Sérsic profile

Surface brightness curve for various Sérsic indices

The Sérsic profile generally describes the distribution of brightness in galaxies , i.e. H. it describes how the surface brightness of a galaxy changes with distance from its center.

The Sérsic profile is a generalization of the De Vaucouleurs profile and was introduced by José Luis Sérsic .

definition

The brightness profile with the Sérsic index has the following mathematical form: ${\ displaystyle n}$

{\ displaystyle \ log \ left ({\ frac {I (R)} {I_ {e}}} \ right) = - b_ {n} \ left [\ left ({\ frac {R} {R_ {e} }} \ right) ^ {\ frac {1} {n}} \, - 1 \ right]}

.

Here, the surface brightness at the location of the effective radius , i.e. H. at the radius within which half the luminosity is emitted. The factor is selected accordingly so that this condition is met. As a good approximation: ${\ displaystyle I_ {e}}$ ${\ displaystyle R_ {e}}$ ${\ displaystyle b_ {n}}$

{\ displaystyle b_ {n} \ approx 1.999 \, n-0.327}

.

The higher the Sérsic index of the distribution considered, the higher the light concentration in the center of the galaxy and the greater the surface brightness for larger radii.

Applications

For the De Vaucouleurs profile results again, which describes the brightness distribution of an elliptical galaxy or the bulge of a spiral galaxy . ${\ displaystyle n = 4}$

An exponential curve is obtained for which is suitable in many cases for the disks of spiral galaxies, for irregular galaxies and for elliptical or lenticular dwarf galaxies . ${\ displaystyle n = 1}$

A classification of galaxies is possible using the Sérsic profile. Thus, by curve fitting the parameters , and modeled for a measured brightness distribution. For some galaxies, especially for spiral galaxies, two different Sérsic profiles are usually assumed, for example for the bulge and for the disk. If the model is applied to the entire galaxy, a correlation between the Sérsic index and the bulge-disk ratio can be observed. ${\ displaystyle n}$ ${\ displaystyle R_ {e}}$ ${\ displaystyle I_ {e}}$

Individual evidence

^ ^A ^b ^c Peter Schneider: Extragalactic Astronomy and Cosmology. An Introduction . 2nd Edition. Springer, 2015, ISBN 978-3-642-54082-0 , pp. 139 ( limited preview in Google Book search).
^ 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. 776 ( limited preview in Google Book search).

[Schneider-1] A ^b ^c Peter Schneider: Extragalactic Astronomy and Cosmology. An Introduction . 2nd Edition. Springer, 2015, ISBN 978-3-642-54082-0 , pp. 139 ( 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. 776 ( limited preview in Google Book search).