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 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 cluster_dynamics(cluster):
orbits = []
dist_dict = dict(cluster[2])
for i in cluster[1]:
ra = float(i[0])
dec = float(i[1])
dist = float(dist_dict[i[-1]])
pmRA = float(i[2])
pmDec = float(i[3])
Vlos = float(i[4])
#only attach where proper motions are available
if dist != 0.0:
if pmRA != 0.0:
if pmDec != 0.0:
orbits.append(
Orbit(vxvv=[ra, dec, dist, pmRA, pmDec, Vlos],
radec=True,
ro=8.,
vo=220.,
solarmotion="schoenrich"))
ts = np.linspace(0, 100, 10000)
mwp = MWPotential2014
print(len(orbits))
#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
mean_js = np.array([])
for o in orbits:
try:
o.integrate(ts, mwp, method='odeint')
delta_o = estimateDeltaStaeckel(MWPotential2014, (o.R()) / ro,
(o.z()) / vo)
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)
#the next line isn't really needed unless js is actually a vector, for t = 0 it is not
mean_o_js = np.array(
[js_o[0].mean(), js_o[1].mean(), js_o[2].mean()])
if mean_js.shape == (0, ):
mean_js = mean_o_js
else:
mean_js = np.vstack([mean_js, mean_o_js])
except:
print("found unbound, discarded")
#in this case the orbit is unbound -- this f***s up the whole thing I know
pass
print(mean_js.shape)
#so for this cluster we have a 3 x cluster length array
cluster_mean_js = np.array(
[mean_js.T[0].mean(), mean_js.T[1].mean(), mean_js.T[2].mean()])
#average_difference
diffs = np.absolute((mean_js - cluster_mean_js)) / cluster_mean_js
dynamics_summary = np.array(
[diffs.T[0].mean(), diffs.T[1].mean(), diffs.T[2].mean()])
return dynamics_summary
def estimate_delta(orbit,
ts=numpy.linspace(0., 20., 1001),
pot=MWPotential2014):
'''
estimate delta for a given orbit instance
'''
orbit.integrate(ts, pot, method='symplec4_c')
return estimateDeltaStaeckel(pot, orbit.R(ts), orbit.z(ts))
def test_staeckel_fudge_delta():
import galpy.potential as galpy_pot
from galpy.actionAngle import estimateDeltaStaeckel
ro = 8.1 * u.kpc
vo = 229 * u.km / u.s
paired_potentials = []
# Miyamoto-Nagai
potential = gp.MiyamotoNagaiPotential(m=6e10 * u.Msun,
a=3 * u.kpc,
b=0.3 * u.kpc,
units=galactic)
amp = (G * potential.parameters['m']).to_value(vo**2 * ro)
a = potential.parameters['a'].to_value(ro)
b = potential.parameters['b'].to_value(ro)
galpy_potential = galpy_pot.MiyamotoNagaiPotential(amp=amp,
a=a,
b=b,
ro=ro,
vo=vo)
paired_potentials.append((potential, galpy_potential))
# Hernquist
potential = gp.HernquistPotential(m=6e10 * u.Msun,
c=0.3 * u.kpc,
units=galactic)
amp = (G * potential.parameters['m']).to_value(vo**2 * ro)
a = potential.parameters['c'].to_value(ro)
galpy_potential = galpy_pot.HernquistPotential(amp=amp, a=a, ro=ro, vo=vo)
paired_potentials.append((potential, galpy_potential))
# NFW
potential = gp.NFWPotential(m=6e11 * u.Msun,
r_s=15.6 * u.kpc,
units=galactic)
amp = (G * potential.parameters['m']).to_value(vo**2 * ro)
a = potential.parameters['r_s'].to_value(ro)
galpy_potential = galpy_pot.NFWPotential(amp=amp, a=a, ro=ro, vo=vo)
paired_potentials.append((potential, galpy_potential))
# TEST:
N = 1024
rnd = np.random.default_rng(42)
w = PhaseSpacePosition(pos=rnd.uniform(-10, 10, size=(3, N)) * u.kpc,
vel=rnd.uniform(-100, 100, size=(3, N)) * u.km /
u.s)
R = w.cylindrical.rho.to_value(ro)
z = w.z.to_value(ro)
for p, galpy_p in paired_potentials:
galpy_deltas = estimateDeltaStaeckel(galpy_p, R, z, no_median=True)
gala_deltas = get_staeckel_fudge_delta(p, w).value
print(p, np.allclose(gala_deltas, galpy_deltas))
assert np.allclose(gala_deltas, galpy_deltas, atol=1e-6)
def 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 params_along_orbit(orbit, ts, pot=MWPotential2014, delta=0.375):
'''
estimate the orbit parameters along an orbit
'''
orbit.integrate(ts, pot, method='symplec4_c')
Rs = orbit.R(ts)
vRs = orbit.vR(ts)
vTs = orbit.vT(ts)
zs = orbit.z(ts)
vzs = orbit.vz(ts)
phis = orbit.phi(ts)
aAS = actionAngleStaeckel(pot=pot, delta=delta)
if delta == 'along':
delta = estimateDeltaStaeckel(pot, Rs, zs, no_median=True)
es, zms, rps, ras = aAS.EccZmaxRperiRap(Rs,
vRs,
vTs,
zs,
vzs,
phis,
delta=delta)
return es, zms, rps, ras
def process_single(i):
vxvv = [ra[i], dec[i], distance[i], pmra[i], pmdec[i], rv[i]]
if not np.all(np.isfinite(vxvv)) or not np.all(np.isfinite(covariance[i])):
return np.ones(56) * np.nan
samp = np.random.multivariate_normal(vxvv, covariance[i], size=1000)
if not (np.all(samp[:, 1] < 90.) & np.all(samp[:, 1] > -90.)):
return np.ones(56) * np.nan
os = Orbit(np.array([
samp[:, 0], samp[:, 1], samp[:, 2], samp[:, 3], samp[:, 4], samp[:, 5]
]).T,
radec=True,
ro=_R0,
vo=_v0,
zo=_z0,
solarmotion=[-11.1, 25.7, 7.25])
sXYZ = np.dstack([os.x(), os.y(), os.z()])[0] / _R0
sRpz = np.dstack([os.R() / _R0, os.phi(), os.z() / _R0])[0]
svRvTvz = np.dstack([os.vR(), os.vT(), os.vz()])[0] / _v0
deltas = estimateDeltaStaeckel(MWPotential2014,
np.median(sRpz[:, 0]),
np.median(sRpz[:, 2]),
no_median=True)
aAS = actionAngleStaeckel(pot=MWPotential2014, delta=np.mean(deltas))
e, zmax, rperi, rap = aAS.EccZmaxRperiRap(sRpz[:, 0],
svRvTvz[:, 0],
svRvTvz[:, 1],
sRpz[:, 2],
svRvTvz[:, 2],
sRpz[:, 1],
delta=deltas)
tcov = np.cov(np.dstack([e, zmax, rperi, rap])[0].T)
errs = np.sqrt(np.diag(tcov))
e_zmax_corr = tcov[0, 1] / (errs[0] * errs[1])
e_rperi_corr = tcov[0, 2] / (errs[0] * errs[2])
e_rap_corr = tcov[0, 3] / (errs[0] * errs[3])
zmax_rperi_corr = tcov[1, 2] / (errs[1] * errs[2])
zmax_rap_corr = tcov[1, 3] / (errs[1] * errs[3])
rperi_rap_corr = tcov[2, 3] / (errs[2] * errs[3])
e_err, zmax_err, rperi_err, rap_err = errs
action = np.array(
aAS.actionsFreqsAngles(sRpz[:, 0], svRvTvz[:, 0], svRvTvz[:, 1],
sRpz[:, 2], svRvTvz[:, 2], sRpz[:, 1]))
tcov_after_action = np.cov(action)
errs = np.sqrt(np.diag(tcov_after_action))
jr_lz_corr = tcov_after_action[0, 1] / (errs[0] * errs[1])
jr_jz_corr = tcov_after_action[0, 2] / (errs[0] * errs[2])
lz_jz_corr = tcov_after_action[1, 2] / (errs[1] * errs[2])
jr_err, lz_err, jz_err, or_err, op_err, oz_err, tr_err, tphi_err, tz_err = errs
Rc = np.array([rl(MWPotential2014, lz) for lz in action[1]]) * _R0
Ec = (evaluatePotentials(MWPotential2014, Rc, 0.) + 0.5 *
(action[1])**2. / Rc**2.) * _v0**2
E = os.E(pot=MWPotential2014)
# galactocentric coord and vel uncertainty
galcen_tcov = np.cov(np.dstack([sRpz[:, 0], sRpz[:, 1], sRpz[:, 2]])[0].T)
galcen_errs = np.sqrt(np.diag(galcen_tcov))
galr_err, galphi_err, galz_err = galcen_errs
galcenv_tcov = np.cov(
np.dstack([svRvTvz[:, 0], svRvTvz[:, 1], svRvTvz[:, 2]])[0].T)
galcenv_errs = np.sqrt(np.diag(galcenv_tcov))
galvr_err, galvt_err, galvz_err = galcenv_errs
galvr_galvt_corr = galcenv_tcov[0, 1] / (galcenv_errs[0] * galcenv_errs[1])
galvr_galvz_corr = galcenv_tcov[0, 2] / (galcenv_errs[0] * galcenv_errs[2])
galvt_galvz_corr = galcenv_tcov[1, 2] / (galcenv_errs[1] * galcenv_errs[2])
# galr mean to avoid issue near GC, error propagation
x_mean = np.nanmean(sXYZ[:, 0])
y_mean = np.nanmean(sXYZ[:, 1])
x_err = np.nanstd(sXYZ[:, 0])
y_err = np.nanstd(sXYZ[:, 1])
x_err_percentage = x_err / np.nanmean(sXYZ[:, 0])
y_err_percentage = y_err / np.nanmean(sXYZ[:, 1])
x2_err = (x_mean**2) * (2 * x_err_percentage)
y2_err = (y_mean**2) * (2 * y_err_percentage)
galr = np.sqrt(x_mean**2 + y_mean**2)
galr2_err = np.sqrt(x2_err**2 + y2_err**2)
galr2_err_percentage = galr2_err / (galr**2)
galr_err = galr * (0.5 * galr2_err_percentage)
# galphi mean to avoid issue near GC, error propagation
galphi = np.arctan2(y_mean, x_mean)
galphi_err_x = (
y_mean /
(x_mean**2 + y_mean**2)) * x_err # error propagation from x_mean
galphi_err_y = (
-x_mean /
(x_mean**2 + y_mean**2)) * y_err # error propagation from y_mean
galphi_err = np.sqrt(galphi_err_x**2 + galphi_err_y**2) # add them up
return np.nanmean(e), \
e_err, \
np.nanmean(zmax) * _R0, \
zmax_err * _R0, \
np.nanmean(rperi) * _R0, \
rperi_err * _R0, \
np.nanmean(rap) * _R0, \
rap_err * _R0, \
e_zmax_corr, \
e_rperi_corr, \
e_rap_corr, \
zmax_rperi_corr, \
zmax_rap_corr, \
rperi_rap_corr, \
np.nanmean(action[0]) * _R0 * _v0, \
jr_err * _R0 * _v0, \
np.nanmean(action[1]) * _R0 * _v0, \
lz_err * _R0 * _v0, \
np.nanmean(action[2]) * _R0 * _v0, \
jz_err * _R0 * _v0, \
jr_lz_corr, \
jr_jz_corr, \
lz_jz_corr, \
np.nanmean(action[3]) * _freq, or_err * _freq, \
np.nanmean(action[4]) * _freq, op_err * _freq, \
np.nanmean(action[5]) * _freq, oz_err * _freq, \
np.nanmean(action[6]), \
tr_err, \
np.nanmean(action[7]), \
tphi_err, \
np.nanmean(action[8]), \
tz_err, \
np.nanmean(Rc), \
np.nanstd(Rc), \
np.nanmean(E), \
np.nanstd(E), \
np.nanmean(E - Ec), \
np.nanstd(E - Ec), \
galr * _R0, \
galphi, \
np.nanmean(sRpz[:, 2]) * _R0, \
np.nanmean(svRvTvz[:, 0]) * _v0, \
np.nanmean(svRvTvz[0, 1]) * _v0, \
np.nanmean(svRvTvz[:, 2]) * _v0, \
galr_err * _R0, \
galphi_err, \
galz_err * _R0, \
galvr_err * _v0, \
galvt_err * _v0, \
galvz_err * _v0, \
galvr_galvt_corr, \
galvr_galvz_corr, \
galvt_galvz_corr
def process_single(i):
vxvv = [ra[i], dec[i], distance[i], pmra[i], pmdec[i], rv[i]]
if not np.all(np.isfinite(vxvv)) or not np.all(np.isfinite(covariance[i])):
return np.ones(56) * np.nan
samp = np.random.multivariate_normal(vxvv, covariance[i], size=1000)
if not (np.all(samp[:, 1] < 90.) & np.all(samp[:, 1] > -90.)):
return np.ones(56) * np.nan
sXYZ, svxyz, sRpz, svRvTvz = obs_to_galcen(samp[:, 0],
samp[:, 1],
samp[:, 2],
samp[:, 3],
samp[:, 4],
samp[:, 5],
ro=_R0,
vo=_v0,
zo=_z0)
deltas = estimateDeltaStaeckel(MWPotential2014, np.median(sRpz[:, 0]), np.median(sRpz[:, 2]), no_median=True)
aAS = actionAngleStaeckel(pot=MWPotential2014, delta=np.mean(deltas))
e, zmax, rperi, rap = aAS.EccZmaxRperiRap(sRpz[:, 0],
svRvTvz[:, 0],
svRvTvz[:, 1],
sRpz[:, 2],
svRvTvz[:, 2],
sRpz[:, 1], delta=deltas)
tcov = np.cov(np.dstack([e, zmax, rperi, rap])[0].T)
errs = np.sqrt(np.diag(tcov))
e_zmax_corr = tcov[0, 1] / (errs[0] * errs[1])
e_rperi_corr = tcov[0, 2] / (errs[0] * errs[2])
e_rap_corr = tcov[0, 3] / (errs[0] * errs[3])
zmax_rperi_corr = tcov[1, 2] / (errs[1] * errs[2])
zmax_rap_corr = tcov[1, 3] / (errs[1] * errs[3])
rperi_rap_corr = tcov[2, 3] / (errs[2] * errs[3])
e_err, zmax_err, rperi_err, rap_err = errs
action = np.array(
aAS.actionsFreqsAngles(sRpz[:, 0], svRvTvz[:, 0], svRvTvz[:, 1], sRpz[:, 2], svRvTvz[:, 2], sRpz[:, 1]))
tcov_after_action = np.cov(action)
errs = np.sqrt(np.diag(tcov_after_action))
jr_lz_corr = tcov_after_action[0, 1] / (errs[0] * errs[1])
jr_jz_corr = tcov_after_action[0, 2] / (errs[0] * errs[2])
lz_jz_corr = tcov_after_action[1, 2] / (errs[1] * errs[2])
jr_err, lz_err, jz_err, or_err, op_err, oz_err, tr_err, tphi_err, tz_err = errs
Rc = np.array([rl(MWPotential2014, lz) for lz in action[1]]) * _R0
Ec = (evaluatePotentials(MWPotential2014, Rc, 0.) + 0.5 * (action[1]) ** 2. / Rc ** 2.) * _v0 ** 2
E = (evaluatePotentials(MWPotential2014, sRpz[:, 0], sRpz[:, 2], phi=sRpz[:, 1]) + np.sum(svRvTvz ** 2 / 2.,
axis=1)) * _v0 ** 2
# galactocentric coord and vel uncertainty
galcen_tcov = np.cov(np.dstack([sRpz[:, 0], sRpz[:, 1], sRpz[:, 2]])[0].T)
galcen_errs = np.sqrt(np.diag(galcen_tcov))
galr_err, galphi_err, galz_err = galcen_errs
galcenv_tcov = np.cov(np.dstack([svRvTvz[:, 0], svRvTvz[:, 1], svRvTvz[:, 2]])[0].T)
galcenv_errs = np.sqrt(np.diag(galcenv_tcov))
galvr_err, galvt_err, galvz_err = galcenv_errs
galvr_galvt_corr = galcenv_tcov[0, 1] / (galcenv_errs[0] * galcenv_errs[1])
galvr_galvz_corr = galcenv_tcov[0, 2] / (galcenv_errs[0] * galcenv_errs[2])
galvt_galvz_corr = galcenv_tcov[1, 2] / (galcenv_errs[1] * galcenv_errs[2])
return np.nanmean(e), e_err, np.nanmean(zmax) * _R0, zmax_err * _R0, np.nanmean(
rperi) * _R0, rperi_err * _R0, np.nanmean(rap) * _R0, rap_err * _R0, \
e_zmax_corr, e_rperi_corr, e_rap_corr, zmax_rperi_corr, zmax_rap_corr, rperi_rap_corr, \
np.nanmean(action[0]) * _R0 * _v0, jr_err * _R0 * _v0, np.nanmean(
action[1]) * _R0 * _v0, lz_err * _R0 * _v0, np.nanmean(action[2]) * _R0 * _v0, jz_err * _R0 * _v0, \
jr_lz_corr, jr_jz_corr, lz_jz_corr, \
np.nanmean(action[3]) * _freq, or_err * _freq, np.nanmean(action[4]) * _freq, op_err * _freq, np.nanmean(
action[5]) * _freq, oz_err * _freq, \
np.nanmean(action[6]), tr_err, np.nanmean(action[7]), tphi_err, np.nanmean(action[8]), tz_err, \
np.nanmean(Rc), np.nanstd(Rc), np.nanmean(E), np.nanstd(E), np.nanmean(E - Ec), np.nanstd(
E - Ec), \
np.nanmean(sRpz[:, 0]) * _R0, \
np.nanmean(sRpz[:, 1]), \
np.nanmean(sRpz[:, 2]) * _R0, \
np.nanmean(svRvTvz[:, 0]) * _v0, \
np.nanmean(svRvTvz[0, 1]) * _v0, \
np.nanmean(svRvTvz[:, 2]) * _v0, \
galr_err * _R0, \
galphi_err, \
galz_err * _R0, \
galvr_err * _v0, \
galvt_err * _v0, \
galvz_err * _v0, \
galvr_galvt_corr, \
galvr_galvz_corr, \
galvt_galvz_corr
delta = (delta_x**2 + delta_y**2 + delta_z**2)**0.5
plt.semilogy(sun.time(ts), delta*1000)
#action angles portion:
#actionanglesAdiabatic for MWpotential2014
#if we want it for comparison:
#aAA_sun = actionAngleAdiabatic(pot=MWPotential2014)
#js_aaa_sun = aAA_sun(sun.R(ts),sun.vR(ts),sun.vT(ts),sun.z(ts),sun.vz(ts))
#
#convert into natural shit
ro = 8
vo = 220
delta_sun = estimateDeltaStaeckel(MWPotential2014,(sun.R(ts))/ro, (sun.z(ts))/vo)
aAS_sun = actionAngleStaeckel(pot=MWPotential2014,delta = delta_sun)
js_sun = aAS_sun((sun.R())/ro,(sun.vR())/vo,(sun.vT())/vo,(sun.z())/ro,(sun.vz())/vo)
mean_js = np.array([js_sun[0].mean(), js_sun[1].mean(), js_sun[2].mean()])
print("going for the big fella")
for o in orbits:
try:
#quick method: only first instance
delta_o = estimateDeltaStaeckel(MWPotential2014,(o.R(ts))/ro,(o.z(ts))/ro)
# plt.plot(js[0] - js_sun[0], ts)
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)
mean_o_js = np.array([js_o[0].mean(), js_o[1].mean(), js_o[2].mean()])
mean_js = np.vstack([mean_js, mean_o_js])
except:
def computeKinematics(ra,
dec,
dist,
pm_ra,
pm_dec,
rv,
R0=8.,
Z0=20.,
V0=240.,
Vlsd=[11.1, 12.24, 7.25]):
'''
Compute kinematics
Parameters
----------
ra : float
Right ascension of the star (in degree)
dec : float
Declination of the star (in degree)
dist : float
Distance to the star (in kpc)
pm_ra : float
Proper motion in right ascension * cos(dec) (in mas/yr)
pm_dec : float
Proper motion in declination (in mas/yr)
rv : float
Radial velocity (km/s)
R0 : float
Radial distance of the Sun from the Galactic center (in kpc)
Z0 : float
Height of the Sun above the Galactic plane (in pc)
V0 : float
Rotational velocity of the Sun (in km/s)
Vlsd : list
Velocity of the Sun w.r.t the local standard of rest (in km/s)
Return
------
pos : array
Position in galactocentric cylindrical coordinate
vel : array
Velocity in galactocentric cylindrical coordinate
act : array
Action in galactocentric cylindrical coordinate
orb : array
Orbital parameters (maximum height and eccentricity)
'''
#-----------------------------------------------------------------------------------------
# Tranform to galactocentric cylindrical coordinate
v_sun = coord.CartesianDifferential([Vlsd[0], V0 + Vlsd[1], Vlsd[2]] *
u.km / u.s)
cs = coord.SkyCoord(ra=ra * u.deg,
dec=dec * u.deg,
distance=dist * u.kpc,
pm_ra_cosdec=pm_ra * u.mas / u.yr,
pm_dec=pm_dec * u.mas / u.yr,
radial_velocity=rv * u.km / u.s,
galcen_distance=R0 * u.kpc,
galcen_v_sun=v_sun,
z_sun=Z0 * u.pc)
gc = coord.Galactocentric(galcen_distance=R0 * u.kpc,
galcen_v_sun=v_sun,
z_sun=Z0 * u.pc)
cs = cs.transform_to(gc)
cs.representation_type = 'cylindrical'
cs.differential_type = 'cylindrical'
# Position in cylindrical coordinate
rho, phi, z = cs.rho.to(u.kpc), cs.phi.to(u.rad), cs.z.to(u.kpc)
pos = np.zeros(1,
dtype={
'names': ['rho', 'phi', 'z'],
'formats': [float, float, float]
})
pos['rho'][0], pos['phi'][0], pos['z'][0] = rho.value, phi.value, z.value
# Velocity in cylindrical coordinate
vrho = cs.d_rho.to(u.km / u.s)
vphi = (cs.d_phi.to(u.mas / u.yr).value * 4.74047 *
cs.rho.to(u.kpc).value * u.km / u.s)
vz = cs.d_z.to(u.km / u.s)
vel = np.zeros(1,
dtype={
'names': ['rho', 'phi', 'z'],
'formats': [float, float, float]
})
vel['rho'][0], vel['phi'][0], vel['z'][
0] = vrho.value, vphi.value, vz.value
# Compute actions
delta = estimateDeltaStaeckel(mw, rho, z)
aAS = actionAngleStaeckel(pot=mw,
delta=delta,
c=True,
ro=R0 * u.kpc,
vo=V0 * u.km / u.s)
jrho, jphi, jz = aAS(rho, vrho, vphi, z, vz, fixed_quad=True)
act = np.zeros(1,
dtype={
'names': ['rho', 'phi', 'z'],
'formats': [float, float, float]
})
act['rho'][0], act['phi'][0], act['z'][
0] = jrho.value, jphi.value, jz.value
# Compute maximum height and eccentricity
o = Orbit([rho, vrho, vphi, z, vz], ro=R0 * u.kpc, vo=V0 * u.km / u.s)
np.seterr(over='raise')
zmax, ecc = -1., -1.
try:
zmax = o.zmax(pot=mw, delta=delta, analytic=True, type='staeckel')
except FloatingPointError:
pass
try:
ecc = o.e(pot=mw, delta=delta, analytic=True, type='staeckel')
except FloatingPointError:
pass
orb = np.zeros(1,
dtype={
'names': ['zmax', 'ecc'],
'formats': [float, float]
})
orb['zmax'][0], orb['ecc'][0] = zmax.value, ecc
return pos, vel, act, orb
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 compute_AA(self, potential, dt=0.01 * u.Myr, AAi=None, method='S'):
'''
Compute action angle coordinates for a propagated orbit.
'''
from galpy.orbit import Orbit
if (AAi is None):
AAi = range(self.size)
AAi = np.atleast_1d(AAi)
# Integration time step
self.dt = dt
nsteps = np.ceil((self.tflight / self.dt).to('1').value)
nsteps[nsteps < 100] = 100
# Initialize position in cylindrical coords
rho = self.r0 * np.sin(self.theta0)
z = self.r0 * np.cos(self.theta0)
phi = self.phi0
#... and velocity
vR = self.v0 * np.sin(self.thetav0) * np.cos(self.phiv0)
vT = self.v0 * np.sin(self.thetav0) * np.sin(self.phiv0)
vz = self.v0 * np.cos(self.thetav0)
# Initialize empty arrays to save orbit data and integration steps
self.orbits = [None] * self.size
AA = [np.zeros((3, int(nsteps[i]))) for i in AAi]
if (method != 'S'):
from galpy.actionAngle import actionAngleIsochroneApprox, actionAngleAdiabatic
aAA = actionAngleIsochroneApprox(pot=potential,
c=True,
ro=8.,
vo=220.)
else:
from galpy.actionAngle import estimateDeltaStaeckel, actionAngleStaeckel
k = 0
for i in AAi:
ts = np.linspace(0, 1, nsteps[i]) * self.tflight[i]
self.orbits[i] = Orbit(
vxvv=[rho[i], vR[i], vT[i], z[i], vz[i], phi[i]],
solarmotion=self.solarmotion)
self.orbits[i].integrate(ts, potential, method='dopr54_c')
if (method == 'S'):
delta = estimateDeltaStaeckel(potential,
self.orbits[i].R(ts) * u.kpc,
self.orbits[i].z(ts) * u.kpc)
aAA = actionAngleStaeckel(pot=potential,
c=True,
ro=8.,
vo=220.,
delta=delta)
AA[k] = aAA(self.orbits[i].R(ts) * u.kpc,
self.orbits[i].vR(ts) * u.km / u.s,
self.orbits[i].vT(ts) * u.km / u.s,
self.orbits[i].z(ts) * u.kpc,
self.orbits[i].vz(ts) * u.km / u.s)
#AA[k] = aAA(self.orbits[i].R(ts)/8, self.orbits[i].vR(ts)/220, self.orbits[i].vT(ts)/220, self.orbits[i].z(ts)/8, self.orbits[i].vz(ts)/220)
k += 1
return AA
