Physics 681 Lecture 1 I' General Properties of the Sun

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Physics 681 Lecture 1I. General Properties of
the Sun
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Sun Overview
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1. Mean Sun-Earth Distance 1AU1.5x108 Km

• Range 1.47x108 km Perihelion, Jan.
• 1.52x108 km Aphelion, July
• The distance can be measured by the Keplers 3rd
  Law

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• Radius r6.96x108 m, However, the radius means
  the photospheric radius
• Sun is expanding at 2.4 cm/year.
• Mean density ?1.408g/cm3
• Gravitation acceleration g274 m/s2
• Luminosity L total photon energy output per unit
  time.
• Solar Constant

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Solar Maximum Mission found
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However, the Earths atmosphere absorbs
significant amount of energy (Fig. 1.2)
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There is a solar cycle variation of Luminosity
peaks at solar maximum (Fig. 1.3)
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Intensity
Stefen-Boltzman Law
Stefen-Boltzman Constant
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Planks Radiation Law (Fig. 1.4)
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Long-wavelength Range
Rayleigh-Jeans Approximation
Example IR case
Example Radio Spectrum (Fig. 1.6)
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Rayleigh-Jeans Regime T (brightness temperature)
changes from
when wavelength changes from 1cm to 1m
Short Wavelength UV, EUV, X-Ray Wien Regime
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Color Indices U-B U 365nm Ultraviolet B-V
B 440nm Blue V 548nm Visible
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II. Stellar Model
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Hertzsprung-Russell Diagram
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H-R Diagram (Hertzsprun-Russell) Energy
Source Thermonuclear fusion Standard Solar
Model(Ignore internal rotation and
magnetic)X H abundance by weightY He
abundanceZ other heavier elementsXYZ 1Z
0.02 (approximately constant)to fit the present
Sun,
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III. Age and Pre-main-Sequence Evolution
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Star forms by gravitation collapse from a cloud,
i.e., self gravitationgtinternal gas pressure
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3 complications Magnetic Fields, Rotation,
Fragmentationat a
contracting cool Star is formed.R is several
times currentIt then continues to contract,
radiation energy comes from gravitational energy
internal energy increases as T increases
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Duration of slow contract phase
is Kelvin-Helmhotz Time where, L is
luminosity For Sun, Then, and nuclear fusion
started to begin the life in main sequence.
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IV. Quantitative Model
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1. Conservation of Mass orwhere rr(t) 2.
Hydrostatic Equilibriumgiven, however,
during the collapsing phase, this relation is
replaced by hydro-dynamics balance equation
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3. Energy Balancewhere, E energy generation
per unit mass S entropy per unit mass 4.
Energy TransportEnergy Flux F luminosity per
unit area transport by radiation transport
by convection
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5. Radiation Transform Equation Intensity
absorption coefficient cross section/mass
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For isotropic radiation would permit no net flux
Combining (2.17)(2.18)(2.13) gives
(2.20) defines Rosseland Mean Absorption
Coefficient
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However, we need to consider conduction and
convection in addition. Diffusion is defined
as a very slow process to move heavier elements
to center, lighter ones to surface.
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6. The Equation of Statepressure where, is
radiation pressure is gas pressure.For the
Sun,For perfect Gas, where, R is gas
constant is mean molecular weight can be
described by chemical composition and degree of
ionization.
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For the neutral gas, For ionized
gas, where, E number of electrons get free by
ionization of H and He divided by number of all
other particles.Degree of ionization is
determined by Saha equation,e.g., where,
is ionization energy is electron
pressure is partition function.
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Electrostatic correction at a given temperature
and density, the pressure is smaller than it
would be for perfect gas.Partial electron
degeneracy - Pauli Exclusion
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V. Nuclear Reaction
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Hydrogen Burning Reaction For the Sun, it
yields 98.8 of energy. (Table 2.1) CNO
chain (Table 2.2)
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VI. Opacity
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1. Bound-Bound AbsorptionPhotons with frequency
can be absorbed when atom is undergoing a
transition between two states ofabsorption
coefficient (cross section)where, oscillator
strength (transition probability) normalized
profile.
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Two Important ProfilesDoppler broadening due to
Maxwell Velocity of absorbing particlesLore
ntz profile due to collision broadening
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Doppler width where, damping constant 2x
effective collision frequency.Usually two
effects are combined and Doppler for core damping
for wings.
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2. Bound-Free Absorption- Photoionization (Fig
2.7)When photo energy gt ionization energy, cause
discontinuity at the ionization
energycross-section(hydrogen like
atom) Gaunt factor - ionization probability
from quantum mechanics
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3. Free-Free AbsorptionA free electron can
absorb a photon, but must have a third particle
(explain why?)
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4. Thomson Scatteringindependent of photon
wavelengthcross section electron is set
into oscillatory motion by electric field of the
incident wave.
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5. Rosseland Mean
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VII. Boundary Condition
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Equations
(Stable Layer)
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Boundary Condition at Center (m0)
Opacity
Surface defined as
at
Method Iteration Method
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VIII. Results for a Standard Solar Model
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Homework set 1

• 1. Derive Keplers 3rd law
• 2. Use T1 year, a 1AU, derive solar mass
• 3. Stix 1.5, 2.2, 2.3