def observed_to_xyzuvw_orbit(obs, ts, lsr_orbit=None):
"""
Convert six-parameter astrometric solution to XYZUVW orbit.
Parameters
----------
obs : [RA (deg), DEC (deg), pi (mas),
mu_ra (mas/yr), mu_dec (mas/yr), vlos (km/s)]
Current kinematics
ts : [ntimes] array
times (in Myr) to traceback to
lsr_orbit : Orbit
the orbit of the local standard of rest for comparison, if None can
calculate on the fly
XYZUVW : [ntimes, 6] array
The space position and velocities of the star in a co-rotating frame
centred on the LSR
"""
#convert times from Myr into bovy_time
bovy_ts = ts / (bovy_conversion.time_in_Gyr(220.,8.)*1000) # bovy-time/Myr
logging.info("max time in Myr: {}".format(np.max(ts)))
logging.info("max time in Bovy time: {}".format(np.max(bovy_ts)))
o = Orbit(vxvv=obs, radec=True, solarmotion='schoenrich')
o.integrate(bovy_ts,mp,method='odeint')
data = o.getOrbit()
XYZUVW = galpy_coords_to_xyzuvw(data, bovy_ts)
return XYZUVW
def sample_los(options,args,dfc):
print "Sampling the LOS ..."
n= 0
out= []
while n < options.nobjects:
thisos= dfc.sampleLOS(los=options.los,n=options.nobjects-n)
#add distance uncertainty
thisout= []
for o in thisos:
basico= Orbit([o.R(),o.vR(),o.vT(),0.,0.,o.phi()])#HACK bc ll does not work in 2D currently
thisd= basico.dist(obs=[1.,0.,0.],ro=1.)
#Add uncertainty logarithmically, like photometric distance uncertainty TO DO
thisd+= nu.random.normal()*thisd*options.distuncertainty
thisout.append(Orbit([basico.ll(obs=[1.,0.,0.],ro=1.)[0],
thisd[0],
basico.pmll(obs=[1.,0.,0.,0.,1.,0.],
ro=1.,vo=1.)[0],
basico.vlos(obs=[1.,0.,0.,0.,1.,0.],
ro=1.,vo=1.)[0]],
lb=True,
solarmotion=[0.,0.,0.],ro=1.,vo=1.))
ds= nu.array([o.dist(obs=[1.,0.,0.],ro=1.) for o in thisout]).flatten()
thisos= [thisout[ii] for ii in range(len(thisout)) \
if (ds[ii] < options.dmax)]
out.extend(thisos)
n+= len(thisos)
if len(out) > options.nobjects:
out= out[0:options.nobjects-1]
#Save
picklefile= open(args[0],'wb')
pickle.dump(out,picklefile)
picklefile.close()
return None
def test_correctInitialSolarMotion():
age = np.pi # Half a galactic revolution
# For reference: the expected solar motion as provided by Schoenrich
REFERENCE_SCHOENRICH_SOLAR_MOTION = np.array([-11.1, -12.24, -7.25])
ntimesteps = 10
# vxvv is in cylindrical coordinates here. [R,vR,vT(,z,vz,phi)]
lsr_orbit = Orbit(vxvv=[1,0,1,0,0,0],vo=220,ro=8,solarmotion='schoenrich')
lsr_orbit.integrate(np.linspace(0.,age,ntimesteps), MWPotential2014)
U = lsr_orbit.U(0)
V = lsr_orbit.V(0)
W = lsr_orbit.W(0)
results = np.array([U, V, W]).reshape(3)
for i, vel in enumerate('UVW'):
print("For velocity {}:".format(vel))
print(" expected: {}".format(REFERENCE_SCHOENRICH_SOLAR_MOTION[i]))
print(" received: {}".format(results[i]))
assert (np.allclose(REFERENCE_SCHOENRICH_SOLAR_MOTION, results)),\
'!!! Using galpy version {} Need galpy version 1.1 !!!'.format(
galpy.__version__
)
def test_estimateDelta():
#_____initialize some KKSPot_____
Delta = 1.0
pot = KuzminKutuzovStaeckelPotential(ac=20.,Delta=Delta,normalize=True)
#_____initialize an orbit (twice)_____
vxvv = [1.,0.1,1.1,0.01,0.1]
o= Orbit(vxvv=vxvv)
#_____integrate the orbit with C_____
ts= numpy.linspace(0,101,100)
o.integrate(ts,pot,method='leapfrog_c')
#____estimate Focal length Delta_____
#for each time step individually:
deltas_estimate = numpy.zeros(len(ts))
for ii in range(len(ts)):
deltas_estimate[ii] = estimateDeltaStaeckel(pot,o.R(ts[ii]),o.z(ts[ii]))
assert numpy.all(numpy.fabs(deltas_estimate - Delta) < 10.**-8), \
'Focal length Delta estimated along the orbit is not constant.'
#for all time steps together:
delta_estimate = estimateDeltaStaeckel(pot,o.R(ts),o.z(ts))
assert numpy.fabs(delta_estimate - Delta) < 10.**-8, \
'Focal length Delta estimated from the orbit is not the same as the input focal length.'
return None
def traceback2(params,times):
"""Trace forward a cluster. First column of returned array is the
position of the cluster at a given age.
Parameters
----------
times: float array
Times to trace forward, in Myr. Note that positive numbers are going
forward in time.
params: float array
[RA,DE,Plx,PM(RA),PM(DE),RV]
RA = Right Ascension (Deg)
DE = Declination (Deg)
Plx = Paralax (Mas)
PM(RA) = Proper motion (Right Ascension) (mas/yr)
PM(DE) = Proper motion (Declination) (mas/yr)
RV = Radial Velocity (km/s)
age: Age of cluster, in Myr
"""
#FIXME: This is very out of date and should be deleted!!!
#Times in Myr
ts = -(times/1e3)/bovy_conversion.time_in_Gyr(220.,8.)
nts = len(times)
#Positions and velocities in the co-rotating solar reference frame.
xyzuvw = np.zeros( (1,nts,6) )
#Trace forward the local standard of rest.
lsr_orbit= Orbit(vxvv=[1.,0,1,0,0.,0],vo=220,ro=8)
lsr_orbit.integrate(ts,MWPotential2014)#,method='odeint')
xyzuvw = integrate_xyzuvw(params,ts,lsr_orbit,MWPotential2014)
return xyzuvw
def trace_cartesian_orbit(xyzuvw_start, times=None, single_age=True,
potential=MWPotential2014, ro=8., vo=220.):
"""
Given a star's XYZUVW relative to the LSR (at any time), project its
orbit forward (or backward) to each of the times listed in *times*
Positive times --> traceforward
Negative times --> traceback
TODO: Primary source of inefficiencies, 1366.2 (s)
Parameters
----------
xyzuvw : [pc,pc,pc,km/s,km/s,km/s]
times : (float) or ([ntimes] float array)
Myr - time of 0.0 must be present in the array. Times need not be
spread linearly.
single_age: (bool) {True}
Set this flag if only providing a single age to trace to
Returns
-------
xyzuvw_tf : [ntimes, 6] array
[pc, pc, pc, km/s, km/s, km/s] - the traced orbit with positions
and velocities
Notes
-----
Profiling comments have been left in for future reference, but note
that the profiling was done with previous versions of coordinate
functions - ones that utilised astropy.units (and thus symbolic algebra)
"""
if single_age:
# replace 0 with some tiny number
if times == 0.:
times = 1e-15
times = np.array([0., times])
else:
times = np.array(times)
xyzuvw_start = np.copy(xyzuvw_start).astype(np.float)
bovy_times = convert_myr2bovytime(times)
# since the LSR is constant in chron coordinates, the starting point
# is always treated as time 0
galpy_coords = convert_cart2galpycoords(xyzuvw_start, ts=0.,
ro=ro, vo=vo)
o = Orbit(vxvv=galpy_coords, ro=ro, vo=vo)
o.integrate(bovy_times, potential, method='odeint')
xyzuvw = convert_galpycoords2cart(o.getOrbit(), bovy_times,
ro=ro, vo=vo)
if single_age:
return xyzuvw[-1]
return xyzuvw
def evolveorbit(icon, ti, tau, pot):
global x
global y
o = Orbit(vxvv=icon) # [R,vR,vT,z,vz,phi]
tf = ti+tau
ts = np.linspace(ti,tf,100)
o.integrate(ts, pot, method = 'leapfrog')
x.append(o.x(ts[0]))
y.append(o.y(ts[0]))
return [o.R(tf),o.vR(tf),o.vT(tf),o.z(tf),o.vz(tf),o.phi(tf)]
def test_orbitint():
import numpy
from galpy.potential import MWPotential2014
from galpy.potential import evaluatePotentials as evalPot
from galpy.orbit import Orbit
E, Lz= -1.25, 0.6
o1= Orbit([0.8,0.,Lz/0.8,0.,numpy.sqrt(2.*(E-evalPot(0.8,0.,MWPotential2014)-(Lz/0.8)**2./2.)),0.])
ts= numpy.linspace(0.,100.,2001)
o1.integrate(ts,MWPotential2014)
o1.plot(xrange=[0.3,1.],yrange=[-0.2,0.2],color='k')
o2= 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.])
o2.integrate(ts,MWPotential2014)
o2.plot(xrange=[0.3,1.],yrange=[-0.2,0.2],color='k')
return None
def get_lsr_orbit(times, Potential=MWPotential2014):
"""Integrate the local standard of rest backwards in time, in order to provide
a reference point to our XYZUVW coordinates.
Parameters
----------
times: numpy float array
Times at which we want the orbit of the local standard of rest.
Potential: galpy potential object.
"""
ts = -(times/1e3)/bovy_conversion.time_in_Gyr(220.,8.)
lsr_orbit= Orbit(vxvv=[1.,0,1,0,0.,0],vo=220,ro=8, solarmotion='schoenrich')
lsr_orbit.integrate(ts,Potential)#,method='odeint')
return lsr_orbit
def calc_delta_MWPotential2014(savefilename,plotfilename):
Lmin, Lmax= 0.01, 10.
if not os.path.exists(savefilename):
#Setup grid
nL, nE= 101,101
Ls= 10.**numpy.linspace(numpy.log10(Lmin),numpy.log10(Lmax),nL)
#Integration times
ts= numpy.linspace(0.,20.,1001)
deltas= numpy.empty((nL,nE))
Einf= evalPot(10.**12.,0.,MWPotential2014)
print Einf
for ii in range(nL):
#Calculate Ec
Rc= rl(MWPotential2014,Ls[ii])
print ii, "Rc = ", Rc*8.
Ec= evalPot(Rc,0.,MWPotential2014)+0.5*Ls[ii]**2./Rc**2.
Es= Ec+(Einf-Ec)*10.**numpy.linspace(-2.,0.,nE)
for jj in range(nE):
#Setup an orbit with this energy and angular momentum
Er= 2.*(Es[jj]-Ec) #Random energy times 2 = vR^2 + vz^2
vR= numpy.sqrt(4./5.*Er)
vz= numpy.sqrt(1./5.*Er)
o= Orbit([Rc,vR,Ls[ii]/Rc,0.,vz,0.])
o.integrate(ts,MWPotential2014,method='symplec4_c')
deltas[ii,jj]= estimateDeltaStaeckel(o.R(ts),o.z(ts),
pot=MWPotential2014)
#Save
save_pickles(savefilename,deltas)
else:
savefile= open(savefilename,'rb')
deltas= pickle.load(savefile)
savefile.close()
#Plot
print numpy.nanmax(deltas)
bovy_plot.bovy_print()
bovy_plot.bovy_dens2d(deltas.T,origin='lower',cmap='jet',
xrange=[numpy.log10(Lmin),numpy.log10(Lmax)],
yrange=[-2,0.],
xlabel=r'$\log_{10} L$',
ylabel=r'$\log_{10}\left(\frac{E-E_c(L)}{E(\infty)-E_c(L)}\right)$',
colorbar=True,shrink=0.78,
zlabel=r'$\mathrm{Approximate\ focal\ length}$',
# interpolation='nearest',
vmin=0.,vmax=0.6)
bovy_plot.bovy_end_print(plotfilename)
return None
def test_actionConservation():
#_____initialize some KKSPot_____
Delta = 1.0
pot = KuzminKutuzovStaeckelPotential(ac=20.,Delta=Delta,normalize=True)
#_____initialize an orbit (twice)_____
vxvv = [1.,0.1,1.1,0.01,0.1]
o= Orbit(vxvv=vxvv)
#_____integrate the orbit with C_____
ts= numpy.linspace(0,101,100)
o.integrate(ts,pot,method='leapfrog_c')
#_____Setup ActionAngle object and calculate actions (Staeckel approximation)_____
aAS = actionAngleStaeckel(pot=pot,delta=Delta,c=True)
jrs,lzs,jzs = aAS(o.R(ts),o.vR(ts),o.vT(ts),o.z(ts),o.vz(ts))
assert numpy.all(numpy.fabs(jrs - jrs[0]) < 10.**-8.), \
'Radial action is not conserved along orbit.'
assert numpy.all(numpy.fabs(lzs - lzs[0]) < 10.**-8.), \
'Angular momentum is not conserved along orbit.'
assert numpy.all(numpy.fabs(jzs - jzs[0]) < 10.**-8.), \
'Vertical action is not conserved along orbit.'
return None
def trace_orbit_xyzuvw(xyzuvw_then, times):
"""
Given a star's XYZUVW relative to the LSR (at any time), project its
orbit forward to each of the times listed in *times*
Parameters
----------
xyzuvw : [pc,pc,pc,km/s,km/s,km/s]
times : [ntimes] array
Myr
Returns
-------
xyzuvw_tf : [ntimes, 6] array
the traced-forward positions and velocities
"""
XYZUVW_sun_now = np.array([0.,0.,0.025,11.1,12.24,7.25])
# convert positions to kpc
xyzuvw_then[:3] *= 1e-3
# convert times from Myr to bovy units
bovy_times = times*1e-3 / bovy_conversion.time_in_Gyr(220., 8.)
logging.debug("Tracing up to {} Myr".format(times[-1]))
logging.debug("Tracing up to {} Bovy yrs".format(bovy_times[-1]))
# Galpy coordinates are from the vantage point of the sun.
# So even though the sun wasn't where it is, we still "observe" the star
# from a solar height and motion
XYZUVW_gp_tf = xyzuvw_then - XYZUVW_sun_now
logging.debug("Galpy vector: {}".format(XYZUVW_gp_tf))
l,b,dist = lbdist_from_XYZ(XYZUVW_gp_tf)
vxvv = [l,b,dist,XYZUVW_gp_tf[3],XYZUVW_gp_tf[4],XYZUVW_gp_tf[5]]
logging.debug("vxvv: {}".format(vxvv))
otf = Orbit(vxvv=vxvv, lb=True, uvw=True, solarmotion='schoenrich')
otf.integrate(bovy_times,mp,method='odeint')
data_tf = otf.getOrbit()
XYZUVW_tf = galpy_coords_to_xyzuvw(data_tf, bovy_times)
logging.debug("Started orbit at {}".format(XYZUVW_tf[0]))
logging.debug("Finished orbit at {}".format(XYZUVW_tf[-1]))
return XYZUVW_tf
def get_initial_condition(to):
"""Find an initial condition near apocenter that ends up today near the end of the stream and is close to a gyrfalcon stepsize
to= Find an apocenter that is just more recent than this time"""
vo, ro= 220., 8.
# Center of the stream
o= Orbit([0.10035165,-0.81302488,0.80986668,0.58024425,0.92753945,
0.88763126],ro=ro,vo=vo)
#Flip for backwards integration
of= o.flip()
ts= numpy.linspace(0.,to/bovy_conversion.time_in_Gyr(vo,ro),10001)
of.integrate(ts,MWPotential2014)
# Find the closest apocenter to the time to
rs= numpy.sqrt(of.R(ts)**2.+of.z(ts)**2.)
drs= rs-numpy.roll(rs,1)
nearApo= (drs < 0.)*(numpy.roll(drs,1) > 0.)
tsNearApo= ts[nearApo]
tsNearApo*= bovy_conversion.time_in_Gyr(vo,ro)
tfgf= numpy.amax(tsNearApo)
#Round to nearest 2.**-8.
tfgf= round(tfgf/2.**-8.)*2.**-8
tf= tfgf/bovy_conversion.time_in_Gyr(vo,ro)
print 'Current: %s,%s,%s,%s,%s,%s' % (of.x()[0], of.y()[0], of.z(), -of.vx()[0], -of.vy()[0], -of.vz())
print 'At %g Gyr: %s,%s,%s,%s,%s,%s' % (tf*bovy_conversion.time_in_Gyr(vo,ro),of.x(tf)[0], of.y(tf)[0], of.z(tf), -of.vx(tf,use_physical=False)[0]*bovy_conversion.velocity_in_kpcGyr(vo,ro), -of.vy(tf,use_physical=False)[0]*bovy_conversion.velocity_in_kpcGyr(vo,ro), -of.vz(tf,use_physical=False)*bovy_conversion.velocity_in_kpcGyr(vo,ro))
return None
def integrate_xyzuvw(params,ts,lsr_orbit,MWPotential2014):
"""Convenience function"""
vxvv = params.copy()
vxvv[2]=1.0/params[2]
o = Orbit(vxvv=vxvv, radec=True, solarmotion='schoenrich')
o.integrate(ts,MWPotential2014,method='odeint')
xyzuvw = np.zeros( (len(ts),6) )
xyzuvw[:,0] = 1e3*(o.x(ts)-lsr_orbit.x(ts))
xyzuvw[:,1] = 1e3*(o.y(ts)-lsr_orbit.y(ts))
xyzuvw[:,2] = 1e3*(o.z(ts))
xyzuvw[:,3] = o.U(ts) - lsr_orbit.U(ts)
xyzuvw[:,4] = o.V(ts) - lsr_orbit.V(ts)
xyzuvw[:,5] = o.W(ts)
return xyzuvw
def test_actionAngleTorus_orbit():
from galpy.actionAngle import actionAngleTorus
from galpy.potential import MWPotential2014
from galpy.orbit import Orbit
# Set up instance
aAT= actionAngleTorus(pot=MWPotential2014,tol=10.**-5.)
jr,jphi,jz= 0.05,1.1,0.025
# First calculate frequencies and the initial RvR
RvRom= aAT.xvFreqs(jr,jphi,jz,
numpy.array([0.]),
numpy.array([1.]),
numpy.array([2.]))
om= RvRom[1:]
# Angles along an orbit
ts= numpy.linspace(0.,100.,1001)
angler= ts*om[0]
anglephi= 1.+ts*om[1]
anglez= 2.+ts*om[2]
# Calculate the orbit using actionAngleTorus
RvR= aAT(jr,jphi,jz,angler,anglephi,anglez).T
# Calculate the orbit using orbit integration
orb= Orbit([RvRom[0][:,0],RvRom[0][:,1],RvRom[0][:,2],
RvRom[0][:,3],RvRom[0][:,4],RvRom[0][:,5]])
orb.integrate(ts,MWPotential2014)
# Compare
tol= -3.
assert numpy.all(numpy.fabs(orb.R(ts)-RvR[0]) < 10.**tol), \
'Integrated orbit does not agree with torus orbit in R'
assert numpy.all(numpy.fabs(orb.vR(ts)-RvR[1]) < 10.**tol), \
'Integrated orbit does not agree with torus orbit in vR'
assert numpy.all(numpy.fabs(orb.vT(ts)-RvR[2]) < 10.**tol), \
'Integrated orbit does not agree with torus orbit in vT'
assert numpy.all(numpy.fabs(orb.z(ts)-RvR[3]) < 10.**tol), \
'Integrated orbit does not agree with torus orbit in z'
assert numpy.all(numpy.fabs(orb.vz(ts)-RvR[4]) < 10.**tol), \
'Integrated orbit does not agree with torus orbit in vz'
assert numpy.all(numpy.fabs(orb.phi(ts)-RvR[5]) < 10.**tol), \
'Integrated orbit does not agree with torus orbit in phi'
return None
def calc_progenitor_actions(savefilename):
# Setup potential
lp = potential.LogarithmicHaloPotential(normalize=1.0, q=0.9)
# Setup orbit
x, z, y, vx, vz, vy = -11.63337239, -10.631736273934635, -20.76235661, -128.8281653, 79.172383882274971, 42.88727925
R, phi, z = bovy_coords.rect_to_cyl(x, y, z)
vR, vT, vz = bovy_coords.rect_to_cyl_vec(vx, vy, vz, R, phi, z, cyl=True)
R /= 8.0
z /= 8.0
vR /= 220.0
vT /= 220.0
vz /= 220.0
o = Orbit([R, vR, vT, z, vz, phi])
ts = numpy.linspace(0.0, 5.125 * 220.0 / 8.0, 1313) # times of the snapshots
o.integrate(ts, lp, method="dopr54_c")
if "aas" in savefilename:
aA = actionAngleStaeckel(pot=lp, delta=1.20, c=True)
else:
aA = actionAngleIsochroneApprox(pot=lp, b=0.8)
# Now calculate actions, frequencies, and angles for all positions
Rs = o.R(ts)
vRs = o.vR(ts)
vTs = o.vT(ts)
zs = o.z(ts)
vzs = o.vz(ts)
phis = o.phi(ts)
csvfile = open(savefilename, "wb")
writer = csv.writer(csvfile, delimiter=",")
for ii in range(len(ts)):
acfs = aA.actionsFreqsAngles(Rs[ii], vRs[ii], vTs[ii], zs[ii], vzs[ii], phis[ii])
writer.writerow(
[acfs[0][0], acfs[1][0], acfs[2][0], acfs[3][0], acfs[4][0], acfs[5][0], acfs[6][0], acfs[7][0], acfs[8][0]]
)
csvfile.flush()
csvfile.close()
return None
def integrate_xyzuvw(params,times,lsr_orbit=None,Potential=MWPotential2014):
"""Convenience function. Integrates the motion of a star backwards in time.
Parameters
----------
params: numpy array
Kinematic parameters (RAdeg,DEdeg,Plx,pmRA,pmDE,RV)
ts: times for back propagation, in Myr.
lsr_orbit:
WARNING: messy...
lsr_orbit= Orbit(vxvv=[1.,0,1,0,0.,0],vo=220,ro=8, solarmotion='schoenrich')
lsr_orbit.integrate(ts,MWPotential2014,method='odeint')
MWPotential2014:
WARNING: messy...
from galpy.potential import MWPotential2014
"""
#We allow MWPotential and lsr_orbit to be passed for speed, but can compute/import
#now.
if not lsr_orbit:
lsr_orbit = get_lsr_orbit(times)
#Convert times to galpy units:
ts = -(times/1e3)/bovy_conversion.time_in_Gyr(220.,8.)
params = np.array(params)
vxvv = params.copy()
#We'd prefer to pass parallax in mas, but distance in kpc is accepted. This
#reciporical could be done elsewhere...
vxvv[2]=1.0/params[2]
o = Orbit(vxvv=vxvv, radec=True, solarmotion='schoenrich')
o.integrate(ts,Potential)#,method='odeint')
xyzuvw = np.zeros( (len(ts),6) )
xyzuvw[:,0] = 1e3*(o.x(ts)-lsr_orbit.x(ts))
xyzuvw[:,1] = 1e3*(o.y(ts)-lsr_orbit.y(ts))
#The lsr_orbit is zero in the z direction by definition - the local standard of
#rest is at the midplane of the Galaxy
xyzuvw[:,2] = 1e3*(o.z(ts))
#UVW is relative to the sun. We *could* have used vx, vy and vz. Would these
#have been relative to the LSR?
xyzuvw[:,3] = o.U(ts) - lsr_orbit.U(ts)
xyzuvw[:,4] = o.V(ts) - lsr_orbit.V(ts)
xyzuvw[:,5] = o.W(ts) - lsr_orbit.W(ts) #NB This line changed !!!
return xyzuvw
def test_surfacesection():
#Preliminary code
import numpy
from galpy.potential import MWPotential2014
from galpy.potential import evaluatePotentials as evalPot
from galpy.orbit import Orbit
E, Lz= -1.25, 0.6
o1= Orbit([0.8,0.,Lz/0.8,0.,numpy.sqrt(2.*(E-evalPot(0.8,0.,MWPotential2014)-(Lz/0.8)**2./2.)),0.])
ts= numpy.linspace(0.,100.,2001)
o1.integrate(ts,MWPotential2014)
o2= 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.])
o2.integrate(ts,MWPotential2014)
def surface_section(Rs,zs,vRs):
# Find points where the orbit crosses z from - to +
shiftzs= numpy.roll(zs,-1)
indx= (zs[:-1] < 0.)*(shiftzs[:-1] > 0.)
return (Rs[:-1][indx],vRs[:-1][indx])
# Calculate and plot the surface of section
ts= numpy.linspace(0.,1000.,20001) # long integration
o1.integrate(ts,MWPotential2014)
o2.integrate(ts,MWPotential2014)
sect1Rs,sect1vRs=surface_section(o1.R(ts),o1.z(ts),o1.vR(ts))
sect2Rs,sect2vRs=surface_section(o2.R(ts),o2.z(ts),o2.vR(ts))
from matplotlib.pyplot import plot, xlim, ylim
plot(sect1Rs,sect1vRs,'bo',mec='none')
xlim(0.3,1.); ylim(-0.69,0.69)
plot(sect2Rs,sect2vRs,'yo',mec='none')
return None
def calc_es():
savefilename= 'myes.sav'
if os.path.exists(savefilename):
savefile= open(savefilename,'rb')
mye= pickle.load(savefile)
e= pickle.load(savefile)
savefile.close()
else:
#Read data
dialect= csv.excel
dialect.skipinitialspace=True
reader= csv.reader(open('../data/Dierickx-etal-tab2.txt','r'),delimiter=' ',dialect=dialect)
vxvs= []
es= []
vphis= []
vxs= []
vys= []
vzs= []
ls= []
for row in reader:
thisra= float(row[3])
thisdec= float(row[4])
thisd= float(row[17])/1000.
thispmra= float(row[13])
thispmdec= float(row[15])
thisvlos= float(row[11])
thise= float(row[26])
vxvs.append([thisra,thisdec,thisd,thispmra,thispmdec,thisvlos])
es.append(thise)
vphis.append(float(row[25]))
vxs.append(float(row[19]))
vys.append(float(row[21]))
vzs.append(float(row[23]))
ls.append(float(row[5]))
vxvv= nu.array(vxvs)
e= nu.array(es)
vphi= nu.array(vphis)
vx= nu.array(vxs)
vy= nu.array(vys)
vz= nu.array(vzs)
l= nu.array(ls)
#Define potential
lp= LogarithmicHaloPotential(normalize=1.)
mp= MiyamotoNagaiPotential(a=0.5,b=0.0375,amp=1.,normalize=.6)
np= NFWPotential(a=4.5,normalize=.35)
hp= HernquistPotential(a=0.6/8,normalize=0.05)
ts= nu.linspace(0.,20.,10000)
mye= nu.zeros(len(e))
for ii in range(len(e)):
#Integrate the orbit
o= Orbit(vxvv[ii,:],radec=True,vo=220.,ro=8.)
o.integrate(ts,lp)
mye[ii]= o.e()
#Save
savefile= open(savefilename,'wb')
pickle.dump(mye,savefile)
pickle.dump(e,savefile)
savefile.close()
#plot
plot.bovy_print()
plot.bovy_plot(nu.array([0.,1.]),nu.array([0.,1.]),'k-',
xlabel=r'$\mathrm{Dierickx\ et\ al.}\ e$',
ylabel=r'$\mathrm{galpy}\ e$')
plot.bovy_plot(e,mye,'k,',overplot=True)
plot.bovy_end_print('myee.png')
plot.bovy_print()
plot.bovy_hist(e,bins=30,xlabel=r'$\mathrm{Dierickx\ et\ al.}\ e$')
plot.bovy_end_print('ehist.png')
plot.bovy_print()
plot.bovy_hist(mye,bins=30,xlabel=r'$\mathrm{galpy}\ e$')
plot.bovy_end_print('myehist.png')
def test_get_physical():
#Test that the get_physical function returns the right scaling parameters
from galpy.util.bovy_conversion import get_physical
# Potential and variations thereof
from galpy.potential import MWPotential2014, DehnenBarPotential
dp = DehnenBarPotential
assert numpy.fabs(
get_physical(MWPotential2014[0]).get('ro') - 8.
) < 1e-10, 'get_physical does not return the correct unit conversion parameter for a Potential'
assert numpy.fabs(
get_physical(MWPotential2014[0]).get('vo') - 220.
) < 1e-10, 'get_physical does not return the correct unit conversion parameter for a Potential'
ro, vo = 9., 230.
dp = DehnenBarPotential(ro=ro, vo=vo)
assert numpy.fabs(
get_physical(dp).get('ro') - ro
) < 1e-10, 'get_physical does not return the correct unit conversion parameter for a Potential'
assert numpy.fabs(
get_physical(dp).get('vo') - vo
) < 1e-10, 'get_physical does not return the correct unit conversion parameter for a Potential'
assert numpy.fabs(
get_physical(MWPotential2014).get('ro') - 8.
) < 1e-10, 'get_physical does not return the correct unit conversion parameter for a Potential'
assert numpy.fabs(
get_physical(MWPotential2014).get('vo') - 220.
) < 1e-10, 'get_physical does not return the correct unit conversion parameter for a Potential'
assert numpy.fabs(
get_physical(MWPotential2014 + dp).get('ro') - 8.
) < 1e-10, 'get_physical does not return the correct unit conversion parameter for a Potential'
assert numpy.fabs(
get_physical(MWPotential2014 + dp).get('vo') - 220.
) < 1e-10, 'get_physical does not return the correct unit conversion parameter for a Potential'
assert numpy.fabs(
get_physical(MWPotential2014 + dp).get('ro') - 8.
) < 1e-10, 'get_physical does not return the correct unit conversion parameter for a Potential'
assert numpy.fabs(
get_physical(MWPotential2014 + dp).get('vo') - 220.
) < 1e-10, 'get_physical does not return the correct unit conversion parameter for a Potential'
# Orbits
from galpy.orbit import Orbit
ro, vo = 10., 210.
o = Orbit(ro=ro, vo=vo)
assert numpy.fabs(
get_physical(o).get('ro') - ro
) < 1e-10, 'get_physical does not return the correct unit conversion parameter for an Orbit'
assert numpy.fabs(
get_physical(o).get('vo') - vo
) < 1e-10, 'get_physical does not return the correct unit conversion parameter for an Orbit'
# even though one shouldn't do this, let's test a list
assert numpy.fabs(
get_physical([o, o]).get('ro') - ro
) < 1e-10, 'get_physical does not return the correct unit conversion parameter for an Orbit'
assert numpy.fabs(
get_physical([o, o]).get('vo') - vo
) < 1e-10, 'get_physical does not return the correct unit conversion parameter for an Orbit'
# actionAngle
from galpy.actionAngle import actionAngleStaeckel
aAS = actionAngleStaeckel(pot=MWPotential2014, delta=0.45)
assert numpy.fabs(
get_physical(aAS).get('ro') - 8.
) < 1e-10, 'get_physical does not return the correct unit conversion parameter for an actionAngle instance'
assert numpy.fabs(
get_physical(aAS).get('vo') - 220.
) < 1e-10, 'get_physical does not return the correct unit conversion parameter for an actionAngle instance'
# This doesn't make much sense, but let's test...
ro, vo = 19., 130.
dp = DehnenBarPotential(ro=ro, vo=vo)
aAS = actionAngleStaeckel(pot=dp, delta=0.45, ro=ro, vo=vo)
assert numpy.fabs(
get_physical(aAS).get('ro') - ro
) < 1e-10, 'get_physical does not return the correct unit conversion parameter for an actionAngle instance'
assert numpy.fabs(
get_physical(aAS).get('vo') - vo
) < 1e-10, 'get_physical does not return the correct unit conversion parameter for an actionAngle instance'
# DF
from galpy.df import quasiisothermaldf
aAS = actionAngleStaeckel(pot=MWPotential2014, delta=0.45)
qdf = quasiisothermaldf(1. / 3.,
0.2,
0.1,
1.,
1.,
aA=aAS,
pot=MWPotential2014)
assert numpy.fabs(
get_physical(qdf).get('ro') - 8.
) < 1e-10, 'get_physical does not return the correct unit conversion parameter for a DF instance'
assert numpy.fabs(
get_physical(qdf).get('vo') - 220.
) < 1e-10, 'get_physical does not return the correct unit conversion parameter for a DF instance'
# non-standard ro,vo
from galpy.potential import MiyamotoNagaiPotential
ro, vo = 4., 330.
mp = MiyamotoNagaiPotential(a=0.5, b=0.1, ro=ro, vo=vo)
aAS = actionAngleStaeckel(pot=mp, delta=0.45, ro=ro, vo=vo)
qdf = quasiisothermaldf(1. / 3.,
0.2,
0.1,
1.,
1.,
aA=aAS,
pot=mp,
ro=ro,
vo=vo)
assert numpy.fabs(
get_physical(qdf).get('ro') - ro
) < 1e-10, 'get_physical does not return the correct unit conversion parameter for a DF instance'
assert numpy.fabs(
get_physical(qdf).get('vo') - vo
) < 1e-10, 'get_physical does not return the correct unit conversion parameter for a DF instance'
return None
def star_to_orbit(star_name, radius = 1.0*u.arcsec):
"""
Given the name of a star, returns a galpy.orbit.Orbit object for that
star using data from the Gaia dr2 catalogue. If no data on the star can
be found from Gaia, then data from SIMBAD is used instead.
"""
# Get data on the star from SIMBAD, for use in epoch adjustment
custom_simbad = Simbad()
custom_simbad.add_votable_fields('pmra', 'pmdec', 'plx', 'rv_value')
simbad_table = custom_simbad.query_object(star_name)
# Convert ra and dec from SIMBAD into a SkyCoord object
# to transform into degrees
simbad_coord = SkyCoord(ra = simbad_table['RA'][0],
dec = simbad_table['DEC'][0],
unit = (u.hourangle, u.deg))
# Store the SIMBAD values in a tuple of the form
# (ra, dec, plx, pmra, pmdec, rv)
simbad_vals = (simbad_coord.ra.value,
simbad_coord.dec.value,
simbad_table['PLX_VALUE'][0],
simbad_table['PMRA'][0],
simbad_table['PMDEC'][0],
simbad_table['RV_VALUE'][0])
# Circle radius to query Gaia, in degrees
radius_deg = radius.to(u.deg)
# Replace masked values from the SIMBAD table with 0.0 for epoch adjustment
epoch_prop_vals = [val if not is_masked(val) else 0.0 for val in simbad_vals]
# Perform a cone search with epoch adjustment
query = """
SELECT source_id, ra, dec, pmra, pmdec, parallax, radial_velocity
FROM gaiadr2.gaia_source
WHERE 1=CONTAINS(
POINT('ICRS',gaiadr2.gaia_source.ra,gaiadr2.gaia_source.dec),
CIRCLE('ICRS',
COORD1(EPOCH_PROP_POS({0},{1},{2},{3},{4},{5},2000,2015.5)),
COORD2(EPOCH_PROP_POS({0},{1},{2},{3},{4},{5},2000,2015.5)), {6}))
""".format(*epoch_prop_vals, radius_deg.value)
# Perfrom the cone search and get the result in a table
job = Gaia.launch_job_async(query)
gaia_table = job.get_results()
# If no Gaia entries are found, use the SIMBAD entries
if len(gaia_table) != 0:
ra = gaia_table['ra'][0]
dec = gaia_table['dec'][0]
plx = gaia_table['parallax'][0]
pmra = gaia_table['pmra'][0]
pmdec = gaia_table['pmdec'][0]
rv = gaia_table['radial_velocity'][0]
else:
ra, dec, plx, pmra, pmdec, rv = simbad_vals
if is_masked(rv) and is_masked(simbad_vals[-1]):
# Set rv to 20.0 if not available in either the Gaia or SIMBAD tables
rv = 20.0
elif is_masked(rv):
# Use the SIMBAD rv if not available in GAIA
rv = simbad_vals[5]
# Generate and return a galpy.orbit.Orbit object
orbit = Orbit(vxvv = (ra, dec, 1/plx, pmra, pmdec, rv), radec = True)
return orbit
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 plot_lb(i, ts, plot_extreme=False, save_name='fwd', zorder=1, **kargs):
# integrate orbit
if RUN:
vxvv = [ra[i], dec[i], d[i], pmra[i], pmde[i], rv[i]]
o = Orbit(vxvv=vxvv, radec=True, ro=ro, vo=vo, solarmotion=solarmotion)
o.integrate(ts, pot, method='leapfrog')
# get orbit l and b
ll = o.ll(ts)
bb = o.bb(ts)
np.save("./Orbits/{}/l{}150Myr.npy".format(star_id[i], save_name), ll)
np.save("./Orbits/{}/b{}150Myr.npy".format(star_id[i], save_name), bb)
else:
ll = np.load("./Orbits/{}/l{}150Myr.npy".format(star_id[i], save_name))
bb = np.load("./Orbits/{}/b{}150Myr.npy".format(star_id[i], save_name))
Npoints = len(ll)
# Find boundary breaks at -180 and 180
boundary_breaks = []
# crossings for 180
for j in range(1, Npoints):
# crossings for 180+
if (ll[j - 1] <= 180) and (ll[j] > 180):
boundary_breaks.append(j)
# crossings for 180-
elif (ll[j - 1] >= 180) and (ll[j] < 180):
boundary_breaks.append(j)
boundary_breaks.append(Npoints)
# fix ll > 180
ll[ll > 180] = ll[ll > 180] - 360
# plots
j0 = 0
for k in range(len(boundary_breaks)):
jf = boundary_breaks[k]
plt.plot(ll[j0:jf] * radconv,
bb[j0:jf] * radconv,
zorder=zorder,
**kargs)
j0 = jf
# plot extremes
if plot_extreme == 'lower':
lower = plt.plot(ll[-1] * radconv,
bb[-1] * radconv,
marker='x',
markersize=4,
color=colors[i],
alpha=1,
zorder=zorder + 1)
return lower
elif plot_extreme == 'upper':
upper = plt.plot(ll[-1] * radconv,
bb[-1] * radconv,
marker='o',
markersize=4,
markeredgecolor=colors[i],
color="#FFFFFF",
alpha=1,
zorder=zorder + 1)
return upper
def test_energy_momentum_of_sun():
o = Orbit() # create sun's orbit
o.turn_physical_off()
ts = np.linspace(0, 1000, 100000)
o.integrate(ts, MWPotential2014)
print('galpy energy = ', o.E())
coord = np.array([o.x(), o.y(), o.z(), o.vx(), o.vy(), o.vz()])
print('my energy = ', Energy(coord))
print(o.E() == Energy(coord))
print('galpy momentum = ', o.L()[0][2])
print('my momentum = ', L_z(coord))
print(o.L()[0][2] == L_z(coord))
import sys
import numpy
from galpy.orbit import Orbit
from galpy.potential import MiyamotoNagaiPotential
if __name__ == '__main__':
# python orbitint4sigint.py symplec4_c full
mp= MiyamotoNagaiPotential(normalize=1.,a=0.5,b=0.05)
ts= numpy.linspace(0.,10000000.,1000001)
if sys.argv[2] == 'full' or sys.argv[2] == 'planar':
if sys.argv[2] == 'full':
o= Orbit([1.,0.1,1.1,0.1,0.1,0.])
elif sys.argv[2] == 'planar':
o= Orbit([1.,0.1,1.1,0.1])
o.integrate(ts,mp,method=sys.argv[1])
elif sys.argv[2] == 'planardxdv':
o= Orbit([1.,0.1,1.1,0.1])
o.integrate_dxdv([0.1,0.1,0.1,0.1],ts,mp,method=sys.argv[1])
sys.exit(0)
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
def pal5_dpmguess(
pot: PotentialType,
doras: Optional[float] = None,
dodecs: Optional[float] = None,
dovloss: Optional[float] = None,
dmin: float = 21.0,
dmax: float = 25.0,
dstep: float = 0.02,
pmmin: float = -0.36,
pmmax: float = 0.36,
pmstep: float = 0.01,
alongbfpm: bool = False,
ro: float = REFR0,
vo: float = REFV0,
) -> tuple:
"""pal5_dpmguess.
Parameters
----------
pot: Potential
doras : float or None, optional
default None
dodecs : float or None, optional
default None
dovloss : float or None, optional
default None
dmin=21 : float or None, optional
default 0
dmax=25 : float or None, optional
default 0
dstep=0 : float or None, optional
default 02
pmmin=-0 : float or None, optional
default 36
pmmax=0 : float or None, optional
default 36
pmstep=0 : float or None, optional
default 01
alongbfpm : float or None, optional
default False
ro : float or None, optional
default REFR0
vo : float or None, optional
default REFV0
Returns
-------
bestd
bestpmoff
lnl
ds
pmoffs
"""
if doras is None:
with open("pal5_stream_orbit_offset.pkl", "rb") as savefile:
doras = pickle.load(savefile)
dodecs = pickle.load(savefile)
dovloss = pickle.load(savefile)
ds = np.arange(dmin, dmax + dstep / 2.0, dstep)
pmoffs = np.arange(pmmin, pmmax + pmstep / 2.0, pmstep)
lnl = np.zeros((len(ds), len(pmoffs)))
pos_radec, rvel_ra = pal5_data_total()
print("Determining good distance and parallel proper motion...")
for ii, d in tqdm(enumerate(ds)):
for jj, pmoff in enumerate(pmoffs):
if alongbfpm:
pm = (d - 24.0) * 0.099 + 0.0769 + pmoff
else:
pm = pmoff
progt = Orbit(
[
229.11,
0.3,
d + 0.3,
-2.27 + pm,
-2.22 + pm * 2.257 / 2.296,
-58.5,
],
radec=True,
ro=ro,
vo=vo,
solarmotion=[-11.1, 24.0, 7.25],
).flip()
ts = np.linspace(0.0, 3.0, 1001)
progt.integrate(ts, pot)
progt._orb.orbit[:, 1] *= -1.0
progt._orb.orbit[:, 2] *= -1.0
progt._orb.orbit[:, 4] *= -1.0
toras, todecs, tovloss = (
progt.ra(ts),
progt.dec(ts),
progt.vlos(ts),
)
# Interpolate onto common RA
ipdec = interpolate.InterpolatedUnivariateSpline(toras, todecs)
ipvlos = interpolate.InterpolatedUnivariateSpline(toras, tovloss)
todecs = ipdec(doras) - dodecs
tovloss = ipvlos(doras) - dovloss
est_trackRADec_trailing = np.zeros((1, len(doras), 2))
est_trackRADec_trailing[0, :, 0] = doras
est_trackRADec_trailing[0, :, 1] = todecs
est_trackRAVlos_trailing = np.zeros((1, len(doras), 2))
est_trackRAVlos_trailing[0, :, 0] = doras
est_trackRAVlos_trailing[0, :, 1] = tovloss
lnl[ii, jj] = (
np.sum(
pal5_lnlike(
pos_radec,
rvel_ra,
est_trackRADec_trailing,
est_trackRADec_trailing, # hack
est_trackRAVlos_trailing,
est_trackRAVlos_trailing, # hack
np.array([0.0]),
np.array([0.0]),
None,
)[0, :3:2]) - 0.5 * pm**2.0 / 0.186**2.0) # pm measurement
# /for
# /for
bestd = ds[np.unravel_index(np.argmax(lnl), lnl.shape)[0]]
if alongbfpm:
bestpmoff = ((bestd - 24.0) * 0.099 + 0.0769 +
pmoffs[np.unravel_index(np.argmax(lnl), lnl.shape)[1]])
else:
bestpmoff = pmoffs[np.unravel_index(np.argmax(lnl), lnl.shape)[1]]
# /if
return bestd, bestpmoff, lnl, ds, pmoffs
def predict_pal5obs(
pot_params: list,
c: float,
b: float = 1.0,
pa: float = 0.0,
sigv: Union[float, list] = 0.2,
td: float = 10.0,
dist: float = 23.2,
pmra: float = -2.296,
pmdec: float = -2.257,
vlos: float = -58.7,
ro: float = REFR0,
vo: float = REFV0,
singlec: bool = False,
interpcs: Optional[float] = None,
interpk: Optional[float] = None,
isob: Optional[float] = None,
nTrackChunks: int = 8,
multi: Optional = None,
trailing_only: bool = False,
useTM: bool = False,
verbose: bool = True,
) -> TrackTuple:
"""Predict Pal 5 Observed.
Function that generates the location and velocity of the Pal 5 stream,
its width, and its length for a given potential and progenitor
phase-space position
Parameters
----------
pot_params: array
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 : float
halo flattening
b : float, optional
(1.) halo-squashed
pa: float, optional
(0.) halo PA
sigv : float, optional
(0.4) velocity dispersion in km/s
(can be array of same len as interpcs)
td : float, optional
(5.) stream age in Gyr (can be array of same len as interpcs)
dist : float, optional
(23.2) progenitor distance in kpc
pmra : float, optional
(-2.296) progenitor proper motion in RA * cos(Dec) in mas/yr
pmdec : float, optional
(-2.257) progenitor proper motion in Dec in mas/yr
vlos : float, optional
(-58.7) progenitor line-of-sight velocity in km/s
ro : float, optional
(project default) distance to the GC in kpc
vo : float, optional
(project default) circular velocity at R0 in km/s
singlec : bool, optional
(False) if True, just compute the observables for a single c
interpcs : float or None, optional
(None) values of c at which to compute the model for interpolation
nTrackChunks : int, optional
(8) nTrackChunks input to streamdf
multi : float or None, optional
(None) multi input to streamdf
isob : float or None, optional
(None) if given, b parameter of actionAngleIsochroneApprox
trailing_only : bool, optional
(False) if True, only predict the trailing arm
useTM : bool, optional
(True) use the TorusMapper to compute the track
verbose : bool, optional
(True) print messages
Returns
-------
trackRADec_trailing_out : array
trailing track in RA, Dec
all arrays with the shape of c
trackRADec_leading_out : array
leading track in RA, Dec
all arrays with the shape of c
trackRAVlos_trailing_out : array
trailing track in RA, Vlos
all arrays with the shape of c
trackRAVlos_leading_out : array
leading track in RA, Vlos
all arrays with the shape of c
width_out : float
trailing width in arcmin
length_out : float
trailing length in deg
interpcs : array
success : bool
"""
# First compute the model for all cs at which we will interpolate
interpcs: list
if singlec:
interpcs = [c]
elif interpcs is None:
interpcs = [
0.5,
0.75,
1.0,
1.25,
1.55,
1.75,
2.0,
2.25,
2.5,
2.75,
3.0,
]
else:
interpcs = copy.deepcopy(interpcs) # bc we might want to remove some
if isinstance(sigv, float):
sigv: list = [sigv for i in interpcs]
if isinstance(td, float):
td: list = [td for i in interpcs]
if isinstance(isob, float) or isob is None:
isob: list = [isob for i in interpcs]
prog: Orbit = Orbit(
[229.018, -0.124, dist, pmra, pmdec, vlos],
radec=True,
ro=ro,
vo=vo,
solarmotion=[-11.1, 24.0, 7.25],
)
# Setup the model
sdf_trailing_varyc: list = []
sdf_leading_varyc: list = []
ii: int = 0
ninterpcs: int = len(interpcs)
this_useTM: bool = copy.deepcopy(useTM)
this_nTrackChunks: int = nTrackChunks
ntries: int = 0
while ii < ninterpcs:
ic = interpcs[ii]
pot = mw_pot.setup_potential(pot_params,
ic,
False,
False,
ro,
vo,
b=b,
pa=pa)
success: bool = True
# wentIn = ntries != 0
# Make sure this doesn't run forever
signal.signal(signal.SIGALRM, timeout_handler)
signal.alarm(300)
try:
tsdf_trailing, tsdf_leading = setup_sdf(
pot,
prog,
sigv[ii],
td[ii],
ro,
vo,
multi=multi,
isob=isob[ii],
nTrackChunks=this_nTrackChunks,
trailing_only=trailing_only,
verbose=verbose,
useTM=this_useTM,
)
except Exception:
# Catches errors and time-outs
success = False
signal.alarm(0)
# Check for calc. issues
if not success or (not this_useTM
and looks_funny(tsdf_trailing, tsdf_leading)):
# Try again with TM
this_useTM = True
this_nTrackChunks = 21 # might as well
# wentIn= True
# print("Here",ntries,success)
# sys.stdout.flush()
ntries += 1
else:
success = not this_useTM
# if wentIn:
# print(success)
# sys.stdout.flush()
ii += 1
# reset
this_useTM = useTM
this_nTrackChunks = nTrackChunks
ntries = 0
# Add to the list
sdf_trailing_varyc.append(tsdf_trailing)
sdf_leading_varyc.append(tsdf_leading)
if not singlec and len(sdf_trailing_varyc) <= 1:
# Almost everything bad!!
return (
np.zeros((len(c), 1001, 2)),
np.zeros((len(c), 1001, 2)),
np.zeros((len(c), 1001, 2)),
np.zeros((len(c), 1001, 2)),
np.zeros((len(c))),
np.zeros((len(c))),
[],
success,
)
# Compute the track properties for each model
trackRADec_trailing: np.ndarray = np.zeros(
(len(interpcs), sdf_trailing_varyc[0].nInterpolatedTrackChunks, 2))
trackRADec_leading: np.ndarray = np.zeros(
(len(interpcs), sdf_trailing_varyc[0].nInterpolatedTrackChunks, 2))
trackRAVlos_trailing: np.ndarray = np.zeros(
(len(interpcs), sdf_trailing_varyc[0].nInterpolatedTrackChunks, 2))
trackRAVlos_leading: np.ndarray = np.zeros(
(len(interpcs), sdf_trailing_varyc[0].nInterpolatedTrackChunks, 2))
# TODO put in distances (can use _interpolatedObsTrackLB[:,2],)
width: np.ndarray = np.zeros(len(interpcs))
length: np.ndarray = np.zeros(len(interpcs))
for ii in range(len(interpcs)):
trackRADec_trailing[ii] = bovy_coords.lb_to_radec(
sdf_trailing_varyc[ii]._interpolatedObsTrackLB[:, 0],
sdf_trailing_varyc[ii]._interpolatedObsTrackLB[:, 1],
degree=True,
)
if not trailing_only:
trackRADec_leading[ii] = bovy_coords.lb_to_radec(
sdf_leading_varyc[ii]._interpolatedObsTrackLB[:, 0],
sdf_leading_varyc[ii]._interpolatedObsTrackLB[:, 1],
degree=True,
)
trackRAVlos_trailing[ii][:, 0] = trackRADec_trailing[ii][:, 0]
trackRAVlos_trailing[ii][:, 1] = sdf_trailing_varyc[
ii]._interpolatedObsTrackLB[:, 3]
if not trailing_only:
trackRAVlos_leading[ii][:, 0] = trackRADec_leading[ii][:, 0]
trackRAVlos_leading[ii][:, 1] = sdf_leading_varyc[
ii]._interpolatedObsTrackLB[:, 3]
width[ii] = width_trailing(sdf_trailing_varyc[ii])
length[ii] = sdf_trailing_varyc[ii].length(ang=True,
coord="customra",
threshold=0.3)
if singlec:
# if wentIn:
# print(success)
# sys.stdout.flush()
return (
trackRADec_trailing,
trackRADec_leading,
trackRAVlos_trailing,
trackRAVlos_leading,
width,
length,
interpcs,
success,
)
# Interpolate; output grids
trackRADec_trailing_out: np.ndarray = np.zeros(
(len(c), sdf_trailing_varyc[0].nInterpolatedTrackChunks, 2))
trackRADec_leading_out: np.ndarray = np.zeros(
(len(c), sdf_trailing_varyc[0].nInterpolatedTrackChunks, 2))
trackRAVlos_trailing_out: np.ndarray = np.zeros(
(len(c), sdf_trailing_varyc[0].nInterpolatedTrackChunks, 2))
trackRAVlos_leading_out: np.ndarray = np.zeros(
(len(c), sdf_trailing_varyc[0].nInterpolatedTrackChunks, 2))
if interpk is None:
interpk = np.amin([len(interpcs) - 1, 3])
for ii in range(sdf_trailing_varyc[0].nInterpolatedTrackChunks):
ip = interpolate.InterpolatedUnivariateSpline(interpcs,
trackRADec_trailing[:,
ii,
0],
k=interpk,
ext=0)
trackRADec_trailing_out[:, ii, 0] = ip(c)
ip = interpolate.InterpolatedUnivariateSpline(interpcs,
trackRADec_trailing[:,
ii,
1],
k=interpk,
ext=0)
trackRADec_trailing_out[:, ii, 1] = ip(c)
ip = interpolate.InterpolatedUnivariateSpline(interpcs,
trackRAVlos_trailing[:,
ii,
0],
k=interpk,
ext=0)
trackRAVlos_trailing_out[:, ii, 0] = ip(c)
ip = interpolate.InterpolatedUnivariateSpline(interpcs,
trackRAVlos_trailing[:,
ii,
1],
k=interpk,
ext=0)
trackRAVlos_trailing_out[:, ii, 1] = ip(c)
if not trailing_only:
ip = interpolate.InterpolatedUnivariateSpline(
interpcs, trackRADec_leading[:, ii, 0], k=interpk, ext=0)
trackRADec_leading_out[:, ii, 0] = ip(c)
ip = interpolate.InterpolatedUnivariateSpline(
interpcs, trackRADec_leading[:, ii, 1], k=interpk, ext=0)
trackRADec_leading_out[:, ii, 1] = ip(c)
ip = interpolate.InterpolatedUnivariateSpline(
interpcs, trackRAVlos_leading[:, ii, 0], k=interpk, ext=0)
trackRAVlos_leading_out[:, ii, 0] = ip(c)
ip = interpolate.InterpolatedUnivariateSpline(
interpcs, trackRAVlos_leading[:, ii, 1], k=interpk, ext=0)
trackRAVlos_leading_out[:, ii, 1] = ip(c)
# /for
ip = interpolate.InterpolatedUnivariateSpline(interpcs,
width,
k=interpk,
ext=0)
width_out = ip(c)
ip = interpolate.InterpolatedUnivariateSpline(interpcs,
length,
k=interpk,
ext=0)
length_out = ip(c)
return TrackTuple(
trackRADec_trailing_out=trackRADec_trailing_out,
trackRADec_leading_out=trackRADec_leading_out,
trackRAVlos_trailing_out=trackRAVlos_trailing_out,
trackRAVlos_leading_out=trackRAVlos_leading_out,
width_out=width_out,
length_out=length_out,
interpcs=interpcs,
success=success,
)
def calc_es():
savefilename = 'myes.sav'
if os.path.exists(savefilename):
savefile = open(savefilename, 'rb')
mye = pickle.load(savefile)
e = pickle.load(savefile)
savefile.close()
else:
#Read data
dialect = csv.excel
dialect.skipinitialspace = True
reader = csv.reader(open('../data/Dierickx-etal-tab2.txt', 'r'),
delimiter=' ',
dialect=dialect)
vxvs = []
es = []
vphis = []
vxs = []
vys = []
vzs = []
ls = []
for row in reader:
thisra = float(row[3])
thisdec = float(row[4])
thisd = float(row[17]) / 1000.
thispmra = float(row[13])
thispmdec = float(row[15])
thisvlos = float(row[11])
thise = float(row[26])
vxvs.append(
[thisra, thisdec, thisd, thispmra, thispmdec, thisvlos])
es.append(thise)
vphis.append(float(row[25]))
vxs.append(float(row[19]))
vys.append(float(row[21]))
vzs.append(float(row[23]))
ls.append(float(row[5]))
vxvv = nu.array(vxvs)
e = nu.array(es)
vphi = nu.array(vphis)
vx = nu.array(vxs)
vy = nu.array(vys)
vz = nu.array(vzs)
l = nu.array(ls)
#Define potential
lp = LogarithmicHaloPotential(normalize=1.)
mp = MiyamotoNagaiPotential(a=0.5, b=0.0375, amp=1., normalize=.6)
np = NFWPotential(a=4.5, normalize=.35)
hp = HernquistPotential(a=0.6 / 8, normalize=0.05)
ts = nu.linspace(0., 20., 10000)
mye = nu.zeros(len(e))
for ii in range(len(e)):
#Integrate the orbit
o = Orbit(vxvv[ii, :], radec=True, vo=220., ro=8.)
o.integrate(ts, lp)
mye[ii] = o.e()
#Save
savefile = open(savefilename, 'wb')
pickle.dump(mye, savefile)
pickle.dump(e, savefile)
savefile.close()
#plot
plot.bovy_print()
plot.bovy_plot(nu.array([0., 1.]),
nu.array([0., 1.]),
'k-',
xlabel=r'$\mathrm{Dierickx\ et\ al.}\ e$',
ylabel=r'$\mathrm{galpy}\ e$')
plot.bovy_plot(e, mye, 'k,', overplot=True)
plot.bovy_end_print('myee.png')
plot.bovy_print()
plot.bovy_hist(e, bins=30, xlabel=r'$\mathrm{Dierickx\ et\ al.}\ e$')
plot.bovy_end_print('ehist.png')
plot.bovy_print()
plot.bovy_hist(mye, bins=30, xlabel=r'$\mathrm{galpy}\ e$')
plot.bovy_end_print('myehist.png')
return lbd[0], lbd[1], lbd[2]
Mbar = 10**10.
pat_speed = 40.
ang = 27.
Ac, As = SCFbar_util.compute_Acos_Asin()
barpot, nobarpot = SCFbar_util.Particle_Spray_MWPotentialSCFbar(mbar=Mbar,
Acos=Ac,
Asin=As,
t_on=-2.)
p5 = Orbit([229.018, -0.124, 23.2, -2.296, -2.257, -58.7],
radec=True,
ro=ro,
vo=vo,
solarmotion=[-11.1, 24., 7.25])
#convert to galpy units
pal5 = Orbit(p5._orb.vxvv)
#mass of Pal 5 from Dehnen https://arxiv.org/pdf/astro-ph/0401422.pdf
spdf = streamspraydf.streamspraydf(60000. * units.Msun,
progenitor=pal5,
pot=nobarpot,
tdisrupt=5. * units.Gyr)
spdft = streamspraydf.streamspraydf(60000. * units.Msun,
progenitor=pal5,
pot=nobarpot,
leading=False,
0.60122692,
0.36273147,
-0.97591502,
-3.34169377,
0.71877924,
-0.01519337,
-0.01928001,
]
pot = MWPotential2014Likelihood.setup_potential(p_b15, 1.0, False, False,
REFR0, REFV0)
prog = Orbit(
[229.018, -0.124, 23.2, -2.296, -2.257, -58.7],
radec=True,
ro=REFR0,
vo=REFV0,
solarmotion=[-11.1, 24.0, 7.25],
)
aAI = actionAngleIsochroneApprox(pot=pot, b=0.8)
sigv = 0.2
# ----------------------------------------------------------
try:
with open("output/sdf_trailing.pkl", "rb") as file:
sdf_trailing = pickle.load(file)
except Exception:
sdf_trailing = streamdf(
sigv / REFV0,
progenitor=prog,
def test_orbitint():
import numpy
from galpy.potential import MWPotential2014
from galpy.potential import evaluatePotentials as evalPot
from galpy.orbit import Orbit
E, Lz = -1.25, 0.6
o1 = Orbit([
0.8, 0., Lz / 0.8, 0.,
numpy.sqrt(2. * (E - evalPot(MWPotential2014, 0.8, 0.) -
(Lz / 0.8)**2. / 2.)), 0.
])
ts = numpy.linspace(0., 100., 2001)
o1.integrate(ts, MWPotential2014)
o1.plot(xrange=[0.3, 1.], yrange=[-0.2, 0.2], color='k')
o2 = Orbit([
0.8, 0.3, Lz / 0.8, 0.,
numpy.sqrt(2. * (E - evalPot(MWPotential2014, 0.8, 0.) -
(Lz / 0.8)**2. / 2. - 0.3**2. / 2.)), 0.
])
o2.integrate(ts, MWPotential2014)
o2.plot(xrange=[0.3, 1.], yrange=[-0.2, 0.2], color='k')
return None
def calc_eccentricity(args, options):
table = os.path.join(args[0],'table2.dat')
readme = os.path.join(args[0],'ReadMe')
dierickx = ascii.read(table, readme=readme)
vxvv = np.dstack([dierickx['RAdeg'], dierickx['DEdeg'], dierickx['Dist']/1e3, dierickx['pmRA'], dierickx['pmDE'], dierickx['HRV']])[0]
ro, vo, zo = 8., 220., 0.025
ra, dec= vxvv[:,0], vxvv[:,1]
lb= bovy_coords.radec_to_lb(ra,dec,degree=True)
pmra, pmdec= vxvv[:,3], vxvv[:,4]
pmllpmbb= bovy_coords.pmrapmdec_to_pmllpmbb(pmra,pmdec,ra,dec,degree=True)
d, vlos= vxvv[:,2], vxvv[:,5]
rectgal= bovy_coords.sphergal_to_rectgal(lb[:,0],lb[:,1],d,vlos,pmllpmbb[:,0], pmllpmbb[:,1],degree=True)
vsolar= np.array([-10.1,4.0,6.7])
vsun= np.array([0.,1.,0.,])+vsolar/vo
X = rectgal[:,0]/ro
Y = rectgal[:,1]/ro
Z = rectgal[:,2]/ro
vx = rectgal[:,3]/vo
vy = rectgal[:,4]/vo
vz = rectgal[:,5]/vo
vsun= np.array([0.,1.,0.,])+vsolar/vo
Rphiz= bovy_coords.XYZ_to_galcencyl(X,Y,Z,Zsun=zo/ro)
vRvTvz= bovy_coords.vxvyvz_to_galcencyl(vx,vy,vz,Rphiz[:,0],Rphiz[:,1],Rphiz[:,2],vsun=vsun,Xsun=1.,Zsun=zo/ro,galcen=True)
#do the integration and individual analytic estimate for each object
ts= np.linspace(0.,20.,10000)
lp= LogarithmicHaloPotential(normalize=1.)
e_ana = numpy.zeros(len(vxvv))
e_int = numpy.zeros(len(vxvv))
print('Performing orbit integration and analytic parameter estimates for Dierickx et al. sample...')
for i in tqdm(range(len(vxvv))):
try:
orbit = Orbit(vxvv[i], radec=True, vo=220., ro=8.)
e_ana[i] = orbit.e(analytic=True, pot=lp, c=True)
except UnboundError:
e_ana[i] = np.nan
orbit.integrate(ts, lp)
e_int[i] = orbit.e(analytic=False)
fig = plt.figure()
fig.set_size_inches(1.5*columnwidth, 1.5*columnwidth)
plt.scatter(e_int, e_ana, s=1, color='Black', lw=0.)
plt.xlabel(r'$\mathrm{galpy\ integrated}\ e$')
plt.ylabel(r'$\mathrm{galpy\ analytic}\ e$')
plt.xlim(0.,1.)
plt.ylim(0.,1.)
fig.tight_layout()
plt.savefig(os.path.join(args[0],'dierickx-integratedeanalytice.png'), format='png', dpi=200)
fig = plt.figure()
fig.set_size_inches(1.5*columnwidth, 1.5*columnwidth)
plt.hist(e_int, bins=30)
plt.xlim(0.,1.)
plt.xlabel(r'$\mathrm{galpy}\ e$')
fig.tight_layout()
plt.savefig(os.path.join(args[0], 'dierickx-integratedehist.png'), format='png', dpi=200)
fig = plt.figure()
fig.set_size_inches(1.5*columnwidth, 1.5*columnwidth)
plt.scatter(dierickx['e'], e_int, s=1, color='Black', lw=0.)
plt.xlabel(r'$\mathrm{Dierickx\ et\ al.}\ e$')
plt.ylabel(r'$\mathrm{galpy\ integrated}\ e$')
plt.xlim(0.,1.)
plt.ylim(0.,1.)
fig.tight_layout()
plt.savefig(os.path.join(args[0],'dierickx-integratedee.png'), format='png', dpi=200)
fig = plt.figure()
fig.set_size_inches(1.5*columnwidth, 1.5*columnwidth)
plt.scatter(dierickx['e'], e_ana, s=1, color='Black', lw=0.)
plt.xlabel(r'$\mathrm{Dierickx\ et\ al.}\ e$')
plt.ylabel(r'$\mathrm{galpy\ estimated}\ e$')
plt.xlim(0.,1.)
plt.ylim(0.,1.)
fig.tight_layout()
plt.savefig(os.path.join(args[0],'dierickx-analyticee.png'), format='png', dpi=200)
arr = numpy.recarray(len(e_ana), dtype=[('analytic_e', float), ('integrated_e', float)])
arr['analytic_e'] = e_ana
arr['integrated_e'] = e_int
with open(os.path.join(args[0],'eccentricities.dat'), 'w') as file:
pickle.dump(arr, file)
file.close()
def test_orbmethods():
from galpy.orbit import Orbit
from galpy.potential import MWPotential2014
# 8/17/2019: added explicit z=0.025, because that was the default at the
# time of the galpy paper, but the default has been changed
o = Orbit([0.8, 0.3, 0.75, 0., 0.2, 0.],
zo=0.025) # setup R,vR,vT,z,vz,phi
times = numpy.linspace(0., 10., 1001) # Output times
o.integrate(times, MWPotential2014) # Integrate
o.E() # Energy
assert numpy.fabs(o.E() + 1.2547650648697966
) < 10.**-5., 'Orbit method does not work as expected'
o.L() # Angular momentum
assert numpy.all(
numpy.fabs(o.L() - numpy.array([[0., -0.16, 0.6]])) < 10.**-5.
), 'Orbit method does not work as expected'
o.Jacobi(OmegaP=0.65) #Jacobi integral E-OmegaP Lz
assert numpy.fabs(o.Jacobi(OmegaP=0.65) - numpy.array([-1.64476506])
) < 10.**-5., 'Orbit method does not work as expected'
o.ER(times[-1]), o.Ez(times[-1]) # Rad. and vert. E at end
assert numpy.fabs(o.ER(times[-1]) + 1.27601734263047
) < 10.**-5., 'Orbit method does not work as expected'
assert numpy.fabs(o.Ez(times[-1]) - 0.021252201847851909
) < 10.**-5., 'Orbit method does not work as expected'
o.rperi(), o.rap(), o.zmax() # Peri-/apocenter r, max. |z|
assert numpy.fabs(o.rperi() - 0.44231993168097
) < 10.**-5., 'Orbit method does not work as expected'
assert numpy.fabs(o.rap() - 0.87769030382105
) < 10.**-5., 'Orbit method does not work as expected'
assert numpy.fabs(o.zmax() - 0.077452357289016
) < 10.**-5., 'Orbit method does not work as expected'
o.e() # eccentricity (rap-rperi)/(rap+rperi)
assert numpy.fabs(o.e() - 0.32982348199330563
) < 10.**-5., 'Orbit method does not work as expected'
o.R(2., ro=8.) # Cylindrical radius at time 2. in kpc
assert numpy.fabs(o.R(2., ro=8.) - 3.5470772876920007
) < 10.**-3., 'Orbit method does not work as expected'
o.vR(5., vo=220.) # Cyl. rad. velocity at time 5. in km/s
assert numpy.fabs(o.vR(5., vo=220.) - 45.202530965094553
) < 10.**-3., 'Orbit method does not work as expected'
o.ra(1.), o.dec(1.) # RA and Dec at t=1. (default settings)
# 5/12/2016: test weakened, because improved galcen<->heliocen
# transformation has changed these, but still close
assert numpy.fabs(o.ra(1.) - numpy.array([288.19277])
) < 10.**-1., 'Orbit method does not work as expected'
assert numpy.fabs(o.dec(1.) - numpy.array([18.98069155])
) < 10.**-1., 'Orbit method does not work as expected'
o.jr(type='adiabatic'), o.jz() # R/z actions (ad. approx.)
assert numpy.fabs(o.jr(type='adiabatic') - 0.05285302231137586
) < 10.**-3., 'Orbit method does not work as expected'
assert numpy.fabs(o.jz() - 0.006637988850751242
) < 10.**-3., 'Orbit method does not work as expected'
# Rad. period w/ Staeckel approximation w/ focal length 0.5,
o.Tr(type='staeckel', delta=0.5, ro=8., vo=220.) # in Gyr
assert numpy.fabs(
o.Tr(type='staeckel', delta=0.5, ro=8., vo=220.) - 0.1039467864018446
) < 10.**-3., 'Orbit method does not work as expected'
o.plot(d1='R', d2='z') # Plot the orbit in (R,z)
o.plot3d() # Plot the orbit in 3D, w/ default [x,y,z]
return None
parser = get_options()
options, args = parser.parse_args()
Mbar = 10**10.
pat_speed = options.pat_speed
ang = 27.
td = options.td
t_on = options.t_on
Ac, As = SCFbar_util.compute_Acos_Asin()
barpot, nobarpot = SCFbar_util.Particle_Spray_MWPotentialSCFbar(
mbar=Mbar, Acos=Ac, Asin=As, t_on=t_on, pat_speed=pat_speed, tstream=td)
p5 = Orbit([229.018, -0.124, 23.2, -2.296, -2.257, -58.7],
radec=True,
ro=ro,
vo=vo,
solarmotion=[-11.1, 24., 7.25])
#convert to galpy units
pal5 = Orbit(p5._orb.vxvv)
#mass of Pal 5 from Dehnen https://arxiv.org/pdf/astro-ph/0401422.pdf
spdf = streamspraydf.streamspraydf(50000. * units.Msun,
progenitor=pal5,
pot=barpot,
tdisrupt=td * units.Gyr)
spdft = streamspraydf.streamspraydf(50000. * units.Msun,
progenitor=pal5,
pot=barpot,
leading=False,
def test_surfacesection():
#Preliminary code
import numpy
from galpy.potential import MWPotential2014
from galpy.potential import evaluatePotentials as evalPot
from galpy.orbit import Orbit
E, Lz = -1.25, 0.6
o1 = Orbit([
0.8, 0., Lz / 0.8, 0.,
numpy.sqrt(2. * (E - evalPot(MWPotential2014, 0.8, 0.) -
(Lz / 0.8)**2. / 2.)), 0.
])
ts = numpy.linspace(0., 100., 2001)
o1.integrate(ts, MWPotential2014)
o2 = Orbit([
0.8, 0.3, Lz / 0.8, 0.,
numpy.sqrt(2. * (E - evalPot(MWPotential2014, 0.8, 0.) -
(Lz / 0.8)**2. / 2. - 0.3**2. / 2.)), 0.
])
o2.integrate(ts, MWPotential2014)
def surface_section(Rs, zs, vRs):
# Find points where the orbit crosses z from - to +
shiftzs = numpy.roll(zs, -1)
indx = (zs[:-1] < 0.) * (shiftzs[:-1] > 0.)
return (Rs[:-1][indx], vRs[:-1][indx])
# Calculate and plot the surface of section
ts = numpy.linspace(0., 1000., 20001) # long integration
o1.integrate(ts, MWPotential2014)
o2.integrate(ts, MWPotential2014)
sect1Rs, sect1vRs = surface_section(o1.R(ts), o1.z(ts), o1.vR(ts))
sect2Rs, sect2vRs = surface_section(o2.R(ts), o2.z(ts), o2.vR(ts))
from matplotlib.pyplot import plot, xlim, ylim
plot(sect1Rs, sect1vRs, 'bo', mec='none')
xlim(0.3, 1.)
ylim(-0.69, 0.69)
plot(sect2Rs, sect2vRs, 'yo', mec='none')
return None
def pass_v(ra, dec, d, pm_ra, pm_dec, V, time, numpoints):
"""
Function to estimate system velocity everytime it passes through the galactic plane.
This velocity is a proxy for system's natal kick. For details, assumptions and caveats
see Atri et al. 2019.
-----
ra,dec,d,pm_ra,pm_dec,V are source orbit parameters for Galpy
time is the age to integrate (Gyr)
numpoints is the number of points in the orbit to integrate.
"""
o = Orbit([
ra * u.deg, dec * u.deg, d * u.kpc, pm_ra * u.mas / u.yr,
pm_dec * u.mas / u.yr, V * u.km / u.s
],
radec=True)
lp = MWPotential2014
ts = np.linspace(0, time, numpoints) * u.Gyr
o.integrate(ts, lp)
pass_t_array = ts[np.where(
np.sign(o.z(ts)[:-1]) - np.sign(o.z(ts)[1:]) != 0)[0]]
results = []
for pass_t in pass_t_array:
o2 = Orbit(vxvv=[o.R(pass_t) / 8.0, 0., 1., 0., 0.,
o.phi(pass_t)],
ro=8.,
vo=220.)
#results.append(np.sqrt((o.U(pass_t)-o2.U(0)+11.1)**2 + (o.V(pass_t)-o2.V(0)+12.24)**2 + (o.W(pass_t)-o2.W(0)+7.25)**2))
results.append(
np.sqrt((o.U(pass_t) - o2.U(0))**2 + (o.V(pass_t) - o2.V(0))**2 +
(o.W(pass_t) - o2.W(0))**2))
return results
def test_adinvariance():
from galpy.potential import IsochronePotential
from galpy.orbit import Orbit
from galpy.actionAngle import actionAngleIsochrone
# Initialize two different IsochronePotentials
ip1 = IsochronePotential(normalize=1., b=1.)
ip2 = IsochronePotential(normalize=0.5, b=1.)
# Use TimeInterpPotential to interpolate smoothly
tip = TimeInterpPotential(ip1, ip2, dt=100., tform=50.)
# Integrate: 1) Orbit in the first isochrone potential
o1 = Orbit([1., 0.1, 1.1, 0.0, 0.1, 0.])
ts = numpy.linspace(0., 50., 1001)
o1.integrate(ts, tip)
o1.plot(d1='x', d2='y', xrange=[-1.6, 1.6], yrange=[-1.6, 1.6], color='b')
# 2) Orbit in the transition
o2 = o1(ts[-1]) # Last time step => initial time step
ts2 = numpy.linspace(50., 150., 1001)
o2.integrate(ts2, tip)
o2.plot(d1='x', d2='y', overplot=True, color='g')
# 3) Orbit in the second isochrone potential
o3 = o2(ts2[-1])
ts3 = numpy.linspace(150., 200., 1001)
o3.integrate(ts3, tip)
o3.plot(d1='x', d2='y', overplot=True, color='r')
# Now we calculate energy, maximum height, and mean radius
print(o1.E(pot=ip1), (o1.rperi() + o1.rap()) / 2, o1.zmax())
assert numpy.fabs(
o1.E(pot=ip1) + 2.79921356237
) < 10.**-4., 'Energy in the adiabatic invariance test is different'
assert numpy.fabs(
(o1.rperi() + o1.rap()) / 2 - 1.07854158141
) < 10.**-4., 'mean radius in the adiabatic invariance test is different'
assert numpy.fabs(
o1.zmax() - 0.106331362938
) < 10.**-4., 'zmax in the adiabatic invariance test is different'
print(o3.E(pot=ip2), (o3.rperi() + o3.rap()) / 2, o3.zmax())
assert numpy.fabs(
o3.E(pot=ip2) + 1.19677002624
) < 10.**-4., 'Energy in the adiabatic invariance test is different'
assert numpy.fabs(
(o3.rperi() + o3.rap()) / 2 - 1.39962036137
) < 10.**-4., 'mean radius in the adiabatic invariance test is different'
assert numpy.fabs(
o3.zmax() - 0.138364269321
) < 10.**-4., 'zmax in the adiabatic invariance test is different'
# The orbit has clearly moved to larger radii,
# the actions are however conserved from beginning to end
aAI1 = actionAngleIsochrone(ip=ip1)
print(aAI1(o1))
js = aAI1(o1)
assert numpy.fabs(
js[0] - numpy.array([0.00773779])
) < 10.**-4., 'action in the adiabatic invariance test is different'
assert numpy.fabs(
js[1] - numpy.array([1.1])
) < 10.**-4., 'action in the adiabatic invariance test is different'
assert numpy.fabs(
js[2] - numpy.array([0.0045361])
) < 10.**-4., 'action in the adiabatic invariance test is different'
aAI2 = actionAngleIsochrone(ip=ip2)
print(aAI2(o3))
js = aAI2(o3)
assert numpy.fabs(
js[0] - numpy.array([0.00773812])
) < 10.**-4., 'action in the adiabatic invariance test is different'
assert numpy.fabs(
js[1] - numpy.array([1.1])
) < 10.**-4., 'action in the adiabatic invariance test is different'
assert numpy.fabs(
js[2] - numpy.array([0.0045361])
) < 10.**-4., 'action in the adiabatic invariance test is different'
return None
def test_physical_compatible_combos():
# Test that physical_compatible acts as expected for combinations of
# different types of objects
from galpy.util.bovy_conversion import physical_compatible
from galpy.potential import HernquistPotential
from galpy.orbit import Orbit
from galpy.actionAngle import actionAngleSpherical
from galpy.df import quasiisothermaldf
# Set up different objects for possible cases
# Potentials
pot_default_phys = HernquistPotential(amp=0.55, a=2., ro=8., vo=220.)
pot_nonstandardro = HernquistPotential(amp=0.55, a=2., ro=9., vo=220.)
pot_nonstandardvo = HernquistPotential(amp=0.55, a=2., ro=8., vo=230.)
pot_nonstandardrovo = HernquistPotential(amp=0.55, a=2., ro=9., vo=230.)
pot_nophys = HernquistPotential(amp=0.55)
pot_default_noro = HernquistPotential(amp=0.55, vo=220.)
pot_default_novo = HernquistPotential(amp=0.55, ro=8.)
pot_nonstandardro_novo = HernquistPotential(amp=0.55, ro=9.)
pot_nonstandardvo_noro = HernquistPotential(amp=0.55, vo=230.)
pot_nonstandardvo_noro = HernquistPotential(amp=0.55, vo=230.)
# Orbits
orb_default_phys = Orbit([1., 0.1, 1.1, 0.1, 0.3, -0.9], ro=8., vo=220.)
orb_nonstandardro = Orbit([1., 0.1, 1.1, 0.1, 0.3, -0.9], ro=9., vo=220.)
orb_nonstandardvo = Orbit([1., 0.1, 1.1, 0.1, 0.3, -0.9], ro=8., vo=230.)
orb_nonstandardrovo = Orbit([1., 0.1, 1.1, 0.1, 0.3, -0.9], ro=9., vo=230.)
orb_nophys = Orbit([1., 0.1, 1.1, 0.1, 0.3, -0.9])
orb_default_noro = Orbit([1., 0.1, 1.1, 0.1, 0.3, -0.9], vo=220.)
orb_nonstandardvo_noro = Orbit([1., 0.1, 1.1, 0.1, 0.3, -0.9], vo=230.)
# aAs
aA_default_phys = actionAngleSpherical(pot=pot_default_phys,
ro=8.,
vo=220.)
aA_nonstandardro = actionAngleSpherical(pot=pot_nonstandardro,
ro=9.,
vo=220.)
aA_nonstandardvo = actionAngleSpherical(pot=pot_nonstandardvo,
ro=8.,
vo=230.)
aA_nonstandardrovo = actionAngleSpherical(pot=pot_nonstandardrovo,
ro=9.,
vo=230.)
aA_nophys = actionAngleSpherical(pot=pot_nophys)
aA_default_novo = actionAngleSpherical(pot=pot_default_novo, ro=8.)
aA_nonstandardvo_noro = actionAngleSpherical(pot=pot_nonstandardvo_noro,
vo=230.)
# DFs
qdf_default_phys = quasiisothermaldf(1. / 3.,
0.2,
0.1,
1.,
1.,
pot=pot_default_phys,
aA=aA_default_phys,
ro=8.,
vo=220.)
qdf_nonstandardro = quasiisothermaldf(1. / 3.,
0.2,
0.1,
1.,
1.,
pot=pot_nonstandardro,
aA=aA_nonstandardro,
ro=9.,
vo=220.)
qdf_nonstandardvo = quasiisothermaldf(1. / 3.,
0.2,
0.1,
1.,
1.,
pot=pot_nonstandardvo,
aA=aA_nonstandardvo,
ro=8.,
vo=230.)
qdf_nonstandardrovo = quasiisothermaldf(1. / 3.,
0.2,
0.1,
1.,
1.,
pot=pot_nonstandardrovo,
aA=aA_nonstandardrovo,
ro=9.,
vo=230.)
qdf_nophys = quasiisothermaldf(1. / 3.,
0.2,
0.1,
1.,
1.,
pot=pot_nophys,
aA=aA_nophys)
# Now do some tests!
assert physical_compatible(pot_default_phys,orb_default_phys), \
"pot_default_phys does not behave as expected for combinations of different objects"
assert physical_compatible(pot_default_phys,aA_default_phys), \
"pot_default_phys does not behave as expected for combinations of different objects"
assert physical_compatible(pot_default_phys,qdf_default_phys), \
"pot_default_phys does not behave as expected for combinations of different objects"
assert physical_compatible(pot_nonstandardro,orb_nonstandardro), \
"pot_default_phys does not behave as expected for combinations of different objects"
assert physical_compatible(pot_nonstandardro,aA_nonstandardro), \
"pot_default_phys does not behave as expected for combinations of different objects"
assert physical_compatible(pot_nonstandardro,qdf_nonstandardro), \
"pot_default_phys does not behave as expected for combinations of different objects"
assert not physical_compatible(pot_default_phys,orb_nonstandardro), \
"pot_default_phys does not behave as expected for combinations of different objects"
assert not physical_compatible(pot_default_phys,aA_nonstandardro), \
"pot_default_phys does not behave as expected for combinations of different objects"
assert not physical_compatible(pot_default_phys,qdf_nonstandardro), \
"pot_default_phys does not behave as expected for combinations of different objects"
assert not physical_compatible(pot_default_phys,orb_nonstandardvo), \
"pot_default_phys does not behave as expected for combinations of different objects"
assert not physical_compatible(pot_default_phys,aA_nonstandardvo), \
"pot_default_phys does not behave as expected for combinations of different objects"
assert not physical_compatible(pot_default_phys,qdf_nonstandardvo), \
"pot_default_phys does not behave as expected for combinations of different objects"
assert not physical_compatible(pot_default_phys,orb_nonstandardrovo), \
"pot_default_phys does not behave as expected for combinations of different objects"
assert not physical_compatible(pot_default_phys,aA_nonstandardrovo), \
"pot_default_phys does not behave as expected for combinations of different objects"
assert not physical_compatible(pot_default_phys,qdf_nonstandardrovo), \
"pot_default_phys does not behave as expected for combinations of different objects"
assert physical_compatible([pot_nophys,pot_nophys],orb_nonstandardrovo), \
"pot_default_phys does not behave as expected for combinations of different objects"
assert physical_compatible(pot_nophys,aA_nonstandardrovo), \
"pot_default_phys does not behave as expected for combinations of different objects"
assert physical_compatible(pot_nophys,qdf_nonstandardrovo), \
"pot_default_phys does not behave as expected for combinations of different objects"
assert physical_compatible(pot_nophys,orb_default_phys), \
"pot_default_phys does not behave as expected for combinations of different objects"
assert physical_compatible(pot_nophys,aA_default_phys), \
"pot_default_phys does not behave as expected for combinations of different objects"
assert physical_compatible(pot_nophys,qdf_default_phys), \
"pot_default_phys does not behave as expected for combinations of different objects"
assert physical_compatible(pot_nophys,orb_nophys), \
"pot_default_phys does not behave as expected for combinations of different objects"
assert physical_compatible(pot_nophys,orb_nophys), \
"pot_default_phys does not behave as expected for combinations of different objects"
assert physical_compatible(pot_nophys,qdf_nophys), \
"pot_default_phys does not behave as expected for combinations of different objects"
assert physical_compatible(pot_default_noro,qdf_nonstandardro), \
"pot_default_phys does not behave as expected for combinations of different objects"
assert physical_compatible(pot_nonstandardro_novo,orb_default_noro), \
"pot_default_phys does not behave as expected for combinations of different objects"
assert physical_compatible(aA_nonstandardvo_noro,orb_nonstandardvo_noro), \
"pot_default_phys does not behave as expected for combinations of different objects"
assert not physical_compatible(aA_default_novo,qdf_nonstandardrovo), \
"pot_default_phys does not behave as expected for combinations of different objects"
# Also test agained None!
assert physical_compatible(None,pot_default_phys), \
"pot_default_phys does not behave as expected for combinations of different objects"
assert physical_compatible(None,orb_default_phys), \
"pot_default_phys does not behave as expected for combinations of different objects"
assert physical_compatible(None,aA_default_phys), \
"pot_default_phys does not behave as expected for combinations of different objects"
assert physical_compatible(None,qdf_default_phys), \
"pot_default_phys does not behave as expected for combinations of different objects"
assert physical_compatible(pot_default_phys,None), \
"pot_default_phys does not behave as expected for combinations of different objects"
assert physical_compatible(orb_default_phys,None), \
"pot_default_phys does not behave as expected for combinations of different objects"
assert physical_compatible(aA_default_phys,None), \
"pot_default_phys does not behave as expected for combinations of different objects"
assert physical_compatible(qdf_default_phys,None), \
"pot_default_phys does not behave as expected for combinations of different objects"
return None
def test_diskdf():
from galpy.df import dehnendf
# Init. dehnendf w/ flat rot., hr=1/3, hs=1, and sr(1)=0.2
df = dehnendf(beta=0., profileParams=(1. / 3., 1.0, 0.2))
# Same, w/ correction factors to scale profiles
dfc = dehnendf(beta=0.,
profileParams=(1. / 3., 1.0, 0.2),
correct=True,
niter=20)
if True:
# Log. diff. between scale and DF surf. dens.
numpy.log(df.surfacemass(0.5) / df.targetSurfacemass(0.5))
assert numpy.fabs(
numpy.log(df.surfacemass(0.5) / df.targetSurfacemass(0.5)) +
0.056954077791649592
) < 10.**-4., 'diskdf does not behave as expected'
# Same for corrected DF
numpy.log(dfc.surfacemass(0.5) / dfc.targetSurfacemass(0.5))
assert numpy.fabs(
numpy.log(dfc.surfacemass(0.5) / dfc.targetSurfacemass(0.5)) +
4.1440377205802041e-06
) < 10.**-4., 'diskdf does not behave as expected'
# Log. diff between scale and DF sr
numpy.log(df.sigmaR2(0.5) / df.targetSigma2(0.5))
assert numpy.fabs(
numpy.log(df.sigmaR2(0.5) / df.targetSigma2(0.5)) +
0.12786083001363127
) < 10.**-4., 'diskdf does not behave as expected'
# Same for corrected DF
numpy.log(dfc.sigmaR2(0.5) / dfc.targetSigma2(0.5))
assert numpy.fabs(
numpy.log(dfc.sigmaR2(0.5) / dfc.targetSigma2(0.5)) +
6.8065001252214986e-06
) < 10.**-4., 'diskdf does not behave as expected'
# Evaluate DF w/ R,vR,vT
df(numpy.array([0.9, 0.1, 0.8]))
assert numpy.fabs(
df(numpy.array([0.9, 0.1, 0.8])) - numpy.array(0.1740247246180417)
) < 10.**-4., 'diskdf does not behave as expected'
# Evaluate corrected DF w/ Orbit instance
from galpy.orbit import Orbit
dfc(Orbit([0.9, 0.1, 0.8]))
assert numpy.fabs(
dfc(Orbit([0.9, 0.1, 0.8])) - numpy.array(0.16834863725552207)
) < 10.**-4., 'diskdf does not behave as expected'
# Calculate the mean velocities
df.meanvR(0.9), df.meanvT(0.9)
assert numpy.fabs(
df.meanvR(0.9)) < 10.**-4., 'diskdf does not behave as expected'
assert numpy.fabs(df.meanvT(0.9) - 0.91144428051168291
) < 10.**-4., 'diskdf does not behave as expected'
# Calculate the velocity dispersions
numpy.sqrt(dfc.sigmaR2(0.9)), numpy.sqrt(dfc.sigmaT2(0.9))
assert numpy.fabs(numpy.sqrt(dfc.sigmaR2(0.9)) - 0.22103383792719539
) < 10.**-4., 'diskdf does not behave as expected'
assert numpy.fabs(numpy.sqrt(dfc.sigmaT2(0.9)) - 0.17613725303902811
) < 10.**-4., 'diskdf does not behave as expected'
# Calculate the skew of the velocity distribution
df.skewvR(0.9), df.skewvT(0.9)
assert numpy.fabs(
df.skewvR(0.9)) < 10.**-4., 'diskdf does not behave as expected'
assert numpy.fabs(df.skewvT(0.9) + 0.47331638366025863
) < 10.**-4., 'diskdf does not behave as expected'
# Calculate the kurtosis of the velocity distribution
df.kurtosisvR(0.9), df.kurtosisvT(0.9)
assert numpy.fabs(df.kurtosisvR(0.9) + 0.13561300880237059
) < 10.**-4., 'diskdf does not behave as expected'
assert numpy.fabs(df.kurtosisvT(0.9) - 0.12612702099300721
) < 10.**-4., 'diskdf does not behave as expected'
# Calculate a higher-order moment of the velocity DF
df.vmomentsurfacemass(1., 6., 2.) / df.surfacemass(1.)
assert numpy.fabs(
df.vmomentsurfacemass(1., 6., 2.) / df.surfacemass(1.) -
0.00048953492205559054
) < 10.**-4., 'diskdf does not behave as expected'
# Calculate the Oort functions
dfc.oortA(1.), dfc.oortB(1.), dfc.oortC(1.), dfc.oortK(1.)
assert numpy.fabs(dfc.oortA(1.) - 0.40958989067012197
) < 10.**-4., 'diskdf does not behave as expected'
assert numpy.fabs(dfc.oortB(1.) + 0.49396172114486514
) < 10.**-4., 'diskdf does not behave as expected'
assert numpy.fabs(
dfc.oortC(1.)) < 10.**-4., 'diskdf does not behave as expected'
assert numpy.fabs(
dfc.oortK(1.)) < 10.**-4., 'diskdf does not behave as expected'
# Sample Orbits from the DF, returns list of Orbits
numpy.random.seed(1)
os = dfc.sample(n=100, returnOrbit=True, nphi=1)
# check that these have the right mean radius = 2hr=2/3
rs = numpy.array([o.R() for o in os])
assert numpy.fabs(numpy.mean(rs) - 2. / 3.) < 0.1
# Sample vR and vT at given R, check their mean
vrvt = dfc.sampleVRVT(0.7, n=500, target=True)
vt = vrvt[:, 1]
assert numpy.fabs(numpy.mean(vrvt[:, 0])) < 0.05
assert numpy.fabs(numpy.mean(vt) - dfc.meanvT(0.7)) < 0.01
# Sample Orbits along a given line-of-sight
os = dfc.sampleLOS(45., n=1000)
return None
print('Using galpy version {}'.format(galpy.__version__))
FORWARD_THROUGH_TIME = False
# Purely for reference: the expected solar motion as provided by Schoenrich
REFERENCE_SCHOENRICH_SOLAR_MOTION = np.array([-11.1, -12.24, -7.25])
# Set the age to be a full galactic revolution
age = 2*np.pi # galpy time units
ntimesteps = 10
forward_times = np.linspace(0.,age,ntimesteps)
backward_times = np.linspace(0.,-age,ntimesteps)
# vxvv is in cylindrical coordinates here. [R,vR,vT(,z,vz,phi)]
lsr_orbit = Orbit(vxvv=[1,0,1,0,0,0],vo=220,ro=8,solarmotion='schoenrich')
back_lsr_orbit = Orbit(vxvv=[1,0,1,0,0,0],vo=220,ro=8,solarmotion='schoenrich')
lsr_orbit.integrate(forward_times, MWPotential2014)
back_lsr_orbit.integrate(backward_times, MWPotential2014)
# # Manually extract the initial velocities
# U = lsr_orbit.U(0)
# V = lsr_orbit.V(0)
# W = lsr_orbit.W(0)
#
# results = np.array([U, V, W]).reshape(3)
# print('-- Inspecting the initialised velocities --')
# for i, vel in enumerate('UVW'):
# print("For velocity {}:".format(vel))
# print(" expected: {}".format(REFERENCE_SCHOENRICH_SOLAR_MOTION[i]))
# print(" received: {}".format(results[i]))
def likelihood_orbit(self,
potential,
ejmodel,
index,
dt=0.005 * u.Myr,
xi=0,
individual=False,
weights=None,
tint_max=None):
'''
Same as likelihood, but returns the lnLikelihood for a single orbit, together with the entire orbit.
Parameters
----------
index : int
Index of the star to propagate
See self.likelihood() for other parameters
Returns
-------
log likelihood values : numpy.array or float
Returns the ln-likelihood of the entire sample or the log-likelihood for every single star if individual
is True.
x, y, z, vx, vy, vz : Quantity
Position and velocity in Galactocentric coordinates.
'''
from galpy.orbit import Orbit
import astropy.coordinates as coord
from hvs.utils import t_MS
if (self.cattype == 0):
raise ValueError(
"The likelihood can be computed only for a propagated sample.")
if (self.size > 1e3):
print(
"You are computing the likelihood of a large sample. This might take a while."
)
weights = np.array(weights)
if ((weights != None) and (weights.size != self.size)):
raise ValueError(
'The length of weights must be equal to the number of HVS in the sample.'
)
self.backwards_orbits = [None] * self.size
self.back_dt = dt
self.lnlike = np.ones(self.size) * (-np.inf)
if (tint_max is None):
lifetime = t_MS(self.m, xi)
lifetime[lifetime > self.T_MW] = self.T_MW
else:
lifetime = np.ones(self.size) * tint_max
nsteps = np.ceil((lifetime / self.back_dt).to('1').value)
nsteps[nsteps < 100] = 100
vSun = [
-self.solarmotion[0], self.solarmotion[1], self.solarmotion[2]
] * u.km / u.s # (U, V, W)
vrot = [0., 220., 0.] * u.km / u.s
RSun = 8. * u.kpc
zSun = 0.025 * u.kpc
v_sun = coord.CartesianDifferential(vrot + vSun)
gc = coord.Galactocentric(galcen_distance=RSun,
z_sun=zSun,
galcen_v_sun=v_sun)
for i in [index]:
ts = np.linspace(0, 1, nsteps[i]) * lifetime[i]
self.backwards_orbits[i] = Orbit(vxvv = [self.ra[i], self.dec[i], self.dist[i], \
self.pmra[i], self.pmdec[i], self.vlos[i]], \
solarmotion=self.solarmotion, radec=True).flip()
self.backwards_orbits[i].integrate(ts,
potential,
method='dopr54_c')
dist, ll, bb, pmll, pmbb, vlos = self.backwards_orbits[i].dist(ts, use_physical=True) * u.kpc, \
self.backwards_orbits[i].ll(ts, use_physical=True) * u.deg, \
self.backwards_orbits[i].bb(ts, use_physical=True) * u.deg, \
self.backwards_orbits[i].pmll(ts, use_physical=True) *u.mas/u.year, \
self.backwards_orbits[i].pmbb(ts, use_physical=True) * u.mas/u.year, \
self.backwards_orbits[i].vlos(ts, use_physical=True) * u.km/u.s
galactic = coord.Galactic(l=ll,
b=bb,
distance=dist,
pm_l_cosb=pmll,
pm_b=pmbb,
radial_velocity=vlos)
gal = galactic.transform_to(gc)
vx, vy, vz = gal.v_x, gal.v_y, gal.v_z
x, y, z = gal.x, gal.y, gal.z
self.lnlike[i] = np.log(
(ejmodel.R(self.m[i], vx, vy, vz, x, y, z) *
ejmodel.g(np.linspace(0, 1, nsteps[i]))).sum())
return self.lnlike[i], x, y, z, vx, vy, vz
def test_orbmethods():
from galpy.orbit import Orbit
from galpy.potential import MWPotential2014
o= Orbit([0.8,0.3,0.75,0.,0.2,0.]) # setup R,vR,vT,z,vz,phi
times= numpy.linspace(0.,10.,1001) # Output times
o.integrate(times,MWPotential2014) # Integrate
o.E() # Energy
assert numpy.fabs(o.E()+1.2547650648697966) < 10.**-5., 'Orbit method does not work as expected'
o.L() # Angular momentum
assert numpy.all(numpy.fabs(o.L()-numpy.array([[ 0. , -0.16, 0.6 ]])) < 10.**-5.), 'Orbit method does not work as expected'
o.Jacobi(OmegaP=0.65) #Jacobi integral E-OmegaP Lz
assert numpy.fabs(o.Jacobi(OmegaP=0.65)-numpy.array([-1.64476506])) < 10.**-5., 'Orbit method does not work as expected'
o.ER(times[-1]), o.Ez(times[-1]) # Rad. and vert. E at end
assert numpy.fabs(o.ER(times[-1])+1.27601734263047) < 10.**-5., 'Orbit method does not work as expected'
assert numpy.fabs(o.Ez(times[-1])-0.021252201847851909) < 10.**-5., 'Orbit method does not work as expected'
o.rperi(), o.rap(), o.zmax() # Peri-/apocenter r, max. |z|
assert numpy.fabs(o.rperi()-0.44231993168097) < 10.**-5., 'Orbit method does not work as expected'
assert numpy.fabs(o.rap()-0.87769030382105) < 10.**-5., 'Orbit method does not work as expected'
assert numpy.fabs(o.zmax()-0.077452357289016) < 10.**-5., 'Orbit method does not work as expected'
o.e() # eccentricity (rap-rperi)/(rap+rperi)
assert numpy.fabs(o.e()-0.32982348199330563) < 10.**-5., 'Orbit method does not work as expected'
o.R(2.,ro=8.) # Cylindrical radius at time 2. in kpc
assert numpy.fabs(o.R(2.,ro=8.)-3.5470772876920007) < 10.**-3., 'Orbit method does not work as expected'
o.vR(5.,vo=220.) # Cyl. rad. velocity at time 5. in km/s
assert numpy.fabs(o.vR(5.,vo=220.)-45.202530965094553) < 10.**-3., 'Orbit method does not work as expected'
o.ra(1.), o.dec(1.) # RA and Dec at t=1. (default settings)
assert numpy.fabs(o.ra(1.)-numpy.array([ 288.19277])) < 10.**-3., 'Orbit method does not work as expected'
assert numpy.fabs(o.dec(1.)-numpy.array([ 18.98069155])) < 10.**-3., 'Orbit method does not work as expected'
o.jr(type='adiabatic'), o.jz() # R/z actions (ad. approx.)
assert numpy.fabs(o.jr(type='adiabatic')-0.05285302231137586) < 10.**-3., 'Orbit method does not work as expected'
assert numpy.fabs(o.jz()-0.006637988850751242) < 10.**-3., 'Orbit method does not work as expected'
# Rad. period w/ Staeckel approximation w/ focal length 0.5,
o.Tr(type='staeckel',delta=0.5,ro=8.,vo=220.) # in Gyr
assert numpy.fabs(o.Tr(type='staeckel',delta=0.5,ro=8.,vo=220.)-0.1039467864018446) < 10.**-3., 'Orbit method does not work as expected'
o.plot(d1='R',d2='z') # Plot the orbit in (R,z)
o.plot3d() # Plot the orbit in 3D, w/ default [x,y,z]
return None
def compute_impact_parameters(timp,
a,
xs,
ys,
zs,
pot=MWPotential2014,
nchunks=16,
sampling_low=128,
imp_fac=5.,
Mmin=10**6.,
rand_rotate=False):
'''
timp : timpacts
a,xs,ys,zs : list of array, each array decribes the stream at that time, no of arrays = timpacts
sampling_low : low timpact object on to which the impacts from high timpact case will be set
imp_fac: X where bmax= X.r_s
Mmin min mass above which all GMCs will be considered for impact
rand_rotate : give the GMCs an ol' shaka shaka along phi
'''
#load the GMCs
M, rs, coord = add_MCs(pot=pot, Mmin=Mmin, rand_rotate=rand_rotate)
#integrate their orbits 5 Gyr back,
t_age = np.linspace(0., 5., 1001) / bovy_conversion.time_in_Gyr(vo, ro)
orbits = []
N = len(M)
for ii in range(N):
orbits.append(Orbit(coord[ii]).flip()
) # flip flips the velocities for backwards integration
orbits[ii].integrate(t_age, pot)
min_sep_matrix = np.empty([N, len(timp)])
apar_matrix = np.empty([N, len(timp)])
#compute min_sep of each MC
for kk in range(len(timp)):
for jj in range(N):
x_mc = orbits[jj].x(timp[kk])
y_mc = orbits[jj].y(timp[kk])
z_mc = orbits[jj].z(timp[kk])
min_sep, apar_min = compute_min_separation(x_mc, y_mc, z_mc, a[kk],
xs[kk], ys[kk], zs[kk])
min_sep_matrix[jj, kk] = min_sep
apar_matrix[jj, kk] = apar_min
impactb = []
impact_angle = []
vx_mc = []
vy_mc = []
vz_mc = []
tmin = []
rs_mc = []
M_mc = []
impactMC_ind = []
if nchunks > 1:
#just to get timpacts
with open(
'pkl_files/pal5pepper_{}sampling_Plummer_MW2014.pkl'.format(
sampling_low), 'rb') as savefile:
sdf_pepper_low = pickle.load(savefile, encoding='latin1')
timpact_low = sdf_pepper_low._timpact
c = 0
for ii in range(len(orbits)):
bmax = imp_fac * rs[ii] / ro
if min(min_sep_matrix[ii]) <= bmax:
c += 1
min_timpact_ind = np.argmin(min_sep_matrix[ii])
impactMC_ind.append(ii)
t_high = timp[min_timpact_ind]
#round t_high to the nearest timpact in the low timpact sampling
t_low = timpact_low[np.argmin(np.abs(timpact_low - t_high))]
tmin.append(t_low)
impactb.append(min_sep_matrix[ii, min_timpact_ind])
impact_angle.append(apar_matrix[
ii, min_timpact_ind]) # _sigMeanSign = -/+ = trail/lead
rs_mc.append(rs[ii] / ro)
M_mc.append(M[ii] / bovy_conversion.mass_in_msol(vo, ro))
#flip velocities
vx_mc.append(-orbits[ii].vx(t_high))
vy_mc.append(-orbits[ii].vy(t_high))
vz_mc.append(-orbits[ii].vz(t_high))
#combine vx,vy,vz to v
v_mc = np.c_[vx_mc, vy_mc, vz_mc]
print("The stream had %i impacts" % c)
else:
c = 0
for ii in range(len(orbits)):
bmax = imp_fac * rs[ii] / ro
if min(min_sep_matrix[ii]) <= bmax:
c += 1
min_timpact_ind = np.argmin(min_sep_matrix[ii])
impactMC_ind.append(ii)
t_imp_min = timp[min_timpact_ind]
tmin.append(t_imp_min)
impactb.append(min_sep_matrix[ii, min_timpact_ind])
impact_angle.append(apar_matrix[
ii, min_timpact_ind]) # _sigMeanSign = -/+ = trail/lead
rs_mc.append(rs[ii] / ro)
M_mc.append(M[ii] / bovy_conversion.mass_in_msol(vo, ro))
#flip velocities
vx_mc.append(-orbits[ii].vx(t_imp_min))
vy_mc.append(-orbits[ii].vy(t_imp_min))
vz_mc.append(-orbits[ii].vz(t_imp_min))
#combine vx,vy,vz to v
v_mc = np.c_[vx_mc, vy_mc, vz_mc]
print("The stream had %i impacts" % c)
return (impactMC_ind, M_mc, rs_mc, v_mc, impactb, impact_angle, tmin)
def test_adinvariance():
from galpy.potential import IsochronePotential
from galpy.orbit import Orbit
from galpy.actionAngle import actionAngleIsochrone
# Initialize two different IsochronePotentials
ip1= IsochronePotential(normalize=1.,b=1.)
ip2= IsochronePotential(normalize=0.5,b=1.)
# Use TimeInterpPotential to interpolate smoothly
tip= TimeInterpPotential(ip1,ip2,dt=100.,tform=50.)
# Integrate: 1) Orbit in the first isochrone potential
o1= Orbit([1.,0.1,1.1,0.0,0.1,0.])
ts= numpy.linspace(0.,50.,1001)
o1.integrate(ts,tip)
o1.plot(d1='x',d2='y',xrange=[-1.6,1.6],yrange=[-1.6,1.6],
color='b')
# 2) Orbit in the transition
o2= o1(ts[-1]) # Last time step => initial time step
ts2= numpy.linspace(50.,150.,1001)
o2.integrate(ts2,tip)
o2.plot(d1='x',d2='y',overplot=True,color='g')
# 3) Orbit in the second isochrone potential
o3= o2(ts2[-1])
ts3= numpy.linspace(150.,200.,1001)
o3.integrate(ts3,tip)
o3.plot(d1='x',d2='y',overplot=True,color='r')
# Now we calculate energy, maximum height, and mean radius
print(o1.E(pot=ip1), (o1.rperi()+o1.rap())/2, o1.zmax())
assert numpy.fabs(o1.E(pot=ip1)+2.79921356237) < 10.**-4., 'Energy in the adiabatic invariance test is different'
assert numpy.fabs((o1.rperi()+o1.rap())/2-1.07854158141) < 10.**-4., 'mean radius in the adiabatic invariance test is different'
assert numpy.fabs(o1.zmax()-0.106331362938) < 10.**-4., 'zmax in the adiabatic invariance test is different'
print(o3.E(pot=ip2), (o3.rperi()+o3.rap())/2, o3.zmax())
assert numpy.fabs(o3.E(pot=ip2)+1.19677002624) < 10.**-4., 'Energy in the adiabatic invariance test is different'
assert numpy.fabs((o3.rperi()+o3.rap())/2-1.39962036137) < 10.**-4., 'mean radius in the adiabatic invariance test is different'
assert numpy.fabs(o3.zmax()-0.138364269321) < 10.**-4., 'zmax in the adiabatic invariance test is different'
# The orbit has clearly moved to larger radii,
# the actions are however conserved from beginning to end
aAI1= actionAngleIsochrone(ip=ip1); print(aAI1(o1))
js= aAI1(o1)
assert numpy.fabs(js[0]-numpy.array([ 0.00773779])) < 10.**-4., 'action in the adiabatic invariance test is different'
assert numpy.fabs(js[1]-numpy.array([ 1.1])) < 10.**-4., 'action in the adiabatic invariance test is different'
assert numpy.fabs(js[2]-numpy.array([ 0.0045361])) < 10.**-4., 'action in the adiabatic invariance test is different'
aAI2= actionAngleIsochrone(ip=ip2); print(aAI2(o3))
js= aAI2(o3)
assert numpy.fabs(js[0]-numpy.array([ 0.00773812])) < 10.**-4., 'action in the adiabatic invariance test is different'
assert numpy.fabs(js[1]-numpy.array([ 1.1])) < 10.**-4., 'action in the adiabatic invariance test is different'
assert numpy.fabs(js[2]-numpy.array([ 0.0045361])) < 10.**-4., 'action in the adiabatic invariance test is different'
return None
def create_frames(basefilename):
"""Create Frames.
Parameters
----------
basefilename : str
Returns
-------
None
"""
pot = IsochronePotential(normalize=1.0, b=1.2)
aAT = actionAngleIsochrone(ip=pot)
bmock = 0.8
aAF = actionAngleIsochrone(b=bmock)
o = Orbit([1.0, 0.3, 0.9, 0.2, 1.0, 0.1])
tfac, skip = 10, 1
ndesired = 30 * 25
times = numpy.linspace(0.0, 7.0, tfac * ndesired) * u.Gyr
# Subsample
otimesIndices = (numpy.arange(len(times)) /
float(len(times) - 1))**10 * (len(times) - 2)
otimesIndices = numpy.unique(numpy.floor(otimesIndices).astype("int"))
if len(otimesIndices) > ndesired:
sfac = int(numpy.floor(len(otimesIndices) / float(ndesired)))
otimesIndices = otimesIndices[::sfac]
otimes = times[otimesIndices]
o.integrate(times, pot)
# Compute all actions in the wrong potential
acfs = aAF.actionsFreqsAngles(
o.R(times),
o.vR(times),
o.vT(times),
o.z(times),
o.vz(times),
o.phi(times),
)
js = (acfs[0], acfs[1], acfs[2])
danglerI = ((numpy.roll(acfs[6], -1) - acfs[6]) % (2.0 * numpy.pi))[:-1]
jrC = numpy.cumsum(acfs[0][:-1] * danglerI) / numpy.cumsum(danglerI)
# And also the actions in the true potential
jsT = aAT(o.R(times), o.vR(times), o.vT(times), o.z(times), o.vz(times))
jrT = numpy.median(jsT[0]) * _RO * _VO
# ---------------------------------------------------------------
# Plotting
# Setup gridspec
gs = gridspec.GridSpec(1, 3, wspace=0.325, bottom=0.2, left=0.075)
# For each time step, plot: orbit, Jr, <Jr>
for ii in tqdm(range(len(otimes))):
bovy_plot.bovy_print(
fig_width=11.2,
fig_height=4.0,
axes_labelsize=17.0,
text_fontsize=12.0,
xtick_labelsize=13.0,
ytick_labelsize=13.0,
)
pyplot.figure()
pyplot.subplot(gs[0])
minIndx = otimesIndices[ii] - 100
if minIndx < 0:
minIndx = 0
bovy_plot.bovy_plot(
[o.x(otimes[ii:ii + 1]) * _RO],
[o.z(otimes[ii:ii + 1]) * _RO],
"o",
ms=15.0,
gcf=True,
xrange=[-19.0, 19.0],
yrange=[-19.0, 19.0],
xlabel=r"$X\,(\mathrm{kpc})$",
ylabel=r"$z\,(\mathrm{kpc})$",
)
if ii > 0:
bovy_plot.bovy_plot(
o.x(times[minIndx:otimesIndices[ii]:skip]) * _RO,
o.z(times[minIndx:otimesIndices[ii]:skip]) * _RO,
"-",
overplot=True,
)
pyplot.subplot(gs[1])
bovy_plot.bovy_plot(
[times[otimesIndices[ii]].value],
[js[0][otimesIndices[ii]] * _RO * _VO],
"o",
ms=15.0,
gcf=True,
xrange=[0.0, 1.0 + times[otimesIndices[ii]].value],
yrange=[0.0, 349.0],
xlabel=r"$\mathrm{time}\,(\mathrm{Gyr})$",
ylabel=r"$J_R\,(\mathrm{kpc\,km\,s}^{-1})$",
)
if ii > 0:
bovy_plot.bovy_plot(
times[:otimesIndices[ii]:skip].value,
js[0][:otimesIndices[ii]:skip] * _RO * _VO,
"-",
overplot=True,
)
pyplot.axhline(jrT, ls="--", color="k")
pyplot.subplot(gs[2])
bovy_plot.bovy_plot(
[otimes[ii].value],
[jrC[otimesIndices[ii]] * _RO * _VO],
"o",
ms=15.0,
gcf=True,
xrange=[0.0, 1.0 + times[otimesIndices[ii]].value],
yrange=[
(otimes[ii] / times[-1])**0.3 * (jrT - 3),
349.0 + (otimes[ii] / times[-1])**0.3 * (jrT + 3 - 349.0),
],
xlabel=r"$\mathrm{time}\,(\mathrm{Gyr})$",
ylabel=r"$J_R\,(\mathrm{kpc\,km\,s}^{-1})$",
)
if ii > 0:
bovy_plot.bovy_plot(
times[:otimesIndices[ii]:skip].value,
jrC[:otimesIndices[ii]:skip] * _RO * _VO,
"-",
overplot=True,
)
pyplot.axhline(jrT, ls="--", color="k")
bovy_plot.bovy_end_print(basefilename + "_%05d.png" % ii)
return None
def plot_aagrid(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.])
delta= 0.434
#Integrate the orbit, setup Staeckel already to calculate the period
aAS= actionAngleStaeckel(pot=MWPotential2014,delta=delta,c=True)
orbt= 2.*numpy.pi/aAS.actionsFreqs(o)[4]
norb= 5.
nt= 501
ts= numpy.linspace(0.,norb*orbt,nt)
o.integrate(ts,MWPotential2014,method='symplec4_c')
#First do adiabatic
aAA= actionAngleAdiabatic(pot=MWPotential2014,gamma=1.,c=True)
aAAG= actionAngleAdiabaticGrid(pot=MWPotential2014,gamma=1.,c=True,
nR=31,nEz=31,nEr=51,nLz=51)
jfa= aAA(o.R(ts),o.vR(ts),o.vT(ts),o.z(ts),o.vz(ts),o.phi(ts))
jfag= aAAG(o.R(ts),o.vR(ts),o.vT(ts),o.z(ts),o.vz(ts),o.phi(ts))
#First do adiabatic
#aAS already setup
aASG= actionAngleStaeckelGrid(pot=MWPotential2014,delta=delta,c=True,
nE=51,npsi=51,nLz=51)
jfs= aAS(o.R(ts),o.vR(ts),o.vT(ts),o.z(ts),o.vz(ts),o.phi(ts))
jfsg= aASG(o.R(ts),o.vR(ts),o.vT(ts),o.z(ts),o.vz(ts),o.phi(ts))
bovy_plot.bovy_print()
line1= bovy_plot.bovy_plot(jfa[0],jfa[2],'r.',
xrange=[0.045,0.055],
yrange=[0.0075,0.011],
xlabel=r'$J_R$',ylabel=r'$J_z$',zorder=2)
line2= bovy_plot.bovy_plot(jfag[0],jfag[2],'rx',overplot=True,zorder=1)
bovy_plot.bovy_plot(jfs[0],jfs[2],'k,',overplot=True)
pyplot.legend((line1[0],line2[0]),
(r'$\mathrm{\texttt{actionAngleAdiabatic}}$',
r'$\mathrm{\texttt{actionAngleAdiabaticGrid}}$',),
loc='upper right',#bbox_to_anchor=(.91,.375),
numpoints=1,
prop={'size':14},
frameon=False)
bovy_plot.bovy_end_print(plotfilename1)
#Zoom of Staeckel
line1= bovy_plot.bovy_plot(jfs[0],jfs[2],'k.',
xrange=[0.05025,0.05145],
yrange=[0.0086,0.00933],
xlabel=r'$J_R$',ylabel=r'$J_z$')
line2= bovy_plot.bovy_plot(jfsg[0],jfsg[2],'kx',overplot=True)
pyplot.legend((line1[0],line2[0]),
(r'$\mathrm{\texttt{actionAngleStaeckel}}$',
r'$\mathrm{\texttt{actionAngleStaeckelGrid}}$',),
loc='upper right',#bbox_to_anchor=(.91,.375),
numpoints=1,
prop={'size':14},
frameon=False)
bovy_plot.bovy_end_print(plotfilename2)
return None
# If we have parallax, then take Gaia proper motions. Otherwise, UCAC5.
if np.isfinite(star["parallax"]):
pmra, e_pmra = ("pmra_gaia", "pmra_error")
pmdec, e_pmdec = ("pmdec_gaia", "pmdec_error")
else:
pmra, e_pmra = ("pmRA", "e_pmRA")
pmdec, e_pmdec = ("pmDE", "e_pmDE")
pm_ra = np.random.normal(star[pmra], star[e_pmra])
pm_dec = np.random.normal(star[pmdec], star[e_pmdec])
v_hel = np.random.normal(star["vrad"], star["e_vrad"])
orbit = Orbit(
vxvv=[star["RA"], star["DEC"], distance, pm_ra, pm_dec, v_hel],
radec=True,
ro=ro,
vo=vo)
orbit.integrate(ts, mw)
orbits.append(orbit)
# Save the xyrz values.
positions \
= np.array([[o.x(ts), o.y(ts), o.z(ts), o.R(ts)] for o in orbits])
properties = np.array([[o.rap(), o.rperi(),
o.e(), o.zmax()] for o in orbits])
with open(output_path, "wb") as fp:
pickle.dump((positions, properties), fp, -1)
# Print some summary things.
def calcOrbits(parser):
options,args= parser.parse_args()
#Read data
XYZ,vxvyvz,cov_vxvyvz,rawdata= readData(metal='allall',
sample=options.sample,
loggmin=4.2,
snmin=15.,
select=options.select)
#Define potential
if options.logp:
pot= LogarithmicHaloPotential(normalize=1.)
else:
pot= MWPotential
ts= numpy.linspace(0.,_MAXT,10000) #times to integrate
if os.path.exists(args[0]):#Load savefile
savefile= open(args[0],'rb')
orbits= pickle.load(savefile)
_ORBITSLOADED= True
try:
samples= pickle.load(savefile)
except EORError:
_SAMPLESLOADED= False
else:
_SAMPLESLOADED= True
finally:
savefile.close()
else:
_ORBITSLOADED= False
if not _ORBITSLOADED:
#First calculate orbits
es, rmeans, rperis, raps, zmaxs = [], [], [], [], []
densrmeans, vzrmeans= [], []
for ii in range(len(rawdata)):
sys.stdout.write('\r'+"Working on object %i/%i" % (ii,len(rawdata)))
sys.stdout.flush()
#Integrate the orbit
data= rawdata[ii]
o= Orbit([data.ra,data.dec,data.dist,data.pmra,data.pmdec,data.vr],
radec=True,vo=220.,ro=8.,zo=_ZSUN)
o.integrate(ts,pot)
es.append(o.e())
rperis.append(o.rperi())
raps.append(o.rap())
zmaxs.append(o.zmax())
rmeans.append(0.5*(o.rperi()+o.rap()))
Rs= o.R(ts)
vz2= o.vz(ts)**2.
dens= evaluateDensities(Rs,0.*Rs,pot)
densrmeans.append(numpy.sum(dens*Rs)/numpy.sum(dens))
vzrmeans.append(numpy.sum(vz2*Rs)/numpy.sum(vz2))
# print " ", rmeans[-1], densrmeans[-1], vzrmeans[-1]
sys.stdout.write('\r'+_ERASESTR+'\r')
sys.stdout.flush()
es= numpy.array(es)
rmeans= numpy.array(rmeans)
rperis= numpy.array(rperis)
raps= numpy.array(raps)
zmaxs= numpy.array(zmaxs)
orbits= _append_field_recarray(rawdata,'e',es)
orbits= _append_field_recarray(orbits,'rmean',rmeans)
orbits= _append_field_recarray(orbits,'rperi',rperis)
orbits= _append_field_recarray(orbits,'rap',raps)
orbits= _append_field_recarray(orbits,'zmax',zmaxs)
orbits= _append_field_recarray(orbits,'densrmean',densrmeans)
orbits= _append_field_recarray(orbits,'vzrmean',vzrmeans)
#Pickle
savefile= open(args[0],'wb')
pickle.dump(orbits,savefile)
savefile.close()
return None
def illustrate_adiabatic_invariance(plotfilename1,plotfilename2):
# Initialize two different IsochronePotentials
ip1= IsochronePotential(normalize=1.,b=1.)
ip2= IsochronePotential(normalize=0.5,b=1.)
# Use TimeInterpPotential to interpolate smoothly between the two
tip= TimeInterpPotential(ip1,ip2,dt=100.,tform=50.)
# Integrate the orbit, in three parts
# 1) Orbit in the first isochrone potential
o1= Orbit([1.,0.1,1.1,0.0,0.1,0.])
ts= numpy.linspace(0.,50.,1001)
o1.integrate(ts,tip)
bovy_plot.bovy_print()
o1.plot(d1='x',d2='y',xrange=[-1.6,1.6],yrange=[-1.6,1.6],color='b',
gcf=True)
# 2) Orbit in the transition
o2= o1(ts[-1]) # Last time step = initial time step of the next integration
ts2= numpy.linspace(50.,150.,1001)
o2.integrate(ts2,tip)
o2.plot(d1='x',d2='y',overplot=True,color='g')
# 3) Orbit in the second isochrone potential
o3= o2(ts2[-1])
ts3= numpy.linspace(150.,200.,1001)
o3.integrate(ts3,ip2)
o3.plot(d1='x',d2='y',overplot=True,color='r')
bovy_plot.bovy_end_print(plotfilename1)
# Also plot the R,z projection
bovy_plot.bovy_print(fig_height=2.3333)
o1.plot(d1='R',d2='z',xrange=[0.9,1.65],yrange=[-.175,.175],color='b',
gcf=True)
o2.plot(d1='R',d2='z',overplot=True,color='g')
o3.plot(d1='R',d2='z',overplot=True,color='r')
bovy_plot.bovy_end_print(plotfilename2)
# Now we calculate the energy, eccentricity, mean radius, and maximum height
print o1.E(pot=ip1), o1.e(), 0.5*(o1.rperi()+o1.rap()), o1.zmax()
print o3.E(pot=ip2), o3.e(), 0.5*(o3.rperi()+o3.rap()), o3.zmax()
# The orbit has clearly moved to larger radii, the actions are however conserved
aAI1= actionAngleIsochrone(ip=ip1)
aAI2= actionAngleIsochrone(ip=ip2)
print aAI1(o1)
print aAI2(o3)
return None
def plot_stream_xz(plotfilename):
#Read stream
data= numpy.loadtxt(os.path.join(_STREAMSNAPDIR,'gd1_evol_hitres_00800.dat'),
delimiter=',')
aadata= numpy.loadtxt(os.path.join(_STREAMSNAPAADIR,
'gd1_evol_hitres_aa_00800.dat'),
delimiter=',')
thetar= aadata[:,6]
thetar= (numpy.pi+(thetar-numpy.median(thetar))) % (2.*numpy.pi)
if 'sim' in plotfilename:
sindx= numpy.fabs(thetar-numpy.pi) > (4.*numpy.median(numpy.fabs(thetar-numpy.median(thetar))))
else:
sindx= numpy.fabs(thetar-numpy.pi) > (1.5*numpy.median(numpy.fabs(thetar-numpy.median(thetar))))
includeorbit= True
if includeorbit:
npts= 201
pot= potential.LogarithmicHaloPotential(normalize=1.,q=0.9)
pts= numpy.linspace(0.,4.,npts)
#Calculate progenitor orbit around this point
pox= numpy.median(data[:,1])
poy= numpy.median(data[:,3])
poz= numpy.median(data[:,2])
povx= numpy.median(data[:,4])
povy= numpy.median(data[:,6])
povz= numpy.median(data[:,5])
pR,pphi,pZ= bovy_coords.rect_to_cyl(pox,poy,poz)
pvR,pvT,pvZ= bovy_coords.rect_to_cyl_vec(povx,povy,povz,pR,
pphi,pZ,cyl=True)
ppo= Orbit([pR/8.,pvR/220.,pvT/220.,pZ/8.,pvZ/220.,pphi])
pno= Orbit([pR/8.,-pvR/220.,-pvT/220.,pZ/8.,-pvZ/220.,pphi])
ppo.integrate(pts,pot)
pno.integrate(pts,pot)
pvec= numpy.zeros((3,npts*2-1))
pvec[0,:npts-1]= pno.x(pts)[::-1][:-1]
pvec[1,:npts-1]= pno.z(pts)[::-1][:-1]
pvec[2,:npts-1]= pno.y(pts)[::-1][:-1]
pvec[0,npts-1:]= ppo.x(pts)
pvec[1,npts-1:]= ppo.z(pts)
pvec[2,npts-1:]= ppo.y(pts)
pvec*= 8.
includetrack= True
if includetrack:
#Setup stream model
lp= potential.LogarithmicHaloPotential(q=0.9,normalize=1.)
aAI= actionAngleIsochroneApprox(b=0.8,pot=lp)
obs= numpy.array([1.56148083,0.35081535,-1.15481504,
0.88719443,-0.47713334,0.12019596])
#Obs is at time 1312, need to go back 2 Gyr to time 800
obs[1]*= -1.
obs[2]*= -1.
obs[4]*= -1.
o= Orbit(obs)
ts= numpy.linspace(0.,2.*977.7922212082034/1000./bovy_conversion.time_in_Gyr(220.,8.),1001)
o.integrate(ts,lp)
obs= o(ts[-1])._orb.vxvv
obs[1]*= -1.
obs[2]*= -1.
obs[4]*= -1.
tdisrupt= 4.5-2.*977.7922212082034/1000.
sdf= streamdf(_SIGV/220.,progenitor=Orbit(obs),pot=lp,aA=aAI,
leading=True,nTrackChunks=_NTRACKCHUNKS,
tdisrupt=tdisrupt/bovy_conversion.time_in_Gyr(220.,8.),
deltaAngleTrack=1.5*3./5.,multi=_NTRACKCHUNKS)
sdft= streamdf(_SIGV/220.,progenitor=Orbit(obs),pot=lp,aA=aAI,
leading=False,nTrackChunks=_NTRACKCHUNKS,
tdisrupt=tdisrupt/bovy_conversion.time_in_Gyr(220.,8.),
deltaAngleTrack=1.5*3./5.,multi=_NTRACKCHUNKS)
if 'sim' in plotfilename:
#Replace data with simulated data
forwardXY= sdf.sample(int(round(numpy.sum(sindx)/2.)),
xy=True)
backwardXY= sdft.sample(int(round(numpy.sum(sindx)/2.)),
xy=True)
data= numpy.empty((forwardXY.shape[1]+backwardXY.shape[1],7))
data[:forwardXY.shape[1],1]= forwardXY[0]*8.
data[:forwardXY.shape[1],2]= forwardXY[2]*8.
data[:forwardXY.shape[1],3]= forwardXY[1]*8.
data[:forwardXY.shape[1],4]= forwardXY[3]*220.
data[:forwardXY.shape[1],5]= forwardXY[5]*220.
data[:forwardXY.shape[1],6]= forwardXY[4]*220.
data[forwardXY.shape[1]:,1]= backwardXY[0]*8.
data[forwardXY.shape[1]:,2]= backwardXY[2]*8.
data[forwardXY.shape[1]:,3]= backwardXY[1]*8.
data[forwardXY.shape[1]:,4]= backwardXY[3]*220.
data[forwardXY.shape[1]:,5]= backwardXY[5]*220.
data[forwardXY.shape[1]:,6]= backwardXY[4]*220.
sindx= numpy.ones(data.shape[0],dtype='bool')
#Plot
bovy_plot.bovy_print()
bovy_plot.bovy_plot(data[sindx,1],data[sindx,2],'k,',ms=2.,
xlabel=r'$X\,(\mathrm{kpc})$',
ylabel=r'$Z\,(\mathrm{kpc})$',
xrange=[-12.5,-3.],
yrange=[-12.5,-7.])
if numpy.sum(True-sindx) > 0:
#Also plot progenitor
pindx= copy.copy(True-sindx)
pindx[0:9900]= False #subsample
bovy_plot.bovy_plot(data[pindx,1],data[pindx,2],
'k,',overplot=True)
if includeorbit:
bovy_plot.bovy_plot(pox,poz,'o',color='0.5',mec='none',overplot=True,ms=8)
bovy_plot.bovy_plot(pvec[0,:],pvec[1,:],'k--',overplot=True,lw=1.)
if 'sim' in plotfilename:
bovy_plot.bovy_text(r'$\mathrm{mock\ stream}$',
bottom_left=True,size=16.)
else:
bovy_plot.bovy_text(r'$N\!\!-\!\!\mathrm{body\ stream}$',
bottom_left=True,size=16.)
if includetrack:
d1= 'x'
d2= 'z'
sdf.plotTrack(d1=d1,d2=d2,interp=True,color='k',spread=0,
overplot=True,lw=1.,scaleToPhysical=True)
sdft.plotTrack(d1=d1,d2=d2,interp=True,color='k',spread=0,
overplot=True,lw=1.,scaleToPhysical=True)
#Also create inset
pyplot.plot([-9.,-9.],[-11.75,-10.3],'k-')
pyplot.plot([-6.,-6.],[-11.75,-10.3],'k-')
pyplot.plot([-9.,-6.],[-11.75,-11.75],'k-')
pyplot.plot([-9.,-6.],[-10.3,-10.3],'k-')
pyplot.plot([-6.,-3.4],[-10.3,-10.],'k:')
pyplot.plot([-9.,-8.85],[-10.3,-10.],'k:')
insetAxes= pyplot.axes([0.42,0.47,0.45,0.42])
pyplot.sca(insetAxes)
bovy_plot.bovy_plot(data[sindx,1],data[sindx,2],'k.',ms=2.,zorder=0.,
overplot=True)
if numpy.sum(True-sindx) > 0:
pindx= copy.copy(True-sindx)
pindx[0:9700]= False #subsample
bovy_plot.bovy_plot(data[pindx,1],data[pindx,2],'k,',
zorder=0.,
overplot=True)
bovy_plot.bovy_plot(pvec[0,:],pvec[1,:],'k--',overplot=True,lw=1.,
zorder=1)
sdf.plotTrack(d1=d1,d2=d2,interp=True,color='k',spread=0,
overplot=True,lw=1.,scaleToPhysical=True,zorder=2)
nullfmt = NullFormatter() # no labels
insetAxes.xaxis.set_major_formatter(nullfmt)
insetAxes.yaxis.set_major_formatter(nullfmt)
insetAxes.set_xlim(-9.,-6.)
insetAxes.set_ylim(-11.75,-10.3)
pyplot.tick_params(\
axis='both', # changes apply to the x-axis
which='both', # both major and minor ticks are affected
bottom='off', # ticks along the bottom edge are off
top='off', # ticks along the top edge are off
left='off', # ticks along the bottom edge are off
right='off') # ticks along the top edge are off
bovy_plot.bovy_end_print(plotfilename)
def plot_liouville(plotfilename):
E, Lz= -1.25, 0.6
aAS= actionAngleStaeckel(pot=MWPotential2014,c=True,delta=0.5)
#planarOrbit w/ the same energy
o= Orbit([0.8,numpy.sqrt(2.*(E-evalPot(0.8,0.,MWPotential2014)-(Lz/0.8)**2./2.)),Lz/0.8,0.])
#For the orbital period
fo= Orbit([0.8,numpy.sqrt(2.*(E-evalPot(0.8,0.,MWPotential2014)-(Lz/0.8)**2./2.)),Lz/0.8,0.,0.001,0.])
orbt= 2.*numpy.pi/aAS.actionsFreqs(fo)[4]
norb= 200.
nt= 20001
ts= numpy.linspace(0.,norb*orbt,nt)
start= time.time()
integrator= 'dopr54_c'
o.integrate_dxdv([1.,0.,0.,0.],ts,MWPotential2014,
method=integrator,
rectIn=True,rectOut=True)
dx= o.getOrbit_dxdv()[:,:]
o.integrate_dxdv([0.,1.,0.,0.],ts,MWPotential2014,
method=integrator,
rectIn=True,rectOut=True)
dy= o.getOrbit_dxdv()[:,:]
o.integrate_dxdv([0.,0.,1.,0.],ts,MWPotential2014,
method=integrator,
rectIn=True,rectOut=True)
dvx= o.getOrbit_dxdv()[:,:]
o.integrate_dxdv([0.,0.,0.,1.],ts,MWPotential2014,
method=integrator,
rectIn=True,rectOut=True)
dvy= o.getOrbit_dxdv()[:,:]
print integrator, time.time()-start
#Calculate Jacobian
jacs= numpy.array([numpy.linalg.det(numpy.array([dx[ii],dy[ii],
dvx[ii],dvy[ii]])) for ii in range(nt)])
breakt= 8.
pts= list(ts[ts < breakt])
pts.extend(list((ts[ts >= breakt])[::10]))
pts= numpy.array(pts)
pjacs= list(jacs[ts < breakt])
pjacs.extend(list((jacs[ts >= breakt])[::10]))
pjacs= numpy.array(pjacs)
print integrator, numpy.mean(jacs)-1.
bovy_plot.bovy_print(fig_width=3.25,fig_height=4.5)
pyplot.subplot(4,1,4)
bovy_plot.bovy_plot(pts/orbt,numpy.fabs(pjacs-1.),color='k',
loglog=True,gcf=True,
xrange=[0.5,norb],
yrange=[10.**-12.,10.**0.],
xlabel=r'$\mathrm{Number\ of\ orbital\ periods}$')
bovy_plot.bovy_text(r'$\texttt{dopr54\_c}$',
top_left=True,size=14.)
bovy_plot.bovy_text(0.1,10.**44.5,
r'$|\mathrm{Determinant\ of\ volume\ transformation}-1|$',
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.])
nullfmt = NullFormatter() # no labels
other_integrators= ['odeint',
'rk4_c','rk6_c']
for ii,integrator in enumerate(other_integrators):
start= time.time()
o.integrate_dxdv([1.,0.,0.,0.],ts,MWPotential2014,
method=integrator,
rectIn=True,rectOut=True)
dx= o.getOrbit_dxdv()[:,:]
o.integrate_dxdv([0.,1.,0.,0.],ts,MWPotential2014,
method=integrator,
rectIn=True,rectOut=True)
dy= o.getOrbit_dxdv()[:,:]
o.integrate_dxdv([0.,0.,1.,0.],ts,MWPotential2014,
method=integrator,
rectIn=True,rectOut=True)
dvx= o.getOrbit_dxdv()[:,:]
o.integrate_dxdv([0.,0.,0.,1.],ts,MWPotential2014,
method=integrator,
rectIn=True,rectOut=True)
dvy= o.getOrbit_dxdv()[:,:]
print integrator, time.time()-start
jacs= numpy.array([numpy.linalg.det(numpy.array([dx[jj],dy[jj],
dvx[jj],dvy[jj]])) for jj in range(nt)])
pts= list(ts[ts < breakt])
pts.extend(list((ts[ts >= breakt])[::10]))
pts= numpy.array(pts)
pjacs= list(jacs[ts < breakt])
pjacs.extend(list((jacs[ts >= breakt])[::10]))
pjacs= numpy.array(pjacs)
print integrator, numpy.mean(jacs)-1.
pyplot.subplot(4,1,ii+1)
if integrator == 'odeint':
yrange=[10.**-8.,10.**4.]
yticks= [10.**-8.,10.**-4.,1.,10.**4.]
else:
yrange=[10.**-12.,10.**0.]
yticks= [10.**-12.,10.**-8.,10.**-4.,1.]
bovy_plot.bovy_plot(pts/orbt,numpy.fabs(pjacs-1.),color='k',
loglog=True,gcf=True,
xrange=[0.5,norb],
yrange=yrange)
thisax= pyplot.gca()
thisax.xaxis.set_major_formatter(nullfmt)
thisax.yaxis.set_ticks(yticks)
bovy_plot.bovy_text(r'$\texttt{%s}$' % (integrator.replace('_','\_')),
top_left=True,size=14.)
bovy_plot.bovy_end_print(plotfilename)
return None
cluster = args[1]
N = int(args[2])
dwarves = int(args[3])
print("Started")
print("Including dwarves: ", dwarves == True)
ts = np.linspace(0., -12 * conv, 1201)
dt = (ts[1] - ts[0]) / 250
# SAGITTARIUS
sgr_M = 1.4E10 * u.Msun
sgr_a = 7 * u.kpc # 6.5kpc from https://arxiv.org/pdf/1608.04743.pdf
sgr_pot = HernquistPotential(amp=sgr_M, a=sgr_a, ro=8., vo=220.)
sgr_orbit = Orbit(vxvv=[283.8313, -30.5453, 26.67, -2.692, -1.359, 140],
radec=True,
ro=8.,
vo=220.)
sgr_orbit.integrate(ts, MWPotential2014, dt=dt)
sgr_potential = MovingObjectPotential(sgr_orbit, pot=sgr_pot)
# LMC
lmc_M = 1E11 * u.Msun # https://arxiv.org/pdf/1608.04743.pdf
lmc_a = 10.2 * u.kpc # https://iopscience.iop.org/article/10.1088/2041-8205/721/2/L97/pdf
lmc_pot = HernquistPotential(amp=lmc_M, a=lmc_a, ro=8., vo=220.)
lmc_orbit = Orbit(vxvv=[78.77, -69.01, 50.1, 1.850, 0.234, 262.2],
radec=True,
ro=8.,
vo=220.)
lmc_orbit.integrate(ts, MWPotential2014, dt=dt)
lmc_potential = MovingObjectPotential(lmc_orbit, pot=lmc_pot)
def action_analysis(cls):
try:
fd = open("data/db_9cl_orbits_good.pkl", "rb")
all_orbits = cp.load(fd)
fd.close()
except:
ucac_dict = ucac_pms()
position_dict = grab_other_spatials(cls)[0]
distance_dict = grab_other_spatials(cls)[1]
all_orbits = []
for cl in cls:
cluster_orbits = []
for star in cl:
try:
ra = float(position_dict[star][0])
dec = float(position_dict[star][1])
dist = float(distance_dict[star])
pmRA = float(ucac_dict[star][0])
pmDec = float(ucac_dict[star][2])
Vlos = float(position_dict[star][2])
#only attach where proper motions are available
if ucac_dict[star][-1] == '1':
cluster_orbits.append(Orbit(vxvv=[ra,dec,dist,pmRA,pmDec,Vlos],radec=True,ro=8.,vo=220., solarmotion = "schoenrich"))
except:
print("bad egg, spitting out")
continue
#only attach where proper motions are available
all_orbits.append(cluster_orbits)
print("ticking: ", len(all_orbits))
fd = open("data/db_9cl_orbits_good.pkl", "wb")
cp.dump(all_orbits, fd)
fd.close()
ts = np.linspace(0,100,10000)
mwp= MWPotential2014
#action angles yay!
#the following gets confusing because we speak of "means" twice
#we want the mean J over each individual orbit, but to measure the spread in the cluster
#we compare to the mean of each J
ro = 8
vo = 220
all_actions = []
fig = 1
for cluster_orbits in all_orbits:
all_js = np.array([])
for o in cluster_orbits:
o.integrate(ts,mwp,method='odeint')
# plt.plot(o.R(ts), o.z(ts))
try:
delta_o = estimateDeltaStaeckel(MWPotential2014,(o.R(ts))/ro,(o.z(ts))/ro)
aAS = actionAngleStaeckel(pot=MWPotential2014,delta = delta_o)
js_o = aAS((o.R())/ro,(o.vR())/vo,(o.vT())/vo,(o.z())/ro,(o.vz())/vo)
# delta_b = estimateBIsochrone(MWPotential2014, (o.R(ts))/ro,(o.z(ts))/ro)
# delta_b = delta_b[1]
# aAIA = actionAngleIsochroneApprox(pot=MWPotential2014,b = delta_b)
# js_o = aAIA((o.R())/ro,(o.vR())/vo,(o.vT())/vo,(o.z())/ro,(o.vz())/vo, nonaxi = True)
# print(js_o)
if all_js.shape == (0,):
all_js = js_o
else:
all_js = np.vstack([all_js, js_o])
except:
print("found unbound, discarded")
print(np.array(all_js).shape)
all_actions.append(all_js)
# plt.xlabel("R distance (kpc)")
# plt.ylabel("z distance (kpc)")
# plt.xlim(0, 20)
# plt.ylim(-5, 5)
# plt.title("Cluster " + str(fig)+ " Rz" + " Orbits")
# fn = open("dbcl_" + str(fig) + "_Rz" + ".png", "wb")
# plt.savefig("dbcl_" + str(fig) + "_Rz" + ".png")
# fn.close()
# plt.close()
fig += 1
return all_actions
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 calc_eccentricity(args, options):
table = os.path.join(args[0], 'table2.dat')
readme = os.path.join(args[0], 'ReadMe')
dierickx = ascii.read(table, readme=readme)
vxvv = np.dstack([
dierickx['RAdeg'], dierickx['DEdeg'], dierickx['Dist'] / 1e3,
dierickx['pmRA'], dierickx['pmDE'], dierickx['HRV']
])[0]
ro, vo, zo = 8., 220., 0.025
ra, dec = vxvv[:, 0], vxvv[:, 1]
lb = bovy_coords.radec_to_lb(ra, dec, degree=True)
pmra, pmdec = vxvv[:, 3], vxvv[:, 4]
pmllpmbb = bovy_coords.pmrapmdec_to_pmllpmbb(pmra,
pmdec,
ra,
dec,
degree=True)
d, vlos = vxvv[:, 2], vxvv[:, 5]
rectgal = bovy_coords.sphergal_to_rectgal(lb[:, 0],
lb[:, 1],
d,
vlos,
pmllpmbb[:, 0],
pmllpmbb[:, 1],
degree=True)
vsolar = np.array([-10.1, 4.0, 6.7])
vsun = np.array([
0.,
1.,
0.,
]) + vsolar / vo
X = rectgal[:, 0] / ro
Y = rectgal[:, 1] / ro
Z = rectgal[:, 2] / ro
vx = rectgal[:, 3] / vo
vy = rectgal[:, 4] / vo
vz = rectgal[:, 5] / vo
vsun = np.array([
0.,
1.,
0.,
]) + vsolar / vo
Rphiz = bovy_coords.XYZ_to_galcencyl(X, Y, Z, Zsun=zo / ro)
vRvTvz = bovy_coords.vxvyvz_to_galcencyl(vx,
vy,
vz,
Rphiz[:, 0],
Rphiz[:, 1],
Rphiz[:, 2],
vsun=vsun,
Xsun=1.,
Zsun=zo / ro,
galcen=True)
#do the integration and individual analytic estimate for each object
ts = np.linspace(0., 20., 10000)
lp = LogarithmicHaloPotential(normalize=1.)
e_ana = numpy.zeros(len(vxvv))
e_int = numpy.zeros(len(vxvv))
print(
'Performing orbit integration and analytic parameter estimates for Dierickx et al. sample...'
)
for i in tqdm(range(len(vxvv))):
try:
orbit = Orbit(vxvv[i], radec=True, vo=220., ro=8.)
e_ana[i] = orbit.e(analytic=True, pot=lp, c=True)
except UnboundError:
e_ana[i] = np.nan
orbit.integrate(ts, lp)
e_int[i] = orbit.e(analytic=False)
fig = plt.figure()
fig.set_size_inches(1.5 * columnwidth, 1.5 * columnwidth)
plt.scatter(e_int, e_ana, s=1, color='Black', lw=0.)
plt.xlabel(r'$\mathrm{galpy\ integrated}\ e$')
plt.ylabel(r'$\mathrm{galpy\ analytic}\ e$')
plt.xlim(0., 1.)
plt.ylim(0., 1.)
fig.tight_layout()
plt.savefig(os.path.join(args[0], 'dierickx-integratedeanalytice.png'),
format='png',
dpi=200)
fig = plt.figure()
fig.set_size_inches(1.5 * columnwidth, 1.5 * columnwidth)
plt.hist(e_int, bins=30)
plt.xlim(0., 1.)
plt.xlabel(r'$\mathrm{galpy}\ e$')
fig.tight_layout()
plt.savefig(os.path.join(args[0], 'dierickx-integratedehist.png'),
format='png',
dpi=200)
fig = plt.figure()
fig.set_size_inches(1.5 * columnwidth, 1.5 * columnwidth)
plt.scatter(dierickx['e'], e_int, s=1, color='Black', lw=0.)
plt.xlabel(r'$\mathrm{Dierickx\ et\ al.}\ e$')
plt.ylabel(r'$\mathrm{galpy\ integrated}\ e$')
plt.xlim(0., 1.)
plt.ylim(0., 1.)
fig.tight_layout()
plt.savefig(os.path.join(args[0], 'dierickx-integratedee.png'),
format='png',
dpi=200)
fig = plt.figure()
fig.set_size_inches(1.5 * columnwidth, 1.5 * columnwidth)
plt.scatter(dierickx['e'], e_ana, s=1, color='Black', lw=0.)
plt.xlabel(r'$\mathrm{Dierickx\ et\ al.}\ e$')
plt.ylabel(r'$\mathrm{galpy\ estimated}\ e$')
plt.xlim(0., 1.)
plt.ylim(0., 1.)
fig.tight_layout()
plt.savefig(os.path.join(args[0], 'dierickx-analyticee.png'),
format='png',
dpi=200)
arr = numpy.recarray(len(e_ana),
dtype=[('analytic_e', float),
('integrated_e', float)])
arr['analytic_e'] = e_ana
arr['integrated_e'] = e_int
with open(os.path.join(args[0], 'eccentricities.dat'), 'w') as file:
pickle.dump(arr, file)
file.close()
def test_orbitIntegrationC():
#_____initialize some KKSPot_____
Delta = 1.0
pot = KuzminKutuzovStaeckelPotential(ac=20.,Delta=Delta,normalize=True)
#_____initialize an orbit (twice)_____
vxvv = [1.,0.1,1.1,0.,0.1]
o_P= Orbit(vxvv=vxvv)
o_C= Orbit(vxvv=vxvv)
#_____integrate the orbit with python and C_____
ts= numpy.linspace(0,100,101)
o_P.integrate(ts,pot,method='leapfrog') #python
o_C.integrate(ts,pot,method='leapfrog_c')#C
for ii in range(5):
exp3= -1.7
if ii == 0: Python, CC, string, exp1, exp2 = o_P.R(ts) , o_C.R(ts) , 'R' , -5., -10.
elif ii == 1: Python, CC, string, exp1, exp2 = o_P.z(ts) , o_C.z(ts) , 'z' , -3.25, -4.
elif ii == 2: Python, CC, string, exp1, exp2 = o_P.vR(ts), o_C.vR(ts), 'vR', -3., -10.
elif ii == 3: Python, CC, string, exp1, exp2, exp3 = o_P.vz(ts), o_C.vz(ts), 'vz', -3., -4., -1.3
elif ii == 4: Python, CC, string, exp1, exp2 = o_P.vT(ts), o_C.vT(ts), 'vT', -5., -10.
rel_diff = numpy.fabs((Python-CC)/CC) < 10.**exp1
abs_diff = (numpy.fabs(Python-CC) < 10.**exp2) * (numpy.fabs(Python) < 10.**exp3)
assert numpy.all(rel_diff+abs_diff), \
'Orbit integration for '+string+' coordinate different in ' + \
'C and Python implementation.'
return None
def plot_sat_cluster(sat_galaxy, name_sat, sat_potential, xaxis_dim, yaxis_dim,
sat_mass, sat_size, x_satgal, y_satgal, z_satgal,
vx_satgal, vy_satgal, vz_satgal, tform, tsteady):
# Function plots orbits of satellite galaxy as well as a star cluster within the satellite galaxy - simulates accretion onto MW
#
# Input:
# sat_galaxy: an orbit object for a given satellite galaxy of the MW
# name_sat: string of the satellite galaxy's name
# sat_potential: potential object modelling the satellite's potential
# x and y axis dimensions to plot in (strings)
# x_satgal, y_satgal, z_satgal: x,y,z positions of the star_cluster within the satellite galaxy's frame of reference
# vx_satgal, vy_satgal, vz_satgal: x,y,z velocities of the star_cluster within the satellite galaxy's frame of reference
# mass and size of satellite to model dynamical friction effects (quantities with units attached)
# tform, tsteady: parameters of the potential, models tidal disruption of satellite galaxy (quantities with units attached)
#
# Output:
#
# end_pos_cluster: the coordinates for star cluster at end of integration (@ time tend: tform+5*units.Gyr)
# end_pos_gal: the coordinates for satellite galaxy at tend
# dswp: wrapper potential object that modifies satelltie galaxy to begin disrupting at tform
# cdf: model for dynamical friction force
t_back = 10.
ts = numpy.linspace(0., -t_back, 1000) * units.Gyr
cdf = ChandrasekharDynamicalFrictionForce(GMs=sat_mass,
rhm=sat_size,
dens=mw)
sat_galaxy.integrate(ts, mw + cdf)
'''
R_sat = sat_galaxy.R(-t_back*units.Gyr) #cylindrical radius at time t
vR_sat = sat_galaxy.vR(-t_back*units.Gyr) #radial velocity at time t
vT_sat = sat_galaxy.vT(-t_back*units.Gyr) #tangential velocity at time t
z_sat = sat_galaxy.z(-t_back*units.Gyr) #vertical height at time t
vz_sat = sat_galaxy.vz(-t_back*units.Gyr) #vertical velocity at time t
phi_sat = sat_galaxy.phi(-t_back*units.Gyr) #azimuth at time t
'''
# Rectangular coordinates and velocities
coord = [
sat_galaxy.x(-t_back * units.Gyr),
sat_galaxy.y(-t_back * units.Gyr),
sat_galaxy.z(-t_back * units.Gyr)
]
vcoord = [
sat_galaxy.vx(-t_back * units.Gyr),
sat_galaxy.vy(-t_back * units.Gyr),
sat_galaxy.vz(-t_back * units.Gyr)
]
t_fwrd = 15
ts_f = numpy.linspace(-t_back, -t_back + t_fwrd, 1000) * units.Gyr
sat_galaxy = sat_galaxy(-t_back * units.Gyr)
sat_galaxy.integrate(ts_f, mw + cdf)
sat_galaxy.plot(
d1=xaxis_dim,
d2=yaxis_dim,
linestyle=':',
color='black',
label='satellite'
) #plots orbit of the satellite galaxy in MW frame of reference
#!!sat_pot = HernquistPotential(amp = 2*sat_mass, a = sat_size, ro = 8., vo=220.)
sat_movingpot = MovingObjectPotential(sat_galaxy, sat_potential)
# Transform from satellite galaxy's frame of reference to Milky Way Galaxy's frame of reference (using Cartesian coordinates)
# Rectangular coordinates of the star cluster in galactocentric frame
x_gal = coord[0] + x_satgal
y_gal = coord[1] + y_satgal
z_gal = coord[2] + z_satgal
# Velocity of the star cluster in galactocentric frame
vx_gal = vcoord[0] + vx_satgal
vy_gal = vcoord[1] + vy_satgal
vz_gal = vcoord[2] + vz_satgal
# Transform to cylindrical coordinate system: R, phi, z
R, phi, z = rect_to_cyl(x_gal, y_gal, z_gal)
vR, vT, vz = rect_to_cyl_vec(vx_gal,
vy_gal,
vz_gal,
x_gal,
y_gal,
z_gal,
cyl=False)
star_cluster = Orbit(vxvv=[R, vR, vT, z, vz, phi], ro=8., vo=220.)
star_cluster.integrate(ts_f, mw + sat_movingpot)
star_cluster.plot(
d1=xaxis_dim,
d2=yaxis_dim,
linestyle='-',
overplot=True,
color='blue',
alpha=0.6,
label='star cluster'
) #plots orbit of the star_cluster in MW frame of reference
plt.title('Orbit of Star Cluster Within Satellite Galaxy: ' + name_sat +
' in Galactocentric Frame')
plt.legend()
plt.show()
plt.close()
# Implement wrapper potential to simulate tidal disruption of satellite galaxy
# Plot orbit of the satellite galaxy and star cluster within sat galaxy in MW frame of reference:
plt.figure(figsize=(12., 10.))
tstart = tform - 5. * units.Gyr
tend = tform + 5. * units.Gyr
time_int = numpy.linspace(tstart.to_value(units.Gyr),
tend.to_value(units.Gyr), 1000) * units.Gyr
if tstart < -t_back * units.Gyr:
# re-integrate satellite galaxy from current time back to tstart
re_time = numpy.linspace(-t_back, tstart.to_value(units.Gyr),
1000) * units.Gyr
sat_galaxy.integrate(re_time, mw + cdf)
# initialize star cluster on orbit in satellite galaxy at time tstart:
# Rectangular coordinates and velocities
coord = [
sat_galaxy.x(tstart),
sat_galaxy.y(tstart),
sat_galaxy.z(tstart)
]
vcoord = [
sat_galaxy.vx(tstart),
sat_galaxy.vy(tstart),
sat_galaxy.vz(tstart)
]
# Transform from satellite galaxy's frame of reference to Milky Way Galaxy's frame of reference (using Cartesian coordinates)
# Rectangular coordinates of the star cluster in galactocentric frame
x_gal = coord[0] + x_satgal
y_gal = coord[1] + y_satgal
z_gal = coord[2] + z_satgal
# Velocity of the star cluster in galactocentric frame
vx_gal = vcoord[0] + vx_satgal
vy_gal = vcoord[1] + vy_satgal
vz_gal = vcoord[2] + vz_satgal
# Transform to cylindrical coordinate system: R, phi, z
R, phi, z = rect_to_cyl(x_gal, y_gal, z_gal)
vR, vT, vz = rect_to_cyl_vec(vx_gal,
vy_gal,
vz_gal,
x_gal,
y_gal,
z_gal,
cyl=False)
# Re-initialize star cluster on orbit at time tstart
star_cluster = Orbit(vxvv=[R, vR, vT, vz, z, phi], ro=8., vo=220.)
else:
# default: star cluster is initialized at -10Gyr in given satellite galaxy
star_cluster = star_cluster(tstart)
sat_galaxy = sat_galaxy(
tstart) #make copy of sat_galaxy orbit at time tstart
sat_galaxy.integrate(time_int,
mw + cdf) # integrate sat_galaxy forward for 10Gyrs
sat_galaxy.plot(d1=xaxis_dim,
d2=yaxis_dim,
linestyle=':',
color='black',
label='satellite galaxy')
sat_movingpot = MovingObjectPotential(sat_galaxy, sat_potential)
dswp = DehnenSmoothWrapperPotential(amp=1.0,
pot=sat_movingpot,
tform=tform,
tsteady=tsteady,
decay=True)
star_cluster.integrate(time_int, mw + dswp)
# star cluster in combined potential: MW galaxy & moving potential of satellite galaxy
star_cluster.plot(d1 = xaxis_dim, d2= yaxis_dim, linestyle = '-', overplot = True, color = 'blue', alpha = 0.6,\
label = 'star cluster')
#plots orbit of the star_cluster in MW frame of reference
plt.legend()
plt.title('Star Cluster Orbit Within: ' + name_sat + ' for Tform = ' +
str(tform) + ' & Tsteady = ' + str(tsteady) +
' in Galactocentric Frame')
plt.savefig('WrapperPotential-Decaying Mass.pdf')
plt.show()
plt.close()
# Figure out where star cluster is at end of integration: at tend
end_pos_cluster = [
star_cluster.R(tend),
star_cluster.vR(tend),
star_cluster.vT(tend),
star_cluster.z(tend),
star_cluster.vz(tend),
star_cluster.phi(tend)
]
# [R,vT,vT,z,vz,phi]
end_pos_gal = [
sat_galaxy.R(tend),
sat_galaxy.vR(tend),
sat_galaxy.vT(tend),
sat_galaxy.z(tend),
sat_galaxy.vz(tend),
sat_galaxy.phi(tend)
]
'''
# Used for finding dswp when integrating satellite galaxy backward in previous version of code
time_intb = numpy.linspace(tend.to_value(units.Gyr), tstart.to_value(units.Gyr), 1000)*units.Gyr
star_cluster_b = Orbit(vxvv = end_pos_cluster, ro=8., vo =220.) #full 6 coordinates
sat_galaxy_b = Orbit(vxvv=end_pos_gal, ro=8., vo =220.)
sat_galaxy_b.integrate(time_intb, mw + cdf)
sat_galaxy_b.plot(d1 = xaxis_dim, d2= yaxis_dim,linestyle = ':', color = 'black', label = 'satellite galaxy')
sat_movingpot_b = MovingObjectPotential(sat_galaxy_b, sat_potential)
#new_tform = tform - end_t
#dswp_back = DehnenSmoothWrapperPotential(amp=1.0, pot = sat_movingpot_b, tform=tform, tsteady=tsteady, decay = True)
star_cluster_b.integrate(time_intb, mw + dswp) # star cluster is in combined potential of MW galaxy and the moving potential of satellite galaxy
star_cluster_b.plot(d1 = xaxis_dim, d2= yaxis_dim, linestyle = '-', overplot = True, color = 'blue', alpha = 0.6,\
label = 'star cluster') # galactocentric radius as a function of time
plt.legend()
plt.title('Orbit of Star Cluster Within Satellite Galaxy for Tform = ' + str(tform) + ' & Tsteady = ' + str(tsteady) + ' (in Galactocentric Frame)')
plt.show()
plt.close()
'''
return end_pos_cluster, end_pos_gal, dswp, cdf
def test_qdf():
from galpy.df import quasiisothermaldf
from galpy.potential import MWPotential2014
from galpy.actionAngle import actionAngleStaeckel
# Setup actionAngle instance for action calcs
aAS = actionAngleStaeckel(pot=MWPotential2014, delta=0.45, c=True)
# Quasi-iso df w/ hr=1/3, hsr/z=1, sr(1)=0.2, sz(1)=0.1
df = quasiisothermaldf(1. / 3.,
0.2,
0.1,
1.,
1.,
aA=aAS,
pot=MWPotential2014)
# Evaluate DF w/ R,vR,vT,z,vz
df(0.9, 0.1, 0.8, 0.05, 0.02)
assert numpy.fabs(
df(0.9, 0.1, 0.8, 0.05, 0.02) - numpy.array([123.57158928])
) < 10.**-4., 'qdf does not behave as expected'
# Evaluate DF w/ Orbit instance, return ln
from galpy.orbit import Orbit
df(Orbit([0.9, 0.1, 0.8, 0.05, 0.02]), log=True)
assert numpy.fabs(
df(Orbit([0.9, 0.1, 0.8, 0.05, 0.02]), log=True) - numpy.array(
[4.81682066])) < 10.**-4., 'qdf does not behave as expected'
# Evaluate DF marginalized over vz
df.pvRvT(0.1, 0.9, 0.9, 0.05)
assert numpy.fabs(df.pvRvT(0.1, 0.9, 0.9, 0.05) - 2. * 23.273310451852243
) < 10.**-4., 'qdf does not behave as expected'
#NOTE: The pvRvT() function has changed with respect to the version used in Bovy (2015).
# As of January 2018, a prefactor of 2 has been added (=nsigma/2 with default nsigma=4),
# to account for the correct Gauss-Legendre integration normalization.
# Evaluate DF marginalized over vR,vT
df.pvz(0.02, 0.9, 0.05)
assert numpy.fabs(df.pvz(0.02, 0.9, 0.05) - 50.949586235238172
) < 10.**-4., 'qdf does not behave as expected'
# Calculate the density
df.density(0.9, 0.05)
assert numpy.fabs(df.density(0.9, 0.05) - 12.73725936526167
) < 10.**-4., 'qdf does not behave as expected'
# Estimate the DF's actual density scale length at z=0
df.estimate_hr(0.9, 0.)
assert numpy.fabs(df.estimate_hr(0.9, 0.) - 0.322420336223
) < 10.**-2., 'qdf does not behave as expected'
# Estimate the DF's actual surface-density scale length
df.estimate_hr(0.9, None)
assert numpy.fabs(df.estimate_hr(0.9, None) - 0.38059909132766462
) < 10.**-4., 'qdf does not behave as expected'
# Estimate the DF's density scale height
df.estimate_hz(0.9, 0.02)
assert numpy.fabs(df.estimate_hz(0.9, 0.02) - 0.064836202345657207
) < 10.**-4., 'qdf does not behave as expected'
# Calculate the mean velocities
df.meanvR(0.9, 0.05), df.meanvT(0.9, 0.05),
df.meanvz(0.9, 0.05)
assert numpy.fabs(df.meanvR(0.9, 0.05) - 3.8432265354618213e-18
) < 10.**-4., 'qdf does not behave as expected'
assert numpy.fabs(df.meanvT(0.9, 0.05) - 0.90840425173325279
) < 10.**-4., 'qdf does not behave as expected'
assert numpy.fabs(df.meanvz(0.9, 0.05) + 4.3579787517991084e-19
) < 10.**-4., 'qdf does not behave as expected'
# Calculate the velocity dispersions
from numpy import sqrt
sqrt(df.sigmaR2(0.9, 0.05)), sqrt(df.sigmaz2(0.9, 0.05))
assert numpy.fabs(sqrt(df.sigmaR2(0.9, 0.05)) - 0.22695537077102387
) < 10.**-4., 'qdf does not behave as expected'
assert numpy.fabs(sqrt(df.sigmaz2(0.9, 0.05)) - 0.094215523962105044
) < 10.**-4., 'qdf does not behave as expected'
# Calculate the tilt of the velocity ellipsoid
# 2017/10-28: CHANGED bc tilt now returns angle in rad, no longer in deg
df.tilt(0.9, 0.05)
assert numpy.fabs(
df.tilt(0.9, 0.05) - 2.5166061974413765 / 180. *
numpy.pi) < 10.**-4., 'qdf does not behave as expected'
# Calculate a higher-order moment of the velocity DF
df.vmomentdensity(0.9, 0.05, 6., 2., 2., gl=True)
assert numpy.fabs(
df.vmomentdensity(0.9, 0.05, 6., 2., 2., gl=True) -
0.0001591100892366438) < 10.**-4., 'qdf does not behave as expected'
# Sample velocities at given R,z, check mean
numpy.random.seed(1)
vs = df.sampleV(0.9, 0.05, n=500)
mvt = numpy.mean(vs[:, 1])
assert numpy.fabs(numpy.mean(vs[:, 0])) < 0.05 # vR
assert numpy.fabs(mvt - df.meanvT(0.9, 0.05)) < 0.01 #vT
assert numpy.fabs(numpy.mean(vs[:, 2])) < 0.05 # vz
return None
def pec_v(ra, dec, d, pm_ra, pm_dec, V):
"""
Function to estimate system peculiar velocity distribution as a function of distance.
ra,dec,d,pm_ra,pm_dec,V are source orbit parameters for Galpy
numpoints is the number of points in the orbit to integrate.
"""
o = Orbit([
ra * u.deg, dec * u.deg, d * u.kpc, pm_ra * u.mas / u.yr,
pm_dec * u.mas / u.yr, V * u.km / u.s
],
radec=True)
o2 = Orbit(vxvv=[o.R(0.) / 8.0, 0., 1., 0., 0., o.phi(0.)], ro=8., vo=220.)
current_vel = np.sqrt((o.U(0.) - o2.U(0) + 11.1)**2 +
(o.V(0.) - o2.V(0) + 12.24)**2 +
(o.W(0.) - o2.W(0) + 7.25)**2)
return current_vel
