Tully-Fisher Relation

A very promising distance determination technique was developed in the 1970's and 1980's by Tully and Fisher. The method has since been improved by several workers and is now one of the more accurate secondary distance indicators for the Universe. The method relies on the fact that there is a relationship between the rate at which a spiral galaxy spins and its intrinsic luminosity. The sense of the relation is that the faster a galaxy spins, the more luminous is the galaxy. How does this work?

Due to the spin of the galaxy, an observer will see part of the galaxy approaching them and part of the galaxy running away. This causes the emission from the galaxy to show redshifted, blueshifted, and no-shifted emission.

The motion will thus cause a narrow line, e.g., a line due to some element like hydrogen, to be smeared out and to appear broad to the external observer. The broader the line, the faster the galaxy must be spinning.

Why is there a correlation between the spin rate and L?

• The gas and stars are in orbit in the galaxy
  • ===> Centrifugal Force and Gravitational Force are in balance ===> v**2 / R - G M(galaxy) / R**2 = 0
  • So, the spin rate ===> M(galaxy) = v**2 x R / G
  So, since the observable light we see is produced by stars, it does not take a stretch of the imagination to infer that the more massive a galaxy is, the brighter it is likely to be. This is borne out by the Tully-Fisher relation, the empirically deduced relation between spin-rate and luminosity. [However, note that theoretically, although the idea is quite plausible, it is more difficult to demonstrate in the sense that it is difficult to derive the precise Tully-Fisher relation.]