The Classification of Stellar Spectra The Formation of Spectral Lines The Hertzsprung-Russell Diagram

Stellar Spectra The 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 ,Results collected into the Henry Draper Catalogue (Betelgeuse = HD39801)

Stellar Spectral Classification 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

Understanding Spectral Lines Need to understand… The atom Statistical Mechanics Atomic Transitions Boltzmann Energy Distribution Saha 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 neticMolecularTheory/Maxwell.htmlhttp:// neticMolecularTheory/Maxwell.html The root-mean-squared is the square root of the average value of v 2

Maxwell-Boltzmann Velocity Distribution Example Determine the fraction of hydrogen atoms in a gas at T=10,000 K with speeds between v 1 and v 2

The Boltzmann Equation T=85,000K n2=n1….for Hydrogen atom But what about Ionization? astr.gsu.edu/hbase/quantum/disfcn.html#c3 The probability distribution of a system occupying a given energy state may be described by the Boltzmann Factor…

The Boltzmann Equation Example At what temperature does N 2 =N 1 for hydrogen ??? Boltzmann Equation Degeneracy of levels 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 – – stro12/L9.htmlhttp:// stro12/L9.html – ectral%20Line%20Formation.htmhttp://personal.tcu.edu/~mfanelli/imastro/Sp ectral%20Line%20Formation.htm

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

X SAHABOLTZMANNX ACTUAL INTENSITY CURVE

EXAMPLE 8.1.5

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… applets/Hr/frame.htmlhttp:// applets/Hr/frame.html

Hertzsprung-Russell diagram Ejnar Hertzsprung ( ) 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

Hertzsprung-Russell diagram Henry Norris Russell independently came to the same conclusions as Hertzsprung …but made a graph!!!! The Hertzsprung-Russell Diagram

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 x Rsun) –Giants –White Dwarfs Example 8.2.1

EXAMPLE 8.2.1

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

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