galpy.potential.scf_compute_coeffs_axi¶
Note: This function computes Acos and Asin as defined in Hernquist & Ostriker (1992), except that we multiply Acos by 2 such that the density from Galpy’s Hernquist Potential corresponds to \(Acos = \delta_{0n}\delta_{0l}\delta_{0m}\).
Further note that this function is a specification of scf_compute_coeffs where \(Acos_{nlm} = 0\) at \(m\neq0\) and \(Asin_{nlm} = None\)
For a given \(\rho(R, z)\) we can compute \(Acos\) and \(Asin\) through the following equation
Where
\(P_{lm}\) is the Associated Legendre Polynomials whereas \(C_{n}^{\alpha}\) is the Gegenbauer polynomial.
Also note \(\xi = \frac{r - a}{r + a}\), and \(n\), \(l\) and \(m\) are integers bounded by \(0 <= n < N\) , \(0 <= l < L\), and \(m = 0\)
- galpy.potential.scf_compute_coeffs_axi(dens, N, L, a=1.0, radial_order=None, costheta_order=None)[source]¶
Numerically compute the expansion coefficients for a given axi-symmetric density
- Parameters:
dens (function) – A density function that takes parameters R and z
N (int) – Size of the Nth dimension of the expansion coefficients
L (int) – Size of the Lth dimension of the expansion coefficients
a (float, optional) – Parameter used to shift the basis functions (default is 1.0)
radial_order (int, optional) – Number of sample points of the radial integral. If None, radial_order=max(20, N + 3/2L + 1) (default is None)
costheta_order (int, optional) – Number of sample points of the costheta integral. If None, If costheta_order=max(20, L + 1) (default is None)
- Returns:
(Acos,Asin) - Expansion coefficients for density dens that can be given to SCFPotential.__init__
- Return type:
tuple
Notes
2016-05-20 - Written - Aladdin Seaifan (UofT)