Astronomy and Astrophysics – Astrophysics
Scientific paper
Jul 1995
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1995a%26as..112..191f&link_type=abstract
Astronomy and Astrophysics Supplement, v.112, p.191
Astronomy and Astrophysics
Astrophysics
4
Line: Profiles, Methods: Analytical, Methods: Numerical
Scientific paper
For numerically reliable line profile modelling as required in a number of astrophysical applications, the distribution of the spatial grid points has to meet certain conditions. In the observer's system macroscopic velocity fields and/or non-homogeneous magnetic field geometries lead - via Doppler shift, magnetic field strength and direction - to local profiles which usually exhibit a non-linear dependency on the position on the visible hemisphere. The simple recipe of using surface elements of equal size and/or of raising the number of grid points as employed by most researchers in the field of line profile modelling clearly does not make use of the known variations of line profile shapes with position, leading to a waste of computer resources at best, to serious numerical errors at worst. Following the ideas of Stift (1985) this paper proposes a method which leads to a distribution of the spatial integration points which is near optimum in the sense that it ensures an upper limit to the variation in the quantities to integrate using an almost minimum number of points. Its design is based on the requirement of a constant change in line intensity between any two adjacent integration points. Simple cases that can be treated analytically illustrate the potential savings possible compared to conventional methods (for rotating and (non-)radially pulsating stars savings of a factor of 6 in CPU time can be achieved) and the fact that (nearly) optimum grids never consist of equally sized surface elements. Finally the flexibility and power of the present approach is illustrated by means of Stift's (1975) eccentric tilted dipole model.
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