Dehnen bar potential¶
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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)¶ Class that implements the Dehnen bar potential (Dehnen 2000)
\[\begin{split}\Phi(R,\phi) = A_b(t)\,\cos\left(2\,(\phi-\Omega_b\,t)\right))\times \begin{cases} -(R_b/R)^3\,, & \text{for}\ R \geq R_b\\ (R/R_b)^3-2\,, & \text{for}\ R\leq R_b. \end{cases}\end{split}\]where
\[A_b(t) = \frac{\alpha}{3\,R_b^3}\,\left(\frac{3}{16}\xi^5-\frac{5}{8}\xi^3+\frac{15}{16}\xi+\frac{1}{2}\right)\,, \xi = 2\frac{t/T_b-t_\mathrm{form}}{T_\mathrm{steady}}-1\,,\ \mathrm{if}\ t_\mathrm{form} \leq \frac{t}{T_b} \leq t_\mathrm{form}+T_\mathrm{steady}\]and
\[\begin{split}A_b(t) = \begin{cases} 0\,, & \frac{t}{T_b} < t_\mathrm{form}\\ \frac{\alpha}{3\,R_b^3}\,, & \frac{t}{T_b} > t_\mathrm{form}+T_\mathrm{steady} \end{cases}\end{split}\]where
\[T_b = \frac{2\pi}{\Omega_b}\]is the bar period.
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__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)¶ NAME:
__init__PURPOSE:
initialize a Dehnen bar potentialINPUT:
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)
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)
tsteady - time at which the bar is fully grown / bar period (default: tform/2)
Either provide:
rolr - radius of the Outer Lindblad Resonance for a circular orbit
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.)
omegab - rotation speed of the bar
rb - bar radius
Af - bar strength
OUTPUT:
(none)HISTORY:
2010-11-24 - Started - Bovy (NYU)
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