Lecture 7 - Stellar Classification (2/2/99)

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ASTR012
Reading:

Chapter 13-2, 13-3, 8-2 (ZG4)


Notes:

pages 24 - 27


The disk of the red supergiant star Betelgeuse, as imaged by HST. The radius of this star would extend beyond the orbit of Jupiter, were it our Sun! (Courtesy NASA/STSCI)
? Key Question: What is the main sequence?
! Key Principle: The H-R Diagram
# Key Problem: What is the origin of the different stellar classes?

Investigations:

  1. Surveying the Stars
  2. The H-R Diagram and Stellar Classification
  3. Spectral Lines and Atomic Physics

Continuum Emission and Blackbody Radiation revisted

Stellar classes are essentially temperature classes. The colors correspond to temperatures through the blackbody relation. Opaque matter at a temperature T (in Kelvin) radiates a continuous spectrum of light caused by the movement and collisions of atoms (and their electrons)

The peak wavelength of the blackbody radiation is inversely proportional to the temperature, and the total power radiated per square meter of surface is proportional to the fourth power of the temperature:

The HR Diagram: Mass-Luminosity-Radii Relations

The Hertzsprung-Russell (HR) diagram is the fundamental "tool" for understanding stellar astrophysics. The fundamental quantities plotted are log L vs. -log T. Variants of the HR diagram include the color-magnitude diagram plotting absolute visual magnitude M_V vs. color B-V. Below is an example of an HR diagram:

Given the luminosity and temperature, which determines a star's locus in the HR diagram, we should then look at the radius and mass. First, we can derive a relation for the radius using the Stefan-Boltzmann relation and the surface flux:

Thus, the lines of constant radius follow roughly the slope of the main sequence. Stars above and to the right are larger (giants and supergiants) and stars below and to the left are smaller (dwarfs). For example, we can apply this to the bright standard star Vega:

The mass of the star roughly increases with luminosity as you move up the main sequence. However, the masses of stars not on the main sequence are problematic. We will leave these until we better understand stellar structure and evolution. There is an approximate power-law relation for stars on the main sequence:

This holds for stars more massive than about 0.4 Msun.

The Atom

Structure of the atom - nucleus and electron "cloud" for hydrogen and helium:

The Bohr model of the atom - electrons as orbiting "planets" in an atomic "solar system":

Stellar Types in Outline:

  1. Thermal Continuum (Blackbody) Radiation
  2. Types of Spectra: Continuum, Emission, Absorption
    • A hot dense (opaque) solid, liquid, or gas will produce a continuous spectrum -> thermal blackbody radiation
    • A low-density gas excited by radiation or collisions will emit spectral lines -> emission line spectrum
    • A low-density cooler gas in front of a hot continuum source will absorb spectral lines -> absorption line spectrum
  3. Spectral Classes of Stars
    • Can classify by the surface temperature T
    • Wavelength of peak of thermal continuum can give rough value for temperature
    • The types of lines seen in spectrum are better indicator of temperature
    • Each specific line is strongest at a particular temperature such that the transition energy is somewhat higher than the mean thermal kinetic energy. Too low temperature, not enough atoms in the lower level of transition beacause they are at lower levels. Too high temperature, they are at higher levels.
    • Can see ionized species of multi-electron atoms at the right temperatures.
    • At the highest temperatures, the hydrogen is ionized, and lines of helium dominate.
    • At the lowest temperatures, molecules can form in the coolest outer parts and molecular absorption lines dominate the spectrum.
    • For most medium temperature stars, the Balmer lines of hydrogen are the most prominent spectral feature
    • Spectral classes: O, B, A, F, G, K, M (decreasing in temperature)
    • Each spectral class divided into sub-classes 0-9
    • The Sun is spectral type G2 (T = 5800 K)
  4. Review of Atomic Structure
    • Levels (orbits) labeled by n = 1,2,3,...
    • Hydrogen Bohr Radius: r = 0.0529 nm n^2
    • Hydrogen Energy Levels: E = -13.6 eV / n^2
    • Wavelengths: 91.18 nm/ L = 1/n_low^2 - 1/n_up^2
    • Ionization = removal of electron
    • Hydrogen Ionization at energy gt; 13.6 eV (91.18 nm)
    • Helium single ionization at 24.6 eV (50.4 nm)
    • Helium fully ionized at 54.4 eV (22.8 nm)
    • You can fit 2n^2 electrons on shell of level n
    • Differentiate and label electrons by quantum numbers n (radial), l and m (angular), and spin s
    • You can put 2 electrons in each orbital (n,l, m) as long as they have opposite spins s=+/- 1/2
    • The number l labels the electron orbits, or where on the shell the electron is localized:
      1. l=0 is the s-orbital, which holds 2 electrons. The s electron is equally likely to be found at any angle on the shell.
      2. l=1 is the p-orbital, which holds 6 electrons. The p electrons are concentrated at either ends of 3 perpendicular axes.
      3. The other orbitals are d (l=2), f (l=3), etc.
    • The chemical properties of an element are determined by the orbitals occupied by the outer valence electrons in the atom. This is how the Periodic Table of the elements is arranged.

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smyers@nrao.edu Steven T. Myers