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Lecture 18 : The Early Universe II. Nucleosynthesis

ªThe structure of “normal” matterªNucleosynthesis and the hot big bangªThe density of baryonic matter in the

Universe, WB

ªStellar nucleosynthesisªRecombination and matter/radiation

decoupling

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A brief look at the stages of the Universe’s life…

ª Crude overview:ª t=0: The Big Bangª For first 400,000 yrs, an expanding “soup”

of tightly coupled radiation and matterª Earliest epochs were “extreme”

physicsª Then more “normal” physics: protons &

neutrons formª Then came nucleosynthesis

ª After 400,000 yrs, atoms form (“recombination”) and radiation and matter “decouple”

ª Following decoupling, matter and radiation evolve independently

ª Galaxies, stars, planets, etc can then form and evolve

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QuizªWhat determines what particles can be

spontaneously generated in the very early universe?

A. TemperatureB. CompositionC. DensityD. Luck

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QuizªWhat determines what particles can be

spontaneously generated in the very early universe?

A. TemperatureB. CompositionC. DensityD. Luck

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QuizªToday most of the mass-energy density of the

universe is in matter. What that always the case?

A. Yes, it was very dense at early timesB. No, the Big Bang was a very energetic

explosionC. Yes, mc2 is always a very big numberD. No, energy density grows faster with redshift

than matter density

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QuizªToday most of the mass-energy density of the

universe is in matter. What that always the case?

A. Yes, it was very dense at early timesB. No, the Big Bang was a very energetic

explosionC. Yes, mc2 is always a very big numberD. No, energy density grows faster with redshift

than matter density

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BACKGROUND: THE STRUCTURE OF MATTER

ªAtom is made up of…ªNucleus (very tiny but contains most off mass)ªElectrons (orbit around the nucleus)

ªAtom held together by attraction between positively-charged nucleus and negatively-charged electrons.

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Atomic nucleiª The nucleus is itself made up

of:ª Protons, p (positively charged)ª Neutrons, n (neutral; no charge)ª Collectively, these particles are

known as baryonsª p is slightly less massive than n

(0.1% difference)ª Protons and neutrons bound

together by the strong nuclear force (exchange of “gluons”)

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Elements & isotopesª Number of protons determines element:

ª Hydrogen – 1 protonª Helium – 2 protonsª Lithium – 3 protonsª Beryllium – 4 protonsª Boron – 5 protonsª Carbon – 6 protonª …

ª Number of neutrons determines the isotopeª e.g., for hydrogen (1 proton), there are three isotopes

ª Normal Hydrogen (H or p) – no neutronsª Deuterium (d) – 1 neutronª Tritium (t) – 2 neutrons

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ªThere’s one more level below this, consisting of quarks… ªProtons & Neutrons are made up of trios

of quarksªUp quarks & Down quarksªProton = 2 up quarks + 1 down quarkªNeutron = 1 up quark + 2 down quarksªThere are other kinds of quarks (strange,

charm, top, bottom quarks) that make up more exotic types of particles…

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Where did all the nuclei of elements come from?

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Nuclear fusion

ªHeavier nuclei can be built up from lighter nuclei (or free n, p) by fusion

ªNeed conditions of very high temperature and density to overcome repulsion of protons

ªThese conditions are present only in cores of stars and… in the early Universe!

ªThe original motivation of Gamow, Alpher, & Herman in advocating big bang was that it could provide conditions conducive to nuclear reactions

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Fission and fusion

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Nuclear fusion

ªHeavier nuclei can be built up from lighter nuclei (or free n, p) by fusion

ªNeed conditions of very high temperature and density to overcome repulsion of protons

ªThese conditions are present only in cores of stars and… in the early Universe!

ªThe original motivation of Gamow, Alpher, & Herman in advocating big bang was that it could provide conditions conducive to nuclear reactions

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Recall timeline for early Universe…ª At t=1s, neutrinos began free-streamingª At t=14s, e± stopped being created and destroyedª Temperature continued to drop until protons and neutrons, if

they combined, were not necessarily broken apart

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NUCLEOSYNTHESIS IN THE EARLY UNIVERSE

ªNucleosynthesis: the production of different elements via nuclear reactions

ªConsider universe at t=180s ª i.e. 3 minutes after big bangªUniverse has cooled down to 1 billion (109) KªFilled with

ªPhotons (i.e. parcels of electromagnetic radiation)ªProtons (p)ªNeutrons (n)ªElectrons (e)ª[also Neutrinos, but these were freely streaming]

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The first three minutes…ª Protons and Neutrons can fuse together to

form deuterium (d)

ªBut, deuterium is quite fragile…ªBefore t=180s, Universe is hotter than 1

billion degrees.ªHigh-T means that photons carry a lot of energyªDeuterium is destroyed by energetic photons as

soon as it forms

n + p®D+ g

D+ g ® n + p

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After the first 3 minutes…ªBut, after t=180s, Universe has cooled to the

point where deuterium can surviveªDeuterium formation is the first step in a

whole sequence of nuclear reactions:ªe.g. Helium-4 (4He) formation:

D+ D®T + p

T + D®4He + n

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ªAn alternative pathway to Helium…

ªThis last series of reactions also produces traces of left over “light” helium (3He)

D+ D®3He + n3He + D®4He + p

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ªFurther reactions can give Lithium (Li)

ªReactions cannot easily proceed beyond Lithium due to the “stability gap”… more about that later

4He + T®7Li + g

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ª If this were all there was to it, then the final mixture of hydrogen & helium would be determined by initial number of p and n.ª If equal number of p and n, everything would

basically turn to 4He… Pairs of protons and pairs of neutrons would team up into stable Helium nuclei.

ªWould have small traces of other speciesªBut we know that most of the universe is

hydrogen… why are there fewer n than p? What else is going on?

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Balance of p and n

Protons are more common than neutrons (86% of baryons are p, 14% are n) because:

1. Protons are lower mass thus favored energetically, so they were more abundant to begin with

2. Free neutrons decay quickly

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Neutron decayª Free neutrons (i.e., neutrons that are not

bound to anything else) are unstable!ªNeutrons spontaneously and randomly decay into

protons, emitting electron and neutrino

ªHalf life for this occurrence is 10.5 mins (i.e., take a bunch of free neutrons… half of them will have decayed after 10.5 mins).

n® p+ e +n

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ªWhile the nuclear reactions are proceeding, supply of “free” neutrons is decaying away.

ª So, speed at which nuclear reactions occur is crucial to final mix of elements

ªWhat factors determine the speed of nuclear reactions?ªDensity (affects chance of p/n hitting each other)ªTemperature (affects how hard they hit)ªExpansion rate of early universe (affects how

quickly everything is cooling off and spreading apart).

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ª Full calculations are complex. Need to:ªWork through all relevant nuclear reactionsªTake account of decreasing density and

decreasing temperature as Universe expandsªTake account of neutron decay

ª Feed this into a computer…ªTurns out that relative elemental abundances

depend upon the quantity WBH2

ªHere, WB is the density of the baryons (everything made of protons+neutrons) relative to the critical density.

WB =rBrcrit

=rB

3H02 /(8pG)

11/4/19 28WBh2Mpcskm

Hh//100

0=

From M.White’s webpage, UC Berkeley

Dependence of abundances on WBH2

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ªWe can use the spectra of stars and nebulae to measure abundances of elementsªThese need to be corrected for reactions in stars

ªBy measuring the abundance of H, D, 3He, 4He, and 7Li, we canªTest the consistency of the big bang model -- are

relative abundances all consistent?ªUse the results to measure the quantity WBh2

11/4/19 30WBh2

Results

ª All things considered, we have WBh2»0.019.

ª If H0=70km/s/Mpc,ª h=0.70ª WB»0.04

ª This is far below W=1!ª Baryons alone would

give open universe

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€

ΩB ≈ 0.049Planck results, 2013

QuizªPrimordial nucleosynthesis is done in first

few minutes after the Big Bang. Why?A. There are only so many protons to react

and create heavy elementsB. The universe is expanding and coolingC. The universe is expanding and becoming

less denseD. Both B and C

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QuizªPrimordial nucleosynthesis is done in first

few minutes after the Big Bang. Why?A. There are only so many protons to react

and create heavy elementsB. The universe is expanding and coolingC. The universe is expanding and becoming

less denseD. Both B and C

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Quiz

ªWhy isn’t He the most abundant element in the universe?

A. The Big Bang wasn’t hot enoughB. There wasn’t enough time to build He

before it cooledC. Neutron decay removed too many neutronsD. The Big Bang wasn’t dense enough

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Quiz

ªWhy isn’t He the most abundant element in the universe?

A. The Big Bang wasn’t hot enoughB. There wasn’t enough time to build He

before it cooledC. Neutron decay removed too many neutronsD. The Big Bang wasn’t dense enough

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End result of big bang nucleosynthesis

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How are other elements formed?

ªBig Bang Nucleosynthesis produces most of the hydrogen & helium observed today.

ªBut what about other elements?ªThere are naturally occurring elements as heavy

as UraniumªSome elements (e.g., Carbon, Nitrogen, Oxygen)

are rather plentiful (1 atom in every 105 atoms)ªAstronomers believe these elements were formed

in the cores of stars long after the big bang ªTheory of stellar nucleosynthesis was first worked out

by Burbidge, Burbidge,Folwer, & Hoyle in 1957

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Fission and fusion

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Fission, fusion, and nuclear mass

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Fusion of more and more massive nuclei

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Elemental abundance in the Sun

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Stellar “burning”ª In the normal life of a

star (main sequence)…ª nuclear fusion turns

Hydrogen into Helium

ª In the late stages of the life of a massive star…ª Helium converted into

heavier elements (carbon, oxygen, …, iron)

ª “Triple-alpha” process bridges stability gap from Be to C

ª At end of star’s life, get an onion-like structure (see picture to right)

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Iron, the most stable nucleus

ªWhat’s special about iron?ª Iron has the most stable nucleusªFusing hydrogen to (eventually) iron releases

energy (thus powers the star)ªFurther fusion of iron to give heavier elements

would require energy to be put in…ªCan only happen in the energetic environment of

a supernova explosion

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Proton-electron interaction produces a neutron (and other stuff)

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Core collapse

Boom!(the star explodes)

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Supernovae briefly outshine their parent galaxies

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ª The Crab Nebula is the remnant of a SN that exploded in 1054 AD

ª We directly see a new generation of heavy elements

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Where did all the nuclei of elements come from?

https://www.caltech.edu/about/news/caltech-led-teams-strike-cosmic-gold-80074

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After nucleosynthesisª Nucleosynthesis was essentially

completed by t=30min ,with free neutron abundance down to <1%

ª Universe continued to expand, with energy density in radiation dropping more rapidly than energy density in matter

ª After t=1012s (30,000yrs), when rrad fell below rmatter , the Universe ceased to be radiation-dominated era and entered the matter-dominated era

ª At this time, the expansion rate of the Universe changed from Rµt1/2 to R µt2/3

ª With faster expansion rate, the radiation temperature began to drop more rapidly

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Recombination and beyondª When radiation temperature reached T=3000K, at t=400,000

yrs, photons were no longer energetic enough to keep electrons from binding to protons

ª This marked the time of “recombination”: ionized plasma of electrons and protons (with some Helium nuclei) combined into mostly neutral hydrogen atoms (with some Helium atoms)

ª Photons interact less with bound electrons than free electrons, so radiation began to stream freely after recombination

ª This marked the event of decoupling of matter and radiationª After decoupling, radiation has been freely-streaming through

Universe. CBR is the redshifted remnant of radiation that was last “in contact” with matter at z~1100

ª Matter also began to evolve freely at that time; when it finally became cool enough, galaxies began to form (more later!)

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Next time…

ªWhat do more observations tell us about the parameters for the real Universe?