Tully–Fisher relation

The Tully–Fisher relation is an empirical correlation between a spiral galaxy’s luminosity and its rotation speed. Its calibrated form lets astronomers estimate distances from a galaxy’s measured rotation.

Galaxy rotation curve: A plot of orbital speed against distance from a galaxy’s center. The outer rotation speed is the key kinematic quantity in the relation.
Cosmic distance ladder: A sequence of methods that calibrate astronomical distances from nearby objects to the distant universe. Tully–Fisher provides a rung for distances beyond the reach of stellar parallax.
Absolute magnitude: The apparent magnitude an object would have at a standard distance of ten parsecs. The relation predicts intrinsic brightness, commonly expressed as absolute magnitude.
Faber–Jackson relation: An empirical relation between the luminosity of an elliptical galaxy and the velocity dispersion of its stars. It is a luminosity–kinematics relation for pressure-supported galaxies rather than rotating disks.
Line width–luminosity relation: A form of the Tully–Fisher relation that connects luminosity with the width of a galaxy’s spectral emission line. Spectral line width provides an observable proxy for rotation speed.
Hubble constant: The present-day expansion rate of the universe, relating cosmic recession velocity to distance. A large sample of Tully–Fisher distances can constrain the expansion rate.
Apparent magnitude: A measure of an object's observed brightness from Earth. Observed brightness is compared with the relation’s predicted intrinsic brightness.
Fundamental plane of elliptical galaxies: A scaling relation linking the size, surface brightness, and velocity dispersion of elliptical galaxies. It extends the elliptical-galaxy scaling approach beyond a single luminosity–speed pairing.
Inclination correction: A correction that accounts for a galaxy’s tilted orientation when estimating its rotation speed from line-of-sight motion. Observed line widths underestimate rotation when a disk is viewed near face-on.
Galaxy peculiar velocity: A galaxy’s motion relative to the smooth expansion of the universe. Distance estimates combined with redshifts reveal deviations from cosmic expansion.

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