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CosmphiDiskPotential.py
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CosmphiDiskPotential.py
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###############################################################################
# CosmphiDiskPotential: cos(mphi) potential
###############################################################################
import numpy
from ..util import conversion
from .planarPotential import planarPotential
_degtorad = numpy.pi / 180.0
class CosmphiDiskPotential(planarPotential):
"""Class that implements the disk potential
.. math::
\\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}
This potential can be grown between :math:`t_{\\mathrm{form}}` and :math:`t_{\\mathrm{form}}+T_{\\mathrm{steady}}` in a similar way as DehnenBarPotential by wrapping it with a DehnenSmoothWrapperPotential
"""
def __init__(
self,
amp=1.0,
phib=25.0 * _degtorad,
p=1.0,
phio=0.01,
m=4,
r1=1.0,
rb=None,
cp=None,
sp=None,
ro=None,
vo=None,
):
"""
Initialize a CosmphiDiskPotential.
Parameters
----------
amp : float, optional
Amplitude to be applied to the potential (default: 1.), degenerate with phio below, but kept for overall consistency with potentials.
m : int, optional
m in cos(m * phi - m * phib).
p : float
Power-law index of the phi(R) = (R/Ro)^p part.
r1 : float or Quantity, optional
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 : float or Quantity, optional
If set, break radius for power-law: potential R^p at R > Rb, R^-p at R < Rb, potential and force continuous at Rb.
phib : float or Quantity, optional
Angle (in rad; default=25 degree).
phio : float or Quantity, optional
Potential perturbation (in terms of phio/vo^2 if vo=1 at Ro=1; or can be Quantity).
cp : float or Quantity, optional
m * phio * cos(m * phib); can be Quantity with units of velocity-squared.
sp : float or Quantity, optional
m * phio * sin(m * phib); can be Quantity with units of velocity-squared.
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 specify (phib, phio) or (cp, sp).
- 2011-10-27 - Started - Bovy (IAS)
- 2017-09-16 - Added break radius rb - Bovy (UofT)
"""
planarPotential.__init__(self, amp=amp, ro=ro, vo=vo)
phib = conversion.parse_angle(phib)
r1 = conversion.parse_length(r1, ro=self._ro)
rb = conversion.parse_length(rb, ro=self._ro)
phio = conversion.parse_energy(phio, vo=self._vo)
cp = conversion.parse_energy(cp, vo=self._vo)
sp = conversion.parse_energy(sp, vo=self._vo)
# Back to old definition
self._r1p = r1**p
self._amp /= self._r1p
self.hasC = False
self._m = int(m) # make sure this is an int
if cp is None or sp is None:
self._phib = phib
self._mphio = phio * self._m
else:
self._mphio = numpy.sqrt(cp * cp + sp * sp)
self._phib = numpy.arctan(sp / cp) / self._m
if m < 2.0 and cp < 0.0:
self._phib = numpy.pi + self._phib
self._p = p
if rb is None:
self._rb = 0.0
self._rbp = 1.0 # never used, but for p < 0 general expr fails
self._rb2p = 1.0
else:
self._rb = rb
self._rbp = self._rb**self._p
self._rb2p = self._rbp**2.0
self._mphib = self._m * self._phib
self.hasC = True
self.hasC_dxdv = True
def _evaluate(self, R, phi=0.0, t=0.0):
if R < self._rb:
return (
self._mphio
/ self._m
* numpy.cos(self._m * phi - self._mphib)
* self._rbp
* (2.0 * self._r1p - self._rbp / R**self._p)
)
else:
return (
self._mphio
/ self._m
* R**self._p
* numpy.cos(self._m * phi - self._mphib)
)
def _Rforce(self, R, phi=0.0, t=0.0):
if R < self._rb:
return (
-self._p
* self._mphio
/ self._m
* self._rb2p
/ R ** (self._p + 1.0)
* numpy.cos(self._m * phi - self._mphib)
)
else:
return (
-self._p
* self._mphio
/ self._m
* R ** (self._p - 1.0)
* numpy.cos(self._m * phi - self._mphib)
)
def _phitorque(self, R, phi=0.0, t=0.0):
if R < self._rb:
return (
self._mphio
* numpy.sin(self._m * phi - self._mphib)
* self._rbp
* (2.0 * self._r1p - self._rbp / R**self._p)
)
else:
return self._mphio * R**self._p * numpy.sin(self._m * phi - self._mphib)
def _R2deriv(self, R, phi=0.0, t=0.0):
if R < self._rb:
return (
-self._p
* (self._p + 1.0)
* self._mphio
/ self._m
* self._rb2p
/ R ** (self._p + 2.0)
* numpy.cos(self._m * phi - self._mphib)
)
else:
return (
self._p
* (self._p - 1.0)
/ self._m
* self._mphio
* R ** (self._p - 2.0)
* numpy.cos(self._m * phi - self._mphib)
)
def _phi2deriv(self, R, phi=0.0, t=0.0):
if R < self._rb:
return (
-self._m
* self._mphio
* numpy.cos(self._m * phi - self._mphib)
* self._rbp
* (2.0 * self._r1p - self._rbp / R**self._p)
)
else:
return (
-self._m
* self._mphio
* R**self._p
* numpy.cos(self._m * phi - self._mphib)
)
def _Rphideriv(self, R, phi=0.0, t=0.0):
if R < self._rb:
return (
-self._p
* self._mphio
/ self._m
* self._rb2p
/ R ** (self._p + 1.0)
* numpy.sin(self._m * phi - self._mphib)
)
else:
return (
-self._p
* self._mphio
* R ** (self._p - 1.0)
* numpy.sin(self._m * phi - self._mphib)
)
class LopsidedDiskPotential(CosmphiDiskPotential):
"""Class that implements the disk potential
.. math::
\\Phi(R,\\phi) = \\mathrm{amp}\\,\\phi_0\\,\\left(\\frac{R}{R_1}\\right)^p\\,\\cos\\left(\\phi-\\phi_b\\right)
Special case of CosmphiDiskPotential with m=1; see documentation for CosmphiDiskPotential
"""
def __init__(
self,
amp=1.0,
phib=25.0 * _degtorad,
p=1.0,
phio=0.01,
r1=1.0,
cp=None,
sp=None,
ro=None,
vo=None,
):
CosmphiDiskPotential.__init__(
self, amp=amp, phib=phib, p=p, phio=phio, m=1.0, cp=cp, sp=sp, ro=ro, vo=vo
)
self.hasC = True
self.hasC_dxdv = True