# 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=)[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).

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

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 $$C_n=$$ 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=)[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 drop-off 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 - 2017-05-12 Jack Hong (UBC)

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