Fundamental level

The title of this article is ambiguous. The reference plane used for calculating solar eclipses is also called the fundamental plane, see Bessel elements .

The fundamental plane is a two-dimensional subspace of the parameter space made up of dynamics ( velocity dispersion σ), brightness ( surface brightness ) and extent ( radius ) in which elliptical galaxies are concentrated.

motivation

Many properties of galaxies correlate. For example, the luminosity is related to the effective radius . The benefit of these correlations is that you can still make plausible assumptions about the distance without knowing the distance to a galaxy.

Fundamental plane in elliptical galaxies

For elliptical galaxies, one observes a dependence of the effective radius on the average surface brightness within the effective radius: ${\displaystyle R_{e}}$ ${\displaystyle \langle I\rangle _{e}}$

${\displaystyle R_{e}\propto \langle I\rangle _{e}^{-0.83}}$.

The relationship then applies accordingly to the luminosity . Using the first relation, the following approximation can be derived: ${\displaystyle L=2\pi R_{e}^{2}\langle I\rangle _{e}}$

${\displaystyle \langle I\rangle _{e}\propto L^{-1.5}}$.

If we now add the Faber-Jackson relationship , i. H. the dependence of the luminosity on the velocity dispersion in the center, one obtains a connection between the three parameters , and , which spans a plane in the three-dimensional parameter space, the so-called fundamental plane. This is defined by ${\displaystyle L\propto \sigma _{0}^{4}}$ ${\displaystyle R_{e}}$ ${\displaystyle \langle I\rangle _{e}}$ ${\displaystyle \sigma _{0}}$

${\displaystyle R_{e}\propto \sigma _{0}^{1.4}\langle I\rangle _{e}^{-0.85}}$,

or, represented in logarithmic form, by

${\displaystyle \log R_{e}=0.34\langle \mu \rangle _{e}+1.4\log \sigma _{0}+{\text{const.}}}$,

where denotes the average surface brightness within , measured in . ${\displaystyle \langle \mu \rangle _{e}}$ ${\displaystyle R_{e}}$ ${\displaystyle {\text{mag/arcsec}}^{2}}$

If the distance to a galaxy is unknown, its luminosity can still be determined via the fundamental plane. The fundamental level can also be observed in the bulges of spiral galaxies .

literature

• J. Binney, M. Merrifield: Galactic Astronomy. Princeton University Press, 1998, ISBN 0-691-00402-1 .

Individual evidence

1. ^ Peter Schneider: Extragalactic Astronomy and Cosmology. An Introduction . 2nd Edition. Springer, 2015, ISBN 978-3-642-54082-0 , pp. 130 f . ( limited preview in Google Book search).
2. ^ Hans-Heinrich Voigt: Outline of the astronomy . Ed .: Hermann-Josef Röser, Werner Tscharnuter. 6th edition. Wiley-VCH, Weinheim 2012, ISBN 978-3-527-40736-1 , pp. 812 ( limited preview in Google Book search).