Tully-Fisher relationship

The Tully-Fisher relationship (published in 1977 by Richard Brent Tully and Richard Fisher ) describes a connection between the rotation speed of spiral galaxies and their luminosity . One can deduce from the shift of their spectral lines and the resulting speed of rotation about their luminosity and thus, if the brightness is known, about their distance.

The Tully-Fisher relationship is:

{\ displaystyle L \ propto (\ mathrm {v} _ {\ mathrm {max}}) ^ {\ beta}}

This empirically found relationship says that the luminosity of a spiral galaxy is proportional to a power of its maximum speed of rotation . The exponent of the power law depends on the spectral range: ${\ displaystyle L}$ ${\ displaystyle \ mathrm {v} _ {\ mathrm {max}}}$ ${\ displaystyle \ beta}$

${\ displaystyle \ beta = 3 {,} 0}$ in the B-band ( ) ${\ displaystyle \ lambda = 400 \, \ mathrm {nm}}$
${\ displaystyle \ beta = 3 {,} 2}$ in the I-band ( ) ${\ displaystyle \ lambda = 800 \, \ mathrm {nm}}$
${\ displaystyle \ beta = 4 {,} 2}$ in the H band ( ). ${\ displaystyle \ lambda = 1.200 \, \ mathrm {nm}}$

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

The calculation is based on the fact that the light from the spiral arms moving towards us experiences a slight blue shift , while the light from the arms moving away from us has a red shift ( Doppler effect ). The faster the rotation, the stronger these shifts and the spectral lines become correspondingly wider; the width is therefore a measure of the speed of rotation. The speed of rotation is in turn directly related to the mass of the galaxy, since gravitation acts as a centripetal force . After all, it is assumed that galaxies with similar masses have a comparable absolute luminosity and that this luminosity increases proportionally to the mass. The distance to the galaxy results from the comparison of the calculated absolute with the apparent (observed) brightness .

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

Web links

Tully: Tully-Fisher relation, Scholarpedia , 2007
Spektrum .de: ... in a galaxy far, far away February 10, 2019