Primordial (Big Bang) Nucleosynthesis

Transcription

1 Primordial (Big Bang) Nucleosynthesis H Li Be Which elements? He METALS : Gamow suggests a Big Bang origin of the elements : Alpher, Bethe & Gamow: all elements are synthesized minutes after BB. - Fermi: no stable nuclei with A=5 and A=8 precludes BBN beyond 4 He : Alpher, Herman & Follin: BBN of large amounts of 4 He and little else : Hoyle, Burbridge, Burbridge & Fowler: stellar nucleosynthesis.

2 Origin of the elements formed in: Big Bang Nucleosynthesis Hot Stars Supernova Explosions Early 1980s: Concordance of predicted & observed abundances of D, 3 He, 4 He, 7 Li BBN a cornerstone of the hot Big Bang model as Standard Cosmology.

3 BBN: generalities BBN : - nonequilibrium process - lasts only a few minutes - in radiation-dominated plasma - high entropy (10 9 photons/baryon) - density ~ 10-5 g/cm 3 - many free neutrons Stellar nucleosynthesis : - occurs in equilibrium - over billions of years - in stellar plasma - low entropy (< 1 photon/baryon) - density ~ 10-2 g/cm 3 - no free neutrons Basic assumptions: - General relativity - Standard Big Bang cosmology - Standard Model of particle physics - Input: nuclear physics, theory & cross sections

4 The thermal bath: t «1 s, T» 1 MeV K - Universe is hot, expanding plasma of radiation & relativistic particles - roughly equal # electrons, positrons, (anti)neutrinos, and photons - nucleons outnumbered by more than a billion to one - no composite nuclei Reactions, e.g.: e + e + γ + γ - Proton-neutron (weak) conversion: ν e + n e + p -ν e + p e + + n - - Neutron (weak) β-decay: n p + e + ν e lifetime: τ 15 min. N n /N p = exp(-q/kt) 1 Q = m n -m p = 1.3 MeV N n /N p 0 as T 0, but: freeze-out!

5 Weak reaction n p rate: Neutron-proton freeze-out Fermi coupling constant: G F ~ E -2 Cross section: σ~ E -2 σ ~ G F 2 T 2 flux ~ N ~ T 3 W = N v σ ~ G F 2 T 5 Expansion rate (radiation-dominated Universe): H ~ (g*) 1/2 T 2 W/H ~ T 3 (g*) -1/2 Freeze-out temperature: T ~ 0.8 MeV drop-out of equilibrium when W ~ H with W/H = (T/0.8 MeV) 3 Initial neutron-proton ratio: N n (0)/N p (0) = exp(-q/kt) = 0.20 At later times: N p (t) = N n (0) exp(-t/τ) N p (t) = N p (0) + N n (0)[1-exp(-t/τ)]

6 Deuteron = nucleus of deuterium (heavy hydrogen, 2 H) = bound state of 1 proton and 1 neutron Binding energy = MeV = Q Synthesis of deuterons: The deuterium bottleneck n + p D + γ + Q neutron capture; deuteron photodisintegration Electromagnetic process with σ ~ 0.1 mb stays in equilibrium much longer. Tail of high-energy photons prevents freeze-out of deuterons until kt Q/ MeV; As soon as photodisintegration of deuterons stops helium can be synthesized. Much larger than weak cross section γ energy distribution n B / n γ ~ E

7 Nucleosynthesis: t 1-3 min, T MeV At kt 0.05 MeV, t 300 s for N ν =3: N n /N p 1/7 Neutron decay: Deuterium (all neutrons): D + n 3 H + γ 3 H + p 4 He + γ D + p 3 He + γ 3 He + n 4 He + γ Helium (~ all deuterons i.e all neutrons + equal # of protons): 2n Helium abundance ~ ~ 0.25 n+p Hydrogen abundance ~ 0.75 Note: η = n B /n γ D bottleneck lasts less long N n /N p 4 He

8 Synthesis of heavier elements No A=5, A=8 stable nuclei + 2-body reactions only 5 Li 4 He + p 5 He 4 He + n 8 Be 4 He + 4 He Bottleneck to further nucleosynthesis: BBN essentially STOPS at 4 He Trace amounts of 7 Li, 7 Be : 4 He + 3 H 7 Li + γ 4 He + 3 He 7 Be + γ 7 Be + γ 6 Li + p

9 Abundances of the light elements Observational concordance Agreement of abundances over ~ 10 orders of magnitude Major success of Big Bang CMB: n γ = 411 cm -3 η = n B /n γ = (4±1)x10-10 η Conclusion of BBN: - most of the baryons is dark - most matter is not baryons

10 Time evolution of BBN Most protons remain free Most neutrons in 4 He nuclei Rest of neutrons decay away After ~ 5 minutes, the elemental composition of the Universe remains unchanged until the first stars form several billion years later

11 BBN and # neutrinos H ~ N ν 1/2 T 2 so more neutrino species higher energy density, faster expansion more neutrons, sooner freeze-out, more 4 He He mass fraction upper limit on He 4 N ν = 3

12 LEP and # light neutrinos LEP: e + + e Z 0 charged leptons hadrons neutrinos ( invisible width) N ν = ± 0.012