.. _scf: 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]_). .. raw:: html 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 `~gala.potential.scf.compute_coeffs` and `~gala.potential.scf.compute_coeffs_discrete`. This implementation uses the notation from [L11]_: all expansion coefficients are real, :math:`S_{nlm}` are the cosine coefficients, and :math:`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 :class:`~gala.potential.scf.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. Examples -------- - :ref:`coeff-particle` - :ref:`coeff-analytic` - :ref:`potential-class` .. toctree:: :hidden: scf-examples API --- .. automodapi:: gala.potential.scf ---------- References ---------- .. [HO92] http://dx.doi.org/10.1086/171025 .. [L11] http://dx.doi.org/10.1111/j.1365-2966.2011.19222.x