Self-consistent field (SCF)
gala.scf contains utilities for evaluating basis function expansions of mass
densities and gravitational potentials with the Self-Consistent Field (SCF)
method of Hernquist & Ostriker (1992; [HO92]). SCF uses Hernquist radial
functions and spherical harmonics for angular functions. This implementation is
based on the formalism described in the original paper but using the notation of
Lowing et al. (2011; [L11]).
Introduction
The two main ways to use gala.potential.scf are:
to compute the expansion coefficients given a continuous density distribution
or discrete samples from a density distribution, then
to evaluate the density, potential, and gradients of a basis function
expansion representation of a density distribution given this set of
coefficients.
To compute expansion coefficients, the relevant functions are
compute_coeffs and
compute_coeffs_discrete. This implementation uses the
notation from [L11]: all expansion coefficients are real, \(S_{nlm}\) are
the cosine coefficients, and \(T_{nlm}\) are the sine coefficients.
Once you have coefficients, there are two ways to evaluate properties of the
potential or the density of the expansion representation. gala provides a
class-based interface SCFPotential that utilizes
the gravitational potential machinery implemented in gala.potential (and
supports all of the standard potential functionality, such as orbit integration
and plotting). The examples below use this interface.
gala.potential.scf Package
Implementation of the Self-Consistent Field (SCF) expansion method.
Functions
compute_coeffs(density_func, nmax, lmax, M, r_s)
|
Compute the expansion coefficients for representing the input density function using a basis function expansion. |
compute_coeffs_discrete(xyz, mass, nmax, ...)
|
Compute the expansion coefficients for representing the density distribution of input points as a basis function expansion. |
Classes
SCFInterpolatedPotential(m, r_s, Sjnlm, ...)
|
A gravitational potential represented as a basis function expansion with the Hernquist basis, but where the coefficients are interpolated with linear interpolation to compute the density, potential, or acceleration at a given time. |
SCFPotential(m, r_s, Snlm, Tnlm[, units, ...])
|
A gravitational potential represented as a basis function expansion. |
Class Inheritance Diagram
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"PotentialBase" -> "CPotentialBase" [arrowsize=0.5,style="setlinewidth(0.5)"];
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"CommonBase" -> "PotentialBase" [arrowsize=0.5,style="setlinewidth(0.5)"];
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"CPotentialBase" -> "SCFInterpolatedPotential" [arrowsize=0.5,style="setlinewidth(0.5)"];
"SCFPotential" [URL="../../api/gala.potential.scf.SCFPotential.html#gala.potential.scf.SCFPotential",fillcolor=white,fontname="Vera Sans, DejaVu Sans, Liberation Sans, Arial, Helvetica, sans",fontsize=10,height=0.25,shape=box,style="setlinewidth(0.5),filled",target="_top",tooltip="SCFPotential(m, r_s, Snlm, Tnlm, units=None, origin=None, R=None)"];
"CPotentialBase" -> "SCFPotential" [arrowsize=0.5,style="setlinewidth(0.5)"];
}