The Cosmological Distance Ladder

Spectroscopic Parallax

It's important to realize that both the horizontal and vertical axis in the HR Diagram are independent of distance.  Hence if one can measure the surface temperature of a star, (technically its luminosity class must be know also), one can use the HR Diagram to determine the star's absolute magnitude, and then the distance equation can be used to determine the distance to the star.  This is the method of spectroscopic parallax.  It really has nothing to do with parallax at all, but the term "parallax" is so associated with distance measurements in astronomy that it is sometimes erroneously used as a synonym.

The method of spectroscopic parallax is shown in the diagram below.  A star's spectrum and apparent magnitude are directly observable.  From the star's spectrum we can determine its luminosity class and spectral class, which places the star on the HR Diagram.  From the HR diagram we find the star's absolute magnitude.  And finally from the star's absolute and apparent magnitude we can find the star's distance from the equation:

Example

The spectrum of a star with an apparent magnitude of 8 is studied and shows the star to be have a luminosity class of V, and a spectral type of A5.  What is the distance to the star?

The luminosity class and spectral type locates the star on the HR Diagram as shown below.

From the HR Diagram, the star can be seen to have an absolute magnitude of 2.5.  The distance to the star is then:

Limitations

The only problem with spectroscopic parallax is that the star being observed must be a "normal" star.  That is it must conform to the the relationships of the HR Diagram.  Most stars will fall into this category, but one never knows for sure.  For this reason, the method of spectroscopic parallax is applied most often to clusters of stars, in which case the method is called Main Sequence fitting which is our next distance measuring tool.