Tully-Fisher relation

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In astronomy, the Tully-Fisher relation, published by astronomers R. Brent Tully and J. Richard Fisher in 1977, is a standard candle that measures the distance to rotating spiral galaxies by the width of the galaxy's spectral lines. The empirically-derived relation states that the luminosity of a galaxy is directly proportional to the fourth power of its rotational velocity, which can be calculated from the width of the spectral line, and uses the distance modulus to find distance from luminosity and apparent magnitude.

The reasoning behind the relation first states that the wider a spectral line for a galaxy, especially the 21-cm hydrogen line, the faster the galaxy is rotating. This is because the side spinning toward us will have a slight blueshift, and the side spinning away from us will have a slight redshift, as compared to the average spectral line position for the galaxy as a whole. Furthermore, since the galaxy's centrifugal force, which depends on rotational velocity, and gravitation, which depends on mass, are in balance, the mass and rotational velocity are related. Then, the relation assumes that more massive galaxies tend to have proportionally greater absolute luminosities, from which the apparent magnitude and the distance to a galaxy can be calculated.