Spectroscopic Parallax

...has nothing to do with parallax! (ain't astronomy great?)

But it is about finding the distance to a star.

How does it work?

Measure a star's apparent magnitude
Take a spectrum of the star and classify it (spectral type and luminosity class).
Figure out the proper absolute magnitude for that type of star
Then use the magnitude equation: m-M = 5log(d) -5

But remember to correct for absorption. How do we do this?

Example:

I am looking at Aldebaran. I measure its apparent magnitude to be m=0.86. I take a spectrum of it and classify it as a K5III (red giant). These stars have absolute magnitude of about -0.2. so m-M = 0.86 - (-0.2) = 1.06. 5log(d)-5 = 1.06 so d=11.5 pc
Well, that's close enough to measure by parallax. What is Aldebaran's distance? d=16 pc. Not very accurate...
What if there was dust involved?

Spectroscopic parallax is not all that accurate for individual stars. There is an intrinsic dispersion of about 1 magnitude in the absolute magnitudes of stars of a given spectral class.

1 magnitude error corresponds to a factor of 2.5 in flux, or a factor of 1.6 in distance.

But it is much better at determining the distance to a cluster of stars, where all the stars are at the same (unknown) distance. Why?