# 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; [1]), generalized to 3D following Monari et al. (2016) [2]

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

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]

Initialize a Dehnen bar potential.

Parameters:
• amp (float, optional) – Amplitude to be applied to the potential (default: 1., see alpha or Ab below).

• omegab (float or Quantity, optional) – Rotation speed of the bar (can be Quantity).

• rb (float or Quantity, optional) – Bar radius (can be Quantity).

• Af (float or Quantity, optional) – Bar strength (can be Quantity).

• chi (float, optional) – Fraction R_bar / R_CR (corotation radius of bar).

• rolr (float or Quantity, optional) – Radius of the Outer Lindblad Resonance for a circular orbit (can be Quantity).

• barphi (float or Quantity, optional) – Angle between sun-GC line and the bar’s major axis (in rad; default=25 degree; or can be Quantity).

• beta (float, optional) – Power law index of rotation curve (to calculate OLR, etc.).

• alpha (float or Quantity, optional) – Relative bar strength (default: 0.01).

• tform (float, optional) – Start of bar growth / bar period (default: -4).

• tsteady (float, optional) – Time from tform at which the bar is fully grown / bar period (default: -tform/2, so the perturbation is fully grown at tform/2).

• ro (float or Quantity, optional) – Distance scale for translation into internal units (default from configuration file).

• vo (float or Quantity, optional) – Velocity scale for translation into internal units (default from configuration file).

Notes

• Either provide (omegab, rb, Af) or (chi, rolr, alpha, beta).

• 2010-11-24 - Started - Bovy (NYU)

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

References