SpringerLink
Forum Springer Astron. Astrophys.
Forum Whats New Search Orders


Astron. Astrophys. 321, 444-451 (1997)

Previous Section Next Section Title Page Table of Contents

4. Thin-disk mass distribution with exponential density

The luminosity profile of many spiral galaxies can be well fitted assuming that the luminous matter is placed along a thin disk with a density that decreases exponentially with the distance to the centre of the galaxy (Kent 1987).

[EQUATION]

being [FORMULA] a normalisation constant with units of a two-dimensional density, related to the total mass of the galaxy by [FORMULA].

Considering a thin-disk distribution and using Eqs. (6), (7) and (17), in Eqs. (4) and (5), the two problems outlined in Sect.  2 can be recast as two integral equations:

(i) Given [FORMULA], defined by (6), find a function [FORMULA] such that:

[EQUATION]

(ii) Given [FORMULA], defined by (7), find a function [FORMULA] such that:

[EQUATION]

In this case the problem cannot be solved exactly. We use an approximation that we call Gaussian as, in the Newtonian case, it is equivalent to use the Gauss' law for calculating the gravitational field.

The calculations are described in detail in Appendix A.2. The solution to the two problems outlined above, in the Gaussian approximation can be summarised as:

(i) Potential problem: (viz. Eqs. (6) and (18))

In this case, the approximate solution to the problem is

[EQUATION]

where the function [FORMULA] has the following behaviour at the origin:

[EQUATION]

(ii) Force and velocity problem: (viz. Eqs. (7), (8) and (19)).

Here, the approximate solution is given by the following expression:

[EQUATION]

and the behaviour of [FORMULA] at the origin is as follows:

[EQUATION]

Previous Section Next Section Title Page Table of Contents

© European Southern Observatory (ESO) 1997

Online publication: June 30, 1998
helpdesk.link@springer.de