The Formation of Hydrogen and Helium

1. The Formation of Hydrogen and Helium Primordial Nucleosynthesis Thomas RussellAstrophysics 302/401 Semester 1, 2008

2. 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

3. 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: [Loss, 2008] *These results vary with each paper Relative elemental abundances in the suns photosphere (normalised to hydrogen). [Brau, 2001]

4. 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]

5. 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+ + e- • At 1012 K ratio of neutrons to protons was 0.985 [Carroll & Ostlie, 1996]

6. Just above T~ 1010 K 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] • 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]

7. 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, 21H+ ) • Formation from the following reactions: 21H+ + 21H+↔ 31H+ + 11H+ 31H+ + 21H+↔ 42He++ + n And 21H+ + 21H+↔ 32He++ + n 32He++ + 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 42H++ + 31H+↔ 73H+3 + γ) [Carrol & Ostlie, 1996]

8. 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 42He++ and the ‘left over’ 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 • Nuclei of A=1-4 exist, A=5 and 8 do not exist, and unstable 63Li+3, 74Be+4 and the stable 73Li+3 do exist • 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]

9. 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

10. References • Carrol. B. W, Ostlie. D.A, 1996, ‘An Introduction To Modern Astrophysics’, Addison- Wesley 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