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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