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Phys 24 (F2011) Nucleosynthesis Sadoulet
Primordial NucleosynthesisTwo forms of energy
Kinetic Energy TemperaturePotential energy Bound system Potential barrier
Production of the light elements= Nucleosynthesis High temperature soup Formation of elements Freeze out
Primordial abundance measurementsD=2H, 4He, 7Li
Comparison with theory, consequences
cf. Weinberg: The First Three Minutes
1
Phys 24 (F2011) Nucleosynthesis Sadoulet
Why the Big Bang?3 pillars
Hubble expansionCosmic Microwave backgroundPrimordial D, He ,Li
Hubble expansion
2
v = Hr
∝ log distance( )
log velocity( )
Phys 24 (F2011) Nucleosynthesis Sadoulet
Cosmic Microwave BackgroundCosmic Microwave background
Very uniform radiation fromprimordial fireball
3
Phys 24 (F2011) Nucleosynthesis Sadoulet
NucleosynthesisPrimordial abundance of light elements
4
Phys 24 (F2011) Nucleosynthesis Sadoulet
+
Need protons and neutronsBut do it fast enough as neutron will decay(half life time 10.6
minutes)
2 body reactionsDensity not large enough for 3 body
+ a number of other possible reactions!Process stopped by Freeze-Out
Temperature and density become too smallNo element heavier than Lithium
3H
Building Nuclei by Fusion
p+n
HydrogenDeuterium=2H
3He
4He
7Li
+2H
5
3H+n
Phys 24 (F2011) Nucleosynthesis Sadoulet
Definition
Relation to temperatureFor a collection of particles in thermal equilibrium, the temperature
is proportional to the average kinetic energy
Note: the particles have a broad distribution of kinetic energy
0
0.1
0.2
0.3
0.4
0.5
0 1 2 3 4 5 6
Boltz
man
dis
tribu
tion
Energy/kT
�
Ekin = 12mv 2 = 3
2kT
Kinetic energy
�
Ekin = 12mv 2
Average
6
Phys 24 (F2011) Nucleosynthesis Sadoulet
Expanding Universe
Density goes down
Temperature goes down
One can show that
�
ρ∝ 1a3 t( )
where a t( ) tracks the expansion (e.g. distance between 2 distant galaxies)
�
ΔE = −pΔV + ΔQ = −pΔV = 0p > 0 =>E decreases,T decreases
T ∝ 1a t( )
7
Phys 24 (F2011) Nucleosynthesis Sadoulet
Potential Energy
Example: Marble at the top of a hill
Trade-off between kinetic energy and potential energyDefine potential energy as the energy necessary to bring the
marble to its position=> The sum of kinetic and potential energy is
constant
Gravitationalfield
Etotal
position
kinetic
potential
8
Phys 24 (F2011) Nucleosynthesis Sadoulet
Nuclear attraction
Requires emission of a photon! Need low enough temperature for n and p to stay bound.
Otherwise
More generally equilibrium function of temperatureCoulomb repulsion e.g. 4He
Need s enough energy to “penetrate” barrier => needs high enough temperature (but not too high lest its dissociates)
How to build Nuclei?Po
tent
ial
rn-p
B
“Potential well”p + n→2 H +γ
p + n↔2 H + γ
p + n←2 H +γ
Epot + Ekin = constant
Deuterium =2H
Binding energy= 2.22 MeV
p
n
γ
Pote
ntia
l
rDD
potential barrier <- Coulomb repulsion
�
2 H + +2 H + →4 He++ + γ
γBinding energy (28MeV)
9
Phys 24 (F2011) Nucleosynthesis Sadoulet
Reaction Rates and Expansion
Strong dependence of reaction rate on temperature
cf. ordinary cooking Breaking of bounds (tenderness) Pressure cooker, refrigerator
Establishing new bounds (e.g. custard)Dependence on density
The particles have to find each other!
In an expanding universe The reaction rate has to be greater than the expansion rate otherwise nuclei are diluted away before having time of reacting!
Freeze-out3 temperature regimes
• At high temperature, nucleus cannot exist <- dissociation• At low temperature: nucleus is stable but not enough energy to be
formed The reactions proceed too slowly :Freeze-out• Intermediate: nucleus can be formed and is stable enough to
survive
�
rate∝ρ1ρ2
10
Phys 24 (F2011) Nucleosynthesis Sadoulet
Need protons and neutronsBut do it fast enough as neutron will decay(half life time 10.6
minutes)
2 body reactionsDensity not large enough for 3 body
+ a number of other possible reactions!Process stopped by Freeze-Out
Temperature and density become too smallNo element heavier than Lithium
Building Nuclei by Fusion
p+n
HydrogenDeuterium=2H
3He
4He
7Li
+
+3He
2H
11
Phys 24 (F2011) Nucleosynthesis Sadoulet
Primordial Nucleosynthesis
2H bottleneck
Freeze out
n depleted by low T
• 4He very much more bound than 2H => higher equilibrium concentration at low temperature But cannot be reached because we have to go through 2-body reactions: deuterium bottleneck! Really starts at 0.150MeV ≈1 minute• everything is over in 5 minutes: stops below carbon Higher A elements will have to be produced in stars and supernovae
Dependent on expansion rate and density of p/n = Ωb
12
Phys 24 (F2011) Nucleosynthesis Sadoulet
DeuteriumLook for isotopic shift in absorption lines along
quasar line of sights e.g. Q1937-1009
D/H=2.3±0.3 10-5
Intergalacticgas cloud≈ primordial
13
Phys 24 (F2011) Nucleosynthesis Sadoulet
4HeMetal poor dwarf emission-line galaxies
But have to correct for production of 4He by stars
Isotov et al. Olive and Steigman
Production of Helium in stars14
Phys 24 (F2011) Nucleosynthesis Sadoulet
7LiObservation: absorption line in hot old stars
7Li/H=1.6 ± 0.4 10-10
A Li( ) ≡ 12 + log LiH
⎛ ⎝
⎞ ⎠
Sean G Ryan Astro-ph/00011230
Spite plateau
Mergers?
Age
15
Phys 24 (F2011) Nucleosynthesis Sadoulet
16
Baryonic Density
Fields &SarkarAstro-ph/0601504
Phys 24 (F2011) Nucleosynthesis Sadoulet17
Nucleosynthesis: A remarkable storyExcellent agreement between theory and observations
=> Universe was indeed very hot Very uniform ≠ quark hadron phase transition
Experimentally, need better measurements of deuteriumTheoretically, still problems with 3He (basically gave up) ,7Li
Very tight constraints
implies that dark matter is non baryonic
Three light neutrino families!D.Schramm et al. 15 years before confirmation by acceleratorVery tight constraint on number of massless particles.
Ωm ≈ 0.25 >>Ωb ≈ 0.04
e.g. CMBR Ωmh2 = 0.127
+0.007−0.013
>>Ωbh2 = 0.0223
+,0007−0.009
Nucleosynthesis Ωbh2 = 0.020 ± .002
Recently confirmed by Cosmic Microwave Background Ωbh2 = 0.0223 ± .0008
=>Ωb = 0.044 ± 0.008 rms dominated by uncertainty on Ho
Phys 24 (F2011) Nucleosynthesis Sadoulet18
A surprising but consistent picture
Ωmatter
ΩΛ
Phys 24 (F2011) Nucleosynthesis Sadoulet19
The Number of Neutrino Families