def make_nondefault_pal5stream(chain_ind,leading=False,timpact=None,b=0.8,hernquist=False,td=5.):
orb,pot,sigv,tvo=set_prog_potential(chain_ind)
try :
sdf= pal5_util.setup_pal5model_MWfit(ro=_REFR0,vo=tvo,timpact=timpact,pot=pot,orb=orb,hernquist=hernquist,leading=leading,age=td,sigv=sigv)
except numpy.linalg.LinAlgError:
print ("using estimateBIsochrone")
ts= numpy.linspace(0.,td,1001)/bovy_conversion.time_in_Gyr(_REFV0, _REFR0)
prog = Orbit(orb,radec=True,ro=_REFR0,vo=tvo,solarmotion=[-11.1,24.,7.25])
prog.integrate(ts,pot)
estb= estimateBIsochrone(pot,prog.R(ts,use_physical=False),
prog.z(ts,use_physical=False),
phi=prog.phi(ts,use_physical=False))
if estb[1] < 0.3: isob= 0.3
elif estb[1] > 1.5: isob= 1.5
else: isob= estb[1]
print ("b=%f"%isob)
sdf=pal5_util.setup_pal5model_MWfit(ro=_REFR0,vo=tvo,leading=leading,pot=pot,orb=orb,timpact=timpact,b=isob,hernquist=hernquist,age=td,sigv=sigv)
return sdf
def setup_sdf(pot,prog,sigv,td,ro,vo,multi=None,nTrackChunks=8,isob=None,
trailing_only=False,verbose=True,useTM=True,logpot=False):
"""Simple function to setup the stream model"""
if isob is None:
if True or logpot:
isob= 0.75
if False:
# Determine good one
ts= numpy.linspace(0.,15.,1001)
# Hack!
epot= copy.deepcopy(pot)
epot[2]._b= 1.
epot[2]._b2= 1.
epot[2]._isNonAxi= False
epot[2]._aligned= True
prog.integrate(ts,pot)
estb= estimateBIsochrone(epot,
prog.R(ts,use_physical=False),
prog.z(ts,use_physical=False),
phi=prog.phi(ts,use_physical=False))
if estb[1] < 0.3: isob= 0.3
elif estb[1] > 1.5: isob= 1.5
else: isob= estb[1]
if verbose: print(pot[2]._c, isob,estb)
if not logpot and numpy.fabs(pot[2]._b-1.) > 0.05:
aAI= actionAngleIsochroneApprox(pot=pot,b=isob,tintJ=1000.,
ntintJ=30000)
else:
ts= numpy.linspace(0.,100.,10000)
aAI= actionAngleIsochroneApprox(pot=pot,b=isob,tintJ=100.,
ntintJ=10000,dt=ts[1]-ts[0])
if useTM:
aAT= actionAngleTorus(pot=pot,tol=0.001,dJ=0.0001)
else:
aAT= False
try:
sdf=\
streamdf(sigv/vo,progenitor=prog,pot=pot,aA=aAI,
useTM=aAT,approxConstTrackFreq=True,
leading=True,nTrackChunks=nTrackChunks,
tdisrupt=td/bovy_conversion.time_in_Gyr(vo,ro),
ro=ro,vo=vo,R0=ro,
vsun=[-11.1,vo+24.,7.25],
custom_transform=_TKOP,
multi=multi,
nospreadsetup=True)
except numpy.linalg.LinAlgError:
sdf=\
streamdf(sigv/vo,progenitor=prog,pot=pot,aA=aAI,
useTM=aAT,approxConstTrackFreq=True,
leading=True,nTrackChunks=nTrackChunks,
nTrackIterations=0,
tdisrupt=td/bovy_conversion.time_in_Gyr(vo,ro),
ro=ro,vo=vo,R0=ro,
vsun=[-11.1,vo+24.,7.25],
custom_transform=_TKOP,
multi=multi)
return sdf
def plot_aaspher_conservation(plotfilename1,plotfilename2):
#Setup orbit
E, Lz= -1.25, 0.6
o= Orbit([0.8,0.3,Lz/0.8,0.,numpy.sqrt(2.*(E-evalPot(0.8,0.,MWPotential2014)-(Lz/0.8)**2./2.-0.3**2./2.)),0.])
#Integrate the orbit to estimate an equivalent b
nt= 1001
ts= numpy.linspace(0.,20.,nt)
o.integrate(ts,MWPotential2014,method='symplec4_c')
b= estimateBIsochrone(o.R(ts),o.z(ts),pot=MWPotential2014)
print b
b= 0.3
#Now integrate the orbit in the isochronePotential
ip= IsochronePotential(normalize=1.,b=b)
aAI= actionAngleIsochrone(ip=ip)
orbt= 2.*numpy.pi/aAI.actionsFreqs(o)[4]
norb= 200.
nt= 20001
ts= numpy.linspace(0.,norb*orbt,nt)
o.integrate(ts,ip,method='symplec4_c')
#Calculate actions, frequencies, and angles
jfa= aAI.actionsFreqsAngles(o.R(ts),o.vR(ts),o.vT(ts),
o.z(ts),o.vz(ts),o.phi(ts))
dJs= numpy.fabs((jfa[0]-numpy.mean(jfa[0]))/numpy.mean(jfa[0]))
dOrs= numpy.fabs((jfa[3]-numpy.mean(jfa[3]))/numpy.mean(jfa[3]))
dOzs= numpy.fabs((jfa[5]-numpy.mean(jfa[5]))/numpy.mean(jfa[5]))
print "frequencies", numpy.mean(dOrs), numpy.mean(dOzs)
ar= dePeriod(numpy.reshape(jfa[6],(1,len(ts)))).flatten()
az= dePeriod(numpy.reshape(jfa[8],(1,len(ts)))).flatten()
danglers= numpy.fabs(ar-numpy.mean(jfa[3])*ts-jfa[6][0])/2./numpy.pi
danglezs= numpy.fabs(az-numpy.mean(jfa[5])*ts-jfa[8][0])/2./numpy.pi
#Break up
breakt= 50.
pts= parse_break(ts,ts < breakt)
pdJs= parse_break(dJs,ts < breakt)
pdanglers= parse_break(danglers,ts < breakt)
pdanglezs= parse_break(danglezs,ts < breakt)
#dAngles
bovy_plot.bovy_print()
pyplot.subplot(2,1,1)
bovy_plot.bovy_plot(pts/orbt,
pdJs,
color='k',loglog=True,gcf=True,
xrange=[0.5,norb],
yrange=[10.**-12.,1.])
bovy_plot.bovy_text(r'$\texttt{actionAngleIsochrone}$',
top_left=True,size=14.)
ax= pyplot.gca()
ax.yaxis.set_ticks([10.**-12.,10.**-8.,10.**-4.,1.])
nullfmt = NullFormatter() # no labels
ax.xaxis.set_major_formatter(nullfmt)
#Same for actionAngleSpherical
aAS= actionAngleSpherical(pot=ip)
tts= ts[::1]
jfa= aAS.actionsFreqsAngles(o.R(tts),o.vR(tts),o.vT(tts),
o.z(tts),o.vz(tts),o.phi(tts),
fixed_quad=True)
#dJr
dJs= numpy.fabs((jfa[0]-numpy.mean(jfa[0]))/numpy.mean(jfa[0]))
dOrs= numpy.fabs((jfa[3]-numpy.mean(jfa[3]))/numpy.mean(jfa[3]))
dOzs= numpy.fabs((jfa[5]-numpy.mean(jfa[5]))/numpy.mean(jfa[5]))
print "frequencies", numpy.mean(dOrs), numpy.mean(dOzs)
#dAngles
ar= dePeriod(numpy.reshape(jfa[6],(1,len(tts)))).flatten()
az= dePeriod(numpy.reshape(jfa[8],(1,len(tts)))).flatten()
danglers= numpy.fabs(ar-numpy.mean(jfa[3])*tts-jfa[6][0])/2./numpy.pi
danglezs= numpy.fabs(az-numpy.mean(jfa[5])*tts-jfa[8][0])/2./numpy.pi
print numpy.mean(danglers)
print numpy.mean(danglezs)
ptts= parse_break(tts,tts < breakt)
pdJs= parse_break(dJs,tts < breakt)
pyplot.subplot(2,1,2)
bovy_plot.bovy_plot(ptts/orbt,
pdJs,
color='k',loglog=True,gcf=True,
xrange=[0.5,norb],
yrange=[10.**-12.,1.],
xlabel=r'$\mathrm{Number\ of\ orbital\ periods}$')
bovy_plot.bovy_text(r'$\texttt{actionAngleSpherical}$',
top_left=True,size=14.)
bovy_plot.bovy_text(0.175,10.**2.,r'$\left|\Delta J_R / J_R\right|$',
fontsize=16.,
rotation='vertical')
ax= pyplot.gca()
ax.xaxis.set_major_formatter(ticker.FormatStrFormatter(r'$%0.f$'))
ax.yaxis.set_ticks([10.**-12.,10.**-8.,10.**-4.,1.])
bovy_plot.bovy_end_print(plotfilename1)
#Now plot the deviations in the angles
bovy_plot.bovy_print()
pyplot.subplot(2,1,1)
liner= bovy_plot.bovy_plot(pts/orbt,
pdanglers,
color='k',ls='-',loglog=True,gcf=True,
xrange=[0.5,norb],
yrange=[10.**-12.,1.])
linez= bovy_plot.bovy_plot(pts/orbt,
pdanglezs,
color='k',ls='--',overplot=True)
legend1= pyplot.legend((liner[0],linez[0]),
(r'$\theta_R$',
r'$\theta_z$'),
loc='lower right',#bbox_to_anchor=(.91,.375),
numpoints=2,
prop={'size':14},
frameon=False)
bovy_plot.bovy_text(r'$\texttt{actionAngleIsochrone}$',
top_left=True,size=14.)
ax= pyplot.gca()
ax.yaxis.set_ticks([10.**-12.,10.**-8.,10.**-4.,1.])
nullfmt = NullFormatter() # no labels
ax.xaxis.set_major_formatter(nullfmt)
#Same for Spherical
pdanglers= parse_break(danglers,tts < breakt)
pdanglezs= parse_break(danglezs,tts < breakt)
pyplot.subplot(2,1,2)
bovy_plot.bovy_plot(ptts/orbt,
pdanglers,
color='k',ls='-',loglog=True,gcf=True,
xrange=[0.5,norb],
yrange=[10.**-12.,1.],
xlabel=r'$\mathrm{Number\ of\ orbital\ periods}$')
bovy_plot.bovy_plot(ptts/orbt,
pdanglezs,
color='k',ls='--',overplot=True)
bovy_plot.bovy_text(r'$\texttt{actionAngleSpherical}$',
top_left=True,size=14.)
bovy_plot.bovy_text(0.175,10.**4.,r'$\left|\Delta \theta_{R,z} / 2\,\pi\right|$',
fontsize=16.,
rotation='vertical')
ax= pyplot.gca()
ax.xaxis.set_major_formatter(ticker.FormatStrFormatter(r'$%0.f$'))
ax.yaxis.set_ticks([10.**-12.,10.**-8.,10.**-4.,1.])
bovy_plot.bovy_end_print(plotfilename2)
return None
def setup_sdf(
pot: Sequence[Potential],
prog: Orbit,
sigv: float,
td: float,
ro: float = REFR0,
vo: float = REFV0,
multi: Optional[Any] = None,
nTrackChunks: int = 8,
isob: Optional[bool] = None,
trailing_only: bool = False,
verbose: bool = True,
useTM: bool = True,
logpot: bool = False,
):
"""Simple function to setup the stream model."""
if isob is None:
if True or logpot: # FIXME, "if True"
isob = 0.75
if isob is False: # FIXME, was "if False"
# Determine good one
ts = np.linspace(0.0, 15.0, 1001)
# Hack!
epot = copy.deepcopy(pot)
epot[2]._b = 1.0
epot[2]._b2 = 1.0
epot[2]._isNonAxi = False
epot[2]._aligned = True
prog.integrate(ts, pot)
estb = estimateBIsochrone(
epot,
prog.R(ts, use_physical=False),
prog.z(ts, use_physical=False),
phi=prog.phi(ts, use_physical=False),
)
if estb[1] < 0.3:
isob = 0.3
elif estb[1] > 1.5:
isob = 1.5
else:
isob = estb[1]
if verbose:
print(pot[2]._c, isob, estb)
if not logpot and np.fabs(pot[2]._b - 1.0) > 0.05:
aAI = actionAngleIsochroneApprox(pot=pot, b=isob, tintJ=1000.0, ntintJ=30000)
else:
ts = np.linspace(0.0, 100.0, 10000)
aAI = actionAngleIsochroneApprox(
pot=pot, b=isob, tintJ=100.0, ntintJ=10000, dt=ts[1] - ts[0]
)
if useTM:
aAT = actionAngleTorus(pot=pot, tol=0.001, dJ=0.0001)
else:
aAT = False
try:
sdf = streamdf(
sigv / vo,
progenitor=prog,
pot=pot,
aA=aAI,
useTM=aAT,
approxConstTrackFreq=True,
leading=True,
nTrackChunks=nTrackChunks,
tdisrupt=td / bovy_conversion.time_in_Gyr(vo, ro),
ro=ro,
vo=vo,
R0=ro,
vsun=[-11.1, vo + 24.0, 7.25],
custom_transform=_TKOP,
multi=multi,
nospreadsetup=True,
)
except np.linalg.LinAlgError:
sdf = streamdf(
sigv / vo,
progenitor=prog,
pot=pot,
aA=aAI,
useTM=aAT,
approxConstTrackFreq=True,
leading=True,
nTrackChunks=nTrackChunks,
nTrackIterations=0,
tdisrupt=td / bovy_conversion.time_in_Gyr(vo, ro),
ro=ro,
vo=vo,
R0=ro,
vsun=[-11.1, vo + 24.0, 7.25],
custom_transform=_TKOP,
multi=multi,
)
return sdf
def setup_streammodel(
obs=None,
pot = MWPotential2014,
leading=False,
timpact=None,
hernquist=True,
age=5.,
sigv=.5,
singleImpact=False,
length_factor=1.,
vsun=[-11.1,V0+24.,7.25],
b=None,
**kwargs):
'''
NAME:
setup_streammodel
PURPOSE:
Initialize a streamdf or streampepperdf instance of stellar stream, depending on its impact history
INPUT:
obs: Orbit instance for progenitor position
pot: host potential
age: stream age in Gyr
sigv: ~ internal velocity dispersion in km/s, controls the stream length in proportion to the age
b: fit parameter for the isochrone approximation, if None it is set automatically
R, R_coord: R_name: a rotation matrix for transformation to stream coordinates,the frame they are
transforming from, and a name for the new coordinate system
custom_transform: depreciated, superseded by the Astropy implementation below
leading: if True, use leading tail, use trailing tail otherwise
hernquist: if True, use Hernquist spheres for subhalos; Plummer otherwise
singleImpact: force use of the streamgapdf instead of streampepperdf
length_factor: consider impacts up to length_factor x length of the stream
streamdf kwargs
OUTPUT:
object
HISTORY:
2016 - Started - Bovy (UofT)
2020-05-08 - Generalized - Hendel (UofT)
'''
#automatically set up potential model
if b==None:
obs.turn_physical_off()
b = estimateBIsochrone(pot, obs.R(), obs.z())
obs.turn_physical_on()
print('Using isochrone approxmation parameter of %1.3f, should typically be between 0.5 and 1'%b)
aAI= actionAngleIsochroneApprox(pot=pot,b=b)
if timpact is None:
sdf= streamdf(sigv/V0,progenitor=obs,
pot=pot,aA=aAI,
leading=leading,nTrackChunks=11,
tdisrupt=age/bovy_conversion.time_in_Gyr(V0,R0),
ro=R0,vo=V0,R0=R0,
vsun=vsun,
custom_transform=None)
elif singleImpact:
sdf= streamgapdf(sigv/V0,progenitor=obs,
pot=pot,aA=aAI,
leading=leading,nTrackChunks=11,
tdisrupt=age/bovy_conversion.time_in_Gyr(V0,R0),
ro=R0,vo=V0,R0=R0,
vsun=vsun,
custom_transform=None,
timpact= 0.3/bovy_conversion.time_in_Gyr(V0,R0),
spline_order=3,
hernquist=hernquist,
impact_angle=0.7,
impactb=0.,
GM= 10.**-2./bovy_conversion.mass_in_1010msol(V0,R0),
rs= 0.625/R0,
subhalovel=np.array([6.82200571,132.7700529,14.4174464])/V0,
**kwargs)
else:
sdf= streampepperdf(sigv/V0,progenitor=obs,
pot=pot,aA=aAI,
leading=leading,nTrackChunks=101,
tdisrupt=age/bovy_conversion.time_in_Gyr(V0,R0),
ro=R0,vo=V0,R0=R0,
vsun=vsun,
custom_transform=None,
timpact=timpact,
spline_order=3,
hernquist=hernquist,
length_factor=length_factor)
sdf.turn_physical_off()
return sdf
def setup_sdf(
pot: potential.Potential,
prog: Orbit,
sigv: float,
td: float,
ro: float = REFR0,
vo: float = REFV0,
multi: Optional[bool] = None,
nTrackChunks: float = 8,
isob=None,
trailing_only: bool = False,
verbose: bool = True,
useTM: bool = True,
) -> Tuple[Optional[streamdf], Optional[streamdf]]:
"""Setup Stream Distribution Function.
Parameters
----------
pot : Potential
prog : Orbit
Progenitor
sigv : float
td : float
ro : float
vo : float
multi
default None
nTrackChunks: float
default 8
isob
default None
trailing_only: bool
default False
verbose: bool
default True
useTM: bool
default True
Returns
-------
sdf_trailing, sdf_leading: streamdf or None
"""
if isob is None:
# Determine good one
ts = np.linspace(0.0, 150.0, 1001)
# Hack!
epot = copy.deepcopy(pot)
epot[2]._b = 1.0
epot[2]._b2 = 1.0
epot[2]._isNonAxi = False
epot[2]._aligned = True
prog.integrate(ts, pot)
estb = estimateBIsochrone(
epot,
prog.R(ts, use_physical=False),
prog.z(ts, use_physical=False),
phi=prog.phi(ts, use_physical=False),
)
if estb[1] < 0.3:
isob = 0.3
elif estb[1] > 1.5:
isob = 1.5
else:
isob = estb[1]
if verbose:
print(pot[2]._c, isob)
if np.fabs(pot[2]._b - 1.0) > 0.05:
aAI = actionAngleIsochroneApprox(pot=pot,
b=isob,
tintJ=1000.0,
ntintJ=30000)
else:
aAI = actionAngleIsochroneApprox(pot=pot, b=isob)
if useTM:
aAT = actionAngleTorus(pot=pot, tol=0.001, dJ=0.0001)
else:
aAT = False
trailing_kwargs = dict(
progenitor=prog,
pot=pot,
aA=aAI,
useTM=aAT,
approxConstTrackFreq=True,
leading=False,
nTrackChunks=nTrackChunks,
tdisrupt=td / bovy_conversion.time_in_Gyr(vo, ro),
ro=ro,
vo=vo,
R0=ro,
vsun=[-11.1, vo + 24.0, 7.25],
custom_transform=_TPAL5,
multi=multi,
)
try:
sdf_trailing = streamdf(sigv / vo, **trailing_kwargs)
except np.linalg.LinAlgError:
sdf_trailing = streamdf(sigv / vo,
nTrackIterations=0,
**trailing_kwargs)
if trailing_only:
sdf_leading = None
else:
leading_kwargs = dict(
progenitor=prog,
pot=pot,
aA=aAI,
useTM=aAT,
approxConstTrackFreq=True,
leading=True,
nTrackChunks=nTrackChunks,
tdisrupt=td / bovy_conversion.time_in_Gyr(vo, ro),
ro=ro,
vo=vo,
R0=ro,
vsun=[-11.1, vo + 24.0, 7.25],
custom_transform=_TPAL5,
multi=multi,
)
try:
sdf_leading = streamdf(sigv / vo, **leading_kwargs)
except np.linalg.LinAlgError:
sdf_leading = streamdf(sigv / vo,
nTrackIterations=0,
**leading_kwargs)
return sdf_trailing, sdf_leading
