General Relativity

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The Stellar Graveyard, Relativity, Dead Stars
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I. What happens to a Sun-like star after the
planetary nebulae stage? II. What happens to a
massive star after it reaches the point where
iron is collecting in its core?
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Degenerate Matter

• Quantum Theory shows that matter can exist in a
  extremely dense state referred to as Degenerate
  Matter
• Loosely interpreted as
• Matter compressed to a density in which there
  is no more free space for the particles to fill

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The term degenerate, as used to describe a state
of matter, has nothing to do with politicians.
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Normal Matter

• In normal matter there is plenty of room for
  the electrons to occupy

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Electron Degeneracy

• If the matter is compressed enough it becomes
  electron degenerate
• The electrons run out of room to move around

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Electron Degeneracy Pressure
When matter is compressed and starts becoming
degenerate, a resistance to further compression
is provided by an outward force known as
Degeneracy Pressure In the case of electron
degenerate matter this pressure is referred to
as Electron Degeneracy Pressure
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Examples of Degenerate Matter

• The inert helium core of most low mass stars (lt
  2.5Msun) is compressed to the point of electron
  degeneracy just before the helium flash stage
• Brown Dwarfs
• White Dwarfs
• Black Dwarfs

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Applying Degeneracy to White Dwarfs

• The concept of electron degeneracy pressure can
  be applied to core-radius of dead sun-like stars
  (white dwarfs)
• The primary factor that decides how small a white
  dwarf will become is its final mass.
• (the mass when nuclear reactions have stopped in
  the core)

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White Dwarfs of Finite Dimension the
Chandrasekhar Limit
How small can a star become? For final masses of
1.4MSun or less, the radius will be finite and
the star will become a White Dwarf. This upper
mass limit for White Dwarf development is known
as the Chandrasekhar Limit
The graph indicates the expected radius (y axis)
of a white dwarf as a function of the stars final
mass. Note that as the mass increases, the final
radius decreases.
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White Dwarfs
A White Dwarf has a final mass similar to our Sun
(up to 1.4MSun). This mass is compressed to a
point where its radius is similar to our Earth.
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The Possible Fates of a White Dwarf
I. A White Dwarf with no companion (not a
multiple star system) Since there are no more
nuclear reactions within the core of the star
and the star cannot shrink any further, the star
will simply radiate off its existing heat energy
into space and slowly fade into a Black Dwarf.
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A fortune awaits (Theoretically)

• Continued
• The core of the star (filled mostly with carbon)
  could potentially crystallize into a diamond.
• Astronomers believe they have discovered just
  such a gem located in the constellation
  Centaurus. Its a mere 50LY away and is
  estimated to be 10 billion, trillion, trillion
  carats!!!

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The Possible Fates of a Dying White Dwarf
II. A White Dwarf with a companion If a companion
star is near (typically when the companion has
entered its giant stages), the white dwarf could
possible accrete material from its neighbor.
This material will be rich in hydrogen and will
pool on the surface of the star. The hydrogen
rich layer could possibly reach temperatures
necessary for hydrogen fusion. When this
happens the dwarf will briefly shine (perhaps a
few weeks) as ALL of hydrogen is burned very
quickly. The dwarfs outer layers will burn as
a NOVA.
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The Possible Fates of a Dying White Dwarf

• A White Dwarf with a companion
• The is process can repeat over and over as the
  dwarf gathers mass for the next nova. It is
  believed that some of the mass from each nova
  remains. Thus, there is a possibility that the
  star will destroy itself by way of a last gasp
  nuclear reaction of carbon if the star can
  collect enough mass to exceed the Chandrasekhar
  Limit. The carbon within the star will fuse and
  the degenerate state of the star will cause the
  ENTIRE dwarf to instantaneously be consumed
  by fusion.
• This is known as a Type Ia Supernova.

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What if the final mass of the star is greater
than the Chandrasekhar Limit?
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Recall that a more massive star will evolve
through a series of nuclear reactions involving
increasingly heavier atomic nuclei. This will
continue until the core begins to accumulate iron.
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As the star reaches the end of its fuel supply
the iron core will continue to contract into a
smaller and smaller core.
If the final mass of this shrinking object is
greater than the Chandrasekhar Limit (1.4MSun),
then electron degeneracy will NOT stop the
continued shrinking of the core.
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Neutron Degeneracy

• Given enough mass, gravity can further compress
  matter beyond electron degeneracy into a state of
  neutron degeneracy

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The laws of physics STILL apply to the electrons
and their necessary space and spin requirements,
but the electrons will eventually (under the
crushing force of gravity) crash into the atomic
nuclei of the atoms within the core of the
star. When this happens, they combine with
protons in the nuclei. The action produces a
neutron and neutrino. (note that charge is
conserved)
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Once the process starts, the entire
core collapses to an even smaller radius within
a single second!!
Tick
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Neutron Degeneracy Halts Collapse
If the final mass of the star is between 1.4 and
3MSun, neutron degeneracy will halt the stars
collapse at a finite dimension. The final
diameter will be about 10 kilometers!! Thats
tiny (astronomically speaking)!!!
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The developing core, just before collapse, is
still enshrouded in the outer gasses of the
star. The degenerate core causes all other
inwardly falling material to rebound off the
core. This rapid halt and rebound sends high
energy particles in the form of a shockwave
radiating away from the core and into any
surrounding stellar material.
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In addition to this shockwave is the release of a
HUGE number of neutrinos (1050, 1 neutrino for
every electron proton combination). The release
of energy that is released during this event is
on the order of 1045 WATTS!!
The explosion of a star in this manner is known
as a type II Supernova.
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Completing the Periodic Table
Supernova produce a lot of high energy
neutrons. These neutrons will smash into
neighboring stellar matter where they change into
protons and electrons. There is enough energy
associated with these particles for the elements
heavier than IRON to be synthesized.
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The only thing left in the core after the
supernova is a rapidly spinning ball of
neutrons. This object is as dense as an atomic
nucleus. At this point, the core is
referred to as a NEUTRON STAR and is the most
dense object in the universe.
Casey-Reed/Penn State
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Neutron Stars Spin Fast and Have Intense Magnetic
Fields
Conservation of angular momentum leads to a
prediction that the neutron star will spin on its
axis EXTREMELY fast (a whole rotation in a
fraction of a second!!) The magnetic field
around a typical neutron star should be amplified
to be about a trillion times stronger than the
Earths magnetic field.
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Charged particles trapped in the intense magnetic
field of the neutron star can emit radiation at
almost any wavelength.
Casey-Reed/Penn State
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Pulsating Radio Star The Pulsar
If the magnetic field around the rotating neutron
star is oriented OFF the axis of rotation (see
below) then from our perspective we can detect
radiation emitted by the regions of the fields
poles as it rotates (note the position of Earth
in the diagram).
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Anthony Hewish
Jocelyn Bell
Pulsars were first spotted in 1967 by English
astronomer Anthony Hewish and his graduate
student Jocelyn Bell. Initially thought to be
alien intelligence, the pulsars where original
termed LGMs (little green men).
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Franco Pacini
Thomas Gold
Astrophysicists Franco Pacini and Thomas Gold
were the first to present the spinning neutron
star model.
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Pulsar in the Crab Nebula
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Recap of the types of death that stars
experience based on their mass. Note that these
masses are INITIAL MASSES, not the stellar mass
at the time of death.
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Some properties of typical white dwarfs and
neutron stars relative to the Suns mass.
Billions of times more dense than water!!
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What if the final mass of the star is greater
than about 3 solar masses?
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a black hole
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Black Holes

• Stars with a final mass of up to 1.4MSun (the
  Chandrasekhar Limit) will become White Dwarfs
• Stars with a final mass between 1.4MSun and 3MSun
  will become Neutron Stars
• What happens to stars with a final mass greater
  than 3MSun? BLACK HOLES

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Black Holes (Classical)

• The force of gravity around a massive object is
  proportional to the objects mass and the
  distance from the objects center of mass
• Thus if the mass increases or more importantly if
  the volume that the mass occupies decreases then
  the force of gravity at the surface of the mass
  increases

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Escape Velocity of Black Holes (Classical)

• In order for an object to ESCAPE the force of a
  star or planets gravity it must reach a certain
  velocity away from the planet or stars surface.
  The velocity is known as the escape velocity.
• The Earth has an escape velocity of about 11km/s
• The Sun has an escape velocity of about 620km/s
• Any projectile object that does not have this
  speed when it leaves the surface is destined to
  fall back into the star or planet

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Black Holes (Classical)

• If the mass increases or the volume that the mass
  occupies decreases then the necessary escape
  velocity from the surface increases.
• An average neutron star has an escape velocity of
  about 50 the speed of light!
• If the mass is sufficient that the core collapses
  smaller and smaller, then there will be a point
  where the escape velocity exceeds the speed of
  light! A black hole is born.
• And since nothing can travel faster than the
  speed of light, nothing escapes!!!

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General Relativity Black Holes
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Einsteins Happiest Thought

• I was sitting in a chair in the Patent Office in
  Bern when all of the sudden a thought occurred to
  meIf a person falls freely he will not feel his
  own weight.
• I was startled. This simple thought made a deep
  impression on me. It impelled me toward a theory
  of gravity.
• Albert Einstein (Fall 1907)

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Gedanken Experimenten

• The initial stages of Einsteins theories are
  based on simple (math-less) logic known as
  thought experiments
• Even though a formal proof demands the
  unambiguous discipline of mathematics, the
  foundation is quite simple

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Principle of Equivalence

• No experiment performed in any single place can
  distinguish between a gravitational field and a
  accelerated reference frame.

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Principle of Equivalence
On the Surface of the Earth under the influence
of its Gravity
In the same box but now in the emptiness of space
and accelerating at 9.81m/s/s
The person inside the box cannot see outside of
the box and, based on the Principle of
Equivalence, has NO means to determine which is
true about his reference frame. Is it
accelerating or is it in a gravity field? The
essence of the equivalence principle.
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Principle of Equivalence
The box in freefall within the Earths gravity
field
The box (not accelerating) in intergalactic space
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Principle of Equivalence
TU Students experiencing firsthand the principle
of equivalence on NASAs affectionately named
vomit comet. The plane flies in a repeated
parabolic patternUp and Down, Up and Down, Up
and mmmblahhh.
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Principle of Equivalence
Simulating zero gravity
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Principle of Equivalence

• If there is no possible distinction between a
  gravity field and an accelerated reference frame
  then
• The results of experiments performed in
  accelerated frames should also be the results of
  experiments performed in equivalent gravity
  fields.
• Let the imagination run wild, lets think of a few
  consequences of this.

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Does Gravity Affect the path of Light?
Consider the following properties of light

• Light travels at about 300 million meters per
  second (180 000 miles per second) relative to
  any observer from any reference point!
• Therefore it takes a finite amount of time for
  light to travel a given distance
• Light has NO mass, thus classical Newtonian
  physics models do not adequately account for
  forces on light.

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Path of light in an accelerated frame of reference
Gus here, is about to undergo extreme
acceleration upwards. A photon leaves a light
source located on the side of his closed
reference frame.
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Path of light in an accelerated frame of reference
From Guss perspective inside the accelerating
box, the light seems to bend as it passes across
the width of the box. What would an non
accelerating observer outside the box say of the
light path?
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Did the light path BEND?

• A thought experiment in this reference frame
  leads to a conclusion that the path of light will
  bend relative to the observer inside the box.

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What does the Equivalence Principle Imply?

• The bending of light shown in the previous figure
  would require MASSIVE quantities of acceleration
  because light travels so fast.
• Based on the principle of equivalence this
  corresponds to a MASSIVE gravity field.

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Light path bent by HUGE Mass

• Gravity is created by mass
• Where could we find a large enough collection of
  mass to test such a theory?
• The Sun has a gravitational field strength (at
  its surface) 28 times greater than Earth

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Bending of Light Path by Massive Objects Gravity
Field
Arthur Eddington, an English Astronomer, realized
that during an upcoming eclipse the Sun would be
totally blocked by the Moon for about 6
minutes. From our perspective on Earth, stars in
the open cluster Hyades should be positioned
around the Sun during the eclipse If a light
path was affected by gravity, the stars of Hyades
should visibly shift position during this eclipse
in a manner similar to the figure shown.
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Validation

• In 1919, Eddington set up an expedition to the
  West coast of Africa and (simultaneously) a
  separate one to Eastern South America to witness
  the event.
• The position of the Hyades shifted in nearly the
  exact amount predicted by Einstein!

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How did gravity alter the light path?

• Did the gravity alter the course of the light by
  pulling on the light?
• Or did gravity alter the region of space that the
  light traveled through.
• According to Einstein, mass warps the space (and
  time) around massive objects such that light
  follows a
• straight path through warped space-time!!

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Newton vs. Einstein

• Newton thought of space as unchanging
• a stage on which motion of massive objects
  occurred
• objects moved in straight line paths unless
  acted on by a force
• Einstein thought of space shaped by the presence
  of mass
• mass moves with inertial motion through warped
  space (gives the appearance of forces)

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Newton vs. Einstein
http//science.nasa.gov/headlines/y2005/images/gam
ma/spacetime_strip.jpg
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The Earth does not stay close to the Sun due to a
force exerted on the Earth by the Sun. The Earth
simply follows a straight line path through
distorted space. In Einsteins worldno forces
are required.
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What does it mean to say that gravity altered
Time as well?

• Consider this gedanken experiment
• A light clock at the top of an accelerating
  frame of reference emits a pulse every second

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Observer Accelerates Relative to Light Clock

• The observer in the bottom of the frame will
  intercept pulse one and start counting time until
  the next.
• But before the next one reaches the observer, he
  has accelerated towards the second pulse by a
  finite amount.

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Time is NOT Same

• Thus the observer in the bottom will say that the
  clock does NOT send a pulse every second.
• It must send a pulse in a time interval shorter
  than a second as measured by the observer
• Thus the clock (relative to the observer) is
  ticking faster than observers watch!

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Consider the Principle of Equivalence

• If clocks tick at different rates in an
  accelerated frame of reference, then, per the
  equivalence principle, should the same happen in
  a gravity field?

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Time is Relative!

• Relative to an observer in a gravity field, time
  will pass faster for events that occur high in
  a gravity field (a gravity field less than the
  observers)
• and
• time will pass slower for events that occur lower
  or deeper in a gravity field (a stronger gravity
  field than the observers)

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Validation

• A test was conducted using identical atomic
  clocks, one placed in a high altitude aircraft
  and one on the Earth.
• Observations of time differences were consistent
  with General Relativity!!

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Gravitational Redshift
Relative to a distant observer, gravity alters
time near a massive object. Imagine a light
source deep in the gravity field The period is
related to the speed and wavelength and inversely
related to the frequency of the light source If
time is slowed (increase in period) near a
gravity field it will have the effect of
lengthening the wavelength (in order to maintain
constant speed of light) thus it will shift the
light towards the red (red shifting) as the light
ascends out of a gravity field
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Black Hole (Relativity)

• Mass warps space-time
• Light is not pulled by the mass but follows a
  straight path through the warped space around a
  massive object
• Could the warped space become so very warped that
  it forms closed paths such that light is forever
  constrained to follow? Thus never leave the space
  around the mass?
• Yes
  

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Black Holes (Relativity)

• Light leaving the surface of the massive object
  follows paths that are so warped that the paths
  lead right back into the object!

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Singularity

• What happens to all of the mass when it collapses
  to a black hole?
• The laws of physics, as we know them, cannot
  explain what happens inside the boundary of the
  black hole. The only properties that exist are
  mass, spin, and charge
• The nature, or form (atoms, neutrons,
  electrons,etc) of the mass is not known for
  certain
• Classically, it is believed that all of the mass
  collapses to an infinitely small volume such that
  the density of the core becomes infinite! (this
  is only a guess because the inside of the black
  hole cannot be probed)

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The Event Horizon

• Karl Schwarzchild calculated a minimum distance
  from the singularity such that light could escape
  into the space around the black hole.
• This distance is known as the Schwarzchild radius
• A concentric surface around the singularity with
  the Schwarzchild radius is known as the EVENT
  HORIZON.
• If we could get close enough to a black hole, the
  hole would appear black indeed and the black area
  would be within the event horizon
• Anything that enters the event horizon will NEVER
  return to our universe

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Question

• What if our Sun became a black hole (use your
  imagination). How would this effect our orbit
  around the Sun?
• For the Sun to become a black hole it would
  shrink to a size of 6km diameter.

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A trip into a Black Hole

• What would a trip into a black hole look like for
  a brave individual who ventures into the event
  horizon how would this individuals suicidal
  venture appear to an outside observer?

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How might we find a Black Hole
To find a black hole, we need a few things to
happen. A near by companion star of the black
hole needs to run through its evolutionary stages
and begin to swell such that some of the matter
closest to the black hole is pulled in.
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Searching for Black Holes

• The velocity of the matter that is spiraling into
  the black hole increases. Thus it heats up.
• As in falling gas heats up it will emit radiation
• If the heat is sufficient, the gas could release
  release large amounts of X-Ray radiation

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X-Ray Binary Systems

• Neutron stars can produce x-ray binaries as well
• The principle is similar to binaries containing
  white dwarfs
• Ultimately, the estimated mass suggests if it is
  a neutron star or black hole

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Have we found Black Hole Candidates?

• Within the constellation Cygnus
• There is a very powerful X-ray source very near
  Eta Cygni

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Masses are Uncertain

• Spectral Analysis yields estimates of the mass of
  the Cygni star/black-hole system.
• Similar to tracking binary stars
• Mass is not known exactly, but the estimates of
  the unseen binary member of Eta Cygni place it
  close to 6-10MSun
• Well beyond the 3 solar mass limit

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Gamma Ray Bursts GRB

• Huge explosions occur in the cosmos every day
• Some of these explosions release tremendous
  energy in the form of gamma rays
• It is possible that, at least some of the GRBs
  are due to the formation of black holes

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Compton Observatory
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Simulation of a star drifting too close to a
black hole.