1
PHYS-4XXX
Nucleosynthesis and the Chemical Evolution of the Universe
Simon Driver ICRAR Ground Floor
[email protected] 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
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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 %& $1.0The seeds of galaxies
2013 Planck
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Cosmic Microwave Background (CMB)
!
Blackbody temperature T = 2.728 K
energy density "# =8$ 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