# Tully–Fisher relation

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The Tully–Fisher relation for spiral galaxies and lenticular galaxies

In astronomy, the Tully–Fisher relation 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). It was first published in 1977 by astronomers R. Brent Tully and J. Richard Fisher. 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 using long-slit spectroscopy.

The term Baryonic Tully–Fisher relation is used when the mass being considered is the baryonic mass of the galaxy, as opposed to the mass value inferred from luminosity alone.[1]

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 enables the difficult-to-observe intrinsic luminosity to be calculated from the relatively easily observable velocity. Use of the observed apparent brightness and the inverse square law enables the distance to the object to be estimated. In astronomical parlance this distance measurement is known as 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.

The relation does not apply to elliptical galaxies which are in general not rotationally supported. However, similar methods exist for them, such as the Faber–Jackson relation and the fundamental plane.