def setup_potential_kuepper(Mhalo: float, a: float) -> List[Potential]:
"""Set up Kuepper et al. (2015) Potential.
Parameters
----------
Mhalo: float
mass / 10^12 Msun
a: float
scale length / kpc,
Returns
-------
potential : list
HernquistPotential + MiyamotoNagaiPotential + NFWPotential
"""
pot: List[Potential] = [
potential.HernquistPotential(amp=3.4e10 * u.Msun, a=0.7 * u.kpc),
potential.MiyamotoNagaiPotential(amp=1e11 * u.Msun,
a=6.5 * u.kpc,
b=0.26 * u.kpc),
potential.NFWPotential(amp=Mhalo * 1e12 * u.Msun, a=a * u.kpc),
]
return pot
def test_nemo_MiyamotoNagaiPotential():
mp = potential.MiyamotoNagaiPotential(normalize=1., a=0.5, b=0.1)
tmax = 4.
vo, ro = 220., 8.
o = Orbit([1., 0.1, 1.1, 0.3, 0.1, 0.4], ro=ro, vo=vo)
run_orbitIntegration_comparison(o, mp, tmax, vo, ro)
return None
def test_staeckel_fudge_delta():
import galpy.potential as galpy_pot
from galpy.actionAngle import estimateDeltaStaeckel
ro = 8.1 * u.kpc
vo = 229 * u.km / u.s
paired_potentials = []
# Miyamoto-Nagai
potential = gp.MiyamotoNagaiPotential(m=6e10 * u.Msun,
a=3 * u.kpc,
b=0.3 * u.kpc,
units=galactic)
amp = (G * potential.parameters['m']).to_value(vo**2 * ro)
a = potential.parameters['a'].to_value(ro)
b = potential.parameters['b'].to_value(ro)
galpy_potential = galpy_pot.MiyamotoNagaiPotential(amp=amp,
a=a,
b=b,
ro=ro,
vo=vo)
paired_potentials.append((potential, galpy_potential))
# Hernquist
potential = gp.HernquistPotential(m=6e10 * u.Msun,
c=0.3 * u.kpc,
units=galactic)
amp = (G * potential.parameters['m']).to_value(vo**2 * ro)
a = potential.parameters['c'].to_value(ro)
galpy_potential = galpy_pot.HernquistPotential(amp=amp, a=a, ro=ro, vo=vo)
paired_potentials.append((potential, galpy_potential))
# NFW
potential = gp.NFWPotential(m=6e11 * u.Msun,
r_s=15.6 * u.kpc,
units=galactic)
amp = (G * potential.parameters['m']).to_value(vo**2 * ro)
a = potential.parameters['r_s'].to_value(ro)
galpy_potential = galpy_pot.NFWPotential(amp=amp, a=a, ro=ro, vo=vo)
paired_potentials.append((potential, galpy_potential))
# TEST:
N = 1024
rnd = np.random.default_rng(42)
w = PhaseSpacePosition(pos=rnd.uniform(-10, 10, size=(3, N)) * u.kpc,
vel=rnd.uniform(-100, 100, size=(3, N)) * u.km /
u.s)
R = w.cylindrical.rho.to_value(ro)
z = w.z.to_value(ro)
for p, galpy_p in paired_potentials:
galpy_deltas = estimateDeltaStaeckel(galpy_p, R, z, no_median=True)
gala_deltas = get_staeckel_fudge_delta(p, w).value
print(p, np.allclose(gala_deltas, galpy_deltas))
assert np.allclose(gala_deltas, galpy_deltas, atol=1e-6)
def accMWpot(x,y,z,alpha=1.8, rc=1.9, a=3., b=0.28):
x = x/kpctocm
y = y/kpctocm
z = z/kpctocm
r = np.sqrt( x**2 + y**2)
bp= gp.PowerSphericalPotentialwCutoff(alpha=1.8,rc=1.9/8.,normalize=0.05)
mp= gp.MiyamotoNagaiPotential(a=a/8.,b=b/8.,normalize=.6)
nfw= gp.NFWPotential(a=16/8.,normalize=.35)
#print(help(MWPotential2014))
#pot = [bp,mp,nfw]
pot = MWPotential2014
az = evaluatezforces(pot,r*u.kpc , z*u.kpc)*bovy_conversion.force_in_kmsMyr(Vlsr/1e5,8.122)
ar = evaluateRforces(pot,r*u.kpc , z*u.kpc)*bovy_conversion.force_in_kmsMyr(Vlsr/1e5,8.122)
ar = ar*1.e5/(1.e6*3.15e7)
az = -az*1.e5/(1.e6*3.15e7)
ax = -ar*x/r
ay = -ar*y/r
return ax,ay,az
def setup_potential(params,c,fitc,dblexp,ro,vo,fitvoro=False,b=1.,pa=0.,
addgas=False):
pot= [potential.PowerSphericalPotentialwCutoff(normalize=1.-params[0]-params[1],
alpha=1.8,rc=1.9/ro)]
if dblexp:
if addgas:
# add 13 Msun/pc^2
gp= potential.DoubleExponentialDiskPotential(\
amp=0.03333*u.Msun/u.pc**3\
*numpy.exp(ro/2./numpy.exp(params[2])/_REFR0),
hz=150.*u.pc,
hr=2.*numpy.exp(params[2])*_REFR0/ro,
ro=ro,vo=vo)
gp.turn_physical_off()
gprf= gp.Rforce(1.,0.)
dpf= params[0]+gprf
if dpf < 0.: dpf= 0.
pot.append(\
potential.DoubleExponentialDiskPotential(\
normalize=dpf,hr=numpy.exp(params[2])*_REFR0/ro,
hz=numpy.exp(params[3])*_REFR0/ro))
else:
pot.append(\
potential.DoubleExponentialDiskPotential(\
normalize=params[0],hr=numpy.exp(params[2])*_REFR0/ro,
hz=numpy.exp(params[3])*_REFR0/ro))
else:
pot.append(\
potential.MiyamotoNagaiPotential(normalize=params[0],
a=numpy.exp(params[2])*_REFR0/ro,
b=numpy.exp(params[3])*_REFR0/ro))
if fitc:
pot.append(potential.TriaxialNFWPotential(\
normalize=params[1],a=numpy.exp(params[4])*_REFR0/ro,
c=params[7+2*fitvoro],b=b,pa=pa))
else:
pot.append(potential.TriaxialNFWPotential(\
normalize=params[1],a=numpy.exp(params[4])*_REFR0/ro,
c=c,b=b,pa=pa))
if addgas:
pot.append(gp) # make sure it's the last
return pot
def setup_potential(
params: Sequence,
c: float,
fitc: bool,
dblexp: bool,
ro: float = REFR0,
vo: float = REFV0,
fitvoro: bool = False,
b: float = 1.0,
pa: float = 0.0,
addgas: bool = False,
) -> PotentialType:
"""Set up potential.
PowerSphericalPotentialwCutoff
MiyamotoNagaiPotential or DoubleExponentialDiskPotential
TriaxialNFWPotential
Parameters
----------
params
c
fitc
dblexp
DoubleExponentialDiskPotential instead if MiyamotoNagaiPotential
ro
vo
fitvoro: bool, optional
default False
b: float, optional
default 1.0
pa: float, optional
Position Angle
default 0.0
addgas: bool, optional
default False
"""
pot: potential.Potential = [
potential.PowerSphericalPotentialwCutoff(
normalize=1.0 - params[0] - params[1], alpha=1.8, rc=1.9 / ro
)
]
if dblexp:
if addgas:
# add 13 Msun/pc^2
gp = potential.DoubleExponentialDiskPotential(
amp=0.03333
* u.Msun
/ u.pc ** 3
* np.exp(ro / 2.0 / np.exp(params[2]) / REFR0),
hz=150.0 * u.pc,
hr=2.0 * np.exp(params[2]) * REFR0 / ro,
ro=ro,
vo=vo,
)
gp.turn_physical_off()
gprf = gp.Rforce(1.0, 0.0)
dpf = params[0] + gprf
if dpf < 0.0:
dpf = 0.0
pot.append(
potential.DoubleExponentialDiskPotential(
normalize=dpf,
hr=np.exp(params[2]) * REFR0 / ro,
hz=np.exp(params[3]) * REFR0 / ro,
)
)
else:
pot.append(
potential.DoubleExponentialDiskPotential(
normalize=params[0],
hr=np.exp(params[2]) * REFR0 / ro,
hz=np.exp(params[3]) * REFR0 / ro,
)
)
else:
pot.append(
potential.MiyamotoNagaiPotential(
normalize=params[0],
a=np.exp(params[2]) * REFR0 / ro,
b=np.exp(params[3]) * REFR0 / ro,
)
)
if fitc:
pot.append(
potential.TriaxialNFWPotential(
normalize=params[1],
a=np.exp(params[4]) * REFR0 / ro,
c=params[7 + 2 * fitvoro],
b=b,
pa=pa,
)
)
else:
pot.append(
potential.TriaxialNFWPotential(
normalize=params[1], a=np.exp(params[4]) * REFR0 / ro, c=c, b=b, pa=pa,
)
)
if addgas:
pot.append(gp) # make sure it's the last
return pot
def test_dynamfric_c():
import copy
from galpy.orbit import Orbit
from galpy.potential.Potential import _check_c
from galpy.potential.mwpotentials import McMillan17
#Basic parameters for the test
times = numpy.linspace(0., -100., 1001) #~3 Gyr at the Solar circle
integrator = 'dop853_c'
py_integrator = 'dop853'
#Define all of the potentials (by hand, because need reasonable setup)
MWPotential3021 = copy.deepcopy(potential.MWPotential2014)
MWPotential3021[2] *= 1.5 # Increase mass by 50%
pots= [potential.LogarithmicHaloPotential(normalize=1),
potential.LogarithmicHaloPotential(normalize=1.3,
q=0.9,b=0.7), #nonaxi
potential.NFWPotential(normalize=1.,a=1.5),
potential.MiyamotoNagaiPotential(normalize=.02,a=10.,b=10.),
potential.MiyamotoNagaiPotential(normalize=.6,a=0.,b=3.), # special case
potential.PowerSphericalPotential(alpha=2.3,normalize=2.),
potential.DehnenSphericalPotential(normalize=4.,alpha=1.2),
potential.DehnenCoreSphericalPotential(normalize=4.),
potential.HernquistPotential(normalize=1.,a=3.5),
potential.JaffePotential(normalize=1.,a=20.5),
potential.DoubleExponentialDiskPotential(normalize=0.2,
hr=3.,hz=0.6),
potential.FlattenedPowerPotential(normalize=3.),
potential.FlattenedPowerPotential(normalize=3.,alpha=0), #special case
potential.IsochronePotential(normalize=2.),
potential.PowerSphericalPotentialwCutoff(normalize=0.3,rc=10.),
potential.PlummerPotential(normalize=.6,b=3.),
potential.PseudoIsothermalPotential(normalize=.1,a=3.),
potential.BurkertPotential(normalize=.2,a=2.5),
potential.TriaxialHernquistPotential(normalize=1.,a=3.5,
b=0.8,c=0.9),
potential.TriaxialNFWPotential(normalize=1.,a=1.5,b=0.8,c=0.9),
potential.TriaxialJaffePotential(normalize=1.,a=20.5,b=0.8,c=1.4),
potential.PerfectEllipsoidPotential(normalize=.3,a=3.,b=0.7,c=1.5),
potential.PerfectEllipsoidPotential(normalize=.3,a=3.,b=0.7,c=1.5,
pa=3.,zvec=[0.,1.,0.]), #rotated
potential.HomogeneousSpherePotential(normalize=0.02,R=82./8), # make sure to go to dens = 0 part,
potential.interpSphericalPotential(\
rforce=potential.HomogeneousSpherePotential(normalize=0.02,
R=82./8.),
rgrid=numpy.linspace(0.,82./8.,201)),
potential.TriaxialGaussianPotential(normalize=.03,sigma=4.,b=0.8,c=1.5,pa=3.,zvec=[1.,0.,0.]),
potential.SCFPotential(Acos=numpy.array([[[1.]]]), # same as Hernquist
normalize=1.,a=3.5),
potential.SCFPotential(Acos=numpy.array([[[1.,0.],[.3,0.]]]), # nonaxi
Asin=numpy.array([[[0.,0.],[1e-1,0.]]]),
normalize=1.,a=3.5),
MWPotential3021,
McMillan17 # SCF + DiskSCF
]
#tolerances in log10
tol = {}
tol['default'] = -7.
# Following are a little more difficult
tol['DoubleExponentialDiskPotential'] = -4.5
tol['TriaxialHernquistPotential'] = -6.
tol['TriaxialNFWPotential'] = -6.
tol['TriaxialJaffePotential'] = -6.
tol['MWPotential3021'] = -6.
tol['HomogeneousSpherePotential'] = -6.
tol['interpSphericalPotential'] = -6. # == HomogeneousSpherePotential
tol['McMillan17'] = -6.
for p in pots:
if not _check_c(p, dens=True): continue # dynamfric not in C!
pname = type(p).__name__
if pname == 'list':
if isinstance(p[0],potential.PowerSphericalPotentialwCutoff) \
and len(p) > 1 \
and isinstance(p[1],potential.MiyamotoNagaiPotential) \
and len(p) > 2 \
and isinstance(p[2],potential.NFWPotential):
pname = 'MWPotential3021' # Must be!
else:
pname = 'McMillan17'
#print(pname)
if pname in list(tol.keys()): ttol = tol[pname]
else: ttol = tol['default']
# Setup orbit, ~ LMC
o = Orbit([
5.13200034, 1.08033051, 0.23323391, -3.48068653, 0.94950884,
-1.54626091
])
# Setup dynamical friction object
if pname == 'McMillan17':
cdf= potential.ChandrasekharDynamicalFrictionForce(\
GMs=0.5553870441722593,rhm=5./8.,dens=p,maxr=500./8,nr=101)
ttimes = numpy.linspace(0., -30.,
1001) #~1 Gyr at the Solar circle
else:
cdf= potential.ChandrasekharDynamicalFrictionForce(\
GMs=0.5553870441722593,rhm=5./8.,dens=p,maxr=500./8,nr=201)
ttimes = times
# Integrate in C
o.integrate(ttimes, p + cdf, method=integrator)
# Integrate in Python
op = o()
op.integrate(ttimes, p + cdf, method=py_integrator)
# Compare r (most important)
assert numpy.amax(numpy.fabs(o.r(ttimes)-op.r(ttimes))) < 10**ttol, \
'Dynamical friction in C does not agree with dynamical friction in Python for potential {}'.format(pname)
return None