The Cosmological Distance Ladder

Main Sequence Fitting

The stars within a cluster are roughly the same age and distance from us.  We can take advantage of this fact and dramatically improve the method of spectroscopic parallax.  This is possible, because if one plots the apparent magnitude of stars within the cluster versus the color index, the pattern will closely resemble some part of the HR Diagram.  The only difference between this plot and the plot of an HR diagram is that the vertical axis scale is in apparent magnitude instead of absolute magnitude; however, since the stars in the cluster are all roughly the same distance away, the difference between their apparent magnitude and their absolute magnitude will all be roughly the same, (which is why the plot of apparent magnitude versus color index results in a pattern resembling some part of the HR Diagram).  It is therefore possible to overlay the HR Diagram using apparent magnitudes with a calibrated HR Diagram using absolute magnitudes, and shift the apparent magnitude plot until the patterns line up.  Once the patterns are lined up, the absolute magnitude of the stars in the cluster can be directly read from the HR Diagram.  This is an improvement over the spectroscopic parallax method because within a cluster of stars all having similar age, it is easy to distinguish the "normal" stars that fit the pattern of the HR diagram, (remember in the spectroscopic method applied to isolated stars and there was no way to  know for sure if there was anything unusual about the star that would cause it to not fit the HR Diagram).

Figure 1.  -- A cluster of Stars

Figure 2 -- A plot of apparent magnitude versus color index for the stars in the cluster.

Figure 3 -- The apparent magnitude plot is overlaid on a calibrated HR Diagram and shifted until the patterns match.  The absolute magnitude of the stars in the cluster are now known, and their distance can be calculated from: