Astronomy and Astrophysics – Astrophysics
Scientific paper
2007-03-23
Astronomy and Astrophysics
Astrophysics
5 pages, 1 figure, accepted for publication in A&A
Scientific paper
10.1051/0004-6361:20077132
We show that the gravitational potential in the plane of an axisymmetrical flat disk where the surface density varies as a power of the radius obeys an inhomogeneous first-order Ordinary Differential Equation (ODE) solvable by standard techniques. The potential being exactly known at the origin for any power index (and at infinity as well), the search for solutions consists of a Two-point Boundary Value Problem (TBVP) with Dirichlet conditions. The computating time is then linear with the number of grid points, instead of quadratic from direct summation methods. Complex mass distributions which can be decomposed into a mixture of power law surface density profiles are easily accessible through the superposition principle. This ODE definitively takes the place of the untractable bidimensional Poisson equation for planar calculations. It opens new horizons to investigate various aspects related to self-gravity in astrophysical disks (force calculations, stability analysis, etc.).
Hersant Franck
Hure Jean-Marc
No associations
LandOfFree
A new equation for the mid-plane potential of power law disks does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with A new equation for the mid-plane potential of power law disks, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A new equation for the mid-plane potential of power law disks will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-164137