def get_gravity_at_point(self, eps, x, y, z):
R = np.sqrt(x.value_in(units.kpc)**2. + y.value_in(units.kpc)**2.)
zed = z.value_in(units.kpc)
phi = np.arctan2(y.value_in(units.kpc), x.value_in(units.kpc))
Rforce = potential.evaluateRforces(self.pot,
R / self.ro,
zed / self.ro,
phi=phi,
t=self.tgalpy)
phiforce = potential.evaluatephiforces(
self.pot, R / self.ro, zed / self.ro, phi=phi,
t=self.tgalpy) / (R / self.ro)
zforce = potential.evaluatezforces(self.pot,
R / self.ro,
zed / self.ro,
phi=phi,
t=self.tgalpy)
ax = (Rforce * np.cos(phi) -
phiforce * np.sin(phi)) * bovy_conversion.force_in_kmsMyr(
ro=self.ro, vo=self.vo) | units.kms * units.myr**-1
ay = (Rforce * np.sin(phi) +
phiforce * np.cos(phi)) * bovy_conversion.force_in_kmsMyr(
ro=self.ro, vo=self.vo) | units.kms * units.myr**-1
az = zforce * bovy_conversion.force_in_kmsMyr(
ro=self.ro, vo=self.vo) | units.kms * units.myr**-1
return ax, ay, az
def force_pal5(pot: PotentialType,
dpal5: float,
ro: float = REFR0,
vo: float = REFV0) -> Tuple[float]:
"""Return the force at Pal5.
Parameters
----------
pot: Potential, list
dpal5: float
ro, vo: float
Return
------
force: tuple
[fx, fy, fz]
"""
from galpy import potential
from galpy.util import bovy_coords
# First compute the location based on the distance
l5, b5 = bovy_coords.radec_to_lb(229.018, -0.124, degree=True)
X5, Y5, Z5 = bovy_coords.lbd_to_XYZ(l5, b5, dpal5, degree=True)
R5, p5, Z5 = bovy_coords.XYZ_to_galcencyl(X5, Y5, Z5, Xsun=ro, Zsun=0.025)
args: list = [pot, R5 / ro, Z5 / ro]
kws: dict = {"phi": p5, "use_physical": True, "ro": ro, "vo": vo}
return (
potential.evaluateRforces(*args, **kws),
potential.evaluatezforces(*args, **kws),
potential.evaluatephiforces(*args, **kws),
)
def force_gd1(pot,ro,vo):
"""Return the force at GD-1"""
# Just use R=12.5 kpc, Z= 6.675 kpc, phi=0
R1= 12.5
Z1= 6.675
p1= 0.
return (potential.evaluateRforces(pot,R1/ro,Z1/ro,phi=p1,
use_physical=True,ro=ro,vo=vo),
potential.evaluatezforces(pot,R1/ro,Z1/ro,phi=p1,
use_physical=True,ro=ro,vo=vo),
potential.evaluatephiforces(pot,R1/ro,Z1/ro,phi=p1,
use_physical=True,ro=ro,vo=vo))
def force_pal5(pot,dpal5,ro,vo):
"""Return the force at Pal5"""
# First compute the location based on the distance
l5, b5= bovy_coords.radec_to_lb(229.018,-0.124,degree=True)
X5,Y5,Z5= bovy_coords.lbd_to_XYZ(l5,b5,dpal5,degree=True)
R5,p5,Z5= bovy_coords.XYZ_to_galcencyl(X5,Y5,Z5,Xsun=ro,Zsun=0.025)
return (potential.evaluateRforces(pot,R5/ro,Z5/ro,phi=p5,
use_physical=True,ro=ro,vo=vo),
potential.evaluatezforces(pot,R5/ro,Z5/ro,phi=p5,
use_physical=True,ro=ro,vo=vo),
potential.evaluatephiforces(pot,R5/ro,Z5/ro,phi=p5,
use_physical=True,ro=ro,vo=vo))
def _getForces(folder):
loc = "SCFAnalysis/Orbits/{0}".format(folder)
Acos = nu.load(loc + "/Acos.npy")
a_nfw = 200./8
orbits_pos =nu.load(TIMEORBITS.format(loc, TIME,0.004,1*units.Myr))
scf = potential.SCFPotential(Acos=Acos, a=a_nfw, normalize=.35)
ps= potential.PowerSphericalPotentialwCutoff(alpha=1.8,rc=1.9/8.,normalize=0.05)
mn= potential.MiyamotoNagaiPotential(a=3./8.,b=0.28/8.,normalize=.6)
MWPotential= [ps,mn,scf]
x,y,z = orbits_pos[-1,1:4]
R, phi, z = rect_to_cyl(x,y,z)
print "(R,z,phi) = ({0}, {1}, {2})".format(R,z,phi)
Rforce = potential.evaluateRforces(MWPotential, R,z,phi)
zforce = potential.evaluatezforces(MWPotential, R,z,phi)
phiforce = potential.evaluatephiforces(MWPotential, R,z,phi)
return Rforce, zforce, phiforce
def force_gd1(pot, ro, vo):
"""Return the force at GD-1.
Parameters
----------
pot: Potential
ro, vo: float
Return
------
force: tuple
[fx, fy, fz]
"""
# Just use R=12.5 kpc, Z= 6.675 kpc, phi=0
R1 = 12.5
Z1 = 6.675
p1 = 0.0
return (
potential.evaluateRforces(pot,
R1 / ro,
Z1 / ro,
phi=p1,
use_physical=True,
ro=ro,
vo=vo),
potential.evaluatezforces(pot,
R1 / ro,
Z1 / ro,
phi=p1,
use_physical=True,
ro=ro,
vo=vo),
potential.evaluatephiforces(pot,
R1 / ro,
Z1 / ro,
phi=p1,
use_physical=True,
ro=ro,
vo=vo),
)
def del_E(coord, custom_potential=None):
"""
NAME:
del_E
PURPOSE:
Given (m,6) array for a list of the position and velocity of stars in
Cartesian coordinate, return the gradient vectors of energy in Cartesian
form, in the corresponding row order.
Assumes input and out put are in natrual unit.
INPUT:
coord = array([[x, y, z, vx, vy, vz], ...])
where each row represents the coordinate of a star
OUTPUT:
del_E = gradient in Cartesian coordinate
where each row represents the gradient of a star
HISTORY:
2018-07-10 - Written - Samuel Wong
2018-07-24 - Changed to an array of points - Samuel Wong
"""
if custom_potential == None:
potential = MWPotential2014
else:
potential = custom_potential
x, y, z, vx, vy, vz = coord.T
R, vR, vT, z, vz, phi = rect_to_cyl(x, y, z, vx, vy, vz).T
# get the force of the potential in cylindrical form
F_phi = evaluatephiforces(potential, R, z, phi) / R
F_R = evaluateRforces(potential, R, z, phi)
F_z = evaluatezforces(potential, R, z, phi)
# return the gradient in Cartesian coordinate
gradient = [
F_phi * np.sin(phi) - F_R * np.cos(phi),
-F_R * np.sin(phi) - F_phi * np.cos(phi), -F_z, vx, vy, vz
]
return np.array(gradient).T