# 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])

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).

$\Phi(R, \phi, z) = -4 \pi GH \,\rho_0 exp \left( -\frac{R-r_{ref}}{R_s} \right) \sum{\frac{C_n}{K_n D_n} \,\cos(n \gamma) \,\mathrm{sech}^{B_n} \left( \frac{K_n z}{B_n} \right)}$

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])
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. ($$amp = 4 \pi G \rho_0$$) distance scales for translation into internal units (default from configuration file) velocity scales for translation into internal units (default from configuration file) number of spiral arms pitch angle of the logarithmic spiral arms in radians (can be Quantity) fiducial radius where $$\rho = \rho_0$$ ($$r_0$$ in the paper by Cox and Gomez) (can be Quantity) reference angle ($$\phi_p(r_0)$$ in the paper by Cox and Gomez) (can be Quantity) radial scale length of the drop-off in density amplitude of the arms (can be Quantity) scale height of the stellar arm perturbation (can be Quantity) list of constants multiplying the $$\cos(n \gamma)$$ terms rotational pattern speed of the spiral arms (can be Quantity)
OUTPUT:
(none)
HISTORY:

Started - 2017-05-12 Jack Hong (UBC)

Completed - 2017-07-04 Jack Hong (UBC)