Softened potentials and the multipolar expansion

F. C. WACHLIN; D. D. CARPINTERO

REVISTA MEXICANA DE ASTRONOMíA Y ASTROFíSICA

Instituto de Astronomía, UNAM

Lugar: México D. F.; Año: 2006 vol. 42 p. 251 - 259

0185-1101

When the gravitational potential is developed in a multipolar series,each multipole is well defined and corresponds to a finite sum of terms in theseries. In order to use the gravitational potential in numerical simulations,however, a multipolar expansion is usually applied to a softenedNewtonian potential. It turns out that the commonly used multipolar expansionin this case no longer isolates each multipole as in the former case; instead,each multipole is spilled over an infinity of terms. In this paper we show howto recover the complete multipoles. Fortunately, the overall effect of usingincomplete multipoles instead of complete ones turns out to be negligible inthe cases of interest, for example, in its use in treecodes.