galpy.potential.scf_compute_coeffs¶
Note: This function computes Acos and Asin as defined in Hernquist & Ostriker (1992), except that we multiply Acos and Asin by 2 such that the density from Galpy’s Hernquist Potential corresponds to \(Acos = \delta_{0n}\delta_{0l}\delta_{0m}\) and \(Asin = 0\).
For a given \(\rho(R, z, \phi)\) 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 \(0 <= m <= l\)
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galpy.potential.
scf_compute_coeffs
(dens, N, L, a=1.0, radial_order=None, costheta_order=None, phi_order=None)¶ NAME:
scf_compute_coeffsPURPOSE:
Numerically compute the expansion coefficients for a given triaxial densityINPUT:
dens - A density function that takes a parameter R, z and phi
N - size of the Nth dimension of the expansion coefficients
L - size of the Lth and Mth dimension of the expansion coefficients
a - parameter used to shift the basis functions
radial_order - Number of sample points of the radial integral. If None, radial_order=max(20, N + 3/2L + 1)
costheta_order - Number of sample points of the costheta integral. If None, If costheta_order=max(20, L + 1)
phi_order - Number of sample points of the phi integral. If None, If costheta_order=max(20, L + 1)
OUTPUT:
(Acos,Asin) - Expansion coefficients for density dens that can be given to SCFPotential.__init__HISTORY:
2016-05-27 - Written - Aladdin