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
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))
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_v_esc(self):
R = z = phi = 1
ve = v_esc(MWPotential2014, [R, z, phi])
orb = Orbit(vxvv=[R/_pc, 0, ve/_kms, z/_pc, 0, phi])
E = orb.E(pot=MWPotential2014)
E_inf = evaluatePotentials(MWPotential2014, 1e+12, 0)
self.assertAlmostEqual(E, E_inf, 10, msg="v_esc returns incorrect "
"escape velocity")
now_r_omega = o.R(ts)[-1] #kpc
now_phi_omega = o.phi(ts)[-1]
nowvr_om = o.vR(ts)[-1]
nowvt_om = o.vT(ts)[-1]
nowvz_om = o.vz(ts)[-1]
#finding velocty components of omega cen now:
now_arrayvr_omega = forward_omega_orbit.vR(-ts)
now_arrayvt_omega = forward_omega_orbit.vT(-ts)
now_arrayvz_omega = forward_omega_orbit.vz(-ts)
now_vr_omega = forward_omega_orbit.vR(-ts)[-1]
now_vt_omega = forward_omega_orbit.vT(-ts)[-1]
now_vz_omega = forward_omega_orbit.vz(-ts)[-1]
#finding energies of omega cen now:
now_arraye_omega = forward_omega_orbit.E(-ts)
now_arrayer_omega = forward_omega_orbit.ER(-ts)
now_arrayez_omega = forward_omega_orbit.Ez(-ts)
now_e_omega = now_arraye_omega[-1]
now_er_omega = now_arrayer_omega[-1]
now_ez_omega = now_arrayez_omega[-1]
#print("current omega cen location according to code:", now_r_omega,now_vr_omega,now_vt_omega,now_z_omega,now_vz_omega,now_phi_omega)
num_stars = 1000
vrom = o.vR()
mu, sigma = (0, 100 / (np.sqrt(3)))
sr = np.random.normal(mu, sigma, num_stars)
vr_omega_array_vr = np.ones(num_stars) * (now_arrayvr_omega[0])
vt_omega_array_vt = np.ones(num_stars) * (now_arrayvt_omega[0])
pmra_mc[dist_mc < 0] = 0.0
vhel_mc[dist_mc < 0] = 0.0
pmdec_mc[dist_mc < 0] = 0.0
dist_mc[dist_mc < 0] = 0.0
for j in range(nmc):
op= Orbit(vxvv=[ra[i],dec[i],dist_mc[j],pmra_mc[j],pmdec_mc[j],vhel_mc[j]],\
radec=True,uvw=False,ro=8.0, vo=220.0,zo=zsun, \
solarmotion=[-usun,vsun,wsun])
op.integrate(ts, MWPotential2014)
rap_mc[j] = op.rap()
rperi_mc[j] = op.rperi()
rmean_mc[j] = 0.5 * (rap_mc[j] + rperi_mc[j])
zmax_mc[j] = op.zmax()
ecc_mc[j] = op.e()
ene_mc[j] = op.E()
lz_mc[j] = op.L(0.0)[0][2]
vphi_mc[j] = op.vphi(0.0)
vrad_mc[j] = op.vR(0.0)
# taking mean and std
rap[i] = rap_mc.mean()
rap_err[i] = rap_mc.std()
rperi[i] = rperi_mc.mean()
rperi_err[i] = rperi_mc.std()
rmean[i] = rmean_mc.mean()
rmean_err[i] = rmean_mc.std()
zmax[i] = zmax_mc.mean()
zmax_err[i] = zmax_mc.std()
ecc[i] = ecc_mc.mean()
ecc_err[i] = ecc_mc.std()
ene[i] = ene_mc.mean()
#This is for observational purposes and to test the code and see stars against one another #star1 star1 = Orbit([(r_omega)*units.kpc, (vr_omega+10)*units.km/units.s, vt_omega*units.km/units.s, z_omega*units.kpc,vz_omega*units.km/units.s, phi_omega*units.deg], ro=8., vo=220., solarmotion='hogg') star1.integrate(-ts,MWPotential2014) #[R,vR,vT(,z,vz,phi)] #finding location of star 1 now: now_arrayz_star1 = star1.z(-ts) now_arrayR_star1 = star1.R(-ts) now_arrayphi_star1 = star1.phi(-ts) #finding velocty components of star 1 now: now_arrayvr_star1 = star1.vR(-ts) now_arrayvt_star1 = star1.vT(-ts) now_arrayvz_star1 = star1.vz(-ts) #finding energies of star 1 now: now_arraye_star1 = star1.E(-ts) now_arrayer_star1 = star1.ER(-ts) now_arrayez_star1 = star1.Ez(-ts) #compared with current orbit of omega cen arrayR_omega = forward_omega_orbit.R(-ts) arrayvr_omega = forward_omega_orbit.vR(-ts) arrayvt_omega = forward_omega_orbit.vT(-ts) arrayvz_omega = forward_omega_orbit.vz(-ts) arrayphi_omega = forward_omega_orbit.phi(-ts) arrayz_omega = forward_omega_orbit.z(-ts) rrr = arrayR_omega[-1] vrvr = arrayvr_omega[-1] vtvt = arrayvt_omega[-1] zzz = arrayz_omega[-1] vzvz = arrayvz_omega[-1]
def estimate_orbit_parameters(star_index, orbit_calculation_input):
"""
Estimate orbit parameters from the given
MC sample of 6D information for the Nr of stars
and save it into orbit_information
"""
# We are creating a dictionary for each star
star_i = dict()
ra = orbit_calculation_input['ra'] *u.deg
dec = orbit_calculation_input['dec'] *u.deg
dist = orbit_calculation_input['distance'] *u.pc
pm_ra = orbit_calculation_input['pmra'] *u.mas/u.year
pm_dec = orbit_calculation_input['pmdec'] *u.mas/u.year
v_los = orbit_calculation_input['vrad'] *u.km/u.s
# Create the Orbit instance
o = Orbit(
vxvv=[ra,dec,dist,pm_ra, pm_dec,v_los],
ro=r_galactic_centre,
vo=v_circular,
zo=z_galactic_plane,
solarmotion=[-11.1, 15.17, 7.25]*u.km/u.s,
radec=True
)
star_i = dict()
#Galactocentric coordinates:
star_i['X_XYZ'] = o.helioX()#*u.kpc
star_i['Y_XYZ'] = o.helioY()#*u.kpc
star_i['Z_XYZ'] = o.helioZ()#*u.kpc
star_i['U_UVW'] = o.U()#*u.km/u.s
star_i['V_UVW'] = o.V()#*u.km/u.s
star_i['W_UVW'] = o.W()#*u.km/u.s
star_i['R_Rzphi'] = o.R()#*u.kpc
star_i['phi_Rzphi'] = o.phi()#*u.rad
star_i['z_Rzphi'] = o.z()#*u.kpc
star_i['vR_Rzphi'] = o.vR()#*u.km/u.s
star_i['vT_Rzphi'] = o.vT()#*u.km/u.s
star_i['vz_Rzphi'] = o.vz()#*u.km/u.s
try:
star_i['J_R'], star_i['L_Z'],star_i['J_Z'], star_i['omega_R'], star_i['omega_phi'], star_i['omega_z'], star_i['angle_R'], star_i['angle_phi'], star_i['angle_z'] = aAS.actionsFreqsAngles(
#R,vR,vT,z,vz[,phi]
star_i['R_Rzphi']*u.kpc,
star_i['vR_Rzphi']*u.km/u.s,
star_i['vT_Rzphi']*u.km/u.s,
star_i['z_Rzphi']*u.kpc,
star_i['vz_Rzphi']*u.km/u.s,
star_i['phi_Rzphi']*u.rad,
ro=r_galactic_centre,vo=v_circular
)
except:
star_i['omega_R'] = [np.nan]
star_i['omega_phi'] = [np.nan]
star_i['omega_z'] = [np.nan]
star_i['angle_R'] = [np.nan]
star_i['angle_phi'] = [np.nan]
star_i['angle_z'] = [np.nan]
try:
star_i['J_R'], star_i['L_Z'],star_i['J_Z'] = aAS(
#R,vR,vT,z,vz[,phi]
star_i['R_Rzphi']*u.kpc,
star_i['vR_Rzphi']*u.km/u.s,
star_i['vT_Rzphi']*u.km/u.s,
star_i['z_Rzphi']*u.kpc,
star_i['vz_Rzphi']*u.km/u.s,
star_i['phi_Rzphi']*u.rad,
ro=r_galactic_centre,vo=v_circular
)
except:
star_i['J_R'] = [np.nan]
star_i['L_Z'] = [np.nan]
star_i['J_Z'] = [np.nan]
try:
star_i['ecc'], star_i['zmax'], star_i['R_peri'], star_i['R_ap'] = aAS.EccZmaxRperiRap(
#R,vR,vT,z,vz[,phi]
star_i['R_Rzphi']*u.kpc,
star_i['vR_Rzphi']*u.km/u.s,
star_i['vT_Rzphi']*u.km/u.s,
star_i['z_Rzphi']*u.kpc,
star_i['vz_Rzphi']*u.km/u.s,
star_i['phi_Rzphi']*u.rad,
ro=r_galactic_centre,vo=v_circular
)
star_i['zmax']
star_i['R_peri']
star_i['R_peri']
except:
star_i['ecc'] = [np.nan]
star_i['zmax'] = [np.nan]
star_i['R_peri'] = [np.nan]
star_i['R_ap'] = [np.nan]
star_i['Energy'] = o.E(pot=pot,ro=r_galactic_centre,vo=v_circular,zo=z_galactic_plane)
return(star_i)
sun['z_Rzphi']*u.kpc,
sun['vz_Rzphi']*u.km/u.s,
sun['phi_Rzphi']*u.rad,
ro=r_galactic_centre,vo=v_circular
)
sun['zmax']
sun['R_peri']
sun['R_peri']
except:
sun['ecc'] = [np.nan]
sun['zmax'] = [np.nan]
sun['R_peri'] = [np.nan]
sun['R_ap'] = [np.nan]
sun['Energy'] = o.E(pot=pot,ro=r_galactic_centre,vo=v_circular,zo=z_galactic_plane)
print('Solar values:')
print('X,Y,Z: '+"{:.2f}".format(sun['X_XYZ'])+' '+"{:.2f}".format(sun['Y_XYZ'])+' '+"{:.2f}".format(sun['Z_XYZ']))
print('U,V,W: '+"{:.2f}".format(sun['U_UVW'])+' '+"{:.2f}".format(sun['V_UVW'])+' '+"{:.2f}".format(sun['W_UVW']))
print('R,phi,z: '+"{:.2f}".format(sun['R_Rzphi'])+' '+"{:.2f}".format(sun['phi_Rzphi'])+' '+"{:.2f}".format(sun['z_Rzphi']))
print('vR,vT,vz: '+"{:.2f}".format(sun['vR_Rzphi'])+' '+"{:.2f}".format(sun['vT_Rzphi'])+' '+"{:.2f}".format(sun['vz_Rzphi']))
print('J_R,L_Z,J_Z: '+"{:.2f}".format(sun['J_R'][0])+' '+"{:.2f}".format(sun['L_Z'][0])+' '+"{:.2f}".format(sun['J_Z'][0]))
print('Omega R/phi/z: '+"{:.2f}".format(sun['omega_R'][0])+' '+"{:.2f}".format(sun['omega_phi'][0])+' '+"{:.2f}".format(sun['omega_z'][0]))
print('Angles R/phi/z: '+"{:.2f}".format(sun['angle_R'][0])+' '+"{:.2f}".format(sun['angle_phi'][0])+' '+"{:.2f}".format(sun['angle_z'][0]))
print('ecc, zmax, R_peri, R_apo: '+"{:.2f}".format(sun['ecc'][0])+' '+"{:.2f}".format(sun['zmax'][0])+' '+"{:.2f}".format(sun['R_peri'][0])+' '+"{:.2f}".format(sun['R_ap'][0]))
print('Energy: '+"{:.2f}".format(sun['Energy']))
# ### Input of 6D information in observable dimensions
