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Astronomy C10/L&S C70U
Stellar Life Cycles and Supernovae
Nicholas McConnell
Like many aspects of nature, star formation and destruction is a cycle. Stars form from clouds of gas,
remain stable for long periods of time, and then expel gas back into space, where it can later form new
stars. Below are four stages in the life of a massive star. Describe what happens in each stage, and
how energy is generated and used up.
Initial formation from a cloud of gas
Description: Once a gas cloud (or a particularly dense region of a much larger cloud) reaches a
certain mass, it begins to collapse in on itself. As it collapses, it heats up. The
collapse continues until the center of the cloud is hot enough to fuse hydrogen into
helium.
Energy Source: Gravitational energy
Energy Released As: Heat in the contracting
cloud, light
Main Sequence lifetime
Description: At the center of the star, it so hot that hydrogen nuclei (protons) are moving fast
enough to overcome their electrostatic repulsion and fuse together. Through a series
of nuclear reactions, four protons become one helium nucleus (2 protons, 2 neutrons).
A small amount of mass is lost in this process; it is converted to pure energy.
Because the interior of the star is very hot, it exerts enough outward pressure to match
the inward force of gravity. This state of balance is known as hydrostatic equilibrium.
Throughout its Main Sequence lifetime, the star is basically stable.
Energy Source: Mass (E = mc2 )
Energy Released As: Light, some neutrinos
Red Giant/Supergiant Phase
Description: Eventually, there is no hydrogen left in the center of the star, and fusion stops. With no
way to maintain outward pressure, the core begins to collapse again, getting hotter and
denser. Eventually, it is hot and dense enough to fuse helium into carbon and oxygen.
In a massive star, this process (contraction, then fusion of new elements) repeats for
heavier and heavier elements. During this phase, the temperature of the core creates
enough pressure to push out on the outer layers of the star. They expand and cool,
creating an enormous, red surface. We view the star as a red supergiant.
Energy Source: Gravitational energy,
then mass ( E = mc2 )
once fusion starts again
Energy Released As: Heat, until fusion can occur again.
Then, light, and work done
to expand the outer layers
Supernova
Description: The final fusion product in the center of a massive star is iron. Iron nuclei cannot fuse
together without losing energy (all previous fusion steps created energy), so fusion stops
altogether. Now, the collapse of the core under gravity is inevitable. Within instants,
the center is compressed into pure nuclear material (neutrons with very little space
between them: much less than the width of an atom). Quantum mechanics dictates that
this state must extert an enormous degeneracy pressure. The rest of the collapsing core
bounces off this neutron center, and the star explodes.
Energy Source: Gravitational energy.
As the core collapses to
very high density, neutron
degeneracy pressure
provides the "bounce."
Energy Released As: Mostly neutrinos.
The explosion also ejects
gas (what used to be the star)
at very high speeds.
Light makes up about 0.01%
of the total energy released.
What happens in low-mass stars (less than about 10 solar masses) instead of a supernova?
In low-mass stars, the core never gets hot or dense enough to fuse carbon and oxygen into heavier
elements. Once the helium is used up, the core is able to stave off gravitational collapse with a new
source of pressure: electron degeneracy pressure. This is a quantum mechanical effect similar to the
neutron degeneracy pressure that creates the "bounce" for a supernova, except electron degeneracy
pressure is less powerful.
Therefore, the core of the low-mass star ultimately stable as a very dense glowing mass of carbon and
oxygen. En route to this final state, instabilities during helium fusion create winds that gradually blow
away the outer layers of the red giant star. In the intermediate phase, we see a so-called planetary
nebula: these escaping layers are illuminated and excited by UV radiation from the core. Eventually,
the layers have been entirely blown away and all that remains is the bare core: a white dwarf, which
cools off over billions of years.
Here's a quick list of qualities that should test your knowledge of two different supernova types. Mark
whether the qualities listed apply to Type Ia supernovae, Type II supernovae, or both. Try to keep in
mind how these relate to the ways in which the two types above are physically different from one
another.
Type Ia
Strong hydrogen lines in spectrum
X
No hydrogen lines in spectrum
X
Only occurs in a binary system
X
Requires a star more massive than 10*MSun
Completely destroys the exploding star
Type II
X
X
Leaves behind a neutron star or black hole
X
Creates heavy elements (including stuff humans are made of)
X
Almost always has a standard, predictable luminosity
X
X
We haven't learned the last one yet, but it will be important later. Alex's research team has used this
fact to show that the universe is expanding faster and faster, rather than slowing down as initially
expected.
Supernovae are extraordinarily energetic events. This next exercise will allow us to compare the
luminosity (energy output per second) of a light bulb, the Sun, all the stars in the Milky Way, and a
typical supernova.
Light bulb vs. Sun:
We know the formula for an object's brightness: b = L / 4d2 . This describes how much light we see,
but the same concept can also describe how much energy we feel as heat. By this token, we can
approximate that a light bulb is as "bright" as the Sun, when we stand close enough to it to feel the
same amount of heat as we would feel from sunlight.
If this is true, then bbulb = bSun, so Lbulb / 4dbulb2 = LSun / 4dSun2 .
Or, (LSun / Lbulb ) = (dSun / dbulb )2 .
There is a 100-Watt light bulb at the front of the classroom. 1 Watt is one Joule of energy released per
second, so Lbulb = 100 J/s.
dSun is 1 A.U., or 1.5 x 1013 cm. Our experiment will give us dbulb. Hold your hand out and approach
the light bulb until its warmth feels about the same as sunlight. Then measure the distance from the
bulb to your hand, in centimeters.
This is subjective, but let's say we measure 7.5 cm.
Now you have Lbulb, dbulb, and dSun. You can plug these values into the bold equation above and
calculate the Sun's luminosity in J/s. Do it!
From (LSun / Lbulb ) = (dSun / dbulb )2 , we get LSun = Lbulb * (dSun / dbulb )2
= 100 J/s * (1.5 x 1013 cm / 7.5 cm )2
= 102 J/s * ( 2 x 1012 )2
= 4 x 1026 J/s , which is very close to the actual
value of LSun.
Sun vs Milky Way:
Your answer above for LSun will depend on what distance you chose for dbulb. The actual value of LSun
is about 1026 Joules per second (!!!). Hopefully your answer was close (1024 - 1028 J/s might be
reasonable, given our method).
In any case, the Milky Way galaxy contains about 100 billion (1011) stars. Some are much more
luminous than the Sun, and many are less luminous, but an acceptable approximation is that the
average luminosity per star is 1 LSun . Therefore, the Milky Way has an approximate luminosity of
1011 * 1026 J/s.
So, LMW = 1037
J/s (one easy step).
Milky Way vs Supernova:
Now, a typical Type II supernova explosion releases 1044 Joules of light (and hundreds or thousands of
times more energy in the form of neutrinos and high-speed gas!) Suppose this release occurs over a
single second. For that initial second, how many times brighter will the supernova be than the entire
Milky Way galaxy?
LSN = 1044 J / 1 s = 1044 J/s
LSN / LMW = (1044 J/s ) / (1037 J/s ) = 107 . In that first second, the supernova is 10 million
times
as luminous as the entire Milky Way galaxy!
Wow!!