Introduction
Trying to push deeper into the universe, astronomers have developed a number of new techniques for determining relative distances to galaxies: these independent relative distance scales now agree to better than 10%. For example, there is a very tight relation, called the Tully-Fisher relation, between the rotational velocity of a spiral galaxy and its luminosity. 1
The Tully-Fisher relation postulates that the rotational velocity of a spiral galaxy is correlated with the total luminosity of the galaxy. Tully-Fisher is a secondary distance indicator. It is useful in measuring the relative distances to galaxies, but not very useful in pinning down the absolute distance. Enter the Hubble Space Telescope: one of HST's key projects is to observe Cepheid variables in about 20 nearby galaxies, and to calibrate the secondary distance indicators such as Tully-Fisher. There is more information on this in the WMAP page on Hubble expansion. 2
The Tully-Fisher Relation is expressed as
L \propto W^{\alpha}
and is a correlation that holds for galaxies with disks stabilized by rotation, between the intrinsic luminosity
L
of the galaxy in optical or near-infrared bands and the rate of rotation
W
. 3
The Tully-Fisher relation was published by astronomers R. Brent Tully and J. Richard Fisher in 1977. It is an empirical relationship between the intrinsic luminosity (proportional to the stellar mass) of a spiral galaxy and its velocity width (the amplitude of its rotation curve). The luminosity is the amount of light energy emitted by the galaxy per unit time; it can be measured using the galaxy's apparent brightness when the distance to the galaxy is known. The velocity width is measured via the width or shift of spectral lines and the Doppler effect.
The quantitative relationship between luminosity and velocity width is a function of the wavelength at which the luminosity is measured, but roughly speaking, luminosity is proportional to velocity to the fourth power.
The relation connects the directly (and relatively easily) observable velocity width to the difficult-to-observe intrinsic luminosity. Because the luminosity is related to the (easily observed) apparent brightness by the distance (squared), the Tully-Fisher relation can be used as a distance measurement, or a "secondary standard candle."
Internal dynamics of stars in galaxies are driven by gravity. For this reason, the amplitude of the galaxy rotation curve is related to the galaxy's mass; the Tully-Fisher relation is a direct observation of a close relationship between galaxy stellar mass (which sets the luminosity) and total gravitational mass (which sets the amplitude of the rotation curve).
The relation is measured and calibrated using primary standard candles.
General process used to measure the distance to a spiral galaxy using the Tully-Fisher Relation:
- Measure the red and blue shifts of the rotation curve.
- Calculate the speed of the stars orbiting the center of the galaxy.
- Calculate the gravitational force acting on the stars.
- Take a 10th of the mass because 90% of the mass of the galaxy is made of dark matter.
- Find the luminosity and combine it with the apparent magnitude to finally get the distance.
The Tully-Fisher relation is useful in measuring distances out to about 10 Mpc (10,000,000 parsecs). However, it does not work for elliptical galaxies which are in general not rotationally supported. 4
References
- How Fast is the Universe Expanding? - Universe 101, NASA Goddard Space Flight Center.
- Local Supercluster Information - NASA High Energy Astrophysics Science Archive Research Center, Goddard Space Flght Center & Smithsonian Astrophysical Observatory.
- Tully-Fisher Relation - by Richard Brent Tully, Scholarpedia.
- Tully-Fisher Relation - Wikipedia.
Preview Image
Tully-Fisher Relation - View full-size image. (Source: Richard Brent Tully, Scholarpedia.)
Citation
Wallace, Matthew H. (Contributing Author); Bernard Haisch (Topic Editor). 2009. "Article Name." In: Encyclopedia of the Cosmos. Eds. Bernard Haisch and Joakim F. Lindblom (Redwood City, CA: Digital Universe Foundation). [First published March 14, 2009].
<http://www.cosmosportal.org/articles/view/138225/>
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