Evolution of Stars, Origin
of the Elements
"In the beginning, there was nothing at all. Earth was not
found, nor Heaven above, a Yawning-Gap there was, but
grass nowhere."
The Edda -- collection of Norse Myths dating to 1200
In this lecture period we learn:
Evolution of stars and the H-R diagram (red giant, supernova, black
hole)
Origin of elements (fusion and neutron capture)
Abundances of elements
Format for printing
Evolution of Stars
The scientific evidence is now overwhelming that the
Universe began with a "Big Bang." What came next?
As the early universe expanded and cooled, matter
and anti-matter collided and "annihilated" in a
massive process, producing radiation. We believe
that there was a slight excess of matter and that
hydrogen and helium atoms were "left over." Vast
clouds of gas spewing into space led to the formation of galaxies
and stars, as matter in local high-density regions collapsed and
coalesced under the influence of gravity. Stars were, and continue
to be, formed in gaseous nebulae. An example is the Great Orion
Nebula, which is one of the youngest features in the sky - thought
to be only 20,000 years old. Our own Sun formed in just such a
nebula.
The Universe is still evolving
New stars are being born in gaseous nebulae all the time. Stars
have life cycles of over billions of years. The details of the life cycle
depend on size and luminosity (brightness). Astronomers have
devised ways of studying stellar evolution and since this plays the
key role in the origin of elements, we discuss it next.
As we saw earlier, the Sun acts as a black body with a temperature
of ~6000 K. Other stars seen in the sky are hotter and cooler.
Hotter stars are bluer and cooler stars are redder. If you look
carefully on a clear and dark night, you can sometimes see these
color differences with the eye. Measurements show that stars are in
the general range of 3000K to over 20,000 K. These measurements
represent the star surface temperatures, not the temperatures
inside, which are much hotter and lead to fusion reactions which
power the star.
Stellar temperatures and luminosity
Another characteristic feature that astronomers can measure is the
brightness of a star - this depends on both how far away the star is
and on characteristics of the star itself. For nearby stars, we can
determine distance by geometry, so the brightness can be turned
into a real measurement of how much radiation the star emits - its
luminosity. For further stars, less direct methods are used.
The most important classification scheme for stars plots surface
temperature against luminosity. This plot is called the HertzprungRussell (H-R) diagram, illustrated below.
Hertzprung-Russell (HR) diagram is a
temperature vs.
luminosity plot of
stars. Some prominent
stars are shown by
name. The visible
colors of stars are
indicated at the top,
and the different
classes of stars are
labeled in the diagram.
The majority of stars
are found to lie on the
Main Sequence. Giants
and supergiants do not
behave as typical
stars.
The radius of a star can be deduced by its position on the H-R
diagram. Can you figure out how, using the Stefan-Boltzmann
equation? The Stefan-Boltzmann law relates luminosity and surface
area to temperature. Stars to the top right of the diagram are
large and stars to the bottom left are small.
Mass also changes as a function of position on the diagram. The
masses of "Main Sequence" stars range from one-tenth of the Sun's
mass at the lowest part, to some 50 or 100 solar masses at the
upper end. Heavier stars burn up their fuel more quickly than the
smaller stars. Happily for us, the Sun has been on the main
sequence for around 4.5 billion years and will remain there for
another 4-5 billion years or so.
Main Sequence Stars
Stellar evolution can be studied using the H-R diagram. The
majority of stars spend most of their time on the main sequence
burning hydrogen to make helium through fusion reactions in the
core. When the hydrogen is used up, the star will move away from
the main sequence. A moderately sized star like the sun will
become a red giant, growing in size to engulf the Earth and burning
helium to make carbon. Following this stage, the outer layers will
be thrown off, and the Sun will end up as a white dwarf, a dim star
with a very small radius and high density - it will eventually cool
and fade from sight.
Solar system
abundances of the
elements. Note that the
1:4 ratio of helium to
hydrogen (by weight) is
what the Big Bang
theory would predict.
But other, heaver
elements must come
from other processes.
More importantly for our discussion of the origin of elements is
what happens to the massive stars. Before discussing these
"supergiants", we need to quickly review the chemical elements.
The Figure shows the measured abundances of the elements in our
solar system. The major elements in the solar system are hydrogen
and helium in exactly the ratio predicted by the Big Bang theory.
We need, however, to explain the existence of the heavier elements
that could not have been synthesized during the Big Bang itself.
Atoms -- a primer
The table below list basic characteristics of the building blocks of
atoms.
Particle
Molar Mass
Electrical Charge
C
g/mol
electron
-1.60217733(49) x E-19
30
0.0005486
Rest Mass
kg
0.91093897(54) x E-
proton
+1.60217733(49) x E-19
1672.6231(10) x E30
1.0072697
neutron
0.0
1674.9543(86) x E30
1.0086650
The atomic number, which is the number of protons, characterizes
an atom. In the case of hydrogen, we have one positively-charged
proton (the nucleus) that is orbited by one negatively-charged
electron. In the other elements, the nucleus of an atom contains
both positively-charged protons and neutrally-charged neutrons.
The mass number of an atom is the combined weight of protons
and neutrons. For our purposes it turns out that electrons have
negligible mass compared to the nucleus. Some atoms can have
different numbers of neutrons, called isotopes, but if we change the
number of protons we change atomic species. The atomic number
of H is 1 and its mass is ~1.67E-24 gram; atomic weight is typically
expressed as reference mass, and is slightly more than 1 for H (it is
1.0079) because of the presence of other H isotopes. The next
element in the periodic system, He, has atomic number 2 (two
protons and 2 neutrons) and a mass of ~6.65E-24 gram (or atomic
weight of about 4). To make one He atom, we therefore need four
H atoms and some modifications. Assuming we are able to
overcome the repelling force of the protons, the combined mass of
4 H atoms equals 6.696E-24gram, which exceeds the mass of He.
The excess mass is released as energy following Albert Einstein’s
well-know E=mc^2 equation; with m is (excess) mass and c is the
speed of light. Small as the mass excess may seem, the energy
release of only a very small amount of H that fuses to create He is
tremendous. This H fusion process is the source of our Sun’s
energy, and has also been used to create the most powerful
weapon of destruction: the hydrogen bomb.
The consequence of the fusion process is a balance between
gravitational contraction and expansion due to heat in the Sun. As
long as H fusion continues heat will be generated, but what if all H
has been converted to He? When H fusion stops, the sun cools and
gravitational collapse occurs. This in turn creates heat from the
restricted motion of atoms. At some point, enough heat may
become available to fuse He atoms, for example into the element C.
This releases excess mass in the form of energy as well. Then we
have a He-fueled star. Why does H fuse before He? The answer lies
in the structure of the nucleus, where a greater number of protons
requires more energy to overcome the repelling forces. When He
fusion occurs in the core of a star, sufficient heat is generated for H
fusion to occur in outer parts of the star. The combined energy
these two fusion processes generate causes the star to expand
enormously, at which stage we call it a Red Giant. When our Sun
reaches this stage 9n 4-5 billion years, its size will exceed the orbit
of Earth.
Origin of "Heavy" Elements
So where do these heavier elements come from? All stars are
continually in a balance between gravitational collapse and outward
pressure forces due to the fusion reactions in the core. If gravity
starts to win, the star collapses and the release of gravitational
potential energy allows the star's core to heat up, releasing more
energy.
Shell structure of a heavy
star (~25 solar masses) at
the end of its evolution, just
prior to a supernova
explosion. The fraction of
the total mass contained in
each shell and the principal
elements present are
shown.
Heavier stars evolve into supergiants, and it is the nuclear reactions
in the interiors of these stars that gave rise to the heavy elements
in the universe. Such massive stars start by burning hydrogen into
helium in the core, then helium to carbon, and then carbon to
heavier elements, all the way up to iron. At each stage, once the
fuel is consumed in the core, the star contracts and gravitational
energy is released, heating the core to temperatures high enough
to enable the next stage to begin. The abundant elements carbon
and oxygen are made by helium fusion, and the elements up to iron
are made in subsequent steps. However, beyond iron most
elements are made by successive "neutral capture", though some
of the rarer nuclides are made by proton capture reactions.
The high temperatures (nearly 1,000,000,000 K) required for this
process can only be reached in stars heavier than about 4 solar
masses. When the core is composed of heavy elements near iron,
no further nuclear fusion is possible and the tendency for the star
to collapse under the tremendous gravitational forces is unchecked.
As the star's heavy core implodes, huge shock waves break the star
apart, spewing the heavier elements out to space in a supernova.
Supernovae are fairly common events in
distant galaxies, but are only seen rarely in
our own, since those within the Milky Way are
often obscured by gas and dust. A recently
observed supernova was seen in the
neighboring Large Magellenic Cloud galaxy (a
diffuse "satellite" galaxy of the Milky Way)
early in 1987 (on left). Perhaps the most
famous supernova was seen by Chinese
astronomers in July 1054 and was
visible for several weeks in broad
daylight. The visible remnant of this
huge explosion is now called the Crab
Nebula. For a detailed view of the
Crab Nebula, look at the recent
Hubble Telescope image. This
supernova remnant is 6,500 light
years away. Another beautiful
example of a supernova remnant is the Cygnus Loop, lying about
2,500 light years away (on right).
The evolution of even more massive stars produce other objects in
our universe. Perhaps the most intriguing object that can form
from a massive collapsing star is a black hole. These object are
invisible because all matter is unable to escape the gravitational
attraction. We use indirect means to recognize their presence and
many galaxies, including our own Milky Way galaxy, may have a
black hole in their core.
Calculations show that only one ninth of the material in the solar
system was generated in supernovae, while the remaining eightninths is hydrogen and helium. It is interesting to note that the
elemental abundances of our planet is notably different in H and He
(below), which we use later to understand the origin of Earth and
her immediate neighbors
Abundances of the
elements in Earth.
Comparison with the
figure above shows
that Earth has lost
most of its primordial
hydrogen and
helium.
Summary
The elements hydrogen and helium were synthesized in the Big
Bang. Higher elements were synthesized in fusion reactions (up to
Fe) and neutron capture reactions within massive stars. These
elements were dispersed in supernovae. About 10% of the material
in the solar system (including the most critical materials making up
our bodies) came from supernovae, the rest from the Big Bang. All
of us come from the stars ....
Suggested Readings
Cox, P. A., The Elements: Their Origin, Abundance, and Distribution
Oxford Scientific Publications, 1989.
Self Test
Take the Self-Test for this lecture.
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