Bellwork: Degenerate Matter (A review form yesterday)

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Nov 29, 2013 (3 years and 8 months ago)

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Bellwork: Degenerate Matter (A review form yesterday)


Pulsar Astronomy

Page
1


All that is left of the star after the outer layers are ejected to space is the core remnant. The core's
gas is super
-
compressed by gravity to form a strange type of gas made of ``degenerate matter''. It
is important to remember that what happens to the co
re depends on the mass of the
core,

rather
than the original mass of the main sequence star from which it came, because the only thing left
for gravity to really compress is the core.

Degenerate matter

When gas become super
-
compressed, particles bump righ
t up against each other to produce a
kind of gas, called a
degenerate
gas
, which

behaves more like a solid. Normal gas exerts higher
pressure when it is heated and expands, but the pressure in a degenerate gas does not depend on
the temperature. The laws o
f quantum mechanics must be used for gases of ultra
-
high densities.


PREDICT:

Why do you think degenerate gas behaves more like a solid than the gas you are familiar
with her on Earth?



The
first rule

is that
only certain energies are permitted in a
closely confined space
. The
particles are arranged in energy levels like rungs of an energy ladder. In ordinary gas, most of the
energy levels are unfilled and the particles are free to move about. But in a degenerate gas, all of
the lower energy levels ar
e filled. The
second rule

is that
only two particles can share the same
energy level in a given volume at one time
. For white dwarfs the degenerate particles are the
electrons. For neutron stars the degenerate particles are neutrons. The
third rule

is that

how
close particles can be spaced depends
inversely

on their masses
. Electrons are spaced further
apart in a degenerate electron gas than the neutrons in a degenerate neutron gas because electrons
are much less massive than neutrons.

Let's see how these rules affect the core remnant.

1.

Degenerate gases strongly resist compression. The
degenerate particles (electrons or neutrons) are locked
into place because all of the lower energy shells are
filled up. The only way they can move is to
absorb
enough energy to get to the upper energy shells. This is
hard

to do! Compressing a degenerate gas requires a
change in the motions of the degenerate particle. But
that requires A LOT of energy. Degenerate particles
have no ``elbow room'' and their j
ostling against each other strongly resists compression.
The degenerate gas is like hardened steel!

Question: Why do degenerate gases resist compression?


Bellwork: Degenerate Matter (A review form yesterday)


Pulsar Astronomy

Page
2


2.

The pressure in a degenerate gas depends only on the speed of the degenerate particles
NOT the
temperature of the gas. But to change the speed of degenerate particles requires
A LOT of energy because they are locked into place against each other.
Adding heat only
causes the non
-
degenerate particles to move faster, but the degenerate ones supplying t
he
pressure are unaffected.

Question: Describe how the source of pressure in normal matter and degenerate matter
differ.

(Which depends on temperature?
-

Remember the Ideal Gas Law


PV= nRT
)




3.

Increasing the mass of the stellar core increases the
compression of the core. The
degenerate particles are forced closer together, but not much closer together because
there is no room left. A more massive stellar core remnant will be
smaller

than a lighter
core remnant. This is the opposite behavior of regu
lar materials: usually adding mass to
something makes it bigger!

Question:
What happens to the volume of a white dwarf or neutron star when mass is
added onto its surface? How is this different from “normal matter”?




White dwarfs form as the outer layers of a low
-
mass red giant star puff out to make a planetary
nebula. Since the lower mass stars make the white dwarfs, this type of remnant is the most
common endpoint for stellar evolution. If the remaining mass of the c
ore is less than 1.4 solar
masses, the pressure from the degenerate electrons (called
electron degeneracy pressure
) is
enough to prevent further collapse.

Question
s
:

1.

What is the name of the 1.4



limit for white dwarf stars? This limit represents

the mass limit in the core of a main sequence star that determines its final evolution.
It is the boundary between what two evolutionary endpoints?






2.

There is a mass limit for neutron stars as well. What is the name and value of this
limit?