def test_ChandrasekharDynamicalFrictionForce_varLambda():
# Test that dynamical friction with variable Lambda for small r ranges
# gives ~ the same result as using a constant Lambda that is the mean of
# the variable lambda
# Also tests that giving an axisymmetric list of potentials for the
# density works
from galpy.util import conversion
from galpy.orbit import Orbit
ro, vo = 8., 220.
# Parameters
GMs = 10.**9. / conversion.mass_in_msol(vo, ro)
r_init = 3.
dt = 2. / conversion.time_in_Gyr(vo, ro)
# Compute evolution with variable ln Lambda
cdf= potential.ChandrasekharDynamicalFrictionForce(\
GMs=GMs,rhm=0.125,
dens=potential.MWPotential2014,sigmar=lambda r: 1./numpy.sqrt(2.))
o = Orbit([r_init, 0., 1., 0., 0., 0.])
ts = numpy.linspace(0., dt, 1001)
o.integrate(ts, [potential.MWPotential2014, cdf], method='odeint')
lnLs = numpy.array([
cdf.lnLambda(r, v) for (r, v) in zip(
o.r(ts), numpy.sqrt(o.vx(ts)**2. + o.vy(ts)**2. + o.vz(ts)**2.))
])
cdfc= potential.ChandrasekharDynamicalFrictionForce(\
GMs=GMs,rhm=0.125,const_lnLambda=numpy.mean(lnLs),
dens=potential.MWPotential2014,sigmar=lambda r: 1./numpy.sqrt(2.))
oc = o()
oc.integrate(ts, [potential.MWPotential2014, cdfc], method='odeint')
assert numpy.fabs(
oc.r(ts[-1]) - o.r(ts[-1])
) < 0.05, 'ChandrasekharDynamicalFrictionForce with variable lnLambda for a short radial range is not close to the calculation using a constant lnLambda'
return None
def test_ChandrasekharDynamicalFrictionForce_constLambda():
# Test that the ChandrasekharDynamicalFrictionForce with constant Lambda
# agrees with analytical solutions for circular orbits:
# assuming that a mass remains on a circular orbit in an isothermal halo
# with velocity dispersion sigma and for constant Lambda:
# r_final^2 - r_initial^2 = -0.604 ln(Lambda) GM/sigma t
# (e.g., B&T08, p. 648)
from galpy.util import conversion
from galpy.orbit import Orbit
ro, vo = 8., 220.
# Parameters
GMs = 10.**9. / conversion.mass_in_msol(vo, ro)
const_lnLambda = 7.
r_init = 2.
dt = 2. / conversion.time_in_Gyr(vo, ro)
# Compute
lp = potential.LogarithmicHaloPotential(normalize=1., q=1.)
cdfc= potential.ChandrasekharDynamicalFrictionForce(\
GMs=GMs,const_lnLambda=const_lnLambda,
dens=lp) # don't provide sigmar, so it gets computed using galpy.df.jeans
o = Orbit([r_init, 0., 1., 0., 0., 0.])
ts = numpy.linspace(0., dt, 1001)
o.integrate(ts, [lp, cdfc], method='odeint')
r_pred = numpy.sqrt(o.r()**2. -
0.604 * const_lnLambda * GMs * numpy.sqrt(2.) * dt)
assert numpy.fabs(
r_pred - o.r(ts[-1])
) < 0.01, 'ChandrasekharDynamicalFrictionForce with constant lnLambda for circular orbits does not agree with analytical prediction'
return None
def test_ChandrasekharDynamicalFrictionForce_pickling():
# Test that ChandrasekharDynamicalFrictionForce objects can/cannot be
# pickled as expected
import pickle
from galpy.util import conversion
ro, vo = 8., 220.
# Parameters
GMs = 10.**9. / conversion.mass_in_msol(vo, ro)
# sigmar internally computed, should be able to be pickled
# Compute evolution with variable ln Lambda
cdf= potential.ChandrasekharDynamicalFrictionForce(\
GMs=GMs,rhm=0.125,
dens=potential.MWPotential2014,
minr=0.5,maxr=2.)
pickled = pickle.dumps(cdf)
cdfu = pickle.loads(pickled)
# Test a few values
assert numpy.fabs(cdf.Rforce(1.,0.2,v=[1.,1.,0.])\
-cdfu.Rforce(1.,0.2,v=[1.,1.,0.])) < 1e-10, 'Pickling of ChandrasekharDynamicalFrictionForce object does not work as expected'
assert numpy.fabs(cdf.zforce(2.,-0.2,v=[1.,1.,0.])\
-cdfu.zforce(2.,-0.2,v=[1.,1.,0.])) < 1e-10, 'Pickling of ChandrasekharDynamicalFrictionForce object does not work as expected'
# Not providing dens = Logarithmic should also work
cdf= potential.ChandrasekharDynamicalFrictionForce(\
GMs=GMs,rhm=0.125,
minr=0.5,maxr=2.)
pickled = pickle.dumps(cdf)
cdfu = pickle.loads(pickled)
# Test a few values
assert numpy.fabs(cdf.Rforce(1.,0.2,v=[1.,1.,0.])\
-cdfu.Rforce(1.,0.2,v=[1.,1.,0.])) < 1e-10, 'Pickling of ChandrasekharDynamicalFrictionForce object does not work as expected'
assert numpy.fabs(cdf.zforce(2.,-0.2,v=[1.,1.,0.])\
-cdfu.zforce(2.,-0.2,v=[1.,1.,0.])) < 1e-10, 'Pickling of ChandrasekharDynamicalFrictionForce object does not work as expected'
# Providing sigmar as a lambda function gives AttributeError
sigmar = lambda r: 1. / r
cdf= potential.ChandrasekharDynamicalFrictionForce(\
GMs=GMs,rhm=0.125,
dens=potential.MWPotential2014,sigmar=sigmar,
minr=0.5,maxr=2.)
if PY3:
with pytest.raises(AttributeError) as excinfo:
pickled = pickle.dumps(cdf)
else:
with pytest.raises(pickle.PicklingError) as excinfo:
pickled = pickle.dumps(cdf)
return None
def test_ChandrasekharDynamicalFrictionForce_evaloutsideminrmaxr():
# Test that dynamical friction returns the expected force when evaluating
# outside of the [minr,maxr] range over which sigmar is interpolated:
# 0 at r < minr
# using sigmar(r) for r > maxr
from galpy.util import conversion
ro, vo = 8., 220.
# Parameters
GMs = 10.**9. / conversion.mass_in_msol(vo, ro)
# Compute evolution with variable ln Lambda
sigmar = lambda r: 1. / r
cdf= potential.ChandrasekharDynamicalFrictionForce(\
GMs=GMs,rhm=0.125,
dens=potential.MWPotential2014,sigmar=sigmar,
minr=0.5,maxr=2.)
# cdf 2 for checking r > maxr of cdf
cdf2= potential.ChandrasekharDynamicalFrictionForce(\
GMs=GMs,rhm=0.125,
dens=potential.MWPotential2014,sigmar=sigmar,
minr=0.5,maxr=4.)
v = [0.1, 0., 0.]
# r < minr
assert numpy.fabs(
cdf.Rforce(0.1, 0., v=v)
) < 1e-16, 'potential.ChandrasekharDynamicalFrictionForce at r < minr not equal to zero'
assert numpy.fabs(
cdf.zforce(0.1, 0., v=v)
) < 1e-16, 'potential.ChandrasekharDynamicalFrictionForce at r < minr not equal to zero'
# r > maxr
assert numpy.fabs(
cdf.Rforce(3., 0., v=v) - cdf2.Rforce(3., 0., v=v)
) < 1e-10, 'potential.ChandrasekharDynamicalFrictionForce at r > maxr not as expected'
assert numpy.fabs(
cdf.zforce(3., 0., v=v) - cdf2.zforce(3., 0., v=v)
) < 1e-10, 'potential.ChandrasekharDynamicalFrictionForce at r > maxr not as expected'
return None
def test_dynamfric_c_minr_warning():
from galpy.orbit import Orbit
times = numpy.linspace(0., 100., 1001) #~3 Gyr at the Solar circle
integrator = 'dop853_c'
pot = potential.LogarithmicHaloPotential(normalize=1)
# Setup orbit
o = Orbit()
# Setup dynamical friction object, with minr = 1, should thus reach it
cdf= potential.ChandrasekharDynamicalFrictionForce(\
GMs=0.5553870441722593,rhm=5./8.,dens=pot,minr=1.)
# Integrate, should raise warning
with pytest.warns(None) as record:
o.integrate(times, pot + cdf, method=integrator)
raisedWarning = False
for rec in record:
# check that the message matches
raisedWarning += (
str(rec.message.args[0]) ==
"Orbit integration with ChandrasekharDynamicalFrictionForce entered domain where r < minr and ChandrasekharDynamicalFrictionForce is turned off; initialize ChandrasekharDynamicalFrictionForce with a smaller minr to avoid this if you wish (but note that you want to turn it off close to the center for an object that sinks all the way to r=0, to avoid numerical instabilities)"
)
assert raisedWarning, "Integrating an orbit that goes to r < minr with dynamical friction should have raised a warning, but didn't"
return None
def test_dynamfric_c_minr():
from galpy.orbit import Orbit
times = numpy.linspace(0., -100., 1001) #~3 Gyr at the Solar circle
integrator = 'dop853_c'
pot = potential.LogarithmicHaloPotential(normalize=1)
# Setup orbit, ~ LMC
o = Orbit([
5.13200034, 1.08033051, 0.23323391, -3.48068653, 0.94950884,
-1.54626091
])
# Setup dynamical friction object, with minr = 130 st always 0 for this orbit
cdf= potential.ChandrasekharDynamicalFrictionForce(\
GMs=0.5553870441722593,rhm=5./8.,dens=pot,minr=130./8.,maxr=500./8)
# Integrate in C with dynamical friction
o.integrate(times, pot + cdf, method=integrator)
# Integrate in C without dynamical friction
op = o()
op.integrate(times, pot, method=integrator)
# Compare r (most important)
assert numpy.amax(numpy.fabs(o.r(times)-op.r(times))) < 10**-8., \
'Dynamical friction in C does not properly use minr'
return None
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
