Stellar remnants and binary stars

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Stellar remnants and binary stars

• Dr Bryce

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Class notices

• Exam 2 31st October
• Homework 7 due 12 noon 29th October
• Homework 6 results
• Majority of homework errors are due to misreading
  i.e.
• The Sun is a main sequence sequence star

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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 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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Radius decreasing with Mass
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The White Dwarf Limit

• Quantum mechanics says that electrons must move
  faster as they are squeezed into a smaller 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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Potential white dwarfs
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Multiple Shell Burning

• Advanced nuclear burning proceeds in a series of
  nested shells

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Iron is dead end for fusion because nuclear
reactions involving iron do not release
energy (Fe has lowest mass per nuclear particle)
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Helium Capture

• High core temperatures allow helium to fuse with
  heavier elements

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Evidence for helium capture Higher abundances
of elements with even numbers of protons
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The end of the nuclear road

• Iron builds up in core until degeneracy pressure
  can no longer resist gravity
• Core then suddenly collapses, creating supernova
  explosion
• Nova means new, but this happening at the end of
  a stars life

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Supernova Explosion

• Core 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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Supernova Explosion
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Energy and neutrons released in supernova
explosion enable elements heavier than iron to
form, including Au and U
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Supernova Remnant

• Energy released by collapse of core drives outer
  layers into space
• The Crab Nebula is the remnant of the supernova
  seen in A.D. 1054

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Supernova 1987A

• The closest supernova in the last four centuries
  was seen in 1987

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Impact of Debris with Rings

• More recent observations are showing the inner
  ring light up as debris crashes into it

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Role of Mass

• A stars mass determines its entire life story
  because it determines its core temperature
• High-mass stars with gt8MSun have short lives,
  eventually becoming hot enough to make iron, and
  end in supernova explosions
• Low-mass stars with lt2MSun have long lives,
  never become hot enough to fuse carbon nuclei,
  and end as white dwarfs
• Intermediate mass stars can make elements heavier
  than carbon but end as 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 neutron star
against gravity
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Neutron Stars

• Typically 10s of km in radius
• Equivalent to Iowa City!
• The force of gravity at the surface is immense
• Electrons and protons can exist on the surface,
  where they form a crust
• The interior is a superfluid consisting of only
  neutrons, no nucleii

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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
• The radiation beams sweep through space like
  lighthouse beams as the neutron star rotates

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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
second Surface Rotation Velocity 60,000
km/s 20 speed of light
escape velocity from NS
Anything larger would be torn to pieces!
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Why so fast?

• Pulsars spin fast because cores spin speeds up
  as it collapses into neutron star
• Conservation of angular momentum

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Neutron Star radii

• Any larger and the star would be torn apart due
  to the high rotation rate

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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
Initial Kinetic Energy
Final Gravitational Potential Energy

(escape velocity)2 G x (mass)

2 (radius)
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Thought Question

• What happens to the escape velocity from an
  object if you shrink it?
• A. It increases
• B. It decreases
• C. It stays the same

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Thought Question

• What happens to the escape velocity from an
  object if you shrink it?
• A. It increases
• B. It decreases
• C. It stays the same
• Hint

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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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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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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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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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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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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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Rubber Sheet Analogy

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

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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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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 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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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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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 gt 180
• Circumference of circle is lt 2pr

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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 lt 180
• Circumference of circle is gt 2pr

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• A black holes mass strongly warps space and time
  in vicinity of event horizon
• 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

Event horizon
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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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Paths in curved Spacetime
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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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Photons in gravitational fields
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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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One famous X-ray binary with a likely black hole
is in the constellation Cygnus
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Binary stars
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The binary star Algol consists of a 3.7 MSun main
sequence star and a 0.8 MSun subgiant star.
Stars in Algol are close enough that matter can
flow from subgiant onto main-sequence star
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Star that is now a subgiant was originally more
massive As it reached the end of its life and
started to grow, it began to transfer mass to its
companion (mass exchange) Now the companion star
is more massive
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Star that started with less mass gains mass from
its companion Eventually the mass-losing star
will become a white dwarf
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Mass transfer
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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

• 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
into a neutron star, causing explosion White
dwarf OR binary supernova Carbon fusion
suddenly begins 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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Neutron Stars in binary systems
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-ray 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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Our model
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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