# Tully-Fisher Relation – Definition & Detailed Explanation – Astrophysics Glossary

## I. What is the Tully-Fisher Relation?

The Tully-Fisher Relation is a fundamental relationship in astrophysics that links the luminosity or brightness of a spiral galaxy to its rotational velocity. In simple terms, it states that the faster a galaxy rotates, the more massive it is. This relationship was first discovered in the late 1970s by astronomers R. Brent Tully and J. Richard Fisher, hence the name Tully-Fisher Relation.

## II. How was the Tully-Fisher Relation discovered?

The Tully-Fisher Relation was discovered through observations of spiral galaxies using radio telescopes. Tully and Fisher noticed a correlation between the luminosity of a galaxy and the width of its 21-cm spectral line, which is a measure of its rotational velocity. By studying a large sample of galaxies, they were able to establish a clear relationship between these two parameters, leading to the discovery of the Tully-Fisher Relation.

## III. What is the significance of the Tully-Fisher Relation in Astrophysics?

The Tully-Fisher Relation is significant in astrophysics because it provides a powerful tool for measuring the mass of galaxies. Since the luminosity of a galaxy can be easily measured from its observed brightness, and the rotational velocity can be determined from the Doppler shift of its spectral lines, the Tully-Fisher Relation allows astronomers to estimate the mass of a galaxy without directly observing its gravitational effects.

## IV. How is the Tully-Fisher Relation used in measuring the mass of galaxies?

To use the Tully-Fisher Relation to measure the mass of a galaxy, astronomers first measure the luminosity of the galaxy using optical telescopes. They then observe the 21-cm spectral line of the galaxy using radio telescopes to determine its rotational velocity. By applying the Tully-Fisher Relation, which is typically expressed as a mathematical formula, astronomers can calculate the mass of the galaxy based on its luminosity and rotational velocity.

## V. What are the limitations of the Tully-Fisher Relation?

While the Tully-Fisher Relation is a valuable tool for estimating the mass of galaxies, it does have some limitations. One major limitation is that it assumes all galaxies have the same intrinsic properties, such as the same relationship between luminosity and rotational velocity. In reality, galaxies can vary significantly in their composition, structure, and evolutionary history, which can affect the accuracy of mass estimates derived from the Tully-Fisher Relation.

## VI. How has the Tully-Fisher Relation contributed to our understanding of the universe?

Despite its limitations, the Tully-Fisher Relation has made significant contributions to our understanding of the universe. By providing a method for estimating the mass of galaxies, it has helped astronomers map the distribution of matter in the universe and study the dynamics of galaxy clusters. The Tully-Fisher Relation has also been used to investigate the relationship between galaxy mass and other properties, such as star formation rates and dark matter content, shedding light on the processes that govern the evolution of galaxies and the structure of the cosmos. Overall, the Tully-Fisher Relation remains a valuable tool for astrophysicists studying the vast and complex universe we inhabit.