A new equation for the mid-plane potential of power law disks

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dc.creatorHuré, J. -M.
dc.creatorHersant, F.
dc.date2007-03-23
dc.date2007-03-26
dc.date.accessioned2026-07-07T07:53:33Z
dc.date.available2026-07-07T07:53:33Z
dc.descriptionWe 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.).
dc.description5 pages, 1 figure, accepted for publication in A&A
dc.identifierhttps://arxiv.org/abs/astro-ph/0703603
dc.identifierhttp://arxiv.org/abs/astro-ph/0703603
dc.identifierdoi:10.1051/0004-6361:20077132
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/126264
dc.subjectAstrophysics
dc.titleA new equation for the mid-plane potential of power law disks
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