Primordial Nucleosynthesis - Berkeley Cosmology...

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


Why the Big Bang?3 pillars

Hubble expansionCosmic Microwave backgroundPrimordial D, He ,Li

Hubble expansion

2

v = Hr

∝ log distance( )

log velocity( )


Cosmic Microwave BackgroundCosmic Microwave background

Very uniform radiation fromprimordial fireball

3


NucleosynthesisPrimordial abundance of light elements

4


+

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


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


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


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


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


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


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


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


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


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


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


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


A surprising but consistent picture

Ωmatter

ΩΛ


The Number of Neutrino Families

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