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

Radiation Era Radiation era (when expansion governed by equivalent mass density of blackbody radiation) 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 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: The temperature of the universe at time t is given by: T(t)=(1.52×10 10 K s 1/2 )t -1/2  Radiation era comes to an end and matter era begins at T~10 5 K [Carroll & Ostlie, 1996]

At T~ 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 (v e, v μ, ﻵ e, ﻵ μ ) The universe contained a mixture of photons (γ), electron-positron pairs (e -, e + ), and electron and muon neutrino ’ s and their anti-particles (v e, v μ, ﻵ e, ﻵ μ ) There were also a small number of protons and neutrons (about 5 for every photons), that were constantly being transformed into each other via reactions: There were also a small number of protons and neutrons (about 5 for every photons), that were constantly being transformed into each other via reactions: n ↔ p + + e - + ﻵ e n ↔ p + + e - + ﻵ e n + e + ↔ p + + ﻵ e n + e + ↔ p + + ﻵ e n + ν e ↔ p + + e - n + ν e ↔ p + + e - At K ratio of neutrons to protons was At K ratio of neutrons to protons was [Carroll & Ostlie, 1996]

T~ K Ratio of neutrons to protons “freezes” at n n /n p = [Carrol & Ostlie, 1996, pg 1291] Ratio of neutrons to protons “freezes” at n n /n p = [Carrol & Ostlie, 1996, pg 1291] Effectively no more neutrons being created Effectively no more neutrons being created However the initial reaction of: However the initial reaction of: n ↔ p + + e - + ﻵ e continued to operate, converting neutrons to protons with a T 1/2 =617 s continued to operate, converting neutrons to protons with a T 1/2 =617 s [Roos, 2003] Just above T~ K Expansion reduced the energy of the neutrinos until they were unable to participate in the previous transformation reactions 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 MeV (threshold for creating electron positron pairs) via: γ → e - + e + Characteristic thermal energy of the photons falls below 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) 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~ 10 9 K Neutrons and protons remained separate until temp dropped to 10 9 K, Neutrons and protons remained separate until temp dropped to 10 9 K, (∆t = 229 s for T K to 10 9 K ) Number of neutrons declined and protons rose to give neutron to proton ratio of Number of neutrons declined and protons rose to give neutron to proton ratio of Below 10 9 K, neutrons and protons readily combined to form as many deuterium nuclei as possible via: Below 10 9 K, neutrons and protons readily combined to form as many deuterium nuclei as possible via: p + + n → d + γ p + + n → d + γ (where d is deuteron, 2 1 H + ) Formation from the following reactions: Formation from the following reactions: 2 1 H H + ↔ 3 1 H H H H + ↔ 4 2 He ++ + n And 2 1 H H + ↔ 3 2 He ++ + n 3 2 He H + ↔ 4 2 He H He H + ↔ 4 2 He H + No other nuclei were formed with abundances approaching that of 4 2 H ++, although traces of 2 1 H +, 3 2 H ++ and 7 3 Li +3 were formed (from the reaction 4 2 H H + ↔ 7 3 H +3 + γ) No other nuclei were formed with abundances approaching that of 4 2 H ++, although traces of 2 1 H +, 3 2 H ++ and 7 3 Li +3 were formed (from the reaction 4 2 H H + ↔ 7 3 H +3 + γ) [Carrol & Ostlie, 1996]

T~ 10 9 K Beta decay has reduced the neutron/proton ratio to its final value of Beta decay has reduced the neutron/proton ratio to its final value of n n /n p = = (1/7) The same number of protons as neutrons go into 4 2 He ++ and the ‘left over’ protons are the nuclei of future hydrogen atoms The same number of protons as neutrons go into 4 2 He ++ and the ‘left over’ protons are the nuclei of future hydrogen atoms End result of this nucleosynthesis (t~ s after big bang), is a universe almost entirely composed of hydrogen and helium nuclei End result of this nucleosynthesis (t~ 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 6 3 Li +3, 7 4 Be +4 and the stable 7 3 Li +3 do exist Nuclei of A=1-4 exist, A=5 and 8 do not exist, and unstable 6 3 Li +3, 7 4 Be +4 and the stable 7 3 Li +3 do exist 3 H ++ decays into 3 He ++ with a 12 year half-life so no 3 H ++ survives to the present, and 7 Be +4 decays into 7 Li +3 with a 53 day half-life and also does not survive 3 H ++ decays into 3 He ++ with a 12 year half-life so no 3 H ++ survives to the present, and 7 Be +4 decays into 7 Li +3 with a 53 day half-life and also does not survive T~ 3000 K (t~ years) Cool enough for hydrogen and helium nuclei to collect electrons and become stable atoms 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’, Addison- Wesley Publishing, U.S.A. Carrol. B. W, Ostlie. D.A, 1996, ‘An Introduction To Modern Astrophysics’, Addison- Wesley Publishing, U.S.A. Roos, M, 2003, ‘Introduction to Cosmology’, 3 rd Edition, John Wiley and Sons Publishing, England Roos, M, 2003, ‘Introduction to Cosmology’, 3 rd Edition, John Wiley and Sons Publishing, England Brau, J, 2001, ‘Galaxies and the Expanding Universe’, Retrieved , from: Brau, J, 2001, ‘Galaxies and the Expanding Universe’, Retrieved , from: CERN, 2000, ‘CERN and the Big Bang’, Retrieved , from: CERN, 2000, ‘CERN and the Big Bang’, Retrieved , from: Wright, E.L, 2004, ‘ Big Bang Nucleosynthesis ’, Retrieved , from: Wright, E.L, 2004, ‘ Big Bang Nucleosynthesis ’, Retrieved , from: NASA – Goddard Space Flight Centre, 2005, ‘ Cosmic Connection to the Elements’, Retrieved , from: NASA – Goddard Space Flight Centre, 2005, ‘ Cosmic Connection to the Elements’, Retrieved , from: Battersby, S, 2006, ‘New Scientist: ‘Instant Expert, Cosmology’, Retrieved , from: Battersby, S, 2006, ‘New Scientist: ‘Instant Expert, Cosmology’, Retrieved , from: Loss, B, 2008, Lecture Slide: ‘Cosmic Abundance Data’, Retrieved , from: Loss, B, 2008, Lecture Slide: ‘Cosmic Abundance Data’, Retrieved , from: Chown, M, 2000, ‘New Scientist: ‘Before the Big Bang’, Retrieved , from: Chown, M, 2000, ‘New Scientist: ‘Before the Big Bang’, Retrieved , from: