Tully–Fisher relation

The Tully -Fisher relation describing a connection speed of rotation of spiral galaxies with their luminosity, which was published by Brent Tully and Richard Fisher in 1977. One can choose from the shift of their spectral lines and the consequent rotation speed on their luminosity, and therefore close with a known brightness to their removal. The Tully -Fisher relation is:

This relationship empirically found stating that the luminosity of a spiral galaxy is proportional to a power of its maximum rotational speed. The exponent of the power law depends on the spectral range, the following applies:

• In the B- band ()
• In the I- band ()
• In the H- band ()

The maximum rotation speed can be calculated from the broadening of the spectral lines. For measuring in particular the 21- cm line is used in the radio range of the hydrogen. For the distance determination, the I-band is used, since all contribute stars to the luminosity, whereas the luminosity is dominated exclusively by young OB stars in the B- band.

This calculation is based on the fact that the light of the spiral arms, which move us, undergoes a slight blue shift, while the light of the arms that move away from us, has a redshift. The faster the rotation the stronger these shifts, and the spectral lines are correspondingly wider; the width is a measure for the rotational speed. The rotation speed is in turn directly related to the mass of the galaxy, since the gravitational acts as centripetal force. Finally, it is assumed that galaxies with similar masses have a similar absolute luminosity and this luminosity grows proportional to the mass. From the comparison of the calculated absolute with the apparent ( observed ) brightness gives the distance to the galaxy.

An analogue of the Tully -Fisher relation for elliptical galaxies, the Faber -Jackson relation, which states that the luminosity is proportional to the fourth power of the velocity dispersion.

• Observation method of Astronomy
• Extragalactic Astronomy