def omegac(Pot,R):
"""
NAME:
omegac
PURPOSE:
calculate the circular angular speed velocity at R in potential Pot
INPUT:
Pot - Potential instance or list of such instances
R - Galactocentric radius
OUTPUT:
circular angular speed
HISTORY:
2011-10-09 - Written - Bovy (IAS)
"""
from galpy.potential import evaluateplanarRforces
try:
return nu.sqrt(-evaluateplanarRforces(R,Pot)/R)
except PotentialError:
from galpy.potential import RZToplanarPotential
Pot= RZToplanarPotential(Pot)
return nu.sqrt(-evaluateplanarRforces(R,Pot)/R)
def dvcircdR(Pot,R):
"""
NAME:
dvcircdR
PURPOSE:
calculate the derivative of the circular velocity wrt R at R in potential Pot
INPUT:
Pot - Potential instance or list of such instances
R - Galactocentric radius
OUTPUT:
derivative of the circular rotation velocity wrt R
HISTORY:
2013-01-08 - Written - Bovy (IAS)
"""
from galpy.potential import evaluateplanarRforces, evaluateplanarR2derivs
from galpy.potential import PotentialError
tvc= vcirc(Pot,R)
try:
return 0.5*(-evaluateplanarRforces(R,Pot)+R*evaluateplanarR2derivs(R,Pot))/tvc
except PotentialError:
from galpy.potential import RZToplanarPotential
Pot= RZToplanarPotential(Pot)
return 0.5*(-evaluateplanarRforces(R,Pot)+R*evaluateplanarR2derivs(R,Pot))/tvc
def vcirc(Pot, R):
"""
NAME:
vcirc
PURPOSE:
calculate the circular velocity at R in potential Pot
INPUT:
Pot - Potential instance or list of such instances
R - Galactocentric radius
OUTPUT:
circular rotation velocity
HISTORY:
2011-10-09 - Written - Bovy (IAS)
"""
from galpy.potential import evaluateplanarRforces
from galpy.potential import PotentialError
try:
return nu.sqrt(-R * evaluateplanarRforces(R, Pot))
except PotentialError:
from galpy.potential import RZToplanarPotential
Pot = RZToplanarPotential(Pot)
return nu.sqrt(-R * evaluateplanarRforces(R, Pot))
def vcirc(Pot,R):
"""
NAME:
vcirc
PURPOSE:
calculate the circular velocity at R in potential Pot
INPUT:
Pot - Potential instance or list of such instances
R - Galactocentric radius (can be Quantity)
OUTPUT:
circular rotation velocity
HISTORY:
2011-10-09 - Written - Bovy (IAS)
"""
from galpy.potential import evaluateplanarRforces
from galpy.potential import PotentialError
try:
return nu.sqrt(-R*evaluateplanarRforces(Pot,R,use_physical=False))
except PotentialError:
from galpy.potential import RZToplanarPotential
Pot= RZToplanarPotential(Pot)
return nu.sqrt(-R*evaluateplanarRforces(Pot,R,use_physical=False))
def dvcircdR(Pot, R, phi=None):
"""
NAME:
dvcircdR
PURPOSE:
calculate the derivative of the circular velocity wrt R at R in potential Pot
INPUT:
Pot - Potential instance or list of such instances
R - Galactocentric radius (can be Quantity)
phi= (None) azimuth to use for non-axisymmetric potentials
OUTPUT:
derivative of the circular rotation velocity wrt R
HISTORY:
2013-01-08 - Written - Bovy (IAS)
2016-06-28 - Added phi= keyword for non-axisymmetric potential - Bovy (UofT)
"""
from galpy.potential import evaluateplanarRforces, evaluateplanarR2derivs
from galpy.potential import PotentialError
tvc = vcirc(Pot, R, phi=phi, use_physical=False)
try:
return (
0.5
* (
-evaluateplanarRforces(Pot, R, phi=phi, use_physical=False)
+ R * evaluateplanarR2derivs(Pot, R, phi=phi, use_physical=False)
)
/ tvc
)
except PotentialError:
from galpy.potential import RZToplanarPotential
Pot = RZToplanarPotential(Pot)
return (
0.5
* (
-evaluateplanarRforces(Pot, R, phi=phi, use_physical=False)
+ R * evaluateplanarR2derivs(Pot, R, phi=phi, use_physical=False)
)
/ tvc
)
def dvcircdR(Pot, R, phi=None):
"""
NAME:
dvcircdR
PURPOSE:
calculate the derivative of the circular velocity wrt R at R in potential Pot
INPUT:
Pot - Potential instance or list of such instances
R - Galactocentric radius (can be Quantity)
phi= (None) azimuth to use for non-axisymmetric potentials
OUTPUT:
derivative of the circular rotation velocity wrt R
HISTORY:
2013-01-08 - Written - Bovy (IAS)
2016-06-28 - Added phi= keyword for non-axisymmetric potential - Bovy (UofT)
"""
from galpy.potential import evaluateplanarRforces, evaluateplanarR2derivs
from galpy.potential import PotentialError
tvc = vcirc(Pot, R, phi=phi, use_physical=False)
try:
return 0.5 * (
-evaluateplanarRforces(Pot, R, phi=phi, use_physical=False) + R *
evaluateplanarR2derivs(Pot, R, phi=phi, use_physical=False)) / tvc
except PotentialError:
from galpy.potential import RZToplanarPotential
Pot = RZToplanarPotential(Pot)
return 0.5 * (
-evaluateplanarRforces(Pot, R, phi=phi, use_physical=False) + R *
evaluateplanarR2derivs(Pot, R, phi=phi, use_physical=False)) / tvc
def vcirc(Pot,R,phi=None,t=0.):
"""
NAME:
vcirc
PURPOSE:
calculate the circular velocity at R in potential Pot
INPUT:
Pot - Potential instance or list of such instances
R - Galactocentric radius (can be Quantity)
phi= (None) azimuth to use for non-axisymmetric potentials
t= time (optional; can be Quantity)
OUTPUT:
circular rotation velocity
HISTORY:
2011-10-09 - Written - Bovy (IAS)
2016-06-15 - Added phi= keyword for non-axisymmetric potential - Bovy (UofT)
"""
from galpy.potential import evaluateplanarRforces
from galpy.potential import PotentialError
try:
return nu.sqrt(-R*evaluateplanarRforces(Pot,R,phi=phi,t=t,
use_physical=False))
except PotentialError:
from galpy.potential import toPlanarPotential
Pot= toPlanarPotential(Pot)
return nu.sqrt(-R*evaluateplanarRforces(Pot,R,phi=phi,t=t,
use_physical=False))
def vcirc(Pot, R, phi=None):
"""
NAME:
vcirc
PURPOSE:
calculate the circular velocity at R in potential Pot
INPUT:
Pot - Potential instance or list of such instances
R - Galactocentric radius (can be Quantity)
phi= (None) azimuth to use for non-axisymmetric potentials
OUTPUT:
circular rotation velocity
HISTORY:
2011-10-09 - Written - Bovy (IAS)
2016-06-15 - Added phi= keyword for non-axisymmetric potential - Bovy (UofT)
"""
from galpy.potential import evaluateplanarRforces
from galpy.potential import PotentialError
try:
return nu.sqrt(-R * evaluateplanarRforces(Pot, R, phi=phi, use_physical=False))
except PotentialError:
from galpy.potential import toPlanarPotential
Pot = toPlanarPotential(Pot)
return nu.sqrt(-R * evaluateplanarRforces(Pot, R, phi=phi, use_physical=False))
def epifreq(Pot,R):
"""
NAME:
epifreq
PURPOSE:
calculate the epicycle frequency at R in the potential Pot
INPUT:
Pot - Potential instance or list thereof
R - Galactocentric radius
OUTPUT:
epicycle frequency
HISTORY:
2012-07-25 - Written - Bovy (IAS)
"""
from galpy.potential_src.planarPotential import planarPotential
if isinstance(Pot,(Potential,planarPotential)):
return Pot.epifreq(R)
from galpy.potential import evaluateplanarRforces, evaluateplanarR2derivs
from galpy.potential import PotentialError
try:
return nu.sqrt(evaluateplanarR2derivs(R,Pot)-3./R*evaluateplanarRforces(R,Pot))
except PotentialError:
from galpy.potential import RZToplanarPotential
Pot= RZToplanarPotential(Pot)
return nu.sqrt(evaluateplanarR2derivs(R,Pot)-3./R*evaluateplanarRforces(R,Pot))
def dvcircdR(Pot, R):
"""
NAME:
dvcircdR
PURPOSE:
calculate the derivative of the circular velocity wrt R at R in potential Pot
INPUT:
Pot - Potential instance or list of such instances
R - Galactocentric radius
OUTPUT:
derivative of the circular rotation velocity wrt R
HISTORY:
2013-01-08 - Written - Bovy (IAS)
"""
from galpy.potential import evaluateplanarRforces, evaluateplanarR2derivs
from galpy.potential import PotentialError
tvc = vcirc(Pot, R)
try:
return 0.5 * (-evaluateplanarRforces(R, Pot) +
R * evaluateplanarR2derivs(R, Pot)) / tvc
except PotentialError:
from galpy.potential import RZToplanarPotential
Pot = RZToplanarPotential(Pot)
return 0.5 * (-evaluateplanarRforces(R, Pot) +
R * evaluateplanarR2derivs(R, Pot)) / tvc