EDP Sciences
Free access
Issue A&A
Volume 507, Number 1, November III 2009
Page(s) 573 - 579
Section Numerical methods and codes
DOI http://dx.doi.org/10.1051/0004-6361/200912348
Published online 03 September 2009

A&A 507, 573-579 (2009)
DOI: 10.1051/0004-6361/200912348

A local prescription for the softening length in self-gravitating gaseous discs

J.-M. Huré1, 2 and A. Pierens3

1  Université de Bordeaux, OASU, France
    e-mail: jean-marc.hure@obs.u-bordeaux1.fr
2  CNRS/INSU-UMR 5804/LAB; BP 89, 33271 Floirac Cedex, France
3  LAL-IMCCE/USTL, 1 Impasse de l'Observatoire, 59000 Lille, France

Received 17 April 2009 / Accepted 2 July 2009

Abstract
In 2D-simulations of self-gravitating gaseous discs, the potential is often computed in the framework of “softened gravity” initially designed for N-body codes. In this special context, the role of the softening length $\lambda$ is twofold: i) to avoid numerical singularities in the integral representation of the potential (i.e., arising when the separation $\vert\vec{r} -\vec{r}'\vert \rightarrow 0$); and ii) to account for stratification of matter in the direction perpendicular to the disc mid-plane. So far, most studies have considered $\lambda$ as a free parameter and various values or formulae have been proposed without much mathematical justification. In this paper, we demonstrate by means of a rigorous calculus that it is possible to define $\lambda$ such that the gravitational potential of a flat disc coincides at order zero with that of a geometrically thin disc of the same surface density. Our prescription for $\lambda$, valid in the local, axisymmetric limit, has the required properties i) and ii). It is mainly an analytical function of the radius and disc thickness, and is sensitive to the vertical stratification. For mass density profiles considered (namely, profiles expandable over even powers of the altitude), we find that $\lambda$: i) is independant of the numerical mesh, ii) is always a fraction of the local thickness H; iii) goes through a minimum at the singularity (i.e., at null separation); and iv) is such that 0.13 $\la$ $\lambda$/H $\la$ 0.29 typically (depending on the separation and on density profile). These results should help us to improve the quality of 2D- and 3D-simulations of gaseous discs in several respects (physical realism, accuracy, and computing time).


Key words: accretion, accretion discs -- gravitation -- methods: numerical



© ESO 2009

What is OpenURL?

The OpenURL standard is a protocol for transmission of metadata describing the resource that you wish to access. An OpenURL link contains article metadata and directs it to the OpenURL server of your choice. The OpenURL server can provide access to the resource and also offer complementary services (specific search engine, export of references...). The OpenURL link can be generated by different means.
  • If your librarian has set up your subscription with an OpenURL resolver, OpenURL links appear automatically on the abstract pages.
  • You can define your own OpenURL resolver with your EDPS Account. In this case your choice will be given priority over that of your library.
  • You can use an add-on for your browser (Firefox or I.E.) to display OpenURL links on a page (see http://www.openly.com/openurlref/). You should disable this module if you wish to use the OpenURL server that you or your library have defined.

Editor-in-Chief: T. Forveille
Letters Editor-in-Chief: J. Alves
Managing Editor: C. Bertout

ISSN: 0004-6361 ; e-ISSN: 1432-0746
Frequency: 12 volumes per year
Published by: EDP Sciences

Mirror sites: CDS | EDP Sciences
  RSS feeds
© The European Southern Observatory (ESO)