The term 'spectroscopic parallax' is misleading because it does not involve parallax at all. It is the procedure whereby the luminosity of a star can be measured from it's spectrum.
We make the assumption that the spectra for distant stars is similar to those from nearby stars. This assumption having been made, we can use the Hertzsprung – Russell diagram for nearby stars to estimate the luminosity of distant stars.
Once the luminosityhas been found, the distanceto the star can be estimated from a measurement of apparent brightness,using the equation
This procedure involves a lot of uncertainty. The main sources of uncertainty are
Dust and gas between the star and us absorbs and scatters some of the stars light, making it appear dimmer than it actually is.
The dust may absorb different frequencies of radiation in different ways, making the identification of spectral class harder.
The Luminosity found from the Hertzsprung – Russell diagram is not exact. Every region on the Hertzsprung – Russell diagram encompasses a range of different conditions corresponding to a range of different luminosities, even for stars of similar temperature.
As the stellar distance increases, the first two reasons above make the uncertainty in the luminosity greater and so the uncertainty in the distance calculation becomes greater. For this reason spectroscopic parallax is limited to measuring stellar distances up to about 10 Mpc.