# Cos(m phi) disk potential¶

Generalization of the lopsided and elliptical disk potentials to any m and to allow for a break radius within which the radial dependence of the potential changes from R^p to R^-p.

class galpy.potential.CosmphiDiskPotential(amp=1.0, phib=0.4363323129985824, p=1.0, phio=0.01, m=4, r1=1.0, rb=None, cp=None, sp=None, ro=None, vo=None)[source]

Class that implements the disk potential

$\begin{split}\Phi(R,\phi) = \mathrm{amp}\,\phi_0\,\,\cos\left[m\,(\phi-\phi_b)\right]\times \begin{cases} \left(\frac{R}{R_1}\right)^p\,, & \text{for}\ R \geq R_b\\ \left[2-\left(\frac{R_b}{R}\right)^p\right]\times\left(\frac{R_b}{R_1}\right)^p\,, & \text{for}\ R\leq R_b. \end{cases}\end{split}$

This potential can be grown between $$t_{\mathrm{form}}$$ and $$t_{\mathrm{form}}+T_{\mathrm{steady}}$$ in a similar way as DehnenBarPotential by wrapping it with a DehnenSmoothWrapperPotential

__init__(amp=1.0, phib=0.4363323129985824, p=1.0, phio=0.01, m=4, r1=1.0, rb=None, cp=None, sp=None, ro=None, vo=None)[source]

NAME:

__init__

PURPOSE:

initialize an cosmphi disk potential

INPUT:

amp= amplitude to be applied to the potential (default: 1.), degenerate with phio below, but kept for overall consistency with potentials

m= cos( m * (phi - phib) ), integer

p= power-law index of the phi(R) = (R/Ro)^p part

r1= (1.) normalization radius for the amplitude (can be Quantity); amp x phio is only the potential at (R,phi) = (r1,pib) when r1 > rb; otherwise more complicated

rb= (None) if set, break radius for power-law: potential R^p at R > Rb, R^-p at R < Rb, potential and force continuous at Rb

Either:

1. phib= angle (in rad; default=25 degree; or can be Quantity)

phio= potential perturbation (in terms of phio/vo^2 if vo=1 at Ro=1; or can be Quantity with units of velocity-squared)

2. cp, sp= m * phio * cos(m * phib), m * phio * sin(m * phib); can be Quantity with units of velocity-squared)

OUTPUT:

(none)

HISTORY:

2011-10-27 - Started - Bovy (IAS)

2017-09-16 - Added break radius rb - Bovy (UofT)