The Formation of Hydrogen and Helium
Primordial Nucleosynthesis
Thomas Russell
Astrophysics 302/401
Semester 1, 2008
Creation of The Universe: The Big Bang

Approximately 13.7 billion years ago, the big bang [New Scientist, 2006],
from Hubble 1929 – Expanding universe [NASA, 2005]

Everything - all matter, energy, space and time - came into being at that
instant

Before the Big Bang – meaningless question “What’s north of the North
Pole” – Hawking [New Scientist, 2000]

Hot Big Bang model accounts for the abundances of the light elements,
High H and He consistent with big bang theory [Kunth, 1986]

However, the lack of stable nuclei with atomic weights of 5 or 8 limited the
Big Bang to producing hydrogen and helium [Wright, 2004]

Scientists believe the instantaneous universe was too hot for anything
other than the most fundamental particles [CERN, 2000]

Ever since, the Universe has been expanding and cooling
Abundance Ratios
•
•
H and He make up over 99% of the
cosmic elemental abundances and
98% of the mass of the known
universe [Carroll & Ostlie, 1996].
Abundances:
Mass
Atom
H
0.71
0.91
He
0.27
0.08
A>2
0.02
0.02
[Loss, 2008]
Relative elemental abundances in the suns
photosphere (normalised to hydrogen).
[Brau, 2001]
*These results
vary with each
paper
Radiation Era

Radiation era (when expansion governed by equivalent mass density of
blackbody radiation)

Hydrogen and Helium formed due to big bang, helium is also formed later
in stellar cores

The temperature of the universe at time t is given by:
T(t)=(1.52×1010 K s1/2)t-1/2

Radiation era comes to an end and matter era begins at T~105 K
[Carroll & Ostlie, 1996]
At T~ 1012 K, (t~10-4 s)


•
The universe contained a mixture of photons (γ), electron-positron pairs
(e-, e+), and electron and muon neutrino’s and their anti-particles (ve, vμ,
‫ﻵ‬e, ‫ﻵ‬μ)
There were also a small number of protons and neutrons (about 5 for
every 1010 photons), that were constantly being transformed into each
other via reactions:
n ↔ p+ + e- + ‫ ﻵ‬e
n + e+ ↔ p+ + ‫ ﻵ‬e
n + νe ↔ p+ + eAt 1012 K ratio of neutrons to protons was 0.985
[Carroll & Ostlie, 1996]
Just above T~ 1010 K



Expansion reduced the energy of the neutrinos until they were unable to
participate in the previous transformation reactions
Characteristic thermal energy of the photons falls below 1.022 MeV
(threshold for creating electron positron pairs) via: γ→ e- + e+
Electrons and positrons annihilated each other without being replaced,
thus leaving only small number of excess electrons (i.e. neutrons could
not keep up with the rate of expansion)
[Carroll & Ostlie, 1996]
•
•
•
T~ 1010 K
Ratio of neutrons to protons “freezes” at nn/np = 0.223 [Carrol & Ostlie,
1996, pg 1291]
Effectively no more neutrons being created
However the initial reaction of:
n ↔ p + + e- + ‫ ﻵ‬e
continued to operate, converting neutrons to protons with a T1/2=617 s
[Roos, 2003]
T~ 109 K



Neutrons and protons remained separate until temp dropped to 109 K,
(∆t = 229 s for T1010 K to 109 K)
Number of neutrons declined and protons rose to give neutron to proton
ratio of 0.163
Below 109 K, neutrons and protons readily combined to form as many
deuterium nuclei as possible via:
p+ + n → d + γ
(where d is deuteron,

2
1H
+
)
Formation from the following reactions:
2 H+ + 2 H+ ↔ 3 H+ + 1 H+
1
1
1
1
3 H+ + 2 H+ ↔ 4 He++ + n
1
1
2
And
2
3

1H
2He
++
+ 21H+ ↔ 32He++ + n
+ 21H+ ↔ 42He++ + 11H+
+
No other nuclei were formed with abundances approaching that of 42H++,
although traces of 21H+, 32H++ and 73Li+3 were formed (from the reaction
4 H++ + 3 H+ ↔ 7 H+3 + γ)
2
1
3
[Carrol & Ostlie, 1996]
T~ 109 K

Beta decay has reduced the neutron/proton ratio to its final value of
nn/np = 0.143 = (1/7)

The same number of protons as neutrons go into
protons are the nuclei of future hydrogen atoms

End result of this nucleosynthesis (t~ 100-700 s after big bang), is a
universe almost entirely composed of hydrogen and helium nuclei


4
++
2He
and the ‘left over’
Nuclei of A=1-4 exist, A=5 and 8 do not exist, and unstable
and the stable 73Li+3 do exist
6
+3 7
+4
3Li , 4Be
3H++
decays into 3He++ with a 12 year half-life so no 3H++ survives to the
present, and 7Be+4 decays into 7Li+3 with a 53 day half-life and also does
not survive
T~ 3000 K (t~700 000 years)

Cool enough for hydrogen and helium nuclei to collect electrons and
become stable atoms
[Roos, 2003]
Conclusion

One important success of the big bang model has been in describing the
abundance of light elements such as hydrogen, helium, and lithium in the
Universe

The above elements are produced in the big bang, and to some degree in
stars. Analysis of the oldest stars, which contain material that is the least
altered from that produced originally in the big bang, indicate abundances
that are in very good agreement with the predictions of the hot big bang

At T~3000K absence of ionized gas makes universe transparent to light for
first time
References

Carrol. B. W, Ostlie. D.A, 1996, ‘An Introduction To Modern Astrophysics’, AddisonWesley Publishing, U.S.A.

Roos, M, 2003, ‘Introduction to Cosmology’, 3rd Edition, John Wiley and Sons
Publishing, England

Brau, J, 2001, ‘Galaxies and the Expanding Universe’, Retrieved 5-4-2008, from:
http://physics.uoregon.edu/~jimbrau/astr123/

CERN, 2000, ‘CERN and the Big Bang’, Retrieved 5-4-2008, from:
http://www.exploratorium.edu/origins/cern/ideas/bang2.html

Wright, E.L, 2004, ‘Big Bang Nucleosynthesis’, Retrieved 4-4-2008, from:
http://www.astro.ucla.edu/~wright/BBNS.html

NASA – Goddard Space Flight Centre, 2005, ‘ Cosmic Connection to the Elements’,
Retrieved 5-4-2008, from:
http://imagine.gsfc.nasa.gov/Images/teachers/posters/elements/Elements_2005.pdf

Battersby, S, 2006, ‘New Scientist: ‘Instant Expert, Cosmology’, Retrieved 5-4-2008,
from: http://www.newscientist.com/article/dn9988-instant-expert-cosmology.html

Loss, B, 2008, Lecture Slide: ‘Cosmic Abundance Data’, Retrieved 4-4-2008, from:
http://webct.curtin.edu.au/SCRIPT/310267_011594_302742_a/scripts/serve_home

Chown, M, 2000, ‘New Scientist: ‘Before the Big Bang’, Retrieved 5-4-2008, from:
http://space.newscientist.com/channel/astronomy/cosmology/mg16622414.400.html