Stars%20II.%20Stellar%20Physics

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StarsII. Stellar Physics
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Overview of the structure of stars Still, First
the Sun as an example
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Overview of basic processes

• Nuclear energy production ? energy transport
  (radiation, convection)
• for a system in a long-time equilibrium, mass
  conservation, energy conservation, force balance.

Mathematically the conditions for the internal
equilibrium of a star can be expressed as four
differential equations governing the distribution
of mass, gas pressure and energy production and
transport in the star. Plus the Equation of
State (Physical State of the Gas) and Boundary
Conditions. These equations will be derived
soon.
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Connections with observations

• Maoz, fig2.4

Energy transport I radiation
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Energy transport IIconvection, sound waves and
helioseismology
The solar convection is visible on the surface as
the granulation. At the bright (high-T) center of
each granule, gas is rising upward, and at the
darker (lower-T) granule boundaries, it is
sinking down again. The size of a granule seen
from the Earth is typically 1, corresponding to
about 1000 km on the solar surface. There is also
a larger scale convection called supergranulation
in the photosphere. The cells of the
supergranulation may be about 1 in diameter.
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The oscillations we see on the surface are due to
sound waves generated and trapped inside the sun.
Sound waves are produced by pressure fluctuations
in the turbulent convective motions of the sun's
interior. Since sound is produced by pressure,
these modes of vibration are called p-modes.
Helioseismology These sound waves, and the modes
of vibration they produce, can be used to probe
the interior of the sun the same way that
geologists uses seismic waves from earthquakes to
probe the inside of the earth. Some of these
waves travel right through the center of the sun.
Others are bent back toward the surface at
shallow depths. Helioseismologists can use the
properties of these waves to determine the
temperature, density, composition, and motion of
the interior of the sun.
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http//solarscience.msfc.nasa.gov/Helioseismology.
shtml
The sound waves set the sun vibrating in millions
of different patterns or modes
One mode of vibration is shown in the preceding
image as a pattern of surface displacements
exaggerated by over 1000 times
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A cylindrical mass element located (r, rdr) from
center of the star
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2. Our goal of this Section

The goal is to understand the inner structure of
stars, their equilibrium configurations, nuclear
burning, energy transport and evolution. In the
standard model, we assume that a star can be
treated as a spherically symmetric gas sphere (no
non-radial motions, no magnetic fields). This is
a reasonably good approximation for most stars.
The task is solved within the approximation when
we have determined
Which equations constrain these parameters?

• (1) Hydrostatic equilibrium
• (2) Mass-density relation

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• (3) Radial luminosity profile, i.e. the
  luminosity produced by nuclear burning
• in a shell of radius r and thickness dr
• ev(?, T) denotes the energy production rate
  per volume, whereas e(?,T) is the energy
• production rate per mass. They can be
  determined by considering all nuclear reaction
• rates at a given temperature and density
  (only valid in inner nuclear reaction core).
• (4) Equation of energy transport (important!
  e.g. inhibiting the energy
• transport would imply zero luminosity and
  the explosion of the star).
• e.g.

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• So, we finally have 5 equations for 5 unknowns
  and we should be able to solve the problem in a
  unique way. The uniqueness of the solution is
  claimed in the Russel-Vogt-Theorem For a star of
  given chemical composition and mass there exists
  only one equilibrium configuration which solves
  the boundary problem of stellar structure.
• In this generality, the theorem is not proven.
  Local uniqueness can be shown, however. Also, the
  theorem is based on the wrong assumption that the
  chemical composition of a star is homogenous.
• That is, all the parameters of a star (its
  spectral type, luminosity, size, radius and
  temperature) are determined primarily by its
  mass. The emphasis on primarily' is important
  since this only applies during the normal' or
  hydrogen burning phase of a star's life.
• ??????????? (AY15204)

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Four boundary conditions

• M(r0) 0
• L(r0) 0
• P(rr) 0
• M(rr) M

???,???? (Vogt-Russell theorem) ????????????

• Standard Solar Model Bahcall Pinsonneault,
  Phys. Lett. B, 433 (1998) 1-8

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Nuclear fusions Summary

• Proton-proton chain
• (Tlt2x107 K stars with MMsun)
• CNO cycle
• (stars with mass1.2Msun)
• Triple-alpha reaction
• (Tgt 108K)
• More reactions at higher temperatures
• Carbon burning Oxygen burning Silicon burning
• (questions how elements heavier than Iron are
  produced? neutron capture see Star III.)

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p-p chain
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CNO cycle
C, N, O as catalysts
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• Triple-alpha
• Carbon burning
• Oxygen burning
• Silicon burning

(He burning)
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Onion Structure of the Massive Star
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Homework Textbook of D. Maoz, p61, 2, 6,9