Two related questions:
1) The WMAP experiment says the first stars ignited about
200 million years after the Big Bang – earlier than previously
thought. What’s our best estimate of the temperature of the
cosmic microwave background radiation at this time?
2) Pfenniger and Puy have suggested that hydrogen cooled to the
point of crystallizing before the first stars ignited:
D. Pfenniger and D. Puy, Possible flakes of molecular hydrogen in
the early Universe, available as astro-ph/0211393.
Has this theory been killed by the WMAP experiment?
In article <bachnr$32…@glue.ucr.edu>, John Baez
<b…@galaxy.ucr.edu> wrote:
>Two related questions:
>1) The WMAP experiment says the first stars ignited about
>200 million years after the Big Bang – earlier than previously
>thought. What’s our best estimate of the temperature of the
>cosmic microwave background radiation at this time?
The relevant number here is the redshift. When cosmologists
talk to newspapers, they identify epochs by times: such-and-such
happened 200 million years after the big bang. When cosmologists
talk to cosmologist, they identify epochs by redshift. When
a cosmologist says that something happened at a redshift z, that
means it happened when the Universe was (1+z) times smaller
than it is today.
In any particular cosmological model (that is, for any particular
choice of parameters like the matter density, the cosmological
constant, and the Hubble parameter), you can convert a redshift to a
time. But for many purposes, it’s nicer just to work with
the redshift. This question is a case in point: the temperature
of the microwave background is related to the redshift
in a very simple way:
T = T0 / (1+z)
where T0 is the present temperature (2.726 K).
According to the WMAP paper (http://arxiv.org/abs/astro-ph/0302207),
the epoch of reionization (which is thought to be when the first stars
formed) was at a redshift of 20 +/- 10. If we take the central value,
the temperature was about 60 K, but there’s a factor of two
uncertainty in that.
Here’s a useful fact to use in figuring out this sort of thing. For
a flat Universe that contains pressureless matter and a cosmological
constant (and nothing else), the scale factor as a function of time is
a(t) = (Omega / (1-Omega))^(1/3) [sinh((3/2)sqrt(1-Omega) H0 t)]^(3/2).
Here Omega is the critical density in ordinary matter. (Since
the Universe is flat, this implies that the density associated
with the cosmological constant is 1-Omega.) H0 is the present-day
Hubble parameter, and the scale factor today is taken to be 1.
In terms of the redshift,
a = 1/(1+z).
Armed with this, you can convert times to redshifts and vice versa.
For instance, starting from the number you gave (t = 200 million
years), and picking reasonable parameters (Omega = 0.3, H=70 km/(s
Mpc), for instance), you get 1+z = 19, which is consistent with what I
got from the WMAP paper.
>2) Pfenniger and Puy have suggested that hydrogen cooled to the
>point of crystallizing before the first stars ignited:
>D. Pfenniger and D. Puy, Possible flakes of molecular hydrogen in
>the early Universe, available as astro-ph/0211393.
>Has this theory been killed by the WMAP experiment?
According to the abstract of this paper (which is all I’ve read), the
action here has to happen at redshifts of 6-12. If you push the WMAP
limit down as far as they’ll allow you (z=10 or so), then they can
overlap a bit, but not for very long.
- -Ted
- —
[E-mail me at n...@domain.edu, as opposed to n...@machine.domain.edu.]
"John Baez" <b…@galaxy.ucr.edu> wrote in message
news:bachnr$32c$1@glue.ucr.edu…
> Two related questions:
> 1) The WMAP experiment says the first stars ignited about
> 200 million years after the Big Bang – earlier than previously
> thought. What’s our best estimate of the temperature of the
> cosmic microwave background radiation at this time?
> 2) Pfenniger and Puy have suggested that hydrogen cooled to the
> point of crystallizing before the first stars ignited:
> D. Pfenniger and D. Puy, Possible flakes of molecular hydrogen in
> the early Universe, available as astro-ph/0211393.
> Has this theory been killed by the WMAP experiment?
Wouldn’t the temperature go inversely as the scale length?
If much of the cooling (of the CMBR) is due to expansion of
the universe stretching the wavelengths, then the Planck’s
law peak should vary accordingly, no?
"John Baez" <b…@galaxy.ucr.edu> wrote:
> D. Pfenniger and D. Puy, Possible flakes of molecular hydrogen in
> the early Universe, available as astro-ph/0211393.
I just thought you might like the NSU on this paper added.
Universe’s first winter was snowy
http://www.nature.com/nsu/021118/021118-8.html
>>>>> "JB" == John Baez <b…@galaxy.ucr.edu> writes:
JB> Two related questions: 1) The WMAP experiment says the first stars
JB> ignited about 200 million years after the Big Bang – earlier than
JB> previously thought. What’s our best estimate of the temperature
JB> of the cosmic microwave background radiation at this time?
The estimate is that reionization took place at a redshift z = 17 +/-
5. The theoretical prediction, for which there is some observational
support (Srianand et al. 2000, <URL:
http://adsabs.harvard.edu/cgi-bin/nph-bib_query?bibcode=2000Natur.408...
>), is that the temperature of the cosmic microwave background is T(z)
= T_0 (1 + z), where T_0 is the current temperature (2.7 K).
At z ~ 17, we expect T ~ 49 K.
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