Stellar Remnants

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Stellar Remnants

• 2950
• Dr Bryce

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Class notices

• Clear Sky Patrol now operates from 9pm to 11pm
• Last week for 3 extra credit
• Preparation for next in-class exam

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White Dwarfs

• White dwarfs are the remaining cores of dead
  stars
  
• Electron degeneracy pressure supports them
  against gravity

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White Dwarfs

• Have very small luminosities, therefore are
  difficult to observe
  
• Easiest to observe as a binary companion of a
  brighter star
  
• Recall spectroscopic binaries
• Well known white dwarfs include Sirius binary
  companion

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White dwarfs cool off and grow dimmer with time


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Size of a White Dwarf

• White dwarfs with same mass as Sun are about same
  size as Earth
  
• Higher mass white dwarfs are smaller

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White dwarfs

• No longer have any useful nuclear fuel
• Gravity has overcome pressure until the point at
  which density is so high that degeneracy pressure
  takes over
  
• Higher mass white dwarfs have smaller radii as
  they experience stronger gravitational forces
  
• Although white dwarfs are very hot they are dim
  due to their very small surface areas.

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The White Dwarf Limit

• Quantum mechanics says that electrons must move
  faster as they are squeezed into a very small
  space
  
• As a white dwarfs mass approaches 1.4MSun, its
  electrons must move at nearly the speed of light
  
  
• Because nothing can move faster than light, a
  white dwarf cannot be more massive than 1.4MSun,
  the white dwarf limit (or Chandrasekhar limit)
  

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Star that started with less mass gains mass from
its companion Eventually the mass-losing star w
ill become a white dwarf
What happens next?
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Accretion Disks

• Mass falling toward a white dwarf from its close
  binary companion has some angular momentum
  
• The matter therefore orbits the white dwarf in an
  accretion disk

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Accretion Disks

• Friction between orbiting rings of matter in the
  disk transfers angular momentum outward and
  causes the disk to heat up and glow
  

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Nova

• The temperature of accreted matter eventually
  becomes hot enough for hydrogen fusion
  
• Fusion begins suddenly and explosively, causing a
  nova

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Nova

• Nova means new
• Although white dwarfs are old stars, the sudden
  brightening would make them appear to be new
  stars to ancient astronomers
  
• The core of the White Dwarf has used up all the
  nuclear fuel but there is a layer on unused
  hydrogen on the stars surface

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Nova

• The nova star system temporarily appears much
  brighter
  
• The explosion drives accreted matter out into
  space

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Two Types of Supernova
Massive star supernova Iron core of massive
star reaches white dwarf limit and collapses i
nto a neutron star, causing explosion White
dwarf supernova Carbon fusion suddenly begi
ns as white dwarf in close binary system reaches
white dwarf limit, causing total explosion
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One way to tell supernova types apart is with a
light curve showing how luminosity changes with
time
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Nova or Supernova?

• Supernovae are MUCH MUCH more luminous!!! (about
  10 million times)
  
• Nova H to He fusion of a layer of accreted
  matter, white dwarf left intact
  
• Supernova complete explosion of white dwarf,
  nothing left behind
  

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Supernova Type Massive Star or White Dwarf?

• Light curves differ
• Spectra differ (exploding white dwarfs dont have
  hydrogen absorption lines)
  

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Potential white dwarfs
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A neutron star is the ball of neutrons left
behind by a massive-star supernova
Degeneracy pressure of neutrons supports a neu
tron star against gravity
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Electron degeneracy pressure goes away because
electrons combine with protons, making neutrons
and neutrinos Neutrons collapse to the center,
forming a neutron star
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Discovery of Neutron Stars

• Using a radio telescope in 1967, Jocelyn Bell
  noticed very regular pulses of radio emission
  coming from a single part of the sky
  
• The pulses were coming from a spinning neutron
  stara pulsar
  

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Pulsar at center of Crab Nebula pulses 30 times
per second
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Pulsars

• A pulsar is a neutron star that beams radiation
  along a magnetic axis that is not aligned with
  the rotation axis

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Pulsars

• 10 - 20 km in radius
• 1.4 2 solar masses
• The fast spin speed is due to the small radius of
  the star
  
• Conservation of angular momentum

• The radiation beams sweep through space like
  lighthouse beams as the neutron star rotates
  
• Periods range from 1.5 ms to 8s

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Why Pulsars must be Neutron Stars
Circumference of NS 2p (radius) 60 km
Spin Rate of Fast Pulsars 1000 cycles per sec
ond Surface Rotation Velocity 60,000 km/s
20 speed of light
escape velocity from NS
Anything else would be torn to pieces!
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Matter falling toward a neutron star forms an
accretion disk, just as in a white-dwarf binary
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Accreting matter adds angular momentum to a
neutron star, increasing its spin
Episodes of fusion on the surface lead to X-ra
y bursts
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X-Ray Bursts

• Matter accreting onto a neutron star can
  eventually become hot enough for helium fusion
  
• The sudden onset of fusion produces a burst of
  X-rays

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A black hole is an object whose gravity is so
powerful that not even light can escape it.
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Escape velocity

• The velocity an object needs to completely
  escape the gravity of a large object
  
• How fast does a rocket need to go to leave the
  Earths surface?
  
• The Moon
• The Sun
• A Neutron star

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Escape Velocity
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Light would not be able to escape Earths surface
if you could shrink it to 34
Surface of a Black Hole

• The surface of a black hole is the radius at
  which the escape velocity equals the speed of
  light.
  
• This spherical surface is known as the event
  horizon.
  
• The radius of the event horizon is known as the
  Schwarzschild radius.
  

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Event horizon is larger for black holes of larger
mass A solar mass black hole would have a radiu
s of about 3 km
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No Escape

• Nothing can escape from within the event horizon
  because nothing can go faster than light.
  
• No escape means there is no more contact with
  something that falls in. It increases the hole
  mass, changes the spin or charge, but otherwise
  loses its identity.

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Neutron Star Limit

• Quantum mechanics says that neutrons in the same
  place cannot be in the same state
  
• Neutron degeneracy pressure can no longer support
  a neutron star against gravity if its mass
  exceeds about 3 Msun
  
• Some massive star supernovae can make black hole
  if enough mass falls onto core
  

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Singularity

• Beyond the neutron star limit, no known force can
  resist the crush of gravity.
  
• As far as we know, gravity crushes all the matter
  into a single point known as a singularity.
  

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To understand more

• We need to turn to Einstein
• Covered in Chapters S2 and S3
• We are going to have a discussion of these today

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Einsteins Theories of Relativity

• Special Theory of Relativity (1905)
• Usual notions of space and time must be revised
  for speeds approaching light speed (c)
  
• E mc2
• General Theory of Relativity (1915)
• Expands the ideas of special theory to include a
  surprising new view of gravity

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Key Ideas of Special Relativity

• No material object can travel faster than light
• If you observe something moving near light
  speed
  
• Its time slows down
• Its length contracts in direction of motion
• Its mass increases
• Whether or not two events are simultaneous
  depends on your perspective
  

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Relativity of Motion

• Motion is not absolutewe must measure speed of
  one object relative to another
  
• Example Plane moving at 1,670 km/hr from E to W
  would appear from space to be standing still

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Absolutes of Relativity

• The laws of nature are the same for everyone
• The speed of light is the same for everyone
• All of relativity follows from these two ideas!

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Thought Experiments

• Einstein explored the consequences of the
  absoluteness of light speed using thought
  experiments
  
• The consequences will be easiest for us to
  visualize with thought experiments involving
  spaceships in freely floating reference frames
  (no gravity or acceleration)

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Relativity of Motion at Low Speeds
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Relativity of Motion at Low Speeds
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Relativity of Motion at High Speeds
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Relativity of Motion at High Speeds
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(No Transcript)
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Time Dilation

• Time will appear to pass more slowly in a moving
  object by an amount depending on its speed
  
• Time almost halts for objects nearing the speed
  of light

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Formulas of Special Relativity
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Tests of Relativity

• First evidence for absoluteness of speed of light
  came from the Michaelson-Morley Experiment
  performed in 1887
  
• Time dilation happens routinely to subatomic
  particles the approach the speed of light in
  accelerators
  
• Time dilation has also been verified through
  precision measurements in airplanes moving at
  much slower speeds
  
• Prediction that Emc2 is verified daily in
  nuclear reactors and in the core of the Sun
  

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Making Sense of Relativity

• According to you, time slows down in a moving
  spaceship
  
• According to someone on that spaceship, your time
  slows down
  
• Who is right?
• You both are, because time is not absolute but
  depends on your perspective
  

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Spacetime

• Special relativity showed that space and time are
  not absolute
  
• Instead they are inextricably linked in a
  four-dimensional combination called spacetime
  

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A Journey to Vega

• The distance to Vega is about 25 light-years
• But if you could travel to Vega at 0.999c, the
  round trip would seem to take only two years!

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A Journey to Vega

• However, your twin on Earth would have aged 50
  years while you aged only 2
  
• Time and space are relative!

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Key Ideas of General Relativity

• Gravity arises from distortions of spacetime
• Time runs slowly in gravitational fields
• Black holes can exist in spacetime
• The universe may have no boundaries and no center
  but may still have finite volume
  
• Rapid changes in the motion of large masses can
  cause gravitational waves
  

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Rubber Sheet Analogy

• Matter distorts spacetime in a manner analogous
  to how heavy weights distort a rubber sheet

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The Equivalence Principle

• Einstein preserved the idea that all motion is
  relative by pointing out that the effects of
  acceleration are exactly equivalent to those of
  gravity

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Perspectives in Space

• A book has a definite three-dimensional shape
• But the book looks different in two-dimensional
  pictures of the book taken from different
  perspectives
  
• Similarly, space and time look different from
  different perspectives in spacetime

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Perspectives in Spacetime

• Observers in relative motion do not share the
  same definitions of x, y, z, and t, taken
  individually
  
• Space is different for different observers.
• Time is different for different observers.
• Spacetime is the same for everyone.

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Rules of Geometry in Flat Space

• Straight line is shortest distance between two
  points
  
• Parallel lines stay same distance apart
• Angles of a triangle sum to 180
• Circumference of circle is 2pr

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Geometry on a Curved Surface

• Straight lines are shortest paths between two
  points in flat space
  
• Great circles are the shortest paths between two
  points on a sphere
  

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Rules of Spherical Geometry

• Great circle is shortest distance between two
  points
  
• Parallel lines eventually converge
• Angles of a triangle sum to 180
• Circumference of circle is

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Rules of Saddle-Shaped Geometry

• Piece of hyperbola is shortest distance between
  two points
  
• Parallel lines diverge
• Angles of a triangle sum to
• Circumference of circle is 2pr

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Geometry of the Universe

• Universe may be either flat, spherical, or
  saddle-shaped depending on how much matter (and
  energy) it contains
  
• Flat and saddle-shaped universe are infinite in
  extent
  
• Spherical universe is finite in extent
• No center and no edge to the universe is
  necessary in any of these cases

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Straight lines in Spacetime

• According to Equivalence Principle
• If you are floating freely, then your worldline
  is following the straightest possible path
  through spacetime
  
• If you feel weight, then you are not on the
  straightest possible path

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Gravity, Newton, and Einstein

• Newton viewed gravity as a mysterious action at
  a distance
  
• Einstein removed the mystery by showing that what
  we perceive as gravity arises from curvature of
  spacetime

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Rubber Sheet Analogy

• On a flat rubber sheet
• Free-falling objects move in straight lines
• Circles all have circumference 2pr

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Rubber Sheet Analogy

• Mass of Sun curves spacetime
• Free-falling objects near Sun follow curved
  paths
  
• Circles near Sun have circumference

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Curvature near Sun

• If we could shrink the Sun without changing its
  mass, curvature of spacetime would become greater
  near its surface, as would strength of gravity

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Curvature near Black Hole

• Continued shrinkage of Sun would eventually make
  curvature so great that it would be like a
  bottomless pit in spacetime a black hole

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Limitations of the Analogy

• Spacetime is so curved near a black hole that
  nothing can escape
  
• The point of no return is called the event
  horizon
  
• Event horizon is a three-dimensional surface

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Time in an Gravitational Field

• Effects of gravity are exactly equivalent to
  those of acceleration
  
• Time must run more quickly at higher altitudes in
  a gravitational field than at lower altitudes

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Gravitational Time Dilation

• Passage of time has been measured at different
  altitudes has been precisely measured
  
• Time indeed passes more slowly at lower altitudes
  in precise agreement with general relativity
  
• Gravitational redshift

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Precession of Mercury

• The major axis of Mercurys elliptical orbit
  precesses with time at a rate that disagrees with
  Newtons laws
  
• General relativity precisely accounts for
  Mercurys precession

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Gravitational Lensing

• Curved spacetime alters the paths of light rays,
  shifting the apparent positions of objects in an
  effect called gravitational lensing
  
• Observed shifts precisely agree with general
  relativity

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Gravitational Lensing

• Gravitational lensing can distort the images of
  objects
  
• Lensing can even make one object appear to be at
  two or more points in the sky

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Gravitational Waves

• General relativity predicts that movements of a
  massive object can produce gravitational waves
  just as movements of a charged particle produce
  light waves
• Gravitational waves have not yet been directly
  detected
  

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Light waves take extra time to climb out of a
deep hole in spacetime leading to a gravitational
redshift
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Time passes more slowly near the event horizon
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• Tidal forces near the event horizon of a
• 3 MSun black hole would be lethal to humans
• Tidal forces would be gentler near a supermassive
  black hole because its radius is much bigger

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If the Sun shrank into a black hole, its gravity
would be different only near the event horizon
Black holes dont suck!
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Black Hole Verification

• Need to measure mass
• Use orbital properties of companion
• Measure velocity and distance of orbiting gas
• Its a black hole if its not a star and its mass
  exceeds the neutron star limit (3 MSun)
  

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Some X-ray binaries contain compact objects of
mass exceeding 3 MSun which are likely to be
black holes
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One famous X-ray binary with a likely black hole
is in the constellation Cygnus
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Gamma-Ray Bursts

• Brief bursts of gamma-rays coming from space were
  first detected in the 1960s
  

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• Observations in the 1990s showed that many
  gamma-ray bursts were coming from very distant
  galaxies
  
• They must be among the most powerful explosions
  in the universecould be the formation of a black
  hole
  

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Supernovae and Gamma-Ray Bursts

• Observations show that at least some gamma-ray
  bursts are produced by supernova explosions
  
• Some others may come from collisions between
  neutron stars

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Our model