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Quiz #10
• What would really happen to you if you were to fall
all the way into the Event Horizon of a black hole?
We know the gravity is unbelievably strong. What
would happen to your body and why? (Note: I am
not looking for a relativity answer here. Just a gravity
answer)
• In the original interaction, star formation can
be set off in the density wave because the gas
and dust are compressed.
• After the interaction, there is continued star
formation along the density wave as
molecular clouds collide with the density wave
and become compressed.
When interactions are not in the plane of the
large galaxy, then warps in the disk ocurr.
The result of the creation of spiral density
waves.
• After the interaction, there will be increased
star formation for quite some time, as
molecular clouds continue to collide with the
spiral density waves.
• Over time, self-sustained star formation and
disruption of the density wave, causes the Sshape density wave to fragment into spurs.
Then there are multiple density wave
fragments.
• Over time, after several orbits of material, the
spiral density wave is lost.
• The result is a slowing of star formation rates.
• Eventually, the disk galaxy has virtually no
recognizable spiral pattern at all.
Galaxy Simulations
• It takes hundreds of millions of years for interactions to
occur between two galaxies.
• When we observe two galaxies interacting we are only
seeing a snapshot of the interaction.
• Fortunately, there are billions of galaxies to observe, and
this is a large enough sample to find galaxy interactions
at many stages, many masses, and many angles of
impact.
• It is also possible, using computers, to model the
interactions of two galaxies, using Newton’s law of
gravity.
http://kristoffer.vinther.name/academia/projects/scicomp/
Composite image on left, and X-ray image on
right. X-ray glow is from extremely hot gas.
What mass should be used for the simulations?
• There are two general methods for estimating the mass
of a galaxy.
• Luminous mass and dynamical mass.
• Luminous mass.
If you measure the apparent brightness of a galaxy it is possible to
determine the total luminosity of the galaxy.
What other parameter would you need to determine the total
luminosity of the galaxy?
What other parameter would you need to determine the
total luminosity of the galaxy?
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1. The total number of
stars.
2. The distance to the
galaxy
3. The number of blue
stars.
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0
33%
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9
10
23
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1
33%
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2
33%
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• Apparent brightness is given by this equation.
B = L/4πd2
where L is the total luminosity of
the galaxy.
If we know the distance, we can compute the total
luminosity.
Suppose a galaxy has a total luminosity that is
Ltot = 3 x 1011 times the Sun’s Luminosity.
Estimate the amount of mass in stars in this
galaxy.
30
30
1. About 3 x 1011 solar
masses.
2. About 100 times the
mass of the Sun.
3. Impossible to say
because most of the
mass is in the central
super massive black
hole.
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2
21
22
0
33%
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1
33%
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2
33%
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3
20
• Although this is just an estimate, you can say, that
the luminosity of the galaxy is the same as if there
where 3 x 1011 Suns in this galaxy. That means it has
about 3 x 1011 times the mass of the Sun.
• To do a better estimate, you look at the luminosity
function, which tells you how many high mass stars,
medium mass stars and low mass stars make up the
galaxy.
• It is also important to determine the amount of mass
that is present from gas and dust. This is typically
only about 10%.
Dynamical Mass.
• This mass determination uses Kepler’s 3rd Law.
• It doesn’t depend on the mass that is giving
off light. It is a direct measure of the mass
that is present.
• (Minterior + m*) P2 = 4π2(r3)/G or
• (Minterior + m*) = r(4π2r2/P2)/G or
• (Minterior + m*) = r(v2)/G we can ignore m*
• So v = (MinteriorG/r)0.5
As you move out in the disk, there are fewer and
fewer stars. The mass interior should not be
changing.
To compute velocities we use the Doppler shift
Rotation curve for nearby M33
Virtually all galaxies show a flat rotation curve.
• Let’s look back at the rotational velocity equation:
•
v = (MinteriorG/r)0.5
• The rotational velocity is constant at big r values.
• What must we conclude?
What must we conclude?
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30
1. The radius in not
decreasing
2. The universal
gravitational constant,
G, is changing
3. More mass is being
added interior to the
orbit.
1
2
21
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0
33%
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1
33%
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2
33%
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• The mass interior to the orbit is still
increasing. Even after the radius r has gone
beyond the last of the stars. It must be
increasing in order to hold v constant.
• This is dark matter.
• We don’t know what it is but it has mass. It
surrounds galaxies in a huge dark matter halo.
• It doesn’t interact with light or we could
observe it. That is true even for gas.
Other ways to detect Dark Matter
• Gravitational lensing. The amount that the
light is bent is directly proportional to the
mass bending the light.
Clusters of Galaxies.
• Galaxies that are in clusters have velocities that are
many orders of magnitude to large to be bound by
the cluster. This means that either, the galaxy
clusters everywhere in the universe are flying apart,
or else there is a huge amount of dark matter
present.
• The results from all these different
observations is that around 90 to 95% of the
mass in the universe is Dark Matter.
• When we look at a galaxy, we are seeing the
luminous matter. But that matter is
embedded in a much larger Dark Matter halo
which contains around 90% of the mass of the
galaxy. And we can’t even see it. We can only
measure its presence using velocities.
So we see this….
But it is only the tip of the iceberg
• In order to model galaxy interactions, it is
necessary to use all the mass, not just the
luminous mass.
• In the simulations we have seen so far, dark
matter is explicitly put into the simulation.
• Let see what will happen some day when the
Milky Way and Andromeda collide.