The Sun s Source of Energy
E= m c2
AND STARS!
Announcements
q  Homework # 5 starts on Thursday, Nov
3th. It is due on Tue, Nov 15th
q  Exam # 2 will take place on Tuesday,
November 8th:
q  Please remember to bring your ID. No ID =
No Exam
q  Please remember to bring a pencil # 2
q  More infos (including lectures and units which
it is based on) on www.astro.umass.edu/
~calzetti/astro100
Assigned Reading
q  Unit 50, 52.1-2-3, 54.1-2-3, 55
Goals for Today
q  Investigate how our Sun produces its
energy
q  To understand how the Sun does not
implode under its own weight.
q  To begin a study of stars – what they’re
made of, what kinds are out there, how
similar or dissimilar they are from the Sun,
how they are born, and how they die
The Sun s Energy Source is in
its Core
The Core is where all the action is.
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The core is the only place in the Sun where the
temperature and density are high enough to
support nuclear fusion.
Every second, about 600 million tons of Hydrogen
are fused into 596 million tons of helium.
The remaining mass (4 million tons) is converted
to energy in line with Einstein’s formula
E = mc2
The Sun is about 5 billions years old, and has
used up about 1/2 of its `fuel’.
Survey Question
The energy emitted by the Sun is produced
1) in a small region at the very center of the Sun.
2) uniformly throughout the entire Sun.
3) throughout the entire Sun but more in the
center than at the surface.
4) from radioactive elements created in the Big
Bang.
Nuclear Fusion in the Sun
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Hydrogen is
constantly being
transformed into
helium in the Sun’s
core.
Energy is produced
because 1 nucleus of He
weights less than 4
protons.
One slide on Neutrinos
-  Neutrinos are generated in the P-P chain in the core of the Sun
-  Neutrinos
-  are thought to only have a tiny mass
-  travel at the speed of light
-  only weakly interact with matter
-  Neutrinos are the only thing that comes directly out of the
core of the Sun without running into other things along the
way.
There are trillions of neutrinos passing through you right
this instant!
The first two people to measure solar neutrinos won the 2002
Nobel Prize in physics (Ray Davis, Masatoshi Koshiba)
An aside about nuclear fusion
as a viable energy source
A few key points about the P-P Chain:
•  It is a “clean” form of energy production.
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Put 4 protons (Hydrogen) in and get one
Helium and some energy back out.
•  Given fuel (in the form of Hydrogen) it is
a self-sustaining reaction.
•  However, it requires *very* high
temperatures (107 K), and large masses
of Hydrogen
Fusion is highly improbable!
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Gravity increases the temperature in the
Sun, which enables protons to overcome
the Coulomb repulsion and have the
strong force take hold
While two protons collide, one must be
transformed into a neutron, which
requires the weak force
For each proton, this happens once every
billion of years.
Without the `weak force bottleneck’, stars
would burn too fast or too slow, and
maybe prevent life on planets.
Nuclear Fusion vs. Fission
Survey Question
The chemical composition of the Sun 3 billion years ago
was different from what it is now in that it had
1)
2)
3)
4)
more hydrogen and more helium
less helium and less hydrogen
more helium and less hydrogen
more hydrogen and less helium
Nuclear Fusion and the Sun
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Nuclear fusion produces energy
The energy heats the gas in the Sun
`Heating of the gas’ means that the
gas particles (electrons and protons)
are accelerated and have more
kinetic energy (called thermal
pressure)
The kinetic energy of the gas
particles compensates for the Sun’s
self-gravity
Hydrostatic Equilibrium in the Sun
Thermal
Pressure
Gravitational
Contraction
What is Hydrostatic Equilibrium?
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A star is a ball of gas held in
hydrostatic equilibrium, which is a
perfect balancing between its own
self-gravity and the thermal pressure
of the hot gas, cooling from center to
the surface
The energy to produce the thermal
pressure comes from nuclear fusion
reactions at the center of the Sun
What is Thermal Pressure?
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Pressure in a gas arises from collisions of atoms
and molecules.
The higher the temperature, the faster the
atoms/molecules in the object are (T ~ v2), thus
more energetic collisions
More energetic collisions result in higher pressure
Think of a hot-air
balloon. To keep it
inflated (high pressure)
you need to keep the air
inside it heated.
How does a
star hold itself?!
This balance between
weight and pressure is
called hydrostatic
equilibrium.
The pressure is provided by the
motions of the very hot gas that
makes the Sun. To keep the gas hot,
the Sun has to produce energy in its
core, and it needs to be hotter in the
center.
The Sun's core, for example, has a
temperature of about 15 million K.
My House’s Thermostat
Air temperature inside drops below
the set point of the thermostat
Electrical signal triggers
ignition of furnace
Furnace shuts off
Furnace burns oil/gas
and generates heat
Air warms thermostat until
electrical signal is shut off
Radiators transfer energy
from water to air
Heat is absorbed by water
running near furnace
causing water temperature
to rise
Hot water is circulated
throughout house
The Solar Thermostat
Outward thermal pressure of core
is larger than inward gravitational
pressure
Core expands
Nuclear fusion rate
rises dramatically
Expanding core cools
Contracting core heats up
Core contracts
Nuclear fusion rate
drops dramatically
Outward thermal pressure
of core drops (and becomes
smaller than inward grav. pressure)
A Balancing Act
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If the Sun contracts, the temperature
goes up, the rate of fusion increases, the
thermal pressure increases, and the Sun
re-expands.
If the Sun expands too much, the
temperature drops, the rate of fusion
drops, the pressure drops, and the Sun
contracts.
Sunshine: Good or Bad?
The Sun’s need to compensate for the contraction
of self-gravity by producing thermal pressure
means:
q  It needs to maintain the thermal pressure, by
keeping its gas hot
q  However, the energy lost via radiation (sunshine)
needs to be replaced (bad for the sun, good for us)
q  The replacement happens in the center of the
Sun, via nuclear fusion
q  As energy flows from hot to cold, the center of
the Sun needs to be hotter than its `surface’ (the
gaseous photosphere).
q  Some evidence….
The Sun is hotter towards the
center:
the limb is slightly darker
Survey Question
Suppose you could magically inject, all at once, a large amount of
energy into the core of the Sun. What would happen?
1) The Sun would contract as the core heated up.
2) The Sun would contract as the energy became gravitational
potential energy and find new equilibrium with the grav.
pressure. The Sun would end up being smaller in size.
3) The injected energy would heat the core, causing the Sun
to expand. The energy would eventually be radiated off
into space and the Sun would return to normal size.
4) The injected energy would heat the core, causing the Sun
to expand. The Sun would find a new equilibrium with
the gravitational pressure and end up being larger in size.
This ends our trip through the Sun
However, the Sun is a star like many….
Let’s expand our horizons:
Stars
n  All
stars (including our Sun) are made
up of the same elements, in roughly the
same proportions:
other
–  Hydrogen (~70%)
–  Helium (~28%)
–  other elements (~2%)
n  All
helium
hydrogen
stars have nuclear fusion going on in
their cores – just like our Sun.
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are four principal characteristics
of a star:
–  Luminosity
–  Surface Temperature
–  Size
–  Mass
Three of them (luminosity, size, and mass)
require
knowledge of the distance of the star from
us.
How do we measure the distance to a
star?
We need it to get: luminosities, radii,
masses
Parallax (a.k.a. triangulation)
For getting distances
Using triangulation
requires:
1.  A baseline (distance
over which observer
moves).
2.  Measurement of angles
to the object from each
end of the baseline.
3.  Mathematical
relationships between
angles and lengths of
sides of triangle. This
is called trigonometry.
Stellar Parallax
The measurements are taken six months apart.
The baseline is the diameter of the Earth’s orbit.
What is seen
What is seen
The ½ of the angle between the current location and the
6-month location is called the stellar parallax = P.
Parallax Distance
1 (AU)
D (in Parsecs) =
P (in arcseconds)
P, the parallax angle, is measured in arcseconds
60 arcseconds = 1 arcminute
60 arcminutes = 1 degree
There are 3600 arcseconds in a degree
The larger P, the smaller D
The smaller P, the larger D
1 parsec = 3.26 light years
= 3.086x1016 meter
Parallax would be easier to measure if
1) the stars were further away.
2) Earth's orbit were larger.
3) Earth moved backwards along its
orbit.
4) none of these.
Parallax would be easier to measure if
1) the stars were further away.
2) Earth's orbit were larger.
3) Earth moved backwards along its
orbit.
4) none of these.
Star A has a parallax angle that is twice that
of Star B. What is the relationship between
their distances?
n  Star
A is closer than Star B
n  Star B is closer than Star A
n  The stars are at the same distance
n  Not enough information is given
Another Method to Measure Distances
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If you can `identify’ a star, i.e., determine its
luminosity (for instance we observe another star
in the distance which has the same color and
spectrum of our Sun, we may infer it has to have
the same luminosity as the Sun), we can derive a
distance from the Inverse Square Law:
d=
√L / 4 π B
L /(4 "B)
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