Lecture 21 - Spectral Classes of Stars (3/1/96)

Seeds: Chapter 6

  1. 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.
  2. Thermal Continuum (Blackbody) Radiation
    • Hot stuff glows
    • The hotter stuff is, the brighter it glows
    • The hotter stuff is, the bluer a color it glows
    • Temperature measures the mean-square velocity (kinetic energy) of the atoms in a substance, which jiggle around
    • Temperature in astronomy is measured in degrees Kelvin (K). A change of 1 K is the same as a change of 1 C. 0 K is absolute zero (no atom movement), 273 K = 0 C (water freezes), 373 K = 100 C (water boils).
    • The characteristic spectrum generated by a hot opaque solid, liquid or gas is called the thermal blackbody spectrum
    • The blackbody spectrum reaches a maximum brightness at a wavelength given by 3x10^6 nm / T
    • The total energy emitted by a blackbody radiator at temperature T is proportional to T^4
    • The measure of radiated energy per unit time is the Watt (W), with 1 W = 1 J/s.
  3. 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
  4. 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)
  5. The Doppler Effect
    • Lines can be used to tell us about the velocity of the gas that emitted it.
    • Because light is a wave, and the speed of light is constant, motion of the source of light can only change the wavelength.
    • If a source is moving toward you, you see a shorter wavelength.
    • If a source is moving away from you, you see a longer wavelength.
    • If a source is moving perpendicular to you, you see no change in wavelength.
    • The fractional change in wavelength is equal to the velocity divided by the speed of light (v/c), at least for v much less than c. When v becomes a significant fraction of c, you need to use Einstein's theory of Relativity to get it right.
    • If you measure a line that you know to be at a certain wavelength (like Lyman Alpha at 91.18 nm) at a slightly different wavelength, you can deduce the velocity of the source relative to us!
    • This velocity induced change in wavelength is called the Doppler Effect.
    • The Doppler Effect is what causes train whistles and car horns to have a higher pitch when approaching, then a lower pitch when passing you and going away.

Next Lecture - The Sun

Review of Atomic Structure

Thermal Continuum (Blackbody) Radiation

It is well-known that if you heat stuff up, it glows! If you turn the burner on your electric stove to high, it starts to glow red. A flame is bright, and burning coals glow red. If you've ever seen iron or steel being heated in a furnace, you know that as you heat it to higher and higher temperatures it glows red, yellow, bluish, then white-hot, and at the same time brighter and brighter.

There is obviously a connection with temperature and light emission. The hotter something is, the brighter it glows, and the "bluer" a color the light that it emits is.

The temperature of a body is a measure of how fast the atoms and molecules in it are jiggling about. Higher temperature means higher average velocity (actually, average squared-velocity). In physics, the temperature is measured using a scale called the Kelvin scale (K). This is the same degrees in the centigrade or Celsius scale (C) (a change of 1 K = 1 C), but measured from absolute zero (zero velocity, 0 K = -273 C = -460 F) instead of from the freezing of water ( 0 Celsius = 273 Kelvin = 32 F). Thus, water boils at 373 K (100 C = 212 F).

When we discussed the energy levels of hydrogen, we used the fact that the kinetic energy of a particle is proportional to the square of the velocity:

E = m v^2 / 2

If you as what the distribution of kinetic energies of atoms in a gas at a temperature T is, you find a distribution that has is peaked at a characteristic kinetic energy, with few atoms at low energies (velocities), and few atoms at high energies (velocities). The average kinetic energy (we denote an average some quantity X by < X >):

< E > = < mv^2/2 > = 3kT/2

where k is Boltzmann's constant (k=8.6 x 10^-5 eV/K). In more useful terms,

< E > = 1.3 eV ( T / 10000 K )

Because the electric force is transmitted by photons, then it turns out that whenever you apply a force to an electron, and it is accelerated, it will emit a photon. The fact that accelerating electrons always emit radiation is an important one in astonomy, and we will return to it more than once. At this point, it is important in that collisions between atoms can cause the electrons in the outer shells to accelerate, and thus emit radiation. The spectrum of this "thermal" radiation depends on the thermal distribution of velocities and thus kinetic energies of the atoms in the material.

If a material is opaque, that is if nearly all the photons emitted by an atom inside the matter will be absorbed and re-emitted by other atoms in the substance before escaping out through the surface, then the energy of the radiation will come to equilibrium with the energy in the thermal motions of the agitated electrons.

Types of Spectra: Continuum, Emission, Absorption

Three types of spectra:

Spectral Classes of Stars

The Doppler Effect

The Doppler effect:

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Steven T. Myers (myers@dept.physics.upenn.edu)
Last revised 04Mar96