def test_nemo_LogarithmicHaloPotential():
lp = potential.LogarithmicHaloPotential(normalize=1.)
tmax = 2.
vo, ro = 210., 8.5
o = Orbit([1., 0.1, 1.1, 0.3, 0.1, 0.4], ro=ro, vo=vo)
run_orbitIntegration_comparison(o, lp, tmax, vo, ro, tol=0.03)
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_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 predict_gd1obs(pot_params,c,b=1.,pa=0.,
sigv=0.4,td=10.,
phi1=0.,phi2=-1.,dist=10.2,
pmphi1=-8.5,pmphi2=-2.05,vlos=-285.,
ro=_REFR0,vo=_REFV0,
isob=None,nTrackChunks=8,multi=None,
useTM=False,
logpot=False,
verbose=True):
"""
NAME:
predict_gd1obs
PURPOSE:
Function that generates the location and velocity of the GD-1 stream (similar to predict_pal5obs), its width, and its length for a given potential and progenitor phase-space position
INPUT:
pot_params- array with the parameters of a potential model (see MWPotential2014Likelihood.setup_potential; only the basic parameters of the disk and halo are used, flattening is specified separately)
c- halo flattening
b= (1.) halo-squashed
pa= (0.) halo PA
sigv= (0.365) velocity dispersion in km/s
td= (10.) stream age in Gyr
phi1= (0.) Progenitor's phi1 position
phi2= (-1.) Progenitor's phi2 position
dist= (10.2) progenitor distance in kpc
pmphi1= (-8.5) progenitor proper motion in phi1 in mas/yr
pmphi2= (-2.) progenitor proper motion in phi2 in mas/yr
vlos= (-250.) progenitor line-of-sight velocity in km/s
ro= (project default) distance to the GC in kpc
vo= (project default) circular velocity at R0 in km/s
nTrackChunks= (8) nTrackChunks input to streamdf
multi= (None) multi input to streamdf
logpot= (False) if True, use a logarithmic potential instead
isob= (None) if given, b parameter of actionAngleIsochroneApprox
useTM= (True) use the TorusMapper to compute the track
verbose= (True) print messages
OUTPUT:
HISTORY:
2016-08-12 - Written - Bovy (UofT)
"""
# Convert progenitor's phase-space position to l,b,...
prog= Orbit(phi12_to_lb_6d(phi1,phi2,dist,pmphi1,pmphi2,vlos),
lb=True,ro=ro,vo=vo,solarmotion=[-11.1,24.,7.25])
if logpot:
pot= potential.LogarithmicHaloPotential(normalize=1.,q=c)
else:
pot= MWPotential2014Likelihood.setup_potential(pot_params,c,
False,False,ro,vo,
b=b,pa=pa)
success= True
this_useTM= useTM
try:
sdf= setup_sdf(pot,prog,sigv,td,ro,vo,multi=multi,
isob=isob,nTrackChunks=nTrackChunks,
verbose=verbose,useTM=useTM,logpot=logpot)
except:
# Catches errors and time-outs
success= False
# Check for calc. issues
if not success:
return (numpy.zeros((1001,6))-1000000.,False)
# Try again with TM
this_useTM= True
this_nTrackChunks= 21 # might as well
sdf= setup_sdf(pot,prog,sigv,td,ro,vo,multi=multi,
isob=isob,nTrackChunks=this_nTrackChunks,
verbose=verbose,useTM=this_useTM,logpot=logpot)
else:
success= not this_useTM
# Compute the track and convert it to phi12
track_phi= convert_track_lb_to_phi12(sdf._interpolatedObsTrackLB)
return (track_phi,success)
tsteady = 3 * u.Gyr
N = 2 # number of arms
alpha = 10 * u.deg # pitch angle, p in the paper
H = 0.18 * u.kpc # arbitrary, not specified in the paper
Rs = 0.38
sp = potential.SpiralArmsPotential(amp=1,
N=N,
alpha=alpha,
H=H,
Rs=Rs,
phi_ref=0)
phi_ref = -minimize(lambda phi: sp.dens(1, 0, phi[0]), x0=[0]).x[0]
dfc = dehnendf(beta=0, profileParams=(1 / 3, 1, 0.01), correct=True, niter=20)
lp = potential.LogarithmicHaloPotential(amp=1, normalize=1)
# 30% density perturbation
sp = potential.SpiralArmsPotential(amp=1,
N=N,
alpha=alpha,
H=H,
Rs=Rs,
phi_ref=phi_ref)
amp30 = abs(lp.dens(R=1, z=0, phi=0) / sp.dens(R=1, z=0, phi=0) * 0.3)
n = 51
omegas = np.linspace(0, 2, 101)
oortA_array = np.empty(len(omegas))
oortB_array = np.empty(len(omegas))
def predict_gd1obs(
pot_params: Sequence[float],
c: float,
b: float = 1.0,
pa: float = 0.0,
sigv: float = 0.4,
td: float = 10.0,
dist: float = 10.2,
pmphi1: float = -8.5,
pmphi2: float = -2.05,
phi1: float = 0.0,
phi2: float = -1.0,
vlos: float = -285.0,
ro: float = REFR0,
vo: float = REFV0,
isob: Optional[bool] = None,
nTrackChunks: int = 8,
multi: Optional[Any] = None,
useTM: bool = False,
logpot: bool = False,
verbose: bool = True,
):
"""Predict GD1-observed.
Function that generates the location and velocity of the GD-1 stream,
its width, and its length for a given potential
and progenitor phase-space position.
Parameters
----------
pot_params
array with the parameters of a potential model
(see mw_pot.setup_potential;
only the basic parameters of the disk and halo are used,
flattening is specified separately)
c
halo flattening
b
(1.) halo-squashed
pa
(0.) halo PA
sigv
(0.365) velocity dispersion in km/s
td
(10.) stream age in Gyr
phi1
(0.) Progenitor's phi1 position
phi2
(-1.) Progenitor's phi2 position
dist
(10.2) progenitor distance in kpc
pmphi1
(-8.5) progenitor proper motion in phi1 in mas/yr
pmphi2
(-2.) progenitor proper motion in phi2 in mas/yr
vlos
(-250.) progenitor line-of-sight velocity in km/s
ro
(project default) distance to the GC in kpc
vo
(project default) circular velocity at R0 in km/s
nTrackChunks
(8) nTrackChunks input to streamdf
multi
(None) multi input to streamdf
logpot
(False) if True, use a logarithmic potential instead
isob
(None) if given, b parameter of actionAngleIsochroneApprox
useTM
(True) use the TorusMapper to compute the track
verbose
(True) print messages
Notes
-----
2016-08-12 - Written - Bovy (UofT)
"""
# Convert progenitor's phase-space position to l,b,...
prog = Orbit(
phi12_to_lb_6d(phi1, phi2, dist, pmphi1, pmphi2, vlos),
lb=True,
ro=ro,
vo=vo,
solarmotion=[-11.1, 24.0, 7.25],
)
if logpot:
pot = potential.LogarithmicHaloPotential(normalize=1.0, q=c)
else:
pot = mw_pot.setup_potential(pot_params, c, False, False, ro, vo, b=b, pa=pa)
success: bool = True
this_useTM = useTM
try:
sdf = setup_sdf(
pot,
prog,
sigv,
td,
ro,
vo,
multi=multi,
isob=isob,
nTrackChunks=nTrackChunks,
verbose=verbose,
useTM=useTM,
logpot=logpot,
)
except:
# Catches errors and time-outs
success: bool = False
# Check for calc. issues
if not success:
return (np.zeros((1001, 6)) - 1000000.0, False)
# Try again with TM
this_useTM = True
this_nTrackChunks = 21 # might as well
sdf = setup_sdf(
pot,
prog,
sigv,
td,
ro,
vo,
multi=multi,
isob=isob,
nTrackChunks=this_nTrackChunks,
verbose=verbose,
useTM=this_useTM,
logpot=logpot,
)
else:
success: bool = not this_useTM
# Compute the track and convert it to phi12
track_phi = convert_track_lb_to_phi12(sdf._interpolatedObsTrackLB)
return track_phi, success
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
