galpy.potential.scf_compute_coeffs_spherical¶
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_axi where \(Acos_{nlm} = 0\) at \(l\neq0\)
For a given \(\rho(r)\) we can compute \(Acos\) and \(Asin\) through the following equation
Where
\(C_{n}^{\alpha}\) is the Gegenbauer polynomial.
Also note \(\xi = \frac{r - a}{r + a}\), and \(n\), \(l\) and \(m\) are integers bounded by \(0 <= n < N\) , \(l = m = 0\)
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galpy.potential.
scf_compute_coeffs_spherical
(dens, N, a=1.0, radial_order=None)[source]¶ NAME:
scf_compute_coeffs_sphericalPURPOSE:
Numerically compute the expansion coefficients for a given spherical densityINPUT:
dens - A density function that takes a parameter R
N - size of expansion coefficients
a= (1.) parameter used to scale the radius
radial_order - Number of sample points of the radial integral. If None, radial_order=max(20, N + 1)
OUTPUT:
(Acos,Asin) - Expansion coefficients for density dens that can be given to SCFPotential.__init__HISTORY:
2016-05-18 - Written - Aladdin Seaifan (UofT)