AS2001

Chemical Evolution

of the UniverseKeith Horne

315a

kdh1@st-and.ac.uk

http://star-www.st-and.ac.uk/~kdh1/ce/ce.html

Origin of Chemical Elements

• Big Bang Nucleosynthesis: t ~ 3 min 1H 2D 3He 4He … 7Li

• Fusion in stars: We are stardust! … 12C 14N 16O … 56Fe

• Fusion in supernova explosions (M* > 8 Msun)

… 56Fe … 235U

• Abundances rise as each generation of stars pollutes the interstellar medium (ISM).

Cosmology Lite• 1925 Galaxy redshifts

– Isotropic expansion. ( Hubble law V = H0 d )– Finite age. ( t0 =13 x 109 yr )

• 1965 Cosmic Microwave Background (CMB)– Isotropic blackbody. T0 = 2.7 K– Hot Big Bang

• 1925 General Relativity Cosmology Models : – Radiation era: R ~ t 1/2 T ~ t -1/2

– Matter era: R ~ t 2/3 T ~ t -2/3

• 1975 Big Bang Nucleosynthesis (BBN)– light elements ( 1H … 7Li ) t ~ 3 min T ~ 109 K

– primordial abundances (75% H, 25% He) as observed!

€

λ = λ 0 1+ z( ) V = c z

Isotropic Expansion

V (

km/s

)

€

Hubble law :

V = H0 d

Hubble constant :

H0 ≈ 500 km s−1Mpc−1

WRONG because distances ~10x too small !

d (Mpc)

HST Key Project

Freedman et al. 2001 ApJ 553, 47.

€

H0 ≈ 72 ± 3 ± 7 km s-1 Mpc−1

Hubble Law --> Finite age.

€

V = H0 d

t0 ≈d

V=

1

H0

=1Mpc

72 km/s

⎛

⎝ ⎜

⎞

⎠ ⎟3×1019km

Mpc

⎛

⎝ ⎜

⎞

⎠ ⎟

1 yr

3×107s

⎛

⎝ ⎜

⎞

⎠ ⎟

≈13×109 yr =13 Gyr.

Gravity decelerates :

t0 ≈2

3

1

H0

.

€

t€

d

€

t0

Hubble Law --> Finite age.

€

V = H0 d

t0 ≈d

V=

1

H0

=1Mpc

72 km/s

⎛

⎝ ⎜

⎞

⎠ ⎟3×1019km

Mpc

⎛

⎝ ⎜

⎞

⎠ ⎟

1 yr

3×107s

⎛

⎝ ⎜

⎞

⎠ ⎟

≈13×109 yr =13 Gyr.

Gravity decelerates :

Dark Energy accelerates

t0 >2

3

1

H0

.

€

t€

d

acceleration

€

t0

Universe expands and cools. 4 forces --> 4 phase transitions. elementary particle soup ( quarks, gluons, leptons, bosons )1. Strong force ( quarks exchange gluons ): quarks -> hadrons ( baryons (qqq), mesons (qq) ) e.g. protons and neutrons ( T ~ 1012 K, t ~ 10-4 s )2. Weak force ( exchange of vector bosons W+,W-,Z0 ): baryons -> atomic nuclei ( ~ 109 K, ~ 3 min )3. Electro-magnetic force ( photons ) : nuclei+electrons -> neutral atoms ( 3000 K, 3x105 yr )4. Gravity ( gravitons ): galaxies of stars, some with planets, some with life.

( --> black holes --> evaporate to elementary particles.)

Self-assembly of complex structures

€

kT ~ E

Universe filled with uniform density fluid [ OK on large scales > 100 Mpc ]

Density Energy density

Critical density: 3 components: 1. Radiation 2. Matter “Dark Matter” baryons 3. “Dark Energy”

Total

€

ΩR ≈ 5 ×10−5

Cosmological Models

€

ΩM ~ 0.3

€

ΩΛ ~ 0.7

€

ρ =Ω ρc

€

ε =ρ c 2

€

ρc ≡3 H0

2

8π G≈10−26kg m−3 ≈

1.4 ×1011Msun

(Mpc)3

€

ΩB ~ 0.04

€

Ω=ΩR + ΩM + ΩΛ =1€

ΩD ~ 0.26

Only ~4% is matter as we know it!

€

{

€

escape velocity :

Vesc2 =

2 G M

R=

2 G

R

4π R3ρ

3

⎛

⎝ ⎜

⎞

⎠ ⎟=

8π G R2ρ

3

Hubble expansion :

V = H0 R

critical density :

Vesc

V

⎛

⎝ ⎜

⎞

⎠ ⎟2

=8π Gρ

3 H02 =

ρ

ρ c

ρ c =3 H0

2

8π G

Critical Density• Newtonian analogy: R

M

€

V < Vesc

€

V > Vesc

€

t

€

R

Cold Matter: ( m > 0, p << mc )

Radiation: ( m = 0 ) Hot Matter: ( m > 0, p >> mc )

€

E ≈ m c 2 = const

εM ≈N m c 2

R3∝ R−3

€

λ ∝ R (wavelengths stretch) :

E = h ν =h c

λ∝ R−1

εR =N h ν

R3∝ R−4

€

volume R3

N particles

€

particle mass m momentum p

energy E = hν = m2c 4 + p2c 2 = m c 2 +p2

2m+ ...

3 Eras: radiation…matter…vacuum

€

radiation : ρ R ∝ R−4

matter : ρ M ∝ R−3

vacuum : ρ Λ = const

€

a ≡R

R0

=1

1+ z

ρ =ρ R ,0

a4+

ρ M ,0

a3+ ρ Λ

ρ R = ρ M at a ~ 10−4 t ~ 104 yr

ρ M = ρ Λ at a ~ 0.7 t ~ 1010 yr

Rlog

ρlog

tlog

Rlog

€

e t

t 2/1

t 3/2

€

ρΛ

€

ρM

€

ρR

Penzias & Wilson

Discovered the CMB1965 The Bell Lab antenna

The CMB spectrum

A perfect Blackbody! 1992 NASA - COBE

COsmic Background Explorer

1992 COBE

€

temperature ripples : ΔT

T~ 10−5

angular resolution : Δθ ≈ 7o

whole sky map

2004 WMAPWilkinson Microwave Anisotropy Probe

€

preferred angular scale : Δθ ≈1o ⇒ Ω ≈1.0

The seeds of galaxies

Cosmic Microwave Background (CMB)

€

Blackbody temperature T = 2.728 K

energy density εν =8π h

c 3

ν 3

exp hν kT( ) −1

ε = εν dν∫ = α T 4 ≈ 4.2 ×10−14 J m−3(Tut. sheet 1)

mean photon energy hν ≈ 3 k T = 7 ×10−4 eV

photon density nγ = εhν

≈ 4 ×108 photons

m3

baryon density nB = ρ Bmp

≈ 0.2baryons

m3

ratio photons

baryons~ 109 Why?

Adiabatic Expansion preserves the Blackbody spectrum

€

T ∝1

Rhν ∝T ε ∝T 4

€

ν€

εν

€

×10−9

€

×10−3€

T

T0

=2700 K

2.7 K

Cooling History: T(t)

€

Radiation era : 1 s

t

⎛

⎝ ⎜

⎞

⎠ ⎟

1/ 2

≈T

2 ×1010K=

k T

2 MeV

log t

log

T

€

~ 3×1011 s

~ 104 yr

€

35,000 K

€

Matter era : 1010 yr

t

⎛

⎝ ⎜

⎞

⎠ ⎟

2 / 3

=T

2.7 K€

matter - radiation equality : ρ M = ρ R

In the early Universe( kT > E ) photons break up atomic nucleibinding energies: Deuterium ~ 2 MeV Iron ~ 7 MeV

Earlier still, neutrons and protons break into quarks

mass energies: neutron ~ 939.6 MeV proton ~ 938.3 MeV

This takes us back to the quark soup!

Next time we will run the clock forward!

€

T ~ 1010 K t ~ 1 s

€

T ~ 1012 K t ~ 10−4 s€

T ~ 109 K t ~ 100 s