Glossary
The Tully-Fisher Relation

This relation holds for Spiral Galaxies and makes use of a relation between the speed V at which the galaxy spins and the (observed flux from or) luminosity L of a galaxy. Specifically the relation is L is proportional to V4.
  • The speed Vc at which the galaxy spins
    • can be determined spectroscopically
      • e.g. narrow emission lines will be broadened due to the Doppler effect
        • emission from approaching side of the galaxy are blueshifted (relative to the line centroid)
        • emission from receding ing side of the galaxy are redshifted (relative to the line centroid)
        the breath of the observed line therefore gives an estimate of the rotation rate of the galaxy
    • which is a function of the central mass M
      for circular motion and a star of mass m at radius R
      m Vc2 / R = G M m / R2
      so M is proportional to Vc2 R
  • the observed flux or Luminosity L of a galaxy
    • can be determined photometrically
      • eg. simply integrating the surface brightness to determine the total flux or Luminosity from the galaxy.
    • which is a function of the (visible) mass
      (more massive - more stars - more emission)
Assuming all galaxies have the same M/L ratio and the same surface brightness, then the ralation L is proportional to Vc4 can be derived (or the Absolute magnitude in some band is proportional to log Vc). Thus the Tully-Fisher relation can be used as a distance indicator.

An example of the Tully Fisher relation

[Image Credit KLUN Group]

 The unbiased KLUN galaxy subsample binned redshifts (in log V, where V is in km/s) vs. distance moduli (µ = 5 log r + 25, derived with the direct B band TF relation). The continuous line shows the best fit Hubble law, H0 = 55 km/s/Mpc. The dotted line, with H0 = 72 km/s/Mpc is shown for comparison.

Another, with different conclusion

[Image Credit:Shoko Sakai, UCLA] The average TF relation for 5 clusters, with H0 = 73 km/s/Mpc shown.

Yet Another Example

TF [Image Credit:Shoko Sakai, UCLA] The TF relation for two clusters (Fornax & Abell 1367) The relative distance between the two clusters is determined from delta D.