The Classification of Stellar Spectra The Formation of Spectral Lines The Hertzsprung-Russell...
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Transcript of The Classification of Stellar Spectra The Formation of Spectral Lines The Hertzsprung-Russell...
The Classification of Stellar Spectra
• The Formation of Spectral Lines
• The Hertzsprung-Russell Diagram
Stellar SpectraThe spectra of stars contain much information about the
properties of stars….What can be learned? First need to observe…Then classify/categorize
The Spectral Types of Stars
• “Spectral Taxonomy”• Temperature Sequence• OBAFGKM-LT• 10 Subdivisions
– A0-A9,B0-B9• Annie Jump Cannon
classified some 200,000 spectra between 1911-1914,Results collected into the Henry Draper Catalogue (Betelgeuse = HD39801)
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Stellar Spectral Classification
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What is the source of the underlying order???
Atomic Physics
Spectral Lines
• Balmer lines are associated with electronic transitions in Hydrogen atom’s first excited state n=2. Balmer lines reach their maximum “intensity” in the spectra of A0 stars with T=9250 K
• Neutral Helium lines are strongest for B2 stars with T=22,000K
• Singly ionized calcium are most intense for K0 stars with T=5250 K
• Another fine astronomical convention: METAL is any element heavier than helium!!!!!!
Gas Discharge Spectra
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Understanding Spectral Lines
Need to understand…• The atom• Statistical Mechanics
Atomic TransitionsBoltzmann Energy DistributionSaha Ionization Equation
First excited state occupancy for hydrogen atom from Boltzmann Equation
Stellar Spectral Lines
• Why do spectral lines depend upon temperature?– Populations of various
atomic states depends upon temperature
• Degeneracy of levels– Stage of Ionization
• Depends on Pressure and density…
• Depends somewhat on composition of star as well
Maxwell-Boltzmann Velocity Distribution
• http://www.chm.davidson.edu/chemistryapplets/KineticMolecularTheory/Maxwell.html
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The root-mean-squared is the square
root of the average value of v2
€
vrms = < v 2 >
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Maxwell-Boltzmann Velocity Distribution
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Example 8.1.1 Determine the fraction of hydrogen atoms in a gas at T=10,000 K with speeds between v1 and v2
The Boltzmann EquationT=85,000K n2=n1….for Hydrogen atom
But what about Ionization?
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http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/disfcn.html#c3
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The probability distribution of a system occupying a given energy state may be
described by the Boltzmann Factor…
The Boltzmann Equation
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Example 8.1.3 At what temperature does N2=N1 for hydrogen ???
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Boltzmann Equation
Degeneracy of levels
€
gn = 2n2
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But… Balmer lines reach maximum intensity at T~9520K!!
What gives?
The Saha Equation
• Ionization levels depend on:
– Temperature
– Density/Pressure
– Ionization Energy from given level
– Degeneracy of levels
• Saha Equation
– http://en.wikipedia.org/wiki/Saha_equation
– http://www.aoc.nrao.edu/~smyers/courses/astro12/L9.html
– http://personal.tcu.edu/~mfanelli/imastro/Spectral%20Line%20Formation.htm
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Number of Excited Hydrogen Atoms
• Convolution of Boltzmann and Saha Equations
• Maximum occurs at 9500K due to lack of un-ionized atoms above this temperature
EXAMPLE 8.1.4
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EXAMPLE 8.1.4
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X
SAHABOLTZMANN X ACTUAL INTENSITYCURVE
EXAMPLE 8.1.5
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EXAMPLE 8.1.5
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EXAMPLE 8.1.5
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Dependence of Spectral Lines vs. Temperature
Line Strength for each element (and ionization level) depends upon temperature as shown above….
Hertzsprung-Russell diagram
• Astronomers started to notice that O stars tended to be brighter and hotter than the other stars.
• With the Mass-Luminosity relation it was noted that O stars were more massive as well
• This led to a theory of stellar evolution that stated that stars began their lives as O stars and as they age became cooler,dimmer and less massive…This theory is no longer accepted…
• http://www.mhhe.com/physsci/astronomy/applets/Hr/frame.html
Hertzsprung-Russell diagram
• Ejnar Hertzsprung (1873-1967) Danish Engineer and amateur astronomer
• 1905 publication confirming correlation between luminosity and spectral type
• Noticed that type G and later stars could have a range of luminosities…The brighter stars of these classes were
GIANTS in order to achieve their brightness at the lower flux at lower temperatures
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Hertzsprung-Russell diagram
• Henry Norris Russell independently came to the same conclusions as Hertzsprung …but made a graph!!!!
The Hertzsprung-Russell Diagram
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H-R diagram
• Many more stars plotted today…!!!
H-R diagram
• Categories– Main Sequence
• “Adult”• Stable• Hydrogen core burning
– Supergiants• 1000x bigger than Sun• Unstable (Betelgeuse
2070 day period 700-1000 x Rsun)
– Giants– White Dwarfs
• Example 8.2.1
EXAMPLE 8.2.1
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Morgan-Keenan Luminosity classes
• Subtle variations in the line widths of spectra can be found for stars with similar effective temperatures but differing luminosities…canbe used for classification
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Spectroscopic Parallax
• Can use H-R diagram to estimate absolute brightness of star given its spectral type
• Use apparent brightness and distance modulus formula
• To obtain distance
• Scatter of +/- 1 magnitude results in factor of 1.6 uncertainty in distance
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