Spiral arms potential¶

class
galpy.potential.
SpiralArmsPotential
(amp=1, ro=None, vo=None, amp_units='density', N=2, alpha=0.2, r_ref=1, phi_ref=0, Rs=0.3, H=0.125, omega=0, Cs=[1])[source]¶ Class that implements the spiral arms potential from (Cox and Gomez 2002). Should be used to modulate an existing potential (density is positive in the arms, negative outside; note that because of this, a contour plot of this potential will appear to have twice as many arms, where half are the underdense regions).
\[\Phi(R, \phi, z) = 4 \pi GH \,\rho_0 exp \left( \frac{Rr_{ref}}{R_s} \right) \sum{\frac{C_n}{K_n D_n} \,\cos(n \gamma) \,\mathrm{sech}^{B_n} \left( \frac{K_n z}{B_n} \right)}\]where
\[\begin{split}K_n &= \frac{n N}{R \sin(\alpha)} \\ B_n &= K_n H (1 + 0.4 K_n H) \\ D_n &= \frac{1 + K_n H + 0.3 (K_n H)^2}{1 + 0.3 K_n H} \\\end{split}\]and
\[\gamma = N \left[\phi  \phi_{ref}  \frac{\ln(R/r_{ref})}{\tan(\alpha)} \right]\]The default of \(C_n=[1]\) gives a sinusoidal profile for the potential. An alternative from Cox and Gomez (2002) creates a density that behaves approximately as a cosine squared in the arms but is separated by a flat interarm region by setting
\[C_n = \left[\frac{8}{3 \pi}\,,\frac{1}{2} \,, \frac{8}{15 \pi}\right]\]
__init__
(amp=1, ro=None, vo=None, amp_units='density', N=2, alpha=0.2, r_ref=1, phi_ref=0, Rs=0.3, H=0.125, omega=0, Cs=[1])[source]¶  NAME:
 __init__
 PURPOSE:
 initialize a spiral arms potential
 INPUT:
amp: amplitude to be applied to the potential (default: 1); can be a Quantity with units of density. (\(amp = 4 \pi G \rho_0\)) ro: distance scales for translation into internal units (default from configuration file) vo: velocity scales for translation into internal units (default from configuration file) N: number of spiral arms alpha: pitch angle of the logarithmic spiral arms in radians (can be Quantity) r_ref: fiducial radius where \(\rho = \rho_0\) (\(r_0\) in the paper by Cox and Gomez) (can be Quantity) phi_ref: reference angle (\(\phi_p(r_0)\) in the paper by Cox and Gomez) (can be Quantity) Rs: radial scale length of the dropoff in density amplitude of the arms (can be Quantity) H: scale height of the stellar arm perturbation (can be Quantity) Cs: list of constants multiplying the \(\cos(n \gamma)\) terms omega: rotational pattern speed of the spiral arms (can be Quantity)  OUTPUT:
 (none)
 HISTORY:
Started  20170512 Jack Hong (UBC)
Completed  20170704 Jack Hong (UBC)
