The Origin of Elements

Last: 10. The Lives of Stars Next: 12. Structure of the Milky Way

The relentless force of gravity determines the fate of the Sun and other stars. But in struggling against gravity, stars may return matter to interstellar space; moreover, they accomplish what alchemists long-ago failed to do: transmute common elements into rare ones.

Topics

Reading

  13.1a-d The Death of the Sun   p. 298-302
  13.2a-e Supernovae: Stellar Fireworks!   p. 303-311

The Life Cycle the Sun


Life cycle of the Sun
Stellar evolution [Wikipedia]

A star with the same mass as the Sun enjoys a long and stable life on the main sequence, but once hydrogen burning in the core comes to an end the star starts to change.

Red Giants

When all the hydrogen in a star's core has been burned to helium, the star begins a dramatic transformation.

An inert helium (He) core sits at the star's center. The core is hot, so energy flows out; in response, it contracts (black arrows), releases gravitational energy, and gets even hotter! Hydrogen burning (4 H → He) continues in a shell around the core.

The total amount of energy produced by the star is now much greater than it was when the star was on the main sequence, and the envelope the star must expand (red arrows) to handle this energy flow. The surface temperature drops from white-hot to red-hot.

  Evolution after H exhaustion

From an external point of view, the star becomes both brighter and cooler; it swells up to about 100 times its main sequence size, becoming a red giant.

Helium Burning

When the core reaches 108 K, helium burning can begin. (Sometimes called the ``triple-alpha process'' because it involves 3 ``alpha particles'' or He nuclei).

Compared to hydrogen burning, helium burning is inefficient. The reaction 3 He → C converts only 0.07% of the mass to energy; that's just a tenth the yield of hydrogen burning.

  The 3He -> C reaction
Triple-alpha process [Wikipedia]

Under slightly hotter conditions, helium and carbon can burn to produce oxygen. The reaction 4 He → O converts about 0.1% of the mass to energy.

When He begins burning in a small (solar-mass) star, it temporarily reverses some of the changes the star's structure. The core expands, the envelope contracts, and the total luminosity drops because the helium-burning core can regulate its energy output. Such a star is called a horizontal branch star.

Late Stages of Low-Mass Stars

A low-mass star has four stages of nuclear burning: main sequence (MS), red giant (RG), horizontal branch (HB), and asymptotic giant (AG).   Key stages in life of solar-mass star

At each stage, key properties of a M = 1 MSun are:

Stage Age
(109 yr)
Diam.
(AU)
Lumin.
(LSun)
Nuclear Reactions
MS 10.9 0.01 2 4 H → He (core)
RG 12.2 1 2000 4 H → He (shell)
HB 12.3 0.1 100 4 H → He (shell) 3 He → C (core)
AG 12.4 2 5000 4 H → He (shell) 3 He → C (shell)

Planetary Nebulae

Helium shell burning in an asymptotic giant star is unstable; instead of burning steadily as a core does, the shell generates brief bursts of power. The star's envelope surges outward with each burst, and some gas is ejected into space.


The Ring Nebula
 
Helium-shell flashes
The Physical Universe, Ch. 8, Fig. 9

The result is called a planetary nebula (though it has nothing to do with planets); the gas fluoresces in the intense UV emitted by the central star, creating a beautifully symmetric nebula.

White Dwarfs

Why doesn't the core of an asymptotic branch star continue contracting, and heat up enough to burn C/O?

A new form of pressure stops contraction.

Core ejects envelope (→ planetary nebula) and remains behind as central star:

No energy sources -- bare core gradually cools off.

Degeneracy Pressure

New form of pressure due to QM behavior of electrons.

Recall ordinary gas pressure implies atoms move with speeds:

v  ∝  1 

R 
 .

QM rules imply electrons must move with speeds

v  ∝  1 

R 
 .

As R → 0, electron speed becomes much greater than atom speed. Eventually, energy cost of promoting electrons to higher speeds exceeds energy release from contraction, and contraction halts.

Sub-Stellar Objects

Degeneracy pressure explains why, for example, a planet like Jupiter does not get hot enough inside to fuse hydrogen and become a star. Jupiter started contracting under its own gravity, but became degenerate and stopped before it could ignite hydrogen.

Objects smaller than 0.08 MSun never get hot enough to burn ordinary hydrogen, but deuterium -- a rare form of hydrogen -- does burn at lower temperatures and provides brown dwarfs with a modest energy source. The smallest objects which can ignite deuterium are about 0.013 MSun, or roughly 13 MJupiter.

Path of the Sun on the Temperature-Luminosity Diagram

The Temperature-Luminosity Diagram (Review)

 
HR Diagram of Hipparcos stars
Hertzsprung-Russell diagram [Wikipedia]

Origin of Elements: Supernovae

Main types of supernovae

There are two possible ways in which stars can explode and return new elements to interstellar space. Both involve a critical mass limit, the Chandrasekhar mass.

The Chandrasekhar Mass

Recall that quantum mechanics requires electrons to move with speeds inversely proportional to the radius of a star:

v  ∝  1 

R 
 .

Also, recall that the more mass a white dwarf has, the smaller its radius. Therefore, the higher the mass of a white dwarf, the faster its electrons must move.

Now, if a star supported by degeneracy pressure is too massive, the electrons would be required to move faster than light. Nothing can move faster than light, so degeneracy pressure cannot support stars above a certain mass. This mass, first computed by Chandrasekhar, is 1.4 MSun.

Portrait of a High-Mass Star

Space telescope images of Betelgeuse, a red supergiant star of high mass. In visible light, this star has a diameter of about 5 AU. However, these UV images show that Betelgeuse's tenuous and irregular envelope extends many times further.   HST images of Betelgeuse

A computer simulation shows how convection in this star's envelope can account for it's irregular appearance.   Simulation of a red supergiant
Simulation of Betelgeuse [Bernd Freytag]

Late Stages of High-Mass Stars

Stars with more than 10 times the Sun's mass reach internal temperatures far higher than temperatures in smaller stars. As a result, they can burn heavier elements:

Reactants Temperature
(°K)
Products
12C + 12C 6×108 24Mg, 23Mg + n, 23Na + H, 20Ne + He, 16O + 2 He
20Ne + He 1.2×109 24Mg
16O + 16O 1.5×109 32S, 31S + n, 31P + H, 28Si + He, 24Mg + 2 He
32S, 28Si, He ~3×109 56Fe, 56Co, 56Ni

However, each stage of burning yields less energy than the stage before, and the iron-group elements (Fe, Co, Ni) yield no energy at all.

As burning proceeds, a degenerate core of Fe builds up at the center of the star...

 
Structure of 20 M_sun star

Type II Supernovae

When the iron core reaches the Chandrasekhar mass, it collapses, falling inward at speeds approaching the speed of light. This produces gravitational energy. Iron nuclei are smashed into neutrons and protons (Fe → n, p), and as the density increases, protons and electrons combine to produce neutrons and neutrinos (p+e → n+&nu). Most of the neutrinos escape, carrying the gravitational energy with them; a mere 1% are absorbed by material surrounding the collapsing core, which is blasted outward...

Supernova collapse
Model of a SN collapse [Adam Burrows]
  Supernova explosion
Model of a SN explosion [Adam Burrows]

SN 1987a: A Recent Supernova


Before SN 1987a   After SN 1987a

A brief pulse of neutrinos was detected several hours before the supernova was first seen in visible light. This strongly supports the basic picture of core collapse in Type II SN.

Supernova Debris

The blast ejects the rest of the star into space at speeds of ~2000 km ⁄ sec. The debris include the carbon, oxygen, silicon, sulfer, and other elements produced in the star before it exploded.

This image of a supernova remnant shows oxygen-rich material (green & blue) and sulfer-rich material (red).

 
HST image of LMC SNR
Oxygen-Rich Supernova Remnant in the Large Magellanic Cloud [STScI]

The Crab Nebula in X-rays, Visible, and IR

The Crab Nebula
Crab Nebula: a Dead Star Creates Celestial Havoc [NASA]

Type Ia Supernovae

A white dwarf orbiting a another star may gain mass from its companion. The stolen mass forms an accretion disk around the white dwarf and slowly spirals in toward the center.   Mass transfer to a white dwarf

When the white dwarf gains enough mass to exceed the Chandrasekhar limit, it begins to collapse. But the carbon and oxygen making up the white dwarf begin to burn as it collapses, and this releases so much nuclear energy that the star is completely destroyed. The nuclear reactions synthesize large amounts of iron-group elements, and some heavier elements as well.

Cosmic Abundances

Some elements are more common than others; the pattern of abundances reflects stellar processes:
  • Li, Be, B are rare; they are not produced in stars.
  • C and O are common products of Type II SN, as are many other light elements with even numbers of protons.
  • Iron-group elements (Fe, Co, Ni) are common products of Type Ia SN.
  • Elements beyond the iron group require energy to create; they are rare.
  • Pb is more common than other heavy elements; it's produced when heavier ones (eg, Th, U) decay.
  Abundances of elements
Abundance of Elements [GreenSpirit]

The Periodic Table of the Elements

1
H

2
He
3
Li
4
Be

5
B
6
C
7
N
8
O
9
F
10
Ne
11
Na
12
Mg

13
Al
14
Si
15
P
16
S
17
Cl
18
Ar
19
K
20
Ca
21
Sc
22
Ti
23
V
24
Cr
25
Mn
26
Fe
27
Co
28
Ni
29
Cu
30
Zn
31
Ga
32
Ge
33
As
34
Se
35
Br
36
Kr
37
Rb
38
Sr
39
Y
40
Zr
41
Nb
42
Mo
43
Tc
44
Ru
45
Rh
46
Pd
47
Ag
48
Cd
49
In
50
Sn
51
Sb
52
Te
53
I
54
Xe
55
Cs
56
Ba
*
72
Hf
73
Ta
74
W
75
Re
76
Os
77
Ir
78
Pt
79
Au
80
Hg
81
Tl
82
Pb
83
Bi
84
Po
85
At
86
Rn
87
Fr
88
Ra
**
104
Rf
105
Db
106
Sg
107
Bh
108
Hs
109
Mt
110
Ds
111
Rg
112
Uub
113
Uut
114
Uuq
115
Uup
116
Uuh
117
Uus
118
Uuo
* Lanthanides 57
La
58
Ce
59
Pr
60
Nd
61
Pm
62
Sm
63
Eu
64
Gd
65
Tb
66
Dy
67
Ho
68
Er
69
Tm
70
Yb
71
Lu
** Actinides 89
Ac
90
Th
91
Pa
92
U
93
Np
94
Pu
95
Am
96
Cm
97
Bk
98
Cf
99
Es
100
Fm
101
Md
102
No
103
Lr

Periodic table [Wikipedia]
Last: 10. The Lives of Stars Next: 12. Structure of the Milky Way

Joshua E. Barnes (barnes@ifa.hawaii.edu)
Last modified: October 31, 2006
http://www.ifa.hawaii.edu/~barnes/ast110_06/tooe.html
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