The Hot Big BangASTR 2120

Sarazin

Final ExamThursday, May 7, start anytime before 8

pm4 hoursYou may not consult the text, your notes,

or any other materials or any personYou can use three of 3x5 cards (both

sides) or 6x5 paper (one side) with equations only

Have pencils, paper, calculator

Final Exam~2/3 Quantitative Problems (like homework

problems)~1/3 Qualitative Questions

Multiple Choice, Short Answer, Fill In the Blank

Test done with Collab Tests & Quizzes ToolQuantitative Problems:

Do work on work sheetsType Answers in Answer Boxes in Collab

Scan/photo worksheets and equation sheets, either upload at Collab Assignments “Final Exam Work Sheets” tool or email to me sarazin@virginia.edu

Final Exam (Cont.)

Material:Final exam will cover the entire semester

Chapters (5), (7), 13-24Stars, Sun ® Cosmology

Extra emphasis on material not on first two testsExtragalactic Distances, Clusters of Galaxies

(problems), AGNs, CosmologyChapters 21, 23, 24Homeworks 9-11

Know pc, AU, Msolar, Lsolar, Rsolar, H0, TCMB

Final Exam ReviewReading DayWednesday, May 610 am – noon

The Hot Big BangASTR 2120

Sarazin

Hot Big Bang

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particle + antiparticle ↔ 2γExample : p + p ↔ 2γN particles ≈ Nantiparticles ≈ Nγ

Bubbling sea of particles and antiparticlesp, p ,n,n ,e− ,e+ ,γ,ν,ν ,π,Ω− , . . . etc.

Thermal History of Universe

t ≲ 10-6 sec, T ≳ 1013 K

Tγ ≈1010 K t−1/2 (t in sec)for Tγ >10, 000 K

10-5 sec ≲ t ≲ 1 sec, 1013 K > T ≳ 1010 KCan’t make most particlesa) Unstable particles decay

Exception: neutron, t1/2 = 11 minutes

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p, p ,n,n ,e− ,e+ ,γ,νe,ν e,νµ ,ν µ ,ντ ,ν τ ,(dark matter particles)

Thermal History of Universe10-5 sec ≲ t ≲ 1 sec, 1013 K > T ≳ 1010 K

b) Antimatter annihilates

If matter/antimatter symmetric, this is very efficientNp/Ng ≲ 10-18, not 10-9 as observed (homework)

If pure matter, Np ~ Ng initially, would still be trueNeed small, but non-zero asymmetry

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p + p → 2γ (no reverse)n + n → 2γ

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N p − N p

N p

~10−9

Thermal History of Universe10-5 sec ≲ t ≲ 1 sec, 1013 K > T ≳ 1010 K

Existence of matter today requires Universe had a small matter/antimatter asymmetry by 1 sec

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N p − N p

N p

~10−9

Thermal History of Universe10-5 sec ≲ t ≲ 1 sec, 1013 K > T ≳ 1010 K

c) Electrons and neutrinos still producedkT >> mec2

d) Protons and neutrons in equilibrium

View p+ & n as different states (isotopic spin) of same particle

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e−,e+ ,νe,ν e

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p+ + e− ↔ n+νep+ +ν e ↔ n+ e+ , etc.

Thermal History of Universe10-5 sec ≲ t ≲ 1 sec, 1013 K > T ≳ 1010 K

View p+ & n as different states (isotopic spin) of same particle

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Nn

Np

= e−ΔE /kT = e−Δmc2 /kT = e−(mn −mp )c

2 /kT

n

p

ΔE=(mn−mp) c2

Thermal History of Universe

1 sec ≲ t ≲ 103 sec, 1010 K > T ≳ 3 x 108 K(mn-mp)c2/k ~ 1010 K

Nn/Np decreasesAfter a few seconds, T < mec2/k ~ 6 x 109 K, can’t

make electrons anymore

Reactions between n, p stop

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Nn

Np

= e−ΔE /kT = e−Δmc2 /kT = e−(mn −mp )c

2 /kT

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e+ + e− → 2γ (no reverse)

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n+ e+ ↔ p+ +ν e, etc. stop

Thermal History of Universe

1 sec ≲ t ≲ 103 sec, 1010 K > T ≳ 3 x 108 KNeutron to proton ratio freezes out at

What happens to neutrons?

If nothing else happened, neutrons would decay away

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Nn

Np

= e−ΔE /kT = e−Δmc2 /kT = e−(mn −mp )c

2 /kT

€

n→ p+ + e− +ν e, beta decay, t1/2 =11 minutes€

Nn ≈ Np / 8

Fusion During Big Bang1 sec ≲ t ≲ 103 sec, 1010 K > T ≳ 3 x 108 K

rbaryons ≲ 10-2 gm/cm3

Hotter, lower density than center of star, but not completely dissimilar

Differences from star:a) Very little time (minutes)

No weak reactionsNo pp reaction (1010 years in Sun)

b) Free neutronsNever true in stars except during SN, only

last 11 minutes

Fusion During Big Bang

Tritium

p+ n→ 2H+γ2H+ n→ 3H+γ2H+ p→ 3He+γ3He+ n→ 4He+γ3H+ p→ 4He+γ 3 H→ 3 He+ e− +νe

t1/2 =12 years

All tritium è Helium-3

Fusion During Big Bang

Fusion During Big Bang

and similar

No significant reactions beyond 4HeIn stars, requires Triple-Alpha reaction, very slow,

not enough time in Big BangLose energy between 4He and 12C, only reaction is

3 4He ® 12C

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p+ n→ 2H+γ2H + p→ 3He+γ3He +n→ 4He+γ

Fusion During Big Bang

3a reaction

Fusion During Big Bang

and similar

No significant reactions beyond 4HeIn stars, requires Triple-Alpha reaction, very slow,

not enough time in Big BangLose energy between 4He and 12C, only reaction is

3 4He ® 12C

€

p+ n→ 2H+γ2H + p→ 3He+γ3He +n→ 4He+γ

Fusion During Big Bang

Fusion During Big BangFusion in Big Bang makes

H & 4HeTraces of 2H & 3HeTiny bits of 6Li, 7Li, 7Be

Fusion During Big BangHow much helium?

Fusion reactions up to helium very efficientAll neutrons ® heliumInitially, Nn ~ Np / 8Do arithmetic (homework problem), findY = 0.22 (mass fraction of helium)X = 0.78 (mass fraction of hydrogen)

Agree with values in oldest stars

Fusion During Big BangHow much 2H (deuterium), 3He (helium-3), Li?

Fusion reaction rate depends on density of baryonsrbaryons

High density = less 2H, 3He, more LiLow density = more 2H, 3He, less Li

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p+ n→ 2H+γ2H + p→ 3He+γ3He +n→ 4He+γ

Fusion During Big Bang

Fusion During Big BangGives rbaryons at t = 1 sec, T = 1010 K

rbaryons (today) = rbaryons (1 sec) x (r / ro)3

= rbaryons (1 sec) x (1 + z)-3

T (1 sec) = T (today) x (1 + z)(1 + z ) = 1010 K / 2.725 Krbaryons (1 sec) gives rbaryons (today)!!

Fusion During Big Bang

Fusion During Big BangGives rbaryons at t = 1 sec, T = 1010 K

rbaryons (today) = rbaryons (1 sec) x (r / ro)3

= rbaryons (1 sec) x (1 + z)-3

T (1 sec) = T (today) x (1 + z)(1 + z ) = 1010 K / 2.725 Krbaryons (1 sec) gives rbaryons (today)!!rbaryons (today) = 3.5 x 10-31 gm/cm3

W (baryons) = rbaryons / rcrit = Wb = 0.046

Fusion During Big BangWb = 0.046 << WM

Dark Matter not anything which was ordinary matter at t = 1 second

Not planets, brown dwarfs (MACHOs)Not black holes from stars or collapse of matter

Dark Matter = weakly interacting particles made in Big Bang!

Cosmological NeutrinosIn early Universe

Decouple at t ~ 1 sec

Nn ~ Ng Tn = (4/11)1/3 TCMB = 1.95 KNeutrinos stable (except for oscillations), still

aroundCosmological background of neutrinosIf mass = 0, just like photons

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2γ ↔ e+ + e− ↔νe +ν e (etc.)

Neutrino Dark Matter?Oscillations of neutrinos ® must have massIf mn > 10 eV, could be Dark MatterTritium decay, cosmology, particle experiments ®

mn < 1 eVProbably not dark matter, but example of potential weakly

interacting dark matter particles from Big Bang

Made in Big Bang• Hot Dark Matter

• kT >> mc2 when decoupled ® v ~ c when formed• mc2 ~ eV• Example: neutrinos• Problem: hard to get to cluster, form superclusters ®

clusters ® galaxies ® stars• But, galaxies old, structure appears to grow small to large

Probably NOT Hot Dark Matter

Particle Dark Matter

• Cold Dark Matter• kT << mc2 when decoupled ® v << c when formed• mc2 ~ 1-1000 GeV = 1 – 1000 mpc2

• Exception: axion• Examples:

• WIMPs = Weakly Interacting Massive Particles• lightest supersymetric particle (gravitino,

neutralino)• axions

• Structure grows hierarchically, small to largeCurrently the favored form of DM

Particle Dark Matter

Leading candidate is lightest supersymmetricparticleSupersymmetry (SUSY):

Every boson (integer spin) has a fermion (half integral spin) supersymmetric partner

Example: photon (spin 1) / photino (spin ½)Every fermion has a boson supersymmetricpartner

Example: electron (spin ½) / selectron (spin 0)

WIMPs

Supersymmetry particles only decay into supersymmetric particlesè Lightest supersymmetric particle is stable, could

be Dark Matter

Leading candidates:gravitino = SUSY partner of graviton, carrier of

gravity forceneutralino = SUSY partner of W0,Z, B, Higgs

WIMPs

Another particle outside of the standard model is the axionAssociated with symmetry which keeps the strong interaction

from violating CP invarianceWeakly interacting, light (10-6 to 1 eV), produced in Big BangCandidate Dark Matter particlesCan be detected due to effect on photons in a strong

magnetic fieldAlso, super-partners (axino, saxino) might be LSP, also Dark

Matter candidates

Axions

• Warm Dark Matter• mc2 ~ keV• Examples: Sterile neutrino

Normal Neutrinos: left handedSterile Neutrinos : right handed

Only left handed neutrinos interact with matter

Particle Dark Matter

Sterile neutrino Normal neutrino

Later Thermal Historyt ~ 50,000 years, z ~ 3600, T ~ 10,000 K

End of radiation-dominated era

t = 370,000 years, z =1100 , T = 3000 KRecombinationPrior to this, matter is mainly p+ & e-

At recombination, p+ + e-® H (hydrogen atoms)

Recombination

Recombinationt = 370,000 years, z =1100 , T = 3000 K

Prior to recombination, p+ & e-

Matter and radiation tightly coupled by electron scattering

e-photon

Recombinationt = 370,000 years, z =1100,

T = 3000 KMatter and radiation decoupled

Matter can separate from radiation, form structures (galaxies, clusters, etc.)

CMB photons all come directly from recombination era, “last scattering surface”

Epoch of ReionizationIntergalactic medium today is completely ionized

againWhen did this happen?

WMAP: started at z ~ 20Quasar spectra: complete by z ~ 6

Due to UV from:stars in newly formed galaxies?quasars from supermassive BHs in centers of newly

formed galaxies?

Epoch of Reionization21 cm line from hydrogen

CHIME Radio Telescope

Later Thermal Historyt ~ 50,000 years, z ~ 3600, T ~ 10,000t = 370,000 years, z =1100 , T = 3000 K

RecombinationT = 9 billion years, z ~ 1, T ~ 6 K

Epoch of Dark Energy Accelerated Expansion

Dark Energy – Accelerated Expansion

tor / ro

t

deceleration

acceleration

Large Scale Structure

13.7 billion years ago

How does the Universe go from looking like this...To looking like this….?

13.7 billion years ago13.5 billion years ago12.7 billion years ago

Millennium Simulation

9 billion years agoNOW

The Universe Evolves

Gravity Rules

Structure FormationNeed fluctuations in density of 10-5 at recombination to

make all the galaxies and clusters of galaxies todayPrediction confirmed by WMAP and Planck

13.7 billion years ago13.5 billion years ago12.7 billion years ago

Millennium Simulation (Springel et al. 2005)

9 billion years agoNOW

Millennium Simulation Sample