Self-Consistent Field Self-Consistent Field
The algorithm used in the SCF code is described in detail in
Hernquist and Ostriker 1992 [5]. The code solves the coupled
Vlasov and Poisson equation for collisionless stellar systems using the
N-body approximation approach. Poisson's equation for gravitational potential
is solved by expanding the
density and potential
in a set of basis functions.
The basis set is
constructed so that the lowest order members well-approximate a galaxy
obeying the de Vaucouleurs
projected density profile law.
The expansions of the density and potential take the following forms:
where
is the radial ``quantum'' number and
and
are quantum numbers
for the angular variables. Generally, the two sums will involve different
expansion coefficients. But the assumption of bi-orthogonality ensures a
one-to-one relationship between terms in the expansions for the density and
potential. The basis sets
and
also
satisfy Poisson's equation:
The basis sets
and
are given by
where
is a number related only to
and
, and
and
are ultrasperical polynomials
and spherical harmonics, respectively. After some algebra, the expansion
coefficients become
where
is a number and
is the mass of the kth
particle. Once
the gravitational potential is found, the gravitational force per unit mass
can be obtained by taking the gradient of the potential and the particles
can be accelerated accordingly.