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Дата изменения: Wed Apr 2 03:06:39 1997 Дата индексирования: Mon Oct 1 23:41:43 2012 Кодировка: Поисковые слова: ultraviolet |
Abundance of the LIght ELements
On the basis of two observations, 1) the Universe is currently in a state of uniform expansion and 2) the Universe is filled with photons that come from background radiation at a temperature of 2.74 K, we can construct our generic cosmological model known as the Hot Big Bang model. This model is but a mere 30 years old so we should not expect it to be a complete description of what we observe and indeed it is not. What the model can explain well is the following:
The CBR is pretty difficult to ignore. Most radial alternative cosmologies can't really predict it. The discovery of the CBR has an interesting history:
Observations of the
excited states of the CN molecule made by McKellar (1941) indicated
excitation by a photon background with a characteristic temperature
of 2.3 K. But since the CN molecule could only be found where the
Galaxy was, the excitation was attributed to the ambient energy
density of starlight in the Galaxy as opposed to being energy external
to the galaxy (\ie the CMB).
Accidentally discovered again in 1965 by Penzias and Wilson (who
won the Nobel Prize). They were employed at Bell Labs and were testing
the feasibility of using Microwaves for communication. The initial measurements (at one frequency only) of Penzias
Wilson indicated that the flux density of photons at their millimeter receiver
was independent of position in the sky. Failing to see any 24 hour
modulation of this signal, the remaining logical conclusion was that
the CMB was indeed of cosmological origin and therefore everywhere.
But shortly after the Universe was discovered to be
expanding, theoretical
arguments for a background of radiation were presented.:
In 1934
Tolman made an analogy between the expanding universe and a thermodynamic
state. Equating expansion with the thermodynamic concept of entropy
led him to conclude that the expansion must cool any background which
has a thermal spectrum.
In 1942, Chandrasekhar and Heinrich
suggested that if the Universe in its early history achieved thermal
equilibrium at conditions of temperature and density near 10$^{10}$ K
and 10$^{7}$ gm cm$^{-3}$ then equilibrium abundances of lighter elements
would have frozen out, in ratios that roughly agreed with observations.
But this argument is only partially correct since the high matter
density at the time would have required rapid expansion (to avoid
early collapse of the Universe) and hence equilibrium calculations
are not appropriate. Gamow (1942, 1946) used this as the basis for
his set of arguments that physical processes in the early universe
were dynamic in nature as they must have occurred in a rapidly expanding
and cooling environment.
Gamow (1948) later reasoned that at sufficiently
high temperatures, (kT in excess of the rest mass energy of a neutron),
the energy density in the photon field must have greatly exceeded the
energy density of the matter field. In such conditions, the radiation
field can photo-dissociate any nuclei, meaning that the early universe
had to consist of photons and free elementary particles.
Gamow used the estimated
abundances of helium to
predict that, at the current epoch, the photon field has been redshifted
to millimeter wavelengths. In fact he predicted, in 1953, a temperature
of 5K for the background.
Hubble made redshift measurements of galaxies and assumed that all galaxies had roughly the same physical size. using the angular size as a measure of distance he showed there was a linear correlation between radial velocity away from the observer and the distance to the galaxy. This is called the Hubble law and the slope of the relation is the Hubble constant whose inverse represents the expansion age of the Universe.
Although the data are quite noisy, there is a general trend for more distance objects to exhibit a larger redshift. These data were sufficient to empirically demonstrate that recessional velocity was proportional to distance and hence that the Universe was in a state of uniform expansion. Einstein's General Relativity and the static Universe could now be resolved - the Universe itself was expanding. This determination of uniform, linear expansion of the Universe has a clear prediction. If galaxies are moving apart from one another today, then in the past they must have been closer together. Indeed, there must have been a time when all the galaxies in the Universe were together in the same space. At this time, the Universe was very dense and in a physical state well-removed from how it is observed to be today.
Abundance of the Light Elements
Universe at expansion
age of about one second was a hot and dense mixture of electrons, protons,
neutrons, neutrinoes and photons. The ratio of protons to neutrons
at this time was unity as interactions with neutrinoes mediated the
neutron to proton and proton to neutron conversion. However, at
expansion age of 2 seconds, the Universe had cooled to the point where
it became transparent to neutrinoes and this mediation was gone.
Since free neutrons decay with 1/2 life of \app 900 seconds, the
proton-to-neutron (P/N) ratio began to increase. As the Universe continued
to expand, it cooled to the point where some the nucleons could fuse
into light elements such as Deuterium and Helium through the same series
of fusion reactions that are presently occuring in our Sun. At the
time of this hydrogen to helium fusion P/N = 7
Making Helium:
But, deuterium is a very fragile nucleus and can easily be broken
apart by a high energy photon:
Now there is an interesting race condition:
Will deuterium combine with another proton to make a nucleus with
3 nucleons or will it be photodissociated before it can do this?
This race condition depends on the density of protons:
So things are trying to proceed as follows:
The end result is the conversion of 2 protons and 2
neutrons into 1 Helium-4 nucleus.
Before the Reaction:
After the reaction
The mass of 1 Helium-4 nucleus is about 4 times the mass
of a proton
Now we can make a prediction:
The helium abundance reflects three things:
pn + photon --> p + n (which will decay in 900 seconds)
1. The p/n ratio at the time that nucleosynthesis starts
Element Production beyond helium:
2. The ratio of photons to baryons
3. The actual baryon density