Physics 321
Astrophysics II:  Lecture #6
Prof. Dale E. Gary

Hertzsprung-Russell Diagrams and
Structure of Spectral Lines

Hertzsprung-Russell Diagram

Luminosity Classes
We have used the terms giant, supergiant, dwarf, without defining them.  Because of the relationship between size and luminosity, the size categories correspond to luminosity class.  The Morgan-Keenan (M-K) system is based on spectra.  One can see subtle differences in spectra of stars of otherwise similar spectral type, due to the different sizes of the stars.  One of the main effects is the width of the spectral lines, which get narrower for more luminous stars, as may be seen below:

Dependence of Spectra on Luminosity Class
Figure 6.3 Spectra near spectral type F5, for different luminosity classes
Adapted from data in the electronic version of "A Library of Stellar Spectra,"
by Jacoby G.H., Hunter D.A., Christian C.A.  Astrophys. J. Suppl. Ser., 56, 257 (1984).

The M-K system of luminosity classes are shown in the table below, and their position on the H-R diagram is shown in Figure 6.4, below.

Figure 6.4 An H-R diagram showing the Morgan-Keenan luminosity classes,
along with locations in the diagram for some nearby or bright stars.


Type of Star
Extreme, luminous supergiants
Luminous supergiants
Less luminous supergiants
Bright giants
Normal giants
Main-sequence (dwarf) stars
White dwarfs

The M-K classification scheme enables astronomers to place a star on the H-R diagram solely on the basis of the star's spectrum.  Once the star is placed on the H-R diagram, one can simply read off the absolute magnitude MV from the vertical scale, and from its measured apparent magnitude find its distance from

mV - MV = 5 - 5 log d
Such a distance determination is called spectroscopic parallax, although note that it has nothing to do with parallax.  It is simply a distance determination based on its spectral type.  Note that because the luminosity classes are of finite extent in magnitude, this method is only good to roughly +/- 1 magnitude, which corresponds to a distance accuracy of about 101/5 = 1.6.

Let's compare spectral types from our catalog with the listed absolute magnitudes.  Star Gl 3 is listed as a K5 V (a K5 main-sequence, or dwarf star), and looking up that spectral type in Table A4.3 of the text, we find a predicted absolute magnitude of 8.0.  The absolute magnitude listed above is 7.1 -- somewhat brighter than predicted.  The star GJ 1003 has a listed spectral type of 'm', which must mean that the spectral type is uncertain, but it is some type of M star.  If we assume that it is luminosity class V, then from its measured absolute magnitude of 12.82 we would predict that it should be somewhere between M5 and M6.  Its B-V color index, however, would place it as about M2 or M3.  You can see that Table A4.3 is not exactly precise, but it makes a useful guide.

The Structure of Spectral Lines
Now let us focus on individual spectral line shapes and see what more they can tell us about the physical conditions in stars.  One simple measurement we can do is the width of the spectral line, but spectral lines can have different shapes.  A precise definition of line width that is independent of line shape is given by the equivalent width, which is defined as
Fc - Fl
W  = 

where Fc is the flux of the continuum, and Fl is the flux elsewhere in the line.  The figure below shows the relationship between the equivalent width and the shape of the line, for a normalized line profile.

Normalized line profile and equivalent width.  Note that the blue-shaded region above the line has the same area as the blue-shaded region below the line, so the equivalent width has the same area as the line itself.

The width of the line is contributed to by three main effects:

Equivalent Width Versus Line Strength