Lectures 14 and 15: Potential theory in non-spherical systems


Binney and Tremaine 2.3, 2.4, 2.5, 2.6, 2.8, 2.9

We will not cover all of the collection of techniques in these sections, though all are worth knowing. We will concentrate on
Plummer-Kuzmin models (2.3.1), logarithmic potentials (2.3.2), the multipole expansion (2.4), disk potentials via Bessel functions (2.6.2),
functional expansions (2.8), and numerical Poisson solvers (2.9).

Optional reading:

Chandrasekhar, S. 1961, Ellipsoidal figures of equilibrium (New Haven: Yale University Press). Classic reference on potential theory for ellipsoids.

Murray, C. D., and Dermott, S. F. 1999, Solar System Dynamics (Cambridge: Cambridge University Press). The best book on dynamics of planetary systems. Describes indirect potential.

Numerical methods:

Henon, M. 1964, Ann d'Astrophys 27, 83 - the first example of an expansion technique (for spherical systems), and one of the earliest N-body simulations of a stellar system. Like many of Henon's papers, this one is ten years ahead of its time. In French, I'm afraid.

Hockney, R. W., and Eastwood, J. W. 1988, Computer simulation using particles (Bristol: Institute of Physics) - the standard reference on grid-based methods

Applegate, J., et al. 1985, IEEE Trans. Computing C34, 822 - the digital orrery

Barnes, J. and Hut, P. 1986, Nature 324, 446 - description of the Barnes-Hut tree code

Dehnen, W. 2001, MNRAS 324, 273 - softening in N-body codes

Sellwood, J. 1987, ARAA 25, 151 - a good review of numerical methods for the N-body problem; though now a little out of date

Makino, J., et al. 2003, astro-ph/0310702 - the GRAPE special-purpose computers

For expansion techniques for solving Poisson's equation see:

- Hernquist, L., and Ostriker, J. P. 1993, ApJ 386, 375
- Saha, P. 1993, MNRAS 262, 1062 - an alternative treatment of the problem of deriving basis functions


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