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Three methods to transport energy.
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Convection – wholesale streaming of a fluid
from hot to cool regions.
Conduction – energy is transported by free
electrons in a metal.
Radiation – Energy is transported by EM
radiation.
Granulated appearance on the
Sun’s surface (photosphere)
Stream of hot gas rises in the center, gives
off energy and sinks at the edges
Sun has a core, radiative zone and a convective
zone. Convection is a very efficient method of
energy transport
Radiation not an efficient way to
transport energy.
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There is little mixing of material in the radiative
zone of the Sun. So hydrogen is not mixed
down into the core of the Sun.
When the core runs out of hydrogen, the rest of
the Sun will still be mostly hydrogen, but there
is no way for the hydrogen to get down into the
core.
How do we know that the convection zone
doesn’t go all the way to the core?
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Theoretical modeling of the Sun’s temperature
and pressure shows that convection will break
down in the inner portions of the Sun.
In the past decade these models have been
verified using helioseismic measures. Just like
on the Earth, where earthquakes passing
through the Earth show use that the inside has
a crust, mantle, outer core and inner core.
Earth’s interior
Probing the Sun’s interior using Sun
Quakes
How can we be sure that the p-p chain is
responsible for the energy generation in the core
of the Sun?
How can we be sure that the p-p chain is
responsible for the energy generation in the core
of the Sun?
 The neutrinos that are produced in every
reaction of the p-p chain, barely interact with
matter. They can pass right from the core out
into space. Unlike light which can take a million
years of absorption and re-emission to finally
make it out of the Sun.
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The detected rates of neutrinos leaving the Sun
is the same rate that is predicted using the p-p
chain to make the internal energy.
A solar neutrino image of the Sun’s core
A hypothetical question
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The reaction rates in the core of the Sun
depend on two parameters.
1) temperature (high enough kinetic energy to
make protons stick together.
2) the density of the particles (particles close
enough together so that collisions are frequent)
One other point: Because of the slow rate of
energy transfer in the radiative zone, any
changes in the nuclear reaction rate will first
effect the core, before any effect to the outer
part of the Sun.
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The Sun does not have exactly the same
number of reactions from day-to-day. It is close
to the same but on any given day there can be
fewer or more than the day before. It is just
based on chance collisions.
Let’s suppose this is a very unlucky day in the
core of the Sun and there are much fewer
reactions today than normal.
What will happen to the core of the Sun?
What would happen to the core of the Sun?
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The core would shrink down
to a very small size and the
Sun would collapse inward
and disappear
The core would expand
outward since it would now
be out of balance with
gravity. The Sun would
explode
The core would shrink
increasing the reaction rates
and then re-expand.
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Sun is in a state of stable equilibrium. It is a self
regulating process.
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IF reaction rates go down in the core, gravity will cause the core
to begin to shrink. (gravity wins)
As the core shrinks the density and temperature of the core
begins to rise.
When these two parameters increase so does the nuclear
reaction rate. (internal pressure wins)
The core re-expands.
Ultimately, it is the mass of the star that controls the reaction
rate in the core. More mass, more reactions. Less mass, fewer
reactions
This means there is a direct relation between the star’s
luminosity and its mass, IF the star is in equilibrium.
We need to see if this theoretical idea is correct or
not. We need stellar masses and stellar
luminosities.
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Remember how the apparent brightness of a star is
related to its luminosity.
B = L/4πd2
B, the apparent brightness, we can find by hooking
detectors to telescopes and making an observation of
the star.
We can get L, the luminosity of the star, if we know the
distance to the star.
L = B(4πd2)
So we need to find the distance to the stars!
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For stars that are near by we can use a
triangulation technique to measure distance.
This technique is called trigonometric parallax.
This is the exact technique that surveyors use
to measure the height of mountains or the
widths of canyons, etc.
It is based on no assumptions other then
trigonometry.
Quiz #5
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Wednesday we learned that the Sun has a total
lifetime of 10 billion years (1 x 1010 years). Suppose
that there is a star elsewhere that has 10 times the
mass of the Sun (10 times the fuel supply) but a
luminosity which is 100,000 times that of the Sun.
(rate of consumption is 100,000 times the Sun’s rate).
What is the lifetime for this star in years? Show your
work and/or explain your reasoning. There will be
partial credit for correct reasoning.
Who discovered that the Earth was round?
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Cortez
Einstein
Columbus
Ancient Greeks
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Erasothene Determines size of
Earth (240 BC)
A well in Cyrene and an obelisk in Alexandria
separated by 440 miles
How do you compute Earth’s
circumference?
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Ratio and proportion.
C/440 miles = 360o/7o
C = 22,628 miles.
Today’s value: C = 24,901.46 miles
How can you find the distance to
the Comet?
I estimate the change in angle to be 6
arcseconds and the distance from
Denmark to Portugal to be 1,700 miles.
How can you find the distance to
the Comet?
I estimate the change in angle to be 6
arcseconds and the distance from
Denmark to Portugal to be 1,700 miles.
Answer: about 58 million miles
What about distance to the stars?
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The stars are too far away to see a shift in position just
using locations on the Earth.
We need a bigger baseline. So we use the entire orbit
of the Earth to do the measurements.
This technique works for nearby stars but eventually the
distance is to great to measure a shift.
Calculating the distance to the stars
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To find the distance to the stars we introduce a new
distance unit called the parsec (pc). For a parallax
angle p = 1 arcsecond, then d = 1 pc.
The equation is:
d = 1/p
where p is in arcseconds.
You can see that when p = 1 arcsecond, d =1 parsec.
1 parsec = 3.26 light years. The closest star besides
the Sun is α Centuari at a distance of 4.5 light years.
If a star has a parallax angle of p = 0.1
arcseconds, how distant is it?
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0.1 parsecs away
2 parsecs away
10 parsecs away
0.5 parsecs away
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α Centuari is 4.5 light years away. 1 parsec = 3.26 light
years. What can you predict about its parallax angle?
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It is less than 1
arcsecond
It is greater than 1
arcsecond
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The Hipparcos Satelite
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Hipparcos is a Earth orbiting satellite which is able to
make extremely accurate measurements of parallax.
Hipparcos can measure parallax angles as small as
0.001 arcseconds, but not as accurately as bigger
shifts.
It mapped the distance to 7,000 stars within about 500
light years of the Earth with very high accuracy.
With this information a Hertzsprung-Russell diagram
can be made. An H-R diagram.
H-R Diagram parameters
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An H-R Diagram plots a star’s luminosity on the y-axis
and the surface temperature on the x-axis.
Surface temperature is found using the stars color, or
using Wein’s Law. T = 3,000,000/λmax
Luminosity is found using the apparent brightness (B)
and the distance (d). L = B(4πd2)
On the Main-sequence we can see there is a direct
relationship between the surface temperature and the
luminosity, in the sense that as the temperature goes
up so does the luminosity.
Characteristics of the H-R Diagram
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Main-sequence stars are stars in equilibrium.
They are converting Hydrogen to Helium in their
cores.
The Main-sequence is really a mass sequence.
On the Main-sequence the stars that have the
highest luminosity are the most massive. The
stars with the lowest luminosity are the least
massive.
Stars not on the Main-sequence have different
energy sources and do not follow the massluminosity relation. The giant stars are dying.
Two star clusters – An open cluster
and a globular cluster
Two H-R diagrams
Which cluster is older?
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The open cluster (#1) because the
high mass stars are still on the
main sequence and they live the
longest.
The globular cluster (#2) because
there are no high mass stars on
the main sequence and they live
the shortest.
They are the same age because
both clusters have main
sequences
There is no way to tell from the
plots.
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Age of the clusters
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The open cluster still has enormously massive
stars on the main-sequence. They are on the
order of 10 times the Sun’s mass and emitting
100,000 times the Sun’s Luminosity.
The globular cluster has many stars that are no
longer on the main-sequence. The most
massive stars on the main sequence are slightly
less massive than the Sun.
The Open cluster is ~1 million years old, and
the globular is > 10 billion years old.
How do we find stellar masses?
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We look at binary stars and measure their orbital
parameters. Then make use of Kepler’s 3rd law.
(M1 + M2)P2 = (4π2/G)a3
Where P is the orbital period, a is the distance to the
center of mass of the system.
Nearly 50% of all stars are in a binary system. Two
stars orbiting about a common center of mass
Three types of binary stars.
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Visual binaries – Stars that are far enough
apart that they can be seen as separate stars
through a telescope. They typically have orbital
periods that are hundreds of years long.
Stars orbit a common center of mass. More
massive star has smaller orbit.
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Spectroscopic Binaries – Much shorter orbital
periods because stars are so close to each
other that they aren’t separable. But the
spectral lines show that there are two stars.
A Delema
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Spectroscopic binaries often show double the
absorption lines of a regular spectrum. But the
wavelength at which a line forms does not
depend on the type of star. It is set by the
element that is giving off the light. Why don’t
the two absorption lines fall right on top of each
other?
A Delema
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Spectroscopic binaries often show double the
absorption lines of a regular spectrum. But the
wavelength at which a line forms does not
depend on the type of star. It is set by the
element that is giving off the light. Why don’t
the two absorption lines fall right on top of each
other?
The reason is the Doppler Shift.
The Doppler shift is a wave phenomenon
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When an object emits a wave, the wave moves
out in all directions with its center at the source.
This is true of water waves, sound waves, and
light waves.
What if the source is moving?
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If a source of the wave is moving, then as the
source emits the wave, the center is
continuously moving.
Here is a real picture of Doppler shift
When a star is moving toward or away from
us Doppler shift is blue-ward (toward) or redward (away) of what it would be if the star
was not moving.
We can see this as a shift in the absorption or emission
lines in a spectrum. The wavelength that absorption
occurs at depends only on the type of atom. But the shift
depends on the motion
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Using the Doppler shift of light from a star we
can not only tell if the star is coming toward us
or going away from us, but we can also
measure the speed at which it is moving toward
or away.
How is the velocity related to the
amount of Doppler shift?
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The faster the object is
moving toward or away from
us the bigger the shift should
be.
The faster the object moves
toward or away from us the
smaller the shift will be.
If an object is moving rapidly
towards us we get a large
speed, but if it is moving
rapidly away we get a small
speed.
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Relation of velocity to Doppler shift
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The bigger the shift the fast the velocity
because the center of the wave is moving
rapidly causing greater compression or
expansion.
v/c = Δλ/λo
where v is the velocity, c is the speed of light,
λo is the rest wavelength and Δλ is the doppler
shift.
Δλ = (λobserved – λo)
What about stars orbiting each
other?
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The result is two absorption lines that have slightly
different wavelengths from what they have in the lab.