Scaling relations describe strong trends that are observed between important physical properties (such as mass, size, luminosity and colours) of galaxies. Both “early-type“cosmos/E/early-type+galaxies (elliptical and S0) and late-type (spiral) galaxies exhibit scaling relations, though different relations are used for each type.

For example, there are a number of important scaling relations for early-type galaxies. These include:

• The Faber-Jackson Relation (FJR): shows a strong correlation between the masses and luminosities of galaxies, with the sense that more massive galaxies are also the more luminous.
• The Colour-Magnitude Relation (CMR): shows a strong correlation between the masses (estimated from luminosity) and the average metallicities of stellar populations (which dictate colour) in galaxies. The relation implies that larger galaxies are better at retaining the metals produced within them than low-mass galaxies.
• The Kormendy Relation: shows a correlation between the effective radii of galaxies and their surface brightnesses at that radius.
• The Fundamental Plane (FP): is a 3-dimensional plane showing strong correlations between the effective radii, luminosities and velocity dispersions of galaxies.

There are also scaling relations for late-type galaxies, the most important of which is the Tully-Fisher Relation. This relation, which can be derived from the virial theorem, relates the rotation speed of the galaxy to its luminosity, and is often used to determine distances in the Universe. It therefore provides an important rung in the distance ladder.

The existence of scaling relations that correlate the physical properties of widely separated galaxies, indicates that the formation processes for all galaxies within a particular galaxy type must be fairly similar. The relations therefore provide insights into both the formation and evolution of galaxies, and many are also used to measure the distances to galaxies.