# Dehnen bar potential¶

class galpy.potential.DehnenBarPotential(amp=1.0, omegab=None, rb=None, chi=0.8, rolr=0.9, barphi=0.4363323129985824, tform=-4.0, tsteady=None, beta=0.0, alpha=0.01, Af=None, ro=None, vo=None)[source]

Class that implements the Dehnen bar potential (Dehnen 2000), generalized to 3D following Monari et al. (2016)

$\begin{split}\Phi(R,z,\phi) = A_b(t)\,\cos\left(2\,(\phi-\Omega_b\,t)\right))\,\left(\frac{R}{r}\right)^2\,\times \begin{cases} -(R_b/r)^3\,, & \text{for}\ r \geq R_b\\ (r/R_b)^3-2\,, & \text{for}\ r\leq R_b. \end{cases}\end{split}$

where $$r^2 = R^2+z^2$$ is the spherical radius and

$A_b(t) = A_f\,\left(\frac{3}{16}\xi^5-\frac{5}{8}\xi^3+\frac{15}{16}\xi+\frac{1}{2}\right)\,, \xi = 2\frac{t/T_b-t_\mathrm{form}}{T_\mathrm{steady}}-1\,,\ \mathrm{if}\ t_\mathrm{form} \leq \frac{t}{T_b} \leq t_\mathrm{form}+T_\mathrm{steady}$

and

$\begin{split}A_b(t) = \begin{cases} 0\,, & \frac{t}{T_b} < t_\mathrm{form}\\ A_f\,, & \frac{t}{T_b} > t_\mathrm{form}+T_\mathrm{steady} \end{cases}\end{split}$

where

$T_b = \frac{2\pi}{\Omega_b}$

is the bar period and the strength can also be specified using $$\alpha$$

$\alpha = 3\,\frac{A_f}{v_0^2}\,\left(\frac{R_b}{r_0}\right)^3\,.$

If the bar’s pattern speed is zero, $$t_\mathrm{form}$$ and $$t_\mathrm{steady}$$ are straight times, not times divided by the bar period.

__init__(amp=1.0, omegab=None, rb=None, chi=0.8, rolr=0.9, barphi=0.4363323129985824, tform=-4.0, tsteady=None, beta=0.0, alpha=0.01, Af=None, ro=None, vo=None)[source]

NAME:

__init__

PURPOSE:

initialize a Dehnen bar potential

INPUT:

amp - amplitude to be applied to the potential (default: 1., see alpha or Ab below)

barphi - angle between sun-GC line and the bar’s major axis (in rad; default=25 degree; or can be Quantity))

tform - start of bar growth / bar period (default: -4)

tsteady - time from tform at which the bar is fully grown / bar period (default: -tform/2, st the perturbation is fully grown at tform/2)

Either provide:

1. rolr - radius of the Outer Lindblad Resonance for a circular orbit (can be Quantity)

chi - fraction R_bar / R_CR (corotation radius of bar)

alpha - relative bar strength (default: 0.01)

beta - power law index of rotation curve (to calculate OLR, etc.)

2. omegab - rotation speed of the bar (can be Quantity)

rb - bar radius (can be Quantity)

Af - bar strength (can be Quantity)

OUTPUT:

(none)

HISTORY:

2010-11-24 - Started - Bovy (NYU)

2017-06-23 - Converted to 3D following Monari et al. (2016) - Bovy (UofT/CCA)