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Discussion
How can we get stars on the main
sequence that are more massive than the
turn-off, which astronomers call blue
stragglers?
Binary stars
Binary stars typically form together, as
collisions between stars are extremely rare.
Discussion
Binary stars with radii bigger than their Roche
lobe cannot form. How then can binary stars
transfer matter between them?
Discussion
What do you think might happen if Sirius A
evolves into a red giant and fills its Roche
lobe?
Nova
Nova T Pyxidis
Discussion
What do you think would happen if the mass
transfer happened so fast that the mass of the
carbon white dwarf star exceeded the 1.4
solar mass limit?
Supernova type Ia
If the mass transferred to the white dwarf is
greater than 1.4 M☉, the electron degeneracy
pressure will not be able to support the weight
of the star and it will collapse.
The sudden collapse of the white dwarf
heats the core which causes core fusion to
start again. This re-ignition of the core
blows the star apart.
SN 1572
SN 1604
Supernovae type Ia and II
Type Ia – caused by white dwarf exceeding
1.4 M☉. Spectrum has weak hydrogen lines.
Type II – caused by massive star forming a
neutron star. Spectrum has strong H lines.
Discussion
Why is it that a supernova type II can form a
neutron star and doesn’t blow itself to bits
like a type Ia supernova?
Gravity wins
Neutron degeneracy pressure has a limit to how
much mass it can support. If the mass of a
neutron star exceeds about 3 M☉, the star will
collapse.
There is no known force that can stop the
collapse and the matter is smashed down to
infinitely small size, a singularity
Discussion
If the matter is smashed down to a single point,
what happens to the surface gravity? What
happens to the escape velocity of such an
object?
Black Holes
Any object that has an escape velocity greater
than the speed of light is called a black hole.
Albert Einstein
Einstein and Black Holes
The existence of black holes is predicted by
Einstein’s General Theory of Relativity.
But black holes are so strange that Einstein
refused to accept that nature would allow
such a thing to exist.
Quark Stars?
Maybe the neutrons can turn into something
that can stop the collapse into a black hole.
Possible, but not much room to do it in. A 1.4
solar mass neutron star radius is 10.4 – 12.9
km while the escape velocity of a 3 solar mass
object equals the speed of light at a radius of
9 km.
Was Einstein wrong?
Today most theorists believe that black holes
must exist, though all the observational
evidence is still indirect.
Introduction to Relativity
Special Theory of Relativity – 1905
Applies to objects moving at a constant
velocity
Discussion
Which way is up? How would you define the
concept of “up?”
Discussion
Suppose a supersonic airplane is flying at a
speed of 1,650 km/hr from Nairobi, Kenya, to
Quito, Ecuador. How fast is the plane going?
Velocity is relative
In order to talk about the speed of an object,
you need to have a reference frame in mind.
The speed something is moving must always
be measured relative to something else.
Discussion
Suppose you are running on a treadmill at 8
miles/hr. How fast are you moving relative to
the ground? What does it mean to say you are
running at 8 miles/hr?
Discussion
I can throw a ball at 30 m/s. If I’m riding on a
train traveling at 10 m/s toward you and I
throw a ball to you standing by the side of the
track as the train comes toward you, how fast
is the ball going when you try and catch it?
Principle of relativity
Newton’s laws are exactly the same whether one
is moving at a constant velocity in an airplane or
at rest of the ground.
Electric and Magnetic Waves
The speed of light is 3.00 × 108 m/sec in a vacuum
Water Waves
Michelson-Morley experiment
Einstein’s postulates
1. The laws of nature are the same for
everyone.
2. The speed of light in a vacuum is constant
for all observers.
Discussion
If Jackie is in a space ship traveling at 1×108
m/s and she turns on her headlights, the light
leaves the ship at 3×108 m/s. If you are in
front of the ship, how fast would you measure
the light to be traveling past you?
The speed of light
All the strange results of Relativity come from
the observation that the speed of light is
constant for all observers.
Discussion
Consider a space ship traveling at a very
high speed (maybe even faster than the
speed of light). It has a light on the front
of it. How fast does the light leave the
ship as measured by those traveling with
the ship?
Discussion
Consider an observer watching the ship pass
at a very high speed. How fast will they
measure the light to be traveling that the
ship has emitted?
Discussion
From the perspective of those on the ship, the
light must always proceed the ship. Is this true
for observers watching the ship pass? What
must they conclude about the speed of the
ship relative to the speed of light?
Bottom line
No matter can ever travel at or faster than the
speed of light.
Discussion
If I’m traveling at high speed, relative to you,
with a laser, I will measure the speed of the light
emitted by it to be c. If you measured the
speed of that same light at the same time, you
would also get c for the speed. How can this be
possible?
Hint: How do we define speed?
Length and time are relative
Speed is a distance traveled in a period of time.
In order to agree on the speed of light, we must
disagree on the distance traveled, or the time it
took or both.
Speed of light is not relative, space and time are
relative
Throwing a ball up
If you throw a ball straight up it will come
straight back down.
If you are standing in an airplane in smooth
and level flight and you throw a ball straight
up what happens?
Throwing a ball up
If I walk at a steady velocity and throw the
ball straight it how will you see the motion
of the ball?
Discussion
Repeat the experiment in the boxcar with light.
Remembering that the speed of light must be
the same for all observers, for which observer
will the light travel time be the greatest?
Explain.
Light clocks
We could make a clock consisting of two
mirrors a fixed distance apart facing each
other. One of the mirrors is only partially
silvered and allows 1% of the light to pass
through. A laser can then be bounced back
and forth between the two mirrors. Each
time the light pulse is detected behind the
partially silvered mirror, the clock records
another tick.
Time dilation
From your point of view, time runs slower in
the reference frame moving relative to you.
The faster it is moving the slower you observe
the time to pass in the other frame.
Discussion
Consider Jackie’s view of your light
experiment as she speeds by you. How will
she measure the time interval for the light to
complete one round trip as compared to
your measurement?