1

PHYS-4XXX

Nucleosynthesis and the Chemical Evolution of the Universe

Simon Driver ICRAR Ground Floor

Simon.Driver@uwa.edu.au 12 Lectures

Course outline Lecture 1: The expanding universe, and the hot big bang Lecture 2: Fundamental particles in the hot Big Bang Lecture 3: Big Bang Nucleosynthesis Lecture 4: Matter-Radiation decoupling and the CMB Lecture 5: Galaxy Formation Lecture 6: Jeans mass Lecture 7: The closed box model Lecture 8: The IMF and Supernova Lecture 9: Supernova rates and the yield Lecture 10: Chemical evolution of galaxies Lecture 11: Ages and metallicites Lecture 12:

The elemental abundance of the solar system (Sun)

Origin of Chemical Elements •  Big Bang Nucleosynthesis: t ~ 3 min

à 1H 2D 3He 4He … 7Li •  Fusion in stars: We are stardust!

à … + 12C 14N 16O … 56Fe

•  Fusion in supernova explosions (M* > 8 Msun) à … 56Fe … 235U

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

2

Cosmology Lite •  Pre-1900 Olber’s Paradox

–  Why is the sky dark at night, infinite fuel supply of stars •  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!

!

" = "0 1+ z( ) V = c z

Isotropic Expansion

Hubble law:V = H0 d

Hubble constant:H0 ! 72 km s"1Mpc"1

V (k

m/s)

d (Mpc)

HST Key Project

Freedman et al. 2001 ApJ 553, 47.

!

H0 " 72 ± 3± 7 km s-1 Mpc#1 Hubble Law à Finite age. V = H0 d

t0 !dV=

1H0

=1 Mpc

72 km / s"

#$

%

&'

3(1019 kmMpc

"

#$

%

&'

1 yr3(107s"

#$

%

&'

!13(109 yr =13 Gyr.

Gravity decelerates:

t0 !23

1H0

= 8.7Gyr

!

t!

d

!

t0

Slope = d/t = V

3

Hubble Law à Finite age. V = H0 d

t0 !dV=

1H0

=1 Mpc

72 km / s"

#$

%

&'

3(1019 kmMpc

"

#$

%

&'

1 yr3(107s"

#$

%

&'

!13(109 yr =13 Gyr.

Gravity decelerates:Dark Energy accelerates

t0 >23

1H0

=13.7Gyr

!

t!

dacceleration

!

t0

Implications of an expanding Universe

•  Expansion à Universe was smaller, denser, and hotter •  Why? Lets think about the contents •  Contents:

–  Dark Energy (Intrinsic property of space-time?) –  Dark Matter (WIMPs) –  Matter (baryons) –  Radiation (photons)

•  How does the density (importance) of each of these contents scale with the expansion?

•  Need to know how density scales with the expansion (scale) factor

An adiabatic expansion?

•  Assume Universe is a uniform medium (fluid) •  1st Law of thermodynamics gives:

•  i.e., expansion is lossless for conservation of energy in a closed system

dE + pdV = TdS = 0

0.00005% Photons

What makes the Universe

Tick (today)

4

!dE = "pdV

But, E =mc2 and V =43!R3 and m = "V

# d 43!R3"c2$

%&'

()= "pd 4

3!R3$

%&'

()#

d("R3)dt

= "pc2d(R3)dt

For Dark Energy:# "=constant (by definition if property of space-time, i.e., trad. cosmological constant)For Dark and normal matter:p * 0 (if uniform, diluted and cold)

!d("R3)dt

= 0, or "+R"3

For Radiation :p = !c2 / 3

d(!R3) = ! !3d(R3)

d(!R3)+ !3d(R3) = 0

!d(R3)+ R3d(!)+ !3d(R3) = 0

R3d(!)+ 43!d(R3) = 0

Now dR3 = 3R2dR, i.e., x = R3, dxdR

= 3R2

4R2!dR+ R3d! = 04R3!dR+ R4d! = 0d(R4!) = 0!"R!4

What made the Universe

Tick (13.7Gyr ago)

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

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

!

E " m c 2 = const

#M "N m c 2

R3$R%3

!

" #R (wavelengths stretch) :

E = h $ =h c"#R%1

&R =N h $R3 #R%4

!

volume R3

N particles

!

particle mass m momentum p

energy E = h" = m2c 4 + p2c 2 = m c 2 +p2

2m+ ...

Energy Density of expanding box

5

3 Eras: radiation…matter…vacuum

!

radiation : "R #R$4

matter : "M #R$3

vacuum : "% = const

!

a " RR0

=1

1+ zz = redshift

# =#R ,0

a4 +#M ,0

a3 + #$

#R = #M at a ~ 10%4 t ~ 104 yr#M = #$ at a ~ 0.7 t ~ 1010 yr

Rlog

!log

tlog

Rlog

!

et

t 2/1

t 3/2

!

"#

!

"M!

"R

6

Penzias & Wilson Discovered the CMB

1965 The Bell Lab antenna

The CMB spectrum A perfect Blackbody!

1992 NASA - COBE COsmic Background Explorer

1992 COBE

!

temperature ripples : "TT

~ 10#5

angular resolution : "$ % 7o

whole sky map

2004  WMAP Wilkinson Microwave Anisotropy Probe

!

preferred angular scale : "# $1o %& $1.0The seeds of galaxies

2013 Planck

7

Cosmic Microwave Background (CMB)

!

Blackbody temperature T = 2.728 K

energy density "# =8$ hc 3

# 3

exp h# kT( ) %1

" = "# d#& =' T 4 ( 4.2 )10%14 J m%3(Tut. sheet 1)

mean photon energy h# ( 3 k T = 7 )10%4 eV

photon density n* = "h# ( 4 )108 photons

m3

baryon density nB = +B mp( 0.2 baryons

m3

ratio photonsbaryons

~ 109 Why?

Adiabatic Expansion preserves the Blackbody spectrum

!

T " 1R

h# "T $ "T 4

!

"!

"#

!

"10#9

!

"10#3!

TT0

=2700 K2.7 K

Cooling History: T(t)

!

Radiation era : 1 st

"

# $

%

& '

1/ 2

(T

2 )1010K=

k T2 MeV

log t

log

T

!

~ 3"1011 s~ 104 yr

!

35,000 K

!

Matter era : 1010 yrt

"

# $

%

& '

2 / 3

=T

2.7 K!

matter - radiation equality : "M = "R

In the early Universe ( kT > E ) photons break up atomic nuclei binding 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 lecture 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

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Universe expands and cools. 4 forces 4 phase transitions when elementary particle soup ( quarks, gluons, leptons, bosons ) 1. Strong force ( quarks exchange gluons ) : quarks à 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 ) : neutrons à protons baryons à 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. ( à black holes à evaporate to elementary particles.)

Self-assembly of compact structures

!

kT ~ EAssume a 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

!

"R # 5 $10%5

Cosmological Models

!

"M ~ 0.3

!

"# ~ 0.7

!

" =# "c

!

" = # c 2

!

"c #3H0

2

8$ G%10&26kg m&3 %

1.4 '1011Msun(Mpc)3

!

"B ~ 0.04

!

" ="R +"M +"# =1!

"D ~ 0.26

Only ~4% is matter as we know it!

!

{

!

escape velocity :

Vesc2 =

2G MR

=2GR

4" R3#3

$

% &

'

( ) =

8" G R2#3

Hubble expansion :V = H0 R

critical density :

Vesc

V$

% &

'

( )

2

=8" G#3H0

2 =##c

#c =3H0

2

8" G

Critical Density •  Newtonian analogy: R

!

"

!

V <Vesc

!

V >Vesc

!

t

!

R