Stellar Evolutionafter the Main

SequenceHigh Mass Stars

The Path to the Main Sequence

O B A F G K M

1

.1

10

.01

100

1000

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

C

Ne

Si

FeO

The sequence of contraction, heating, ignition continues until we have a set of shells:H HeHe CC NeNe OO SiSi 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!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.

12C4He

8Be

16O

56Fe

1HBind

ing

ener

gy p

er n

ucle

on

Atomic weight

fusion fission

Iron Core CollapseHowever, 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

AftermathThe result is a Type II

supernovaIt 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.

SupernovaThe 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 ADAt 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 SupernovaDate (AD)

Constellation ApparentMagnitude

Distancekpc

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

A sugar cube of neutron star

All of humanity

A cubic centimeter of neutron star weighs† as much as all of humanity

Neutron Stars

†On the surface of the Earth

LGMsA 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

InterludeBefore 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

RelativityEinstein'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.

RelativityFor 10 years, Einstein worked to extend his ideas to

non-uniform motion. The result was 1915's General Theory of Relativity

Recall that some time ago we discussed Newton's laws and wrote down:

F = m a INERTIAL mass

and

F = G m M/r2GRAVITATIONAL mass

General RelativityThe 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 curveCurved space-time tells mass-energy how to

move

The Tao of NewtonConsider 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 EinsteinConsider the same small mass passing near the

same larger one:

The large mass causes space-time to curve about it – similar to the effect of a heavy ball placed on a thin rubber sheet.

In deep space, away from any other masses, space-time is "flat" and the small mass moves in a straight line.

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 StarlightWhile 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 LensingAn object located behind

a massive compact object will have multiple images formed

Einstein’s Cross an Einstein ringgalaxy directly behind a galaxy

Gravitational RedshiftGeneral 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.

There is a border within which nothing can escape, the Event Horizon.

Outside of the event horizon, it is just a mass --- but inside!

Complete Gravitational Collapse

Black HoleA 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-

e+

A 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 RadiationWhat 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

WormholesGeneral 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 WavesRipples in the curvature of space-timeThe 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