5 July 28th 04 10:05 AM
Apollo Buzz alDredge UK Astronomy 5 July 28th 04 10:05 AM
The Apollo Hoax FAQ darla Astronomy Misc 15 July 25th 04 02:57 PM
The Apollo Hoax FAQ darla Misc 10 July 25th 04 02:57 PM


All times are GMT +1. The time now is 09:45 AM.


Powered by vBulletin® Version 3.6.4
Copyright ©2000 - 2024, Jelsoft Enterprises Ltd.
Copyright ©2004-2024 SpaceBanter.com.
The comments are property of their posters.