The Sun and other stars

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The Sun and other stars
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The physics of stars

• A star begins simply as a roughly spherical ball
  of (mostly) hydrogen gas, responding only to
  gravity and its own pressure.
• To understand how this simple system behaves,
  however, requires an understanding of
• Fluid mechanics
• Electromagnetism
• Thermodynamics
• Special relativity
• Chemistry
• Nuclear physics
• Quantum mechanics

X-ray ultraviolet infrared
radio
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The Sun

• The Solar luminosity is 3.8x1026 W
• The surface temperature is about 5700 K
• From Weins Law

• Most of the luminosity comes out at about 509 nm
  (green light)

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The nature of stars

• Stars have a variety of brightnesses and colours
• Betelgeuse is a red giant, and one of the
  largest stars known
• Rigel is one of the brightest stars in the sky
  blue-white in colour

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The Hertzsprung-Russell diagram

• The colours and luminosities of stars are
  strongly correlated
• The Hertzsprung-Russel (1914) diagram proved to
  be the key that unlocked the secrets of stellar
  evolution
• Principle feature is the main sequence
• The brighter stars are known as giants

Luminosity
BLUE Colour RED
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Types of Stars

• Assuming stars are approximately blackbodies

Means bluer stars are hotter
Means brighter stars are larger
Betelgeuse is cool and very, very large
White Dwarfs are hot and tiny
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Types of stars
Intrinsically faint stars are more common than
luminous stars
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Hydrostatic equilibrium

• The force of gravity is always directed toward
  the centre of the star. Why does it not
  collapse?
• The opposing force is the gas pressure. As the
  star collapses, the pressure increases, pushing
  the gas back out.

• How must pressure vary with depth to remain in
  equilibrium?

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Hydrostatic equilibrium

• Consider a small cylinder at distance r from the
  centre of a spherical star.
• Pressure acts on both the top and bottom of the
  cylinder.
• By symmetry the pressure on the sides cancels out

• It is the pressure gradient that supports the
  star against gravity
• The derivative is always negative. Pressure must
  get stronger toward the centre

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Stellar Structure Equations
Hydrostatic equilibrium
Mass conservation
Equation of state

• These equations can be combined to determine the
  pressure or density as a function of radius, if
  the temperature gradient is known
• This depends on how energy is generated and
  transported through the star.

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Stellar structure

• Making the very unrealistic assumption of a
  constant density star, solve the stellar
  structure equations.

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The solar interior

• Observationally, one way to get a good look
  into the interior is using helioseismology
• Vibrations on the surface result from sound waves
  propagating through the interior

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The solar interior

• Another way to test our models of the solar
  interior are to look at the Solar neutrinos

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Break
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Stellar luminosity

• Where does this energy come from? Possibilities
• Gravitational potential energy (energy is
  released as star contracts)
• Chemical energy (energy released when atoms
  combine)
• Nuclear energy (energy released when atoms form)

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Gravitational potential

• So how much energy can we get out of gravity?
• Assume the Sun was originally much larger than it
  is today, and contracted. This releases
  gravitational potential energy on the
  Kelvin-Helmholtz timescale
• .

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Chemical energy

• Chemical reactions are based on the interactions
  of orbital electrons in atoms. Typical energy
  differences between atomic orbitals are 10 eV.

e.g. assume the Sun is pure hydrogen. The total
number of atoms is therefore
If each atom releases 10 eV of energy due to
chemical reactions, this means the total amount
of chemical energy available is
This is 100 times less than the gravitational
potential energy available, and would be radiated
in only 100,000 years at the present solar
luminosity
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Binding energy

• There is a binding energy associated with the
  nucleons themselves. Making a larger nucleus out
  of smaller ones is a process known as fusion.
• For example

0.7 of the H mass is converted into energy,
releasing 26.71 MeV.
E.g. Assume the Sun was originally 100
hydrogen, and converted the central 10 of H into
helium. How much energy would it produce in its
lifetime?