Line Spectra

Part I

From the last presentation we see that each element should present a unique pattern of spectral lines. Thus composition can be determined.

Temperature can also be learned from the spectral lines. Each element has a temperature at which it is most prominent. Hotter than this temperature and the element begins to become ionized, the pattern of stable orbits is altered, and the spectral lines caused by this element have reduced strength. At cooler temperatures the electron receive insufficient stimulation to take upward transitions. Without these upward transitions we will not see the downward transitions that result in the lines in the spectrum.

Real stars range in temperature from about 35,000 K to 3,000 K. For the hottest stars most elements are ionized and the spectrum is relatively bare, almost no spectral lines are present. Lines due to the exceptionally stable helium may be present. Hydrogen lines can be seen in the spectrum of most stars because of its great abundance. The hydrogen lines are most prominent for stars at about 10,000 K.

As we progress to cooler stars, many elements come into prominence. Lines due to heavy elements (heavier than helium) become prominent in stars with temperatures like the Sun. For the very coolest stars, lines due to simple molecules are present. So the temperature of a star comes by comparing the relative prominence of lines due to a variety of elements.

In the early part of the 20^th century, the Harvard College Observatory was the site where most of the early stellar spectra were classified. The bulk of this work was done by female astronomers, Annie J. Cannon and Henrietta Leavett being the most active. The original classification was based on the prominence of the hydrogen lines and was alphabetical. A type stars had the strongest lines of hydrogen – B stars had lines somewhat weaker, and so forth. Cannon reordered this scheme to reflect a temperature scale. Only seven of the original types survived:

O – hottest stars (35,000 K)

A – still the strongest H lines

G – the Sun falls here

M – coolest stars (3,000 K)

In the 1930's a decimal subdivision was introduced for more precision. Each major class is subdivided into 10 subclasses, 0 – 9, so that the Sun (with a surface temperature of 5800 K) became a G2 star (0.2 from a G0 to a K0 star). The spectra of the hot O and B stars are relatively simple, while the cooler stars have very complex spectra, due to the many neutral elements that can exist at lower temperatures.

Part II

The next important thing we learn from the study of spectral lines is motion. This comes from the study of the Doppler Effect. Doppler noticed that for all wave phenomena, the motion of the source of the waves (or the receiver) affected the wavelength of the waves. If the source moves at the observer, the waves bunch up, the measured wavelength is shorter than the "rest" wavelength. For sound we hear a higher pitch. For light the wavelengths are shifted toward the blue (a "blue-shift"). If the source moves away from the observer, the waves spread out and the wavelength is longer than the rest wavelength. For sound the pitch decreases. For light the wavelengths are shifted toward the red (a "red-shift"). The shifts observed are very small and do not affect the color of the object. "Blue-shift" or "Red-shift" refer to motion, not color. The Doppler Effect helps us measure "radial velocity" - velocity in the line of sight, but cannot measure tangential velocity.

The Doppler Effect also explains the shock wave that trails behind an object that exceeds the local speed of sound. Please refer to the "Doppler Effect" animation to see this.

The true or "space velocity" of a star has to be done is two different ways. The Doppler Effect can measure the radial velocity. This is done by taking the spectrum of the star and noting how the lines are shifted from their laboratory wavelengths. This single measurement determines the radial velocity to high precision. In contrast the tangential velocity can only be measured by noting how fast the star moves across the sky (the proper motion) and combining that with the distance to the star. Both of these are exceedingly difficult measurements to make.

Note that the measurement of the Doppler Effect gives two pieces of information. If the lines are shifted toward the red, we know the object is receding. Likewise a blue-shift indicates that the star is approaching. The size of the shift gives us the radial velocity itself. So the Doppler Effect allows us to measure the radial velocity of a star.

The Doppler Effect also is used to measure the rotation rate of a star. All stars (except the Sun) are points of light and to measure the spectrum we must accept light from all over the surface simultaneously. If the star is rotating, parts of the star will be moving away from us and will induce a red-shift in the spectral lines. Other parts of the star will be moving towards us and will induce a blue-shift in the spectral lines. Thus each spectral line is a combination of a range of Doppler shifts. The net result is that the lines are broadened (Doppler Broadening).

Pressure broadening allows us to measure the radius of a star. Recall that the difference between a source that gives an emission spectrum and a source that gives a continuous spectrum is density. Imagine moving with an atom of a typical gas. Your world is very lonely because the distances between atoms is much greater than the size of the atoms. The transition of the electron that gives rise to the spectral lines are exactly in agreement with the simple theory we have discussed. Spectral lines are at well-defined wavelengths. As the pressure of the gas increases, the average distance between atoms decreases. The atom now has nearest neighbors, which can distort the shape of the stable electron orbits. Now when transitions occur, they may be a variety of wavelengths emitted, close to the original wavelength. To our instruments of limited resolution, it appears that the line is broadened. For stars the mechanism to rise or lower the pressure is gravity. Gravity depends on the mass and inversely as the square of the radius. Small stars like our Sun have high surface gravity (high pressure) and, therefore, broad spectral lines. Large stars have low surface gravity and thin spectral lines.

Magnetic fields can also be determined by the Zeeman Effect. When light passes through regions of high magnetic fields, spectral lines become split into fine components. The amount of the splitting is a measure of the magnetic field strength.