Download Stellar Evolution after the Main Sequence

Stellar Evolution
after the Main Sequence
High Mass Stars
The Path to the Main Sequence
1000
100
10
1
.1
.01
O
B
A
F
G
K
M
After the Main Sequence
• As the star ages (at a much faster rate),
the process begins in the same manner as
for a low-mass star.
– H  He which forms an inert core
• After the He core becomes substantial,
then things begin to happen differently.
• The star heats and compresses faster, the
He doesn't get a chance to form the
electron gas and so there is no He flash.
• Instead, the He reaches the 100 million K
needed to begin He  C
More Nucleosyntheis…
• The Carbon core in turn becomes substantial,
but if the star is massive enough, it begins to
react turning Carbon into Neon and Oxygen
• Once the Oxygen core begins to become
substantial gravity again begins compressing
and heating it until it achieves temperatures
sufficient to change Oxygen into Silicon
A Many-layered Star
H
He
Si
C
Ne
O
Fe
The sequence of
contraction, heating,
ignition continues until
we have a set of shells:
H He
He  C
C  Ne
Ne  O
O  Si
Si  Fe
Example: Stars of 11 – 50 Msun
Step
Core Temp
(K)
Time
(years)
H-burning
40 million
70 million
He-burning
200 million
500 thousand
C-burning
600 million
600
Ne-burning
1.2 billion
1
O-burning
1.5 billion
1/2
Si-burning
2.7 billion
1 day
A day later!
You can see that the Silicon  Iron stage takes place in a single
day.
It's here that there is A Serious Problem for our massive star.
Iron occupies a rather special place for the elements. Iron is at
the top of the "Binding Energy Curve". This means creating all
of the elements by nuclear fusion has released energy. This
energy in the form of radiation and therefore heat has balanced
the force of gravity.
However, in order to create elements above Iron (26Fe) we have to
ADD ENERGY. This means that iron is the heaviest element we
can create which will give off energy to balance against gravity.
It takes about a day for the iron core to reach 1.4 Solar masses.
When this (Chanrasekhar's Limit) is exceeded, the electron
pressure cannot withstand gravity any longer.
The Core Collapses!
A day later!
Binding energy per nucleon
You can see that the Silicon  Iron stage takes place in a single day.
It's here that there is A Serious Problem for our massive star.
Iron occupies a rather special place for the elements. Iron is at the top
of the "Binding Energy Curve". This means creating all of the elements
by nuclear fusion has released energy. This energy in the form of
radiation and therefore heat has balanced the force of gravity.
56Fe
16O
12C
4He
8Be
fusion
fission
1H
Atomic weight
Iron Core Collapse
However, in order to create elements above Iron (26Fe) we
have to ADD ENERGY. This means that iron is the
heaviest element we can create which will give off
energy to balance against gravity.
It takes about a day for the iron core to reach 1.4 Solar
masses. When this (Chandrasekhar's Limit) is
exceeded, the electron pressure cannot withstand
gravity any longer.
The Core Collapses!
Danger, Will Robinson!!
Step
Core Temp (K)
Time
(years)
H-burning
40 million
70 million
He-burning
200 million
500 thousand
C-burning
600 million
600
Ne-burning
1.2 billion
1
O-burning
1.5 billion
1/2
Si-burning
2.7 billion
1 day
Fe Core Collapse
5.4 billion
0.2 seconds
Core 'Bounce'
23 billion
1 millionth second
"Boom"
1 billion
10 seconds
Aftermath
The result is a Type II
supernova
It is up to 100 billion times
more luminous than the
Sun
The light rapidly rises to
maximum brightness then
gradually decreases over
several weeks to months
This happens in a galaxy
similar to the Milkyway
about once every fifty
years on the average.
Supernova
The image here and on the
last slide is that of the
Crab Nebula (M1).
It is about 6300 lightyears
away, but was so bright
that it could be seen during
the day when its
appearance was recorded by
Chinese astronomers in
1054 AD
At this time it is about 6 lightyears in diameter and
still spreading out.
The average rate is about 30,000 miles/second
High-Mass Evolution
Historical Supernova
Date (AD)
Constellation
Apparent
Magnitude
Distance
kpc
Observers
185
Centaurus
-6
2.5
China
369
Cassiopeia
-3
10
China
1006
Lupus
-5
3.3
Asia, Europe,
Arabia
1054
Taurus (Crab)
-5
2
China,
North
America,
Arabia
1572
Cassiopeia
-4
5
Europe
(Tycho, et al)
1604
Ophiuchus
-2
6
Europe
(Kepler, et al)
1987
LMC
+3
50
The world
More supernovae
These exploded in 2001
What about the rest of the elements?
If iron is the heaviest element a star can
create, how is gold, silver, uranium, and the
rest of the periodic table formed?
The answer is in those
brief seconds of the
Supernova explosion
when there is more
than enough energy
available.
You are made up of StarStuff
– the results of the death of a massive star
What's Left…
• After the massive star implodes (followed by the
supernova explosion) the inner part of the star
remains.
• If the mass of this inner core is less than about 4
solar masses then it becomes stable.
• What's left is about the size of Manhattan Island
(with up to 4 times the mass of the sun
compressed into it)
• The immense gravity is balanced by degenerate
neutron pressure. When the protons and
electrons were forced too close they were
transformed into neutrons which are capable of
withstanding more pressure than the electron gas
holding apart the white dwarf.
• These stars are now Neutron Stars
Neutron Stars
• Stellar core squeezed together to neutrons
• Supported by neutron degeneracy pressure
• Astonishingly small size and large density
Neutron star
Mt. Everest
Neutron Stars
All of humanity
A sugar cube of neutron star
A cubic centimeter of neutron star weighs† as much
as all of humanity
†On the surface of the Earth
LGMs
A young graduate student,
Jocelyn Bell, was using a
radio telescope and found
that there was a strange
signal.
The first thought was this was a radio beacon from LGMs
(that is… Little Green Men)
Pulsars
• The source instead is a rapidly rotating
neutron star
• Its radio signal similar to the light beam
from a lighthouse
– As the beam sweeps by you get a pulse
M > 4 Msun
What if the remainder from the supernova
has more than 3-4 solar masses?
Then the neutron pressure cannot withstand
the force of gravity and the core collapses.
What can withstand these pressures and
bring the star's core back into balance?
Nothing
Interlude
Before we can discuss the region of space near the Black Hole, we
first have to deal with the nature of time and space.
In 1905, Albert Einstein realized that Newton's view of the
universe was not quite correct.
In Newton's Universe, space had 3
dimensions where objects were
located.
They moved from point to point in
time according to some absolute, or
universal clock which was
independent of space.
In Einstein's Universe, space and time are linked; time is another
dimension and objects are located and move in Spacetime
Relativity
Einstein's 1905 joining of space and time is
known as the Special Theory of Relativity.
Another way of looking at this is that for
Newton, there is some absolute frame of
reference, at rest, from which everything can
be measured. For Einstein, there is no such
reference - all things have the same status;
everything must be measured relative to each
other
It is 'Special' in the sense that it is 'limited' –
It does not deal with non-uniform motion.
Relativity
For 10 years, Einstein worked to extend his ideas to nonuniform motion.
The result was 1915's General Theory of Relativity
Recall that some time ago we discussed Newton's laws and
wrote down:
INERTIAL mass
F = m a
and
F = G m M/r2
GRAVITATIONAL mass
General Relativity
The General Theory of Relativity is based on the
"Principle of Equivalence"
That is,
Inertial Mass = Gravitational Mass
General Relativity
Essentially, this means you cannot tell the difference between
accelerating or being in a gravitational field.
Suppose you were enclosed in a windowless box (an elevator cage,
for example). You could be out in space being pushed by a
rocket or sitting on earth – there would be no way to
determine which is the truth
Newton versus Einstein
The Tao of Newton:
Mass tells gravity how to exert a force
Force tells mass how to move
The Tao of Einstein:
Mass-energy tells space-time how to curve
Curved space-time tells mass-energy how to move
The Tao of Newton
Consider a small mass passing near a larger one:
The masses create a force
according to the law:
F = GmM/r2
As they get closer, the force
increases between the masses
The masses accelerate according to F = m a,
causing them to move (the smaller mass
curves about the larger)
"Houston, There's a problem"
How does the force communicate across the distance
separating the masses?
According to Newton, it acts instantaneously so that
for each 'update' of positions, the force changes
and can act on the masses immediately.
But, according to Special Relativity, nothing can move faster
than the speed of light – so nothing is instantaneous
"What we have here is a failure to communicate"
So how does it work?
The Tao of Einstein
Consider the same small mass passing near the same
larger one:
In deep space, away from
any other masses, spacetime is "flat" and the small
mass moves in a straight
line.
The large mass causes
space-time to curve about it
– similar to the effect of a
heavy ball placed on a thin
rubber sheet.
The small mass simply follows the curve of space-time,
altering its path and ending up swinging around the large
one. Not because of any instantaneous forces, but
simply following the "landscape"
Tests of General Relativity
•
•
•
•
Precession of the Perihelion of Mercury
Bending of Starlight
Binary Pulsars
Gravitational Redshift
Precession of the Perihelion of Mercury
Instead of Mercury's orbit being stable and retracing
its path, it precesses. Some of this can be explained by
Newton's theory, but there is still an error of
42.98"±0.04"/century left unexplained. General
Relativity predicts the precession to be 42.98"/century.
Bending of Starlight
While photons do not have mass, they do have mass-energy,
therefore the curvature of space-time should cause them
to curve about a massive object
During a total solar eclipse
a star was observed next
to the Sun, however, the
actual position of the star
was behind the Sun…The
path the starlight took
followed the curving
'landscape'
The predicted deflection and
matching measurement was
1.75"
Bending of Starlight
The starlight just follows “the shortest path”
Gravitational Lensing
An object located behind a
massive compact object
will have multiple images
formed
Einstein’s Cross
an Einstein ring
galaxy directly behind a galaxy
Gravitational Redshift
General relativity also predicts that photons, since they must use
energy to "climb out of the gravitational well" formed by the
curved space-time will exhibit this energy loss by shifting their
wavelength toward the red end of the spectrum.
Again, this can be measured experimentally and agrees with the
prediction to within 2x10-4
Object
Gravitational Redshift
Earth
10-9
Sun
10-6
White dwarf
10-4
Neutron Star
10-3
Black hole
LARGE: Proportional to mass/radius
The Ultimate Redshift
• In 1783, John Mitchell, an English clergyman and
amateur astronomer, determined the escape velocity
for several objects:
– He calculated that to escape Earth's gravitational pull an
object must accelerate to 25/1000 the speed of light
(about 11 km/sec).
– He then further postulated that to escape the Sun's
gravitational pull and object must accelerate to 1/500 the
speed of light (618 km/sec).
– Intrigued, he wrote that if the sun's mass was increased by
a factor of 500, the escape velocity would equal that of the
speed of light.
– In a letter to a colleague he wrote, "all light emitted from
such a body would be made to return toward it by its own
proper gravity."
Complete Gravitational Collapse
If the core undergoes complete
gravitational collapse, space and time
warp.
The gravity gets so strong that not
even light can escape.
This is a Black Hole.
Complete Gravitational Collapse
There is a border within which nothing can
escape, the Event Horizon.
Outside of the event horizon, it is just a
mass --- but inside!
Black Hole
A black hole is not a cosmic vacuum cleaner!
It is not some colossal drain into which all the
Universe is flowing!
Beyond its event horizon, it acts like any other
mass. You could safely orbit as long as you don't
get inside the event horizon.
Once inside, however, there is no escape
Black Holes
Vacuum Fluctuations
Let’s pause for a moment and instead of
thinking about the large-scale universe we
consider the smallest scales possible.
In classical physics, the vacuum is totally
empty; it is the absence of everything
In quantum physics, the vacuum is a seething
hotbed of activity.
The vacuum is filled with virtual photons
continually creating/destroying pairs of
particles. This pair creation/annihilation is
known as the Vacuum Fluctuation.
Vacuum Fluctuations
Vacuum fluctuations can be pictured as:
e+
eA virtual photon creates an electron/positron pair, which
immediately annihilate each other to become a virtual
photon.
This has been measured in the laboratory as the
Casimir Effect
Hawking Radiation
What does vacuum fluctuations and other quantum
‘weirdness' have to do with Black holes?
Suppose the virtual pair was produced just outside the
event horizon of a black hole.
One member of the pair could fall in while the other
escape.
Conservation of mass-energy then requires the black
hole to shrink a bit
The radiation from this is named after its discoverer,
Stephen Hawking.
A black hole will evaporate in a time proportional to M3
Wormholes
General relativity also predicts the existence of
connections between ‘folds’ of the Universe.
This could permit time-travel and therefore
paradoxes. Hawking feels that quantum theory will
prohibit wormholes and avoid the paradoxes.
Gravitational Waves
Ripples in the curvature of space-time
The observational evidence is their emission by binary
pulsars.
The first studied was the PSR1913+16 which is formed
by two neutron stars, Hulse and Taylor were able to
measure its orbital parameters and found that the
two bodies are spiraling one into the other as they
lose energy by emission of gravitational waves.
These measurements are in excellent agreement with
the prediction of General Relativity