View source for Tully-Fisher relation

== Distance Measurements ==

In the 1970s the situation regarding the extragalactic distance scale was in a sorry state.  The characterization of this scale, the Hubble constant <math> {\rm H}_0 = <V_i/d_i> </math> is the ratio of the cosmic expansion velocity to the distance from us averaged over a fair sample of targets.  There was a debate over the value of this constant at the level of a factor two.  At its core was a critical issue.  The standard cosmological model at the time held that the primary constituents of the universe were particles of matter that had been acting since the Big Bang to slow the cosmic expansion.  The "theory of inflation" 
anticipated that the density of matter amounted to the "critical value" required to give a flat topology.  This model implies a specific link between the age of the universe and the expansion scale.  The age of
the universe was reasonably constrained by the age-dating of stellar populations in globular clusters.  The theoretically preferred model required that the Hubble constant be at the very lowest of the range being seriously discussed at the end of the 20th Century.  If <math> {\rm H}_0 </math> lay in the mid to upper range then the theorist's preferred model was excluded.

For some 20 years after its inception, the Tully-Fisher relation was generally considered to give the best distances to galaxies in the range required to define <math> {\rm H}_0 \ .</math>  There was controversy [7,8].  Other methodologies
emerged, such as the use of the bright end cutoff in the luminosities of planetary nebulae [9] and "surface brightness fluctuations" caused by the distribution of the brightest stars in galaxies dominated by old
populations [10].  There was a general, but not unanimous, agreement among specialist observers that <math> {\rm H}_0 </math>  was being measured at a value that precluded the standard model.

A paradigm shift came with the evidence from observations of supernovae of type Ia that the universe appears to be accelerating [11,12].  It seems that a repulsive dark energy is dynamically dominant.  The relationship between ages and expansion rate is altered.  <math> {\rm H}_0 </math> is now compatible with the new preferred model.

New methods to measure distance become available.  The use of supernovae is particularly accurate.  If the brightest red giant branch stars are resolved in the image of a galaxy, the known luminosities of these stars
gives a good distance [13]. However each of the various methods has a weakness: targets arise serendipitously, or only include certain types of galaxies, or are required to be very nearby.  There is still an important role for the Tully-Fisher relation.  It is no longer the most accurate method on a single case basis but since the application is to normal disk systems, with little restriction in range, it enables the determination of distances to many thousands of galaxies in all the environments that galaxies are found [14,15].  

Independent of the value of the Hubble Constant, the Tully-Fisher relation can be used to measure peculiar velocities, motions of galaxies that are deviations from the linear Hubble expansion.  These motions are thought to be due to the gravitational influence of over- and under-densities of matter.  There is an extensive literature discussing the relationship between the peculiar velocities of galaxies measured via the Tully-Fisher relation and the large-scale distribution of galaxies.