The Hertzsprung-Russell diagram is a graph illustrating star luminosity versus temperature. It is explored thoroughly in the NAAP Hertzsprung-Russell Diagram Module. It is a significant tool in distance determination because astronomers assume that stars nearby the earth are essentially like the stars very far from the earth. Thus, if one can plot a star's location on the HR Diagram, its absolute magnitude can be read off. Two different distance methods make use of the HR Diagram: spectroscopic parallax and main sequence fitting.
It should first be noted that spectroscopic parallax has nothing to do with trigonometric parallax. The use of the word parallax here is simply a reference to the goal of finding distances. The spectroscopic parallax technique requires that a star's apparent magnitude and its spectrum have been observed. Information garnered from the spectrum is used to find the star's position on the HR Diagram.
The types of spectral lines in the star's spectrum allow astronomers to determine the spectral type which determines the location of the star horizontally on the HR Diagram. Determining the vertical location of the star requires scrutinizing the thickness (range over which wavelengths are absorbed) of the spectral lines. The thickness of lines is described by the star's Luminosity Class – a roman numeral between I and V appended to the spectral class. This effect is determined by the density of atoms doing the absorbing in the outer parts of the star since nearby atoms distort the energy levels of an atom allowing photons with a wider range of energies to be absorbed. A main sequence star (lumininosity class V) will have very thick absorption lines in its spectra since the density of atoms in the outer layers of the star is high. While a supergiant star (luminosity class I) will have very narrow spectral lines because of the low density of the absorbing atoms. The luminosity class of the star pins down the vertical position of the star on the HR Diagram. Once the star's position on the HR Diagram is identified by the intersection of its spectral class and luminosity class, one can read off its absolute magnitude.
Once the absolute magnitude is known, it is combined with the already observed apparent magnitude and the distance modulus provides the distance to the star.