def evolve_quadruple(N_output, end_time, m1, m2, m3, m4, aA, aB, aC, eA, eB, eC, iA, iB, iC, ApA, ApB, ApC, LANA, LANB, LANC):
masses = [m1, m2, m3, m4]
semimajor_axis = [aA, aB, aC]
eccentricity = [eA, eB, eC]
inclination = numpy.deg2rad([iA, iB, iC])
argument_of_percienter = numpy.deg2rad([ApA, ApB, ApC])
longitude_of_ascending_node = numpy.deg2rad([LANA, LANB, LANC])
print longitude_of_ascending_node
N_bodies = 4
N_binaries = N_bodies-1
particles, binaries = initialize_multiple_system(N_bodies, masses, semimajor_axis, eccentricity, inclination, argument_of_percienter, longitude_of_ascending_node)
code = SecularMultiple()
code.particles.add_particles(particles)
channel_from_particles_to_code = particles.new_channel_to(code.particles)
channel_from_code_to_particles = code.particles.new_channel_to(particles)
channel_from_particles_to_code.copy()
### set up some arrays for plotting ###
print_smas_AU = [[] for x in range(N_binaries)]
print_rps_AU = [[] for x in range(N_binaries)]
print_parent_is_deg = [[] for x in range(N_binaries)]
print_times_Myr = []
time = 0.0|units.yr
output_time_step = end_time/float(N_output)
while time <= end_time:
time += output_time_step
code.evolve_model(time)
channel_from_code_to_particles.copy()
print '='*50
print 't/Myr',time.value_in(units.Myr)
print 'e',binaries.eccentricity
print 'i/deg', numpy.rad2deg(binaries.inclination)
print 'AP/deg', \
numpy.rad2deg(binaries.argument_of_pericenter)
print 'LAN/deg', \
numpy.rad2deg(binaries.longitude_of_ascending_node)
### write to output arrays ###
print_times_Myr.append(time.value_in(units.Myr))
for index_binary in range(N_binaries):
print_smas_AU[index_binary].append( binaries[index_binary].semimajor_axis.value_in(units.AU) )
print_rps_AU[index_binary].append( binaries[index_binary].semimajor_axis.value_in(units.AU)*(1.0 - binaries[index_binary].eccentricity) )
print_parent_is_deg[index_binary].append( numpy.rad2deg(binaries[index_binary].inclination_relative_to_parent) )
### compute the `canonical' maximum eccentricity/periapsis distance that applies in the quadrupole-order test-particle limit if the `outer' binary is replaced by a point mass ###
print inclination[0],inclination[2],longitude_of_ascending_node[0],longitude_of_ascending_node[2]
i_AC_init = compute_mutual_inclination(inclination[0],inclination[2],longitude_of_ascending_node[0],longitude_of_ascending_node[2])
i_BC_init = compute_mutual_inclination(inclination[1],inclination[2],longitude_of_ascending_node[1],longitude_of_ascending_node[2])
canonical_rp_min_A_AU = (semimajor_axis[0]*(1.0 - numpy.sqrt( 1.0 - (5.0/3.0)*numpy.cos(i_AC_init)**2 ) )).value_in(units.AU)
canonical_rp_min_B_AU = (semimajor_axis[1]*(1.0 - numpy.sqrt( 1.0 - (5.0/3.0)*numpy.cos(i_BC_init)**2 ) )).value_in(units.AU)
data = print_times_Myr,print_smas_AU,print_rps_AU,print_parent_is_deg,canonical_rp_min_A_AU,canonical_rp_min_B_AU
return data
def test7(self):
"""
test collision detection in 3-body system
"""
particles = create_nested_multiple(3,[1.0|units.MSun, 1.2|units.MSun, 0.9|units.MSun], [1.0|units.AU, 100.0|units.AU], [0.1, 0.5], [0.01, 80.0*numpy.pi/180.0], [0.01, 0.01], [0.01, 0.01])
binaries = particles[particles.is_binary]
stars = particles - binaries
binaries.check_for_physical_collision_or_orbit_crossing = True
stars.radius = 0.03 | units.AU
code = SecularMultiple(redirection='none')
code.particles.add_particles(particles)
channel_to_code = particles.new_channel_to(code.particles)
channel_from_code = code.particles.new_channel_to(particles)
channel_to_code.copy()
t = 0.0 | units.Myr
dt = 1.0e-2 | units.Myr
tend = 1.0e-1 | units.Myr
t_print_array = quantities.AdaptingVectorQuantity()
a_print_array = quantities.AdaptingVectorQuantity()
e_print_array = quantities.AdaptingVectorQuantity()
while (t<tend):
t+=dt
code.evolve_model(t)
flag = code.flag
channel_from_code.copy()
print 'secular_breakdown_has_occurred',binaries.secular_breakdown_has_occurred
print 'dynamical_instability_has_occurred',binaries.dynamical_instability_has_occurred
print 'physical_collision_or_orbit_crossing_has_occurred',binaries.physical_collision_or_orbit_crossing_has_occurred
print 'minimum_periapse_distance_has_occurred',binaries.minimum_periapse_distance_has_occurred
print 'RLOF_at_pericentre_has_occurred',binaries.RLOF_at_pericentre_has_occurred
if flag == 2:
print 'root found'
break
print 't_end',code.model_time.value_in(units.Myr)
t_print_array.append(t)
a_print_array.append(binaries[0].semimajor_axis)
e_print_array.append(binaries[0].eccentricity | units.none)
if HAS_MATPLOTLIB == True:
fig = pyplot.figure()
plot = fig.add_subplot(2,1,1)
plot.plot(t_print_array.value_in(units.Myr),e_print_array.value_in(units.none))
plot = fig.add_subplot(2,1,2)
plot.plot(t_print_array.value_in(units.Myr),a_print_array.value_in(units.AU)*(1.0-e_print_array.value_in(units.none)))
plot.axhline(y = stars[0].radius.value_in(units.AU) + stars[1].radius.value_in(units.AU),color='k')
pyplot.show()
def test1(self):
"""
test reference system of Naoz et al. (2009)
"""
particles = create_nested_multiple(3,[1.0|units.MSun, 1.0|units.MJupiter, 40.0|units.MJupiter], [6.0|units.AU,100.0|units.AU], [0.001,0.6], [0.0001,65.0*numpy.pi/180.0],[45.0*numpy.pi/180.0,0.0001],[0.01,0.01])
binaries = particles[particles.is_binary]
binaries.include_pairwise_1PN_terms = False
code = SecularMultiple(redirection='none')
code.particles.add_particles(particles)
channel_to_code = particles.new_channel_to(code.particles)
channel_from_code = code.particles.new_channel_to(particles)
channel_to_code.copy()
self.assertEquals(0.6, code.particles[particles.is_binary][1].eccentricity)
t = 0.0 | units.Myr
dt = 1.0e-2 | units.Myr
tend = 3.0e0 | units.Myr
t_print_array = quantities.AdaptingVectorQuantity()
a_print_array = quantities.AdaptingVectorQuantity()
e_print_array = quantities.AdaptingVectorQuantity()
INCL_print_array = quantities.AdaptingVectorQuantity()
AP_print_array = quantities.AdaptingVectorQuantity()
N = 0
while (t<tend):
t+=dt
N+=1
code.evolve_model(t)
print 't/Myr = ',code.model_time.value_in(units.Myr)
channel_from_code.copy()
t_print_array.append(t)
a_print_array.append(binaries[0].semimajor_axis)
e_print_array.append(binaries[0].eccentricity | units.none)
INCL_print_array.append(binaries[0].inclination_relative_to_parent | units.none)
AP_print_array.append(binaries[0].argument_of_pericenter | units.none)
if HAS_MATPLOTLIB == True:
fig = pyplot.figure(figsize=(16,10))
plot1 = fig.add_subplot(2,1,1)
plot2 = fig.add_subplot(2,1,2,yscale="log")
plot1.plot(t_print_array.value_in(units.Myr),(180.0/numpy.pi)*INCL_print_array.value_in(units.none), color='k')
plot2.plot(t_print_array.value_in(units.Myr),1.0-e_print_array.value_in(units.none), color='k')
fontsize = 15
plot1.set_ylabel("$i$",fontsize=fontsize)
plot2.set_ylabel("$1-e$",fontsize=fontsize)
plot2.set_xlabel("$t/\mathrm{Myr}$",fontsize=fontsize)
pyplot.show()
def test8(self):
"""
test minimum periapse occurrence
"""
particles = create_nested_multiple(
3, [1.0 | units.MSun, 1.2 | units.MSun, 0.9 | units.MSun],
[1.0 | units.AU, 100.0 | units.AU], [0.1, 0.5],
[0.01, 80.0 * numpy.pi / 180.0], [0.01, 0.01], [0.01, 0.01])
binaries = particles[particles.is_binary]
stars = particles - binaries
binaries.check_for_minimum_periapse_distance = True
rp_min = 0.1 | units.AU
binaries.check_for_minimum_periapse_distance_value = rp_min
code = SecularMultiple(redirection='none')
code.particles.add_particles(particles)
channel_to_code = particles.new_channel_to(code.particles)
channel_from_code = code.particles.new_channel_to(particles)
channel_to_code.copy()
t = 0.0 | units.Myr
dt = 5.0e-3 | units.Myr
tend = 1.0e-1 | units.Myr
t_print_array = quantities.AdaptingVectorQuantity()
a_print_array = quantities.AdaptingVectorQuantity()
e_print_array = quantities.AdaptingVectorQuantity()
while (t < tend):
t += dt
code.evolve_model(t)
flag = code.flag
channel_from_code.copy()
print('secular_breakdown_has_occurred',
binaries.secular_breakdown_has_occurred)
print('dynamical_instability_has_occurred',
binaries.dynamical_instability_has_occurred)
print('physical_collision_or_orbit_crossing_has_occurred',
binaries.physical_collision_or_orbit_crossing_has_occurred)
print('minimum_periapse_distance_has_occurred',
binaries.minimum_periapse_distance_has_occurred)
print('RLOF_at_pericentre_has_occurred',
binaries.RLOF_at_pericentre_has_occurred)
if flag == 2:
print('root found')
break
print('t_end', code.model_time.value_in(units.Myr))
t_print_array.append(t)
a_print_array.append(binaries[0].semimajor_axis)
e_print_array.append(binaries[0].eccentricity | units.none)
def test3(self):
"""
test GW emission in 2-body system + collision detection
"""
particles = create_nested_multiple(
2, [1.0 | units.MSun, 1.0 | units.MJupiter], [0.1 | units.AU],
[0.994], [0.01], [0.01], [0.01])
binaries = particles[particles.is_binary]
stars = particles - binaries
stars.radius = 0.0001 | units.AU
binaries.check_for_physical_collision_or_orbit_crossing = True
binaries.include_pairwise_25PN_terms = True
code = SecularMultiple(redirection='none')
code.particles.add_particles(particles)
channel_to_code = particles.new_channel_to(code.particles)
channel_from_code = code.particles.new_channel_to(particles)
channel_to_code.copy()
t_print_array = quantities.AdaptingVectorQuantity()
a_print_array = quantities.AdaptingVectorQuantity()
e_print_array = quantities.AdaptingVectorQuantity()
AP_print_array = quantities.AdaptingVectorQuantity()
tend = 1.0 | units.Gyr
N = 0
t = 0.0 | units.Myr
dt = 100.0 | units.Myr
while (t < tend):
t += dt
N += 1
code.evolve_model(t)
flag = code.flag
if flag == 2:
print('root found')
break
channel_from_code.copy()
t_print_array.append(t)
a_print_array.append(binaries[0].semimajor_axis)
e_print_array.append(binaries[0].eccentricity | units.none)
AP_print_array.append(binaries[0].argument_of_pericenter
| units.none)
print('e', binaries.eccentricity, 'a/AU',
binaries.semimajor_axis.value_in(units.AU), 'rp/AU',
(binaries.semimajor_axis *
(1.0 - binaries.eccentricity)).value_in(units.AU))
def test2(self):
"""
test 1PN precession in 2-body system
"""
particles = create_nested_multiple(
2, [1.0 | units.MSun, 1.0 | units.MJupiter], [1.0 | units.AU],
[0.99], [0.01], [0.01], [0.01])
binaries = particles[particles.is_binary]
binaries.include_pairwise_1PN_terms = True
code = SecularMultiple(redirection='none')
code.particles.add_particles(particles)
channel_to_code = particles.new_channel_to(code.particles)
channel_from_code = code.particles.new_channel_to(particles)
channel_to_code.copy()
t = 0.0 | units.Myr
dt = 1.0e-1 | units.Myr
tend = 1.0e0 | units.Myr
t_print_array = quantities.AdaptingVectorQuantity()
a_print_array = quantities.AdaptingVectorQuantity()
e_print_array = quantities.AdaptingVectorQuantity()
AP_print_array = quantities.AdaptingVectorQuantity()
N = 0
while (t < tend):
t += dt
N += 1
code.evolve_model(t)
channel_from_code.copy()
print('t/Myr', t.value_in(units.Myr), 'omega',
binaries[0].argument_of_pericenter | units.none)
t_print_array.append(t)
a_print_array.append(binaries[0].semimajor_axis)
e_print_array.append(binaries[0].eccentricity | units.none)
AP_print_array.append(binaries[0].argument_of_pericenter
| units.none)
a = binaries[0].semimajor_axis
e = binaries[0].eccentricity
M = binaries[0].mass
rg = constants.G * M / (constants.c**2)
P = 2.0 * numpy.pi * numpy.sqrt(a**3 / (constants.G * M))
t_1PN = (1.0 / 3.0) * P * (1.0 - e**2) * (a / rg)
def test1(self):
"""
test reference system of Naoz et al. (2009)
"""
particles = create_nested_multiple(
3, [1.0 | units.MSun, 1.0 | units.MJupiter, 40.0 | units.MJupiter],
[6.0 | units.AU, 100.0 | units.AU], [0.001, 0.6],
[0.0001, 65.0 * numpy.pi / 180.0],
[45.0 * numpy.pi / 180.0, 0.0001], [0.01, 0.01])
binaries = particles[particles.is_binary]
binaries.include_pairwise_1PN_terms = False
code = SecularMultiple(redirection='none')
code.particles.add_particles(particles)
channel_to_code = particles.new_channel_to(code.particles)
channel_from_code = code.particles.new_channel_to(particles)
channel_to_code.copy()
self.assertEqual(0.6,
code.particles[particles.is_binary][1].eccentricity)
t = 0.0 | units.Myr
dt = 1.0e-2 | units.Myr
tend = 3.0e0 | units.Myr
t_print_array = quantities.AdaptingVectorQuantity()
a_print_array = quantities.AdaptingVectorQuantity()
e_print_array = quantities.AdaptingVectorQuantity()
INCL_print_array = quantities.AdaptingVectorQuantity()
AP_print_array = quantities.AdaptingVectorQuantity()
N = 0
while (t < tend):
t += dt
N += 1
code.evolve_model(t)
print('t/Myr = ', code.model_time.value_in(units.Myr))
channel_from_code.copy()
t_print_array.append(t)
a_print_array.append(binaries[0].semimajor_axis)
e_print_array.append(binaries[0].eccentricity | units.none)
INCL_print_array.append(binaries[0].inclination_relative_to_parent
| units.none)
AP_print_array.append(binaries[0].argument_of_pericenter
| units.none)
def test7(self):
"""
test collision detection in 3-body system
"""
particles = create_nested_multiple(
3, [1.0 | units.MSun, 1.2 | units.MSun, 0.9 | units.MSun],
[1.0 | units.AU, 100.0 | units.AU], [0.1, 0.5],
[0.01, 80.0 * numpy.pi / 180.0], [0.01, 0.01], [0.01, 0.01])
binaries = particles[particles.is_binary]
stars = particles - binaries
binaries.check_for_physical_collision_or_orbit_crossing = True
stars.radius = 0.03 | units.AU
code = SecularMultiple(redirection='none')
code.particles.add_particles(particles)
channel_to_code = particles.new_channel_to(code.particles)
channel_from_code = code.particles.new_channel_to(particles)
channel_to_code.copy()
t = 0.0 | units.Myr
dt = 1.0e-2 | units.Myr
tend = 1.0e-1 | units.Myr
t_print_array = quantities.AdaptingVectorQuantity()
a_print_array = quantities.AdaptingVectorQuantity()
e_print_array = quantities.AdaptingVectorQuantity()
while (t < tend):
t += dt
code.evolve_model(t)
flag = code.flag
channel_from_code.copy()
print('secular_breakdown_has_occurred',
binaries.secular_breakdown_has_occurred)
print('dynamical_instability_has_occurred',
binaries.dynamical_instability_has_occurred)
print('physical_collision_or_orbit_crossing_has_occurred',
binaries.physical_collision_or_orbit_crossing_has_occurred)
print('minimum_periapse_distance_has_occurred',
binaries.minimum_periapse_distance_has_occurred)
print('RLOF_at_pericentre_has_occurred',
binaries.RLOF_at_pericentre_has_occurred)
if flag == 2:
print('root found')
break
print('t_end', code.model_time.value_in(units.Myr))
t_print_array.append(t)
a_print_array.append(binaries[0].semimajor_axis)
e_print_array.append(binaries[0].eccentricity | units.none)
if HAS_MATPLOTLIB == True:
fig = pyplot.figure()
plot = fig.add_subplot(2, 1, 1)
plot.plot(t_print_array.value_in(units.Myr),
e_print_array.value_in(units.none))
plot = fig.add_subplot(2, 1, 2)
plot.plot(
t_print_array.value_in(units.Myr),
a_print_array.value_in(units.AU) *
(1.0 - e_print_array.value_in(units.none)))
plot.axhline(y=stars[0].radius.value_in(units.AU) +
stars[1].radius.value_in(units.AU),
color='k')
pyplot.show()
def test6(self):
"""
test precession due to rotation
"""
M = 1.0 | units.MJupiter
R = 1.5 | units.RJupiter
m_per = 1.0 | units.MSun
a0 = 30.0 | units.AU
e0 = 0.999
P0 = 2.0 * numpy.pi * numpy.sqrt(a0**3 / (constants.G * (M + m_per)))
n0 = 2.0 * numpy.pi / P0
aF = a0 * (1.0 - e0**2)
nF = numpy.sqrt(constants.G * (M + m_per) / (aF**3))
particles = create_nested_multiple(2, [m_per, M], [a0], [e0], [1.0e-5],
[1.0e-5], [1.0e-5])
binaries = particles[particles.is_binary]
particles[0].radius = 1.0 | units.RSun
particles[1].radius = R
particles[1].spin_vec_x = 0.0 | 1.0 / units.day
particles[1].spin_vec_y = 0.0 | 1.0 / units.day
Omega_PS0 = n0 * (33.0 / 10.0) * pow(a0 / aF, 3.0 / 2.0)
particles[1].spin_vec_z = Omega_PS0
k_L = 0.51
k_AM = k_L / 2.0
rg = 0.25
particles[1].tides_method = 1
particles[1].include_tidal_friction_terms = False
particles[1].include_tidal_bulges_precession_terms = False
particles[1].include_rotation_precession_terms = True
particles[1].minimum_eccentricity_for_tidal_precession = 1.0e-5
particles[1].tides_apsidal_motion_constant = k_AM
particles[1].tides_gyration_radius = rg
code = SecularMultiple(redirection='none')
code.particles.add_particles(particles)
channel_to_code = particles.new_channel_to(code.particles)
channel_from_code = code.particles.new_channel_to(particles)
channel_to_code.copy()
t = 0.0 | units.Myr
dt = 1.0e1 | units.Myr
tend = 1.0e2 | units.Myr
t_print_array = quantities.AdaptingVectorQuantity()
a_print_array = quantities.AdaptingVectorQuantity()
e_print_array = quantities.AdaptingVectorQuantity()
AP_print_array = quantities.AdaptingVectorQuantity()
Omega_vec = [
particles[1].spin_vec_x, particles[1].spin_vec_y,
particles[1].spin_vec_z
]
Omega = numpy.sqrt(Omega_vec[0]**2 + Omega_vec[1]**2 + Omega_vec[2]**2)
print('Omega/n', Omega / n0)
g_dot_rot = n0 * (1.0 + m_per / M) * k_AM * pow(
R / a0, 5.0) * (Omega / n0)**2 / ((1.0 - e0**2)**2)
t_rot = 2.0 * numpy.pi / g_dot_rot
print('t_rot/Myr', t_rot.value_in(units.Myr))
N = 0
while (t < tend):
t += dt
code.evolve_model(t)
print('flag', code.flag, t, binaries[0].semimajor_axis,
binaries[0].eccentricity)
channel_from_code.copy()
t_print_array.append(t)
a_print_array.append(binaries[0].semimajor_axis)
e_print_array.append(binaries[0].eccentricity | units.none)
AP_print_array.append(binaries[0].argument_of_pericenter
| units.none)
N += 1
if HAS_MATPLOTLIB == True:
fig = pyplot.figure(figsize=(16, 10))
plot1 = fig.add_subplot(4, 1, 1)
plot2 = fig.add_subplot(4, 1, 2, yscale="log")
plot3 = fig.add_subplot(4, 1, 3, yscale="log")
plot4 = fig.add_subplot(4, 1, 4, yscale="log")
plot1.plot(t_print_array.value_in(units.Myr),
AP_print_array.value_in(units.none),
color='r')
points = numpy.linspace(0.0, tend.value_in(units.Myr), N)
AP = 0.01 + 2.0 * numpy.pi * points / (t_rot.value_in(units.Myr))
AP = (AP + numpy.pi) % (2.0 *
numpy.pi) - numpy.pi ### -pi < AP < pi
plot1.plot(points, AP, color='g')
plot2.plot(t_print_array.value_in(units.Myr),
numpy.fabs(
(AP - AP_print_array.value_in(units.none)) / AP),
color='r')
plot3.plot(t_print_array.value_in(units.Myr),
numpy.fabs((a0 - a_print_array) / a0),
color='r')
plot4.plot(t_print_array.value_in(units.Myr),
numpy.fabs((e0 - e_print_array) / e0),
color='r')
fontsize = 15
plot1.set_ylabel("$\omega$", fontsize=fontsize)
plot2.set_ylabel("$|(\omega_p-\omega)/\omega_p|$",
fontsize=fontsize)
plot3.set_ylabel("$|(a_0-a)/a_0|$", fontsize=fontsize)
plot4.set_ylabel("$|(e_0-e)/e_0|$", fontsize=fontsize)
pyplot.show()
def test4(self):
"""
test tidal friction in 2-body system
"""
M = 1.0 | units.MJupiter
R = 40.0 | units.RJupiter
m_per = 1.0 | units.MSun
m = m_per
mu = m * M / (m + M)
a0 = 0.1 | units.AU
e0 = 0.3
P0 = 2.0 * numpy.pi * numpy.sqrt(a0**3 / (constants.G * (M + m_per)))
n0 = 2.0 * numpy.pi / P0
aF = a0 * (1.0 - e0**2)
nF = numpy.sqrt(constants.G * (M + m_per) / (aF**3))
particles = create_nested_multiple(2, [m_per, M], [a0], [e0], [0.01],
[0.01], [0.01])
binaries = particles[particles.is_binary]
particles[0].radius = 1.0 | units.RSun
particles[1].radius = R
particles[1].spin_vec_x = 0.0 | 1.0 / units.day
particles[1].spin_vec_y = 0.0 | 1.0 / units.day
particles[1].spin_vec_z = 4.0e-2 | 1.0 / units.day
k_L = 0.38
k_AM = k_L / 2.0
rg = 0.25
tau = 0.66 | units.s
I = rg * M * R**2
alpha = I / (mu * a0**2)
T = R**3 / (constants.G * M * tau)
t_V = 3.0 * (1.0 + 1.0 / k_L) * T
particles[1].tides_method = 2
particles[1].include_tidal_friction_terms = True
particles[1].include_tidal_bulges_precession_terms = False
particles[1].include_rotation_precession_terms = False
particles[1].minimum_eccentricity_for_tidal_precession = 1.0e-8
particles[1].tides_apsidal_motion_constant = k_AM
particles[1].tides_viscous_time_scale = t_V
particles[1].tides_gyration_radius = rg
tD = M * aF**8 / (3.0 * k_L * tau * constants.G * m_per *
(M + m_per) * R**5)
particles[2].check_for_physical_collision_or_orbit_crossing = True
code = SecularMultiple(redirection='none')
code.particles.add_particles(particles)
code.parameters.relative_tolerance = 1.0e-14
channel_to_code = particles.new_channel_to(code.particles)
channel_from_code = code.particles.new_channel_to(particles)
channel_to_code.copy()
t = 0.0 | units.Myr
dt = 1.0e-5 | units.Myr
tend = 1.0e-4 | units.Myr
t_print_array = quantities.AdaptingVectorQuantity()
a_print_array = quantities.AdaptingVectorQuantity()
n_print_array = quantities.AdaptingVectorQuantity()
e_print_array = quantities.AdaptingVectorQuantity()
AP_print_array = quantities.AdaptingVectorQuantity()
spin_print_array = quantities.AdaptingVectorQuantity()
while (t < tend):
t += dt
code.evolve_model(t)
print('flag', code.flag, t, 'a/AU', binaries[0].semimajor_axis,
'e', binaries[0].eccentricity)
channel_from_code.copy()
t_print_array.append(t)
a_print_array.append(binaries[0].semimajor_axis)
n_print_array.append(
numpy.sqrt(constants.G * (M + m) /
(binaries[0].semimajor_axis**3)))
e_print_array.append(binaries[0].eccentricity | units.none)
AP_print_array.append(binaries[0].argument_of_pericenter
| units.none)
spin_print_array.append(
numpy.sqrt(particles[1].spin_vec_x**2 +
particles[1].spin_vec_y**2 +
particles[1].spin_vec_z**2))
binaries = particles[particles.is_binary]
bodies = particles - binaries
print('S_x', bodies.spin_vec_x.value_in(1.0 / units.day))
print('S_y', bodies.spin_vec_y.value_in(1.0 / units.day))
print('S_z', bodies.spin_vec_z.value_in(1.0 / units.day))
print('=' * 50)
if HAS_MATPLOTLIB == True:
fig = pyplot.figure()
fontsize = 12
N_p = 4
plot1 = fig.add_subplot(N_p, 1, 1)
plot1.plot(t_print_array.value_in(units.Myr),
a_print_array.value_in(units.AU),
color='r')
plot1.set_ylabel("$a/\mathrm{AU}$", fontsize=fontsize)
plot2 = fig.add_subplot(N_p, 1, 2)
plot2.plot(t_print_array.value_in(units.Myr),
e_print_array.value_in(units.none),
color='k')
plot2.set_ylabel("$e$", fontsize=fontsize)
plot3 = fig.add_subplot(N_p, 1, 3, yscale="log")
plot3.plot(t_print_array.value_in(units.Myr),
a_print_array.value_in(units.AU) *
(1.0 - e_print_array.value_in(units.none)**2),
color='k')
plot3.axhline(y=a0.value_in(units.AU) * (1.0 - e0**2), color='k')
plot3.set_ylabel("$a(1-e^2)/\mathrm{AU}$", fontsize=fontsize)
plot4 = fig.add_subplot(N_p, 1, 4)
plot4.plot(t_print_array.value_in(units.Myr),
spin_print_array / n_print_array)
plot4.set_ylabel("$\Omega/n$", fontsize=fontsize)
plot4.set_xlabel("$t/\mathrm{Myr}$", fontsize=fontsize)
pyplot.show()
def test3(self):
"""
test GW emission in 2-body system + collision detection
"""
particles = create_nested_multiple(
2, [1.0 | units.MSun, 1.0 | units.MJupiter], [0.1 | units.AU],
[0.994], [0.01], [0.01], [0.01])
binaries = particles[particles.is_binary]
stars = particles - binaries
stars.radius = 0.0001 | units.AU
binaries.check_for_physical_collision_or_orbit_crossing = True
binaries.include_pairwise_25PN_terms = True
code = SecularMultiple(redirection='none')
code.particles.add_particles(particles)
channel_to_code = particles.new_channel_to(code.particles)
channel_from_code = code.particles.new_channel_to(particles)
channel_to_code.copy()
t_print_array = quantities.AdaptingVectorQuantity()
a_print_array = quantities.AdaptingVectorQuantity()
e_print_array = quantities.AdaptingVectorQuantity()
AP_print_array = quantities.AdaptingVectorQuantity()
tend = 1.0 | units.Gyr
N = 0
t = 0.0 | units.Myr
dt = 100.0 | units.Myr
while (t < tend):
t += dt
N += 1
code.evolve_model(t)
flag = code.flag
if flag == 2:
print('root found')
break
channel_from_code.copy()
t_print_array.append(t)
a_print_array.append(binaries[0].semimajor_axis)
e_print_array.append(binaries[0].eccentricity | units.none)
AP_print_array.append(binaries[0].argument_of_pericenter
| units.none)
print('e', binaries.eccentricity, 'a/AU',
binaries.semimajor_axis.value_in(units.AU), 'rp/AU',
(binaries.semimajor_axis *
(1.0 - binaries.eccentricity)).value_in(units.AU))
if HAS_MATPLOTLIB == True:
fig = pyplot.figure(figsize=(16, 10))
plot1 = fig.add_subplot(2, 1, 1)
plot2 = fig.add_subplot(2, 1, 2, yscale="log")
plot1.plot(t_print_array.value_in(units.Myr),
e_print_array.value_in(units.none),
color='r')
plot2.plot(t_print_array.value_in(units.Myr),
a_print_array.value_in(units.AU),
color='r')
fontsize = 15
plot1.set_ylabel("$e$", fontsize=fontsize)
plot2.set_ylabel("$a/\mathrm{AU}$", fontsize=fontsize)
plot2.set_xlabel("$t/\mathrm{Myr}$", fontsize=fontsize)
pyplot.show()
def test2(self):
"""
test 1PN precession in 2-body system
"""
particles = create_nested_multiple(
2, [1.0 | units.MSun, 1.0 | units.MJupiter], [1.0 | units.AU],
[0.99], [0.01], [0.01], [0.01])
binaries = particles[particles.is_binary]
binaries.include_pairwise_1PN_terms = True
code = SecularMultiple(redirection='none')
code.particles.add_particles(particles)
channel_to_code = particles.new_channel_to(code.particles)
channel_from_code = code.particles.new_channel_to(particles)
channel_to_code.copy()
t = 0.0 | units.Myr
dt = 1.0e-1 | units.Myr
tend = 1.0e0 | units.Myr
t_print_array = quantities.AdaptingVectorQuantity()
a_print_array = quantities.AdaptingVectorQuantity()
e_print_array = quantities.AdaptingVectorQuantity()
AP_print_array = quantities.AdaptingVectorQuantity()
N = 0
while (t < tend):
t += dt
N += 1
code.evolve_model(t)
channel_from_code.copy()
print('t/Myr', t.value_in(units.Myr), 'omega',
binaries[0].argument_of_pericenter | units.none)
t_print_array.append(t)
a_print_array.append(binaries[0].semimajor_axis)
e_print_array.append(binaries[0].eccentricity | units.none)
AP_print_array.append(binaries[0].argument_of_pericenter
| units.none)
a = binaries[0].semimajor_axis
e = binaries[0].eccentricity
M = binaries[0].mass
rg = constants.G * M / (constants.c**2)
P = 2.0 * numpy.pi * numpy.sqrt(a**3 / (constants.G * M))
t_1PN = (1.0 / 3.0) * P * (1.0 - e**2) * (a / rg)
if HAS_MATPLOTLIB == True:
fig = pyplot.figure(figsize=(16, 10))
plot1 = fig.add_subplot(4, 1, 1)
plot2 = fig.add_subplot(4, 1, 2, yscale="log")
plot3 = fig.add_subplot(4, 1, 3, yscale="log")
plot4 = fig.add_subplot(4, 1, 4, yscale="log")
plot1.plot(t_print_array.value_in(units.Myr),
AP_print_array.value_in(units.none),
color='r')
points = numpy.linspace(0.0, tend.value_in(units.Myr), N)
AP = 0.01 + 2.0 * numpy.pi * points / (t_1PN.value_in(units.Myr))
AP = (AP + numpy.pi) % (2.0 *
numpy.pi) - numpy.pi ### -pi < AP < pi
plot1.plot(points, AP, color='g')
plot2.plot(t_print_array.value_in(units.Myr),
numpy.fabs(
(AP - AP_print_array.value_in(units.none)) / AP),
color='r')
plot3.plot(t_print_array.value_in(units.Myr),
numpy.fabs((a - a_print_array) / a),
color='r')
plot4.plot(t_print_array.value_in(units.Myr),
numpy.fabs((e - e_print_array) / e),
color='r')
fontsize = 15
plot1.set_ylabel("$\omega$", fontsize=fontsize)
plot2.set_ylabel("$|(\omega_p-\omega)/\omega_p|$",
fontsize=fontsize)
plot3.set_ylabel("$|(a_0-a)/a_0|$", fontsize=fontsize)
plot4.set_ylabel("$|(e_0-e)/e_0|$", fontsize=fontsize)
pyplot.show()
def test1(self):
"""
test reference system of Naoz et al. (2009)
"""
particles = create_nested_multiple(
3, [1.0 | units.MSun, 1.0 | units.MJupiter, 40.0 | units.MJupiter],
[6.0 | units.AU, 100.0 | units.AU], [0.001, 0.6],
[0.0001, 65.0 * numpy.pi / 180.0],
[45.0 * numpy.pi / 180.0, 0.0001], [0.01, 0.01])
binaries = particles[particles.is_binary]
binaries.include_pairwise_1PN_terms = False
code = SecularMultiple(redirection='none')
code.particles.add_particles(particles)
channel_to_code = particles.new_channel_to(code.particles)
channel_from_code = code.particles.new_channel_to(particles)
channel_to_code.copy()
self.assertEqual(0.6,
code.particles[particles.is_binary][1].eccentricity)
t = 0.0 | units.Myr
dt = 1.0e-2 | units.Myr
tend = 3.0e0 | units.Myr
t_print_array = quantities.AdaptingVectorQuantity()
a_print_array = quantities.AdaptingVectorQuantity()
e_print_array = quantities.AdaptingVectorQuantity()
INCL_print_array = quantities.AdaptingVectorQuantity()
AP_print_array = quantities.AdaptingVectorQuantity()
N = 0
while (t < tend):
t += dt
N += 1
code.evolve_model(t)
print('t/Myr = ', code.model_time.value_in(units.Myr))
channel_from_code.copy()
t_print_array.append(t)
a_print_array.append(binaries[0].semimajor_axis)
e_print_array.append(binaries[0].eccentricity | units.none)
INCL_print_array.append(binaries[0].inclination_relative_to_parent
| units.none)
AP_print_array.append(binaries[0].argument_of_pericenter
| units.none)
if HAS_MATPLOTLIB == True:
fig = pyplot.figure(figsize=(16, 10))
plot1 = fig.add_subplot(2, 1, 1)
plot2 = fig.add_subplot(2, 1, 2, yscale="log")
plot1.plot(t_print_array.value_in(units.Myr), (180.0 / numpy.pi) *
INCL_print_array.value_in(units.none),
color='k')
plot2.plot(t_print_array.value_in(units.Myr),
1.0 - e_print_array.value_in(units.none),
color='k')
fontsize = 15
plot1.set_ylabel("$i$", fontsize=fontsize)
plot2.set_ylabel("$1-e$", fontsize=fontsize)
plot2.set_xlabel("$t/\mathrm{Myr}$", fontsize=fontsize)
pyplot.show()
def test2(self):
"""
test 1PN precession in 2-body system
"""
particles = create_nested_multiple(2,[1.0|units.MSun, 1.0|units.MJupiter], [1.0|units.AU], [0.99], [0.01], [0.01], [0.01])
binaries = particles[particles.is_binary]
binaries.include_pairwise_1PN_terms = True
code = SecularMultiple(redirection='none')
code.particles.add_particles(particles)
channel_to_code = particles.new_channel_to(code.particles)
channel_from_code = code.particles.new_channel_to(particles)
channel_to_code.copy()
t = 0.0 | units.Myr
dt = 1.0e-1 | units.Myr
tend = 1.0e0 | units.Myr
t_print_array = quantities.AdaptingVectorQuantity()
a_print_array = quantities.AdaptingVectorQuantity()
e_print_array = quantities.AdaptingVectorQuantity()
AP_print_array = quantities.AdaptingVectorQuantity()
N = 0
while (t<tend):
t+=dt
N+=1
code.evolve_model(t)
channel_from_code.copy()
print 't/Myr',t.value_in(units.Myr),'omega',binaries[0].argument_of_pericenter | units.none
t_print_array.append(t)
a_print_array.append(binaries[0].semimajor_axis)
e_print_array.append(binaries[0].eccentricity | units.none)
AP_print_array.append(binaries[0].argument_of_pericenter | units.none)
a = binaries[0].semimajor_axis
e = binaries[0].eccentricity
M = binaries[0].mass
rg = constants.G*M/(constants.c**2)
P = 2.0*numpy.pi*numpy.sqrt(a**3/(constants.G*M))
t_1PN = (1.0/3.0)*P*(1.0-e**2)*(a/rg)
if HAS_MATPLOTLIB == True:
fig = pyplot.figure(figsize=(16,10))
plot1 = fig.add_subplot(4,1,1)
plot2 = fig.add_subplot(4,1,2,yscale="log")
plot3 = fig.add_subplot(4,1,3,yscale="log")
plot4 = fig.add_subplot(4,1,4,yscale="log")
plot1.plot(t_print_array.value_in(units.Myr),AP_print_array.value_in(units.none), color='r')
points = numpy.linspace(0.0,tend.value_in(units.Myr),N)
AP = 0.01 +2.0*numpy.pi*points/(t_1PN.value_in(units.Myr))
AP = (AP+numpy.pi)%(2.0*numpy.pi) - numpy.pi ### -pi < AP < pi
plot1.plot(points,AP,color='g')
plot2.plot(t_print_array.value_in(units.Myr),numpy.fabs( (AP - AP_print_array.value_in(units.none))/AP ), color='r')
plot3.plot(t_print_array.value_in(units.Myr),numpy.fabs((a-a_print_array)/a), color='r')
plot4.plot(t_print_array.value_in(units.Myr),numpy.fabs((e-e_print_array)/e), color='r')
fontsize = 15
plot1.set_ylabel("$\omega$",fontsize=fontsize)
plot2.set_ylabel("$|(\omega_p-\omega)/\omega_p|$",fontsize=fontsize)
plot3.set_ylabel("$|(a_0-a)/a_0|$",fontsize=fontsize)
plot4.set_ylabel("$|(e_0-e)/e_0|$",fontsize=fontsize)
pyplot.show()
def test6(self):
"""
test precession due to rotation
"""
M = 1.0 | units.MJupiter
R = 1.5 | units.RJupiter
m_per = 1.0 | units.MSun
a0 = 30.0 | units.AU
e0 = 0.999
P0 = 2.0 * numpy.pi * numpy.sqrt(a0**3 / (constants.G * (M + m_per)))
n0 = 2.0 * numpy.pi / P0
aF = a0 * (1.0 - e0**2)
nF = numpy.sqrt(constants.G * (M + m_per) / (aF**3))
particles = create_nested_multiple(2, [m_per, M], [a0], [e0], [1.0e-5],
[1.0e-5], [1.0e-5])
binaries = particles[particles.is_binary]
particles[0].radius = 1.0 | units.RSun
particles[1].radius = R
particles[1].spin_vec_x = 0.0 | 1.0 / units.day
particles[1].spin_vec_y = 0.0 | 1.0 / units.day
Omega_PS0 = n0 * (33.0 / 10.0) * pow(a0 / aF, 3.0 / 2.0)
particles[1].spin_vec_z = Omega_PS0
k_L = 0.51
k_AM = k_L / 2.0
rg = 0.25
particles[1].tides_method = 1
particles[1].include_tidal_friction_terms = False
particles[1].include_tidal_bulges_precession_terms = False
particles[1].include_rotation_precession_terms = True
particles[1].minimum_eccentricity_for_tidal_precession = 1.0e-5
particles[1].tides_apsidal_motion_constant = k_AM
particles[1].tides_gyration_radius = rg
code = SecularMultiple(redirection='none')
code.particles.add_particles(particles)
channel_to_code = particles.new_channel_to(code.particles)
channel_from_code = code.particles.new_channel_to(particles)
channel_to_code.copy()
t = 0.0 | units.Myr
dt = 1.0e1 | units.Myr
tend = 1.0e2 | units.Myr
t_print_array = quantities.AdaptingVectorQuantity()
a_print_array = quantities.AdaptingVectorQuantity()
e_print_array = quantities.AdaptingVectorQuantity()
AP_print_array = quantities.AdaptingVectorQuantity()
Omega_vec = [
particles[1].spin_vec_x, particles[1].spin_vec_y,
particles[1].spin_vec_z
]
Omega = numpy.sqrt(Omega_vec[0]**2 + Omega_vec[1]**2 + Omega_vec[2]**2)
print('Omega/n', Omega / n0)
g_dot_rot = n0 * (1.0 + m_per / M) * k_AM * pow(
R / a0, 5.0) * (Omega / n0)**2 / ((1.0 - e0**2)**2)
t_rot = 2.0 * numpy.pi / g_dot_rot
print('t_rot/Myr', t_rot.value_in(units.Myr))
N = 0
while (t < tend):
t += dt
code.evolve_model(t)
print('flag', code.flag, t, binaries[0].semimajor_axis,
binaries[0].eccentricity)
channel_from_code.copy()
t_print_array.append(t)
a_print_array.append(binaries[0].semimajor_axis)
e_print_array.append(binaries[0].eccentricity | units.none)
AP_print_array.append(binaries[0].argument_of_pericenter
| units.none)
N += 1
def test5(self):
"""
test precession due to tidal bulges
"""
M = 1.0 | units.MJupiter
R = 1.0 | units.RJupiter
m_per = 1.0 | units.MSun
a0 = 30.0 | units.AU
e0 = 0.999
P0 = 2.0 * numpy.pi * numpy.sqrt(a0**3 / (constants.G * (M + m_per)))
n0 = 2.0 * numpy.pi / P0
particles = create_nested_multiple(2, [m_per, M], [a0], [e0], [0.01],
[0.01], [0.01])
binaries = particles[particles.is_binary]
particles[0].radius = 1.0 | units.RSun
particles[1].radius = R
k_L = 0.41
k_AM = k_L / 2.0
particles[1].tides_method = 0
particles[1].include_tidal_friction_terms = False
particles[1].include_tidal_bulges_precession_terms = True
particles[1].include_rotation_precession_terms = False
particles[1].minimum_eccentricity_for_tidal_precession = 1.0e-5
particles[1].tides_apsidal_motion_constant = k_AM
particles[1].tides_gyration_radius = 0.25
code = SecularMultiple(redirection='none')
code.particles.add_particles(particles)
channel_to_code = particles.new_channel_to(code.particles)
channel_from_code = code.particles.new_channel_to(particles)
channel_to_code.copy()
t = 0.0 | units.Myr
dt = 1.0e1 | units.Myr
tend = 1.0e2 | units.Myr
t_print_array = quantities.AdaptingVectorQuantity()
a_print_array = quantities.AdaptingVectorQuantity()
e_print_array = quantities.AdaptingVectorQuantity()
AP_print_array = quantities.AdaptingVectorQuantity()
g_dot_TB = (15.0 / 8.0) * n0 * (8.0 + 12.0 * e0**2 + e0**4) * (
m_per / M) * k_AM * pow(R / a0, 5.0) / pow(1.0 - e0**2, 5.0)
t_TB = 2.0 * numpy.pi / g_dot_TB
N = 0
while (t < tend):
t += dt
code.evolve_model(t)
print('flag', code.flag, t, binaries[0].semimajor_axis,
binaries[0].eccentricity)
channel_from_code.copy()
t_print_array.append(t)
a_print_array.append(binaries[0].semimajor_axis)
e_print_array.append(binaries[0].eccentricity | units.none)
AP_print_array.append(binaries[0].argument_of_pericenter
| units.none)
N += 1
def test3(self):
"""
test GW emission in 2-body system + collision detection
"""
particles = create_nested_multiple(2,[1.0|units.MSun, 1.0|units.MJupiter], [0.1|units.AU], [0.994], [0.01], [0.01], [0.01])
binaries = particles[particles.is_binary]
stars = particles - binaries
stars.radius = 0.0001 | units.AU
binaries.check_for_physical_collision_or_orbit_crossing = True
binaries.include_pairwise_25PN_terms = True
code = SecularMultiple(redirection='none')
code.particles.add_particles(particles)
channel_to_code = particles.new_channel_to(code.particles)
channel_from_code = code.particles.new_channel_to(particles)
channel_to_code.copy()
t_print_array = quantities.AdaptingVectorQuantity()
a_print_array = quantities.AdaptingVectorQuantity()
e_print_array = quantities.AdaptingVectorQuantity()
AP_print_array = quantities.AdaptingVectorQuantity()
tend = 1.0 | units.Gyr
N = 0
t = 0.0 | units.Myr
dt = 100.0 | units.Myr
while (t<tend):
t+=dt
N+=1
code.evolve_model(t)
flag = code.flag
if flag == 2:
print 'root found'
break
channel_from_code.copy()
t_print_array.append(t)
a_print_array.append(binaries[0].semimajor_axis)
e_print_array.append(binaries[0].eccentricity | units.none)
AP_print_array.append(binaries[0].argument_of_pericenter | units.none)
print 'e',binaries.eccentricity,'a/AU',binaries.semimajor_axis.value_in(units.AU),'rp/AU',(binaries.semimajor_axis*(1.0-binaries.eccentricity)).value_in(units.AU)
if HAS_MATPLOTLIB == True:
fig = pyplot.figure(figsize=(16,10))
plot1 = fig.add_subplot(2,1,1)
plot2 = fig.add_subplot(2,1,2,yscale="log")
plot1.plot(t_print_array.value_in(units.Myr),e_print_array.value_in(units.none), color='r')
plot2.plot(t_print_array.value_in(units.Myr),a_print_array.value_in(units.AU), color='r')
fontsize = 15
plot1.set_ylabel("$e$",fontsize=fontsize)
plot2.set_ylabel("$a/\mathrm{AU}$",fontsize=fontsize)
plot2.set_xlabel("$t/\mathrm{Myr}$",fontsize=fontsize)
pyplot.show()
def test4(self):
"""
test tidal friction in 2-body system
"""
M = 1.0|units.MJupiter
R = 40.0|units.RJupiter
m_per = 1.0|units.MSun
m = m_per
mu = m*M/(m+M)
a0 = 0.1 | units.AU
e0 = 0.3
P0 = 2.0*numpy.pi*numpy.sqrt(a0**3/(constants.G*(M+m_per)))
n0 = 2.0*numpy.pi/P0
aF = a0*(1.0-e0**2)
nF = numpy.sqrt( constants.G*(M+m_per)/(aF**3) )
particles = create_nested_multiple(2, [m_per, M], [a0], [e0], [0.01], [0.01], [0.01])
binaries = particles[particles.is_binary]
particles[0].radius = 1.0 | units.RSun
particles[1].radius = R
particles[1].spin_vec_x = 0.0 | 1.0/units.day
particles[1].spin_vec_y = 0.0 | 1.0/units.day
particles[1].spin_vec_z = 4.0e-2 | 1.0/units.day
k_L = 0.38
k_AM = k_L/2.0
rg = 0.25
tau = 0.66 | units.s
I = rg*M*R**2
alpha = I/(mu*a0**2)
T = R**3/(constants.G*M*tau)
t_V = 3.0*(1.0 + 1.0/k_L)*T
particles[1].tides_method = 2
particles[1].include_tidal_friction_terms = True
particles[1].include_tidal_bulges_precession_terms = False
particles[1].include_rotation_precession_terms = False
particles[1].minimum_eccentricity_for_tidal_precession = 1.0e-8
particles[1].tides_apsidal_motion_constant = k_AM
particles[1].tides_viscous_time_scale = t_V
particles[1].tides_gyration_radius = rg
tD = M*aF**8/(3.0*k_L*tau*constants.G*m_per*(M+m_per)*R**5)
particles[2].check_for_physical_collision_or_orbit_crossing = True
code = SecularMultiple(redirection='none')
code.particles.add_particles(particles)
code.parameters.relative_tolerance = 1.0e-14
channel_to_code = particles.new_channel_to(code.particles)
channel_from_code = code.particles.new_channel_to(particles)
channel_to_code.copy()
t = 0.0 | units.Myr
dt = 1.0e-5 | units.Myr
tend = 1.0e-4 | units.Myr
t_print_array = quantities.AdaptingVectorQuantity()
a_print_array = quantities.AdaptingVectorQuantity()
n_print_array = quantities.AdaptingVectorQuantity()
e_print_array = quantities.AdaptingVectorQuantity()
AP_print_array = quantities.AdaptingVectorQuantity()
spin_print_array = quantities.AdaptingVectorQuantity()
while (t<tend):
t+=dt
code.evolve_model(t)
print 'flag',code.flag,t,'a/AU',binaries[0].semimajor_axis,'e',binaries[0].eccentricity
channel_from_code.copy()
t_print_array.append(t)
a_print_array.append(binaries[0].semimajor_axis)
n_print_array.append(numpy.sqrt(constants.G*(M+m)/(binaries[0].semimajor_axis**3)))
e_print_array.append(binaries[0].eccentricity | units.none)
AP_print_array.append(binaries[0].argument_of_pericenter | units.none)
spin_print_array.append( numpy.sqrt( particles[1].spin_vec_x**2 + particles[1].spin_vec_y**2 + particles[1].spin_vec_z**2) )
binaries = particles[particles.is_binary]
bodies = particles - binaries
print 'S_x',bodies.spin_vec_x.value_in(1.0/units.day)
print 'S_y',bodies.spin_vec_y.value_in(1.0/units.day)
print 'S_z',bodies.spin_vec_z.value_in(1.0/units.day)
print '='*50
if HAS_MATPLOTLIB == True:
fig = pyplot.figure()
fontsize=12
N_p = 4
plot1 = fig.add_subplot(N_p,1,1)
plot1.plot(t_print_array.value_in(units.Myr),a_print_array.value_in(units.AU), color='r')
plot1.set_ylabel("$a/\mathrm{AU}$",fontsize=fontsize)
plot2 = fig.add_subplot(N_p,1,2)
plot2.plot(t_print_array.value_in(units.Myr),e_print_array.value_in(units.none),color='k')
plot2.set_ylabel("$e$",fontsize=fontsize)
plot3 = fig.add_subplot(N_p,1,3,yscale="log")
plot3.plot(t_print_array.value_in(units.Myr),a_print_array.value_in(units.AU)*(1.0-e_print_array.value_in(units.none)**2),color='k')
plot3.axhline(y = a0.value_in(units.AU)*(1.0 - e0**2), color='k')
plot3.set_ylabel("$a(1-e^2)/\mathrm{AU}$",fontsize=fontsize)
plot4 = fig.add_subplot(N_p,1,4)
plot4.plot(t_print_array.value_in(units.Myr),spin_print_array/n_print_array)
plot4.set_ylabel("$\Omega/n$",fontsize=fontsize)
plot4.set_xlabel("$t/\mathrm{Myr}$",fontsize=fontsize)
pyplot.show()
def test5(self):
"""
test precession due to tidal bulges
"""
M = 1.0 | units.MJupiter
R = 1.0 | units.RJupiter
m_per = 1.0 | units.MSun
a0 = 30.0 | units.AU
e0 = 0.999
P0 = 2.0 * numpy.pi * numpy.sqrt(a0**3 / (constants.G * (M + m_per)))
n0 = 2.0 * numpy.pi / P0
particles = create_nested_multiple(2, [m_per, M], [a0], [e0], [0.01],
[0.01], [0.01])
binaries = particles[particles.is_binary]
particles[0].radius = 1.0 | units.RSun
particles[1].radius = R
k_L = 0.41
k_AM = k_L / 2.0
particles[1].tides_method = 0
particles[1].include_tidal_friction_terms = False
particles[1].include_tidal_bulges_precession_terms = True
particles[1].include_rotation_precession_terms = False
particles[1].minimum_eccentricity_for_tidal_precession = 1.0e-5
particles[1].tides_apsidal_motion_constant = k_AM
code = SecularMultiple(redirection='none')
code.particles.add_particles(particles)
channel_to_code = particles.new_channel_to(code.particles)
channel_from_code = code.particles.new_channel_to(particles)
channel_to_code.copy()
t = 0.0 | units.Myr
dt = 1.0e1 | units.Myr
tend = 1.0e2 | units.Myr
t_print_array = quantities.AdaptingVectorQuantity()
a_print_array = quantities.AdaptingVectorQuantity()
e_print_array = quantities.AdaptingVectorQuantity()
AP_print_array = quantities.AdaptingVectorQuantity()
g_dot_TB = (15.0 / 8.0) * n0 * (8.0 + 12.0 * e0**2 + e0**4) * (
m_per / M) * k_AM * pow(R / a0, 5.0) / pow(1.0 - e0**2, 5.0)
t_TB = 2.0 * numpy.pi / g_dot_TB
N = 0
while (t < tend):
t += dt
code.evolve_model(t)
print 'flag', code.flag, t, binaries[0].semimajor_axis, binaries[
0].eccentricity
channel_from_code.copy()
t_print_array.append(t)
a_print_array.append(binaries[0].semimajor_axis)
e_print_array.append(binaries[0].eccentricity | units.none)
AP_print_array.append(binaries[0].argument_of_pericenter
| units.none)
N += 1
if HAS_MATPLOTLIB == True:
fig = pyplot.figure(figsize=(16, 10))
plot1 = fig.add_subplot(4, 1, 1)
plot2 = fig.add_subplot(4, 1, 2, yscale="log")
plot3 = fig.add_subplot(4, 1, 3, yscale="log")
plot4 = fig.add_subplot(4, 1, 4, yscale="log")
plot1.plot(t_print_array.value_in(units.Myr),
AP_print_array.value_in(units.none),
color='r')
points = numpy.linspace(0.0, tend.value_in(units.Myr), N)
AP = 0.01 + 2.0 * numpy.pi * points / (t_TB.value_in(units.Myr))
AP = (AP + numpy.pi) % (2.0 *
numpy.pi) - numpy.pi ### -pi < AP < pi
plot1.plot(points, AP, color='g')
plot2.plot(t_print_array.value_in(units.Myr),
numpy.fabs(
(AP - AP_print_array.value_in(units.none)) / AP),
color='r')
plot3.plot(t_print_array.value_in(units.Myr),
numpy.fabs((a0 - a_print_array) / a0),
color='r')
plot4.plot(t_print_array.value_in(units.Myr),
numpy.fabs((e0 - e_print_array) / e0),
color='r')
fontsize = 15
plot1.set_ylabel("$\omega$", fontsize=fontsize)
plot2.set_ylabel("$|(\omega_p-\omega)/\omega_p|$",
fontsize=fontsize)
plot3.set_ylabel("$|(a_0-a)/a_0|$", fontsize=fontsize)
plot4.set_ylabel("$|(e_0-e)/e_0|$", fontsize=fontsize)
pyplot.show()
def run_secularmultiple(particle_set, end_time, start_time=(0 |units.Myr), \
N_output=100, debug_mode=False, genT4System=False, \
exportData=True, useAMD=True, GCode = None, \
KeySystemID=None, SEVCode=None):
'''Does what it says on the tin.'''
try:
hierarchical_test = [x for x in particle_set if x.is_binary == True]
print("The supplied set has", len(hierarchical_test),
"node particles and is a tree.")
py_particles = particle_set
except:
print("The supplied set is NOT a tree set! Building tree ...")
py_particles = get_full_hierarchical_structure(particle_set,
KeySystemID=KeySystemID,
SEVCode=SEVCode)
hierarchical_test = [x for x in py_particles if x.is_binary == True]
print("Tree has been built with", len(hierarchical_test),
"node particles.")
nodes = py_particles.select(lambda x: x == True, ["is_binary"])
Num_nodes = len(nodes)
stellarCollisionOccured = False
if GCode == None:
code = SecularMultiple()
else:
code = GCode
if exportData:
plot_a_AU = defaultdict(list)
plot_e = defaultdict(list)
plot_peri_AU = defaultdict(list)
plot_stellar_inc_deg = defaultdict(list)
if useAMD:
plot_AMDBeta = defaultdict(list)
plot_times_Myr = []
if genT4System:
print(nodes.inclination)
nodes.inclination = [-18.137, 0.0, 23.570] | units.deg
print(nodes.inclination)
if debug_mode:
print('=' * 50)
print('t/kyr', 0.00)
print('a/AU', nodes.semimajor_axis)
print('p/day', nodes.period)
print('e', nodes.eccentricity)
print('i/deg', nodes.inclination)
print('AP/deg', \
nodes.argument_of_pericenter)
print('LAN/deg', \
nodes.longitude_of_ascending_node)
#print(py_particles)
code.particles.add_particles(py_particles)
#code.commit_particles()
#print(code.particles.semimajor_axis)
code.model_time = start_time
#print(py_particles.id, py_particles.semimajor_axis)
channel_from_particles_to_code = py_particles.new_channel_to(
code.particles)
channel_from_code_to_particles = code.particles.new_channel_to(
py_particles)
#print(py_particles.id, py_particles.semimajor_axis)
channel_from_particles_to_code.copy(
) #copy_attributes(['semimajor_axis', 'eccentricity', \
#'longitude_of_ascending_node', 'argument_of_pericenter', 'inclination'])
#print('This is After the First Channel Copy:', code.particles.semimajor_axis)
time = start_time
if useAMD:
#print(py_particles.id, py_particles.mass)
jovianParent = get_jovian_parent(py_particles)
output_time_step = 1000 * jovianParent.period.value_in(
units.Myr) | units.Myr
PS = initialize_PlanetarySystem_from_HierarchicalSet(py_particles)
PS.get_SystemBetaValues()
if exportData:
for planet in PS.planets:
plot_AMDBeta[planet.id].append(planet.AMDBeta)
else:
output_time_step = end_time / float(N_output)
if exportData:
plot_times_Myr.append(time.value_in(units.Myr))
for i, node in enumerate(nodes):
plot_a_AU[node.child2.id].append(
node.semimajor_axis.value_in(units.AU))
plot_e[node.child2.id].append(node.eccentricity)
plot_peri_AU[node.child2.id].append(
node.semimajor_axis.value_in(units.AU) *
(1.0 - node.eccentricity))
plot_stellar_inc_deg[node.child2.id].append(
node.inclination.value_in(units.deg))
counter = 0
while time <= end_time:
#print('Start of Time Loop')
#print(output_time_step)
time += output_time_step
counter += 1
#print(time)
#print(code.model_time)
#print(code.particles.semimajor_axis)
code.evolve_model(time)
#print('Evolved model to:', time.value_in(units.Myr), "Myr")
#print(code.particles.semimajor_axis)
channel_from_code_to_particles.copy()
#channel_from_code_to_particles.copy_attributes(['semimajor_axis', 'eccentricity', \
#'longitude_of_ascending_node', 'argument_of_pericenter', 'inclination'])
#print('Hello')
py_particles.time = time
if exportData:
plot_times_Myr.append(time.value_in(units.Myr))
nodes = py_particles.select(lambda x: x == True, ["is_binary"])
for i, node in enumerate(nodes):
plot_a_AU[node.child2.id].append(
node.semimajor_axis.value_in(units.AU))
plot_e[node.child2.id].append(node.eccentricity)
plot_peri_AU[node.child2.id].append(
node.semimajor_axis.value_in(units.AU) *
(1.0 - node.eccentricity))
plot_stellar_inc_deg[node.child2.id].append(
node.inclination.value_in(units.deg))
if time == end_time + output_time_step:
map_node_oe_to_lilsis(py_particles)
if debug_mode:
if time == end_time or time == output_time_step:
print('=' * 50)
print('t/kyr', time.value_in(units.kyr))
print('a/AU', nodes.semimajor_axis)
print('p/day', nodes.period)
print('e', nodes.eccentricity)
print('i/deg', nodes.inclination)
print('AP/deg', \
nodes.argument_of_pericenter)
print('LAN/deg', \
nodes.longitude_of_ascending_node)
# Check for Planet Destruction from Star
#print(py_particles.id, py_particles.semimajor_axis)
temp = check_for_stellar_collision(py_particles)
#print(temp)
# Returns 'None' if No Destruction!
if temp != None:
code.stop()
code = SecularMultiple()
code.model_time = time
py_particles = Particles()
py_particles.add_particles(temp)
code.particles.add_particles(py_particles)
py_particles.time = time
#code.commit_particles()
channel_from_particles_to_code = py_particles.new_channel_to(
code.particles)
channel_from_code_to_particles = code.particles.new_channel_to(
py_particles)
channel_from_particles_to_code.copy()
nodes = py_particles.select(lambda x: x == True, ["is_binary"])
stellarCollisionOccured = True
if useAMD:
PS = initialize_PlanetarySystem_from_HierarchicalSet(
py_particles)
#channel_from_code_to_particles.copy_attributes(['semimajor_axis', 'eccentricity', \
#'longitude_of_ascending_node', 'argument_of_pericenter', 'inclination'])
#print(code.particles.semimajor_axis)
# AMD Checking
if useAMD:
PS = update_oe_for_PlanetarySystem(PS, py_particles)
PS.get_SystemBetaValues()
if exportData:
for planet in PS.planets:
plot_AMDBeta[planet.id].append(planet.AMDBeta)
if counter % 100 == 0 and len(
PS.planets.select(lambda x: x < 1.0, ["AMDBeta"])) > 1:
break
if GCode == None:
code.stop()
else:
code = reset_secularmultiples(code)
if exportData:
if useAMD:
data = plot_times_Myr, plot_a_AU, plot_e, plot_peri_AU, plot_stellar_inc_deg, plot_AMDBeta
else:
data = plot_times_Myr, plot_a_AU, plot_e, plot_peri_AU, plot_stellar_inc_deg
else:
data = None
# Set the Output Code to be the New Code if a Stellar Collision Occured.
if stellarCollisionOccured:
newcode = code
else:
newcode = None
return py_particles, data, newcode
def evolve_quadruple(N_output, end_time, m1, m2, m3, m4, aA, aB, aC, eA, eB,
eC, iA, iB, iC, ApA, ApB, ApC, LANA, LANB, LANC):
masses = [m1, m2, m3, m4]
semimajor_axis = [aA, aB, aC]
eccentricity = [eA, eB, eC]
inclination = numpy.deg2rad([iA, iB, iC])
argument_of_percienter = numpy.deg2rad([ApA, ApB, ApC])
longitude_of_ascending_node = numpy.deg2rad([LANA, LANB, LANC])
print longitude_of_ascending_node
N_bodies = 4
N_binaries = N_bodies - 1
particles, binaries = initialize_multiple_system(
N_bodies, masses, semimajor_axis, eccentricity, inclination,
argument_of_percienter, longitude_of_ascending_node)
code = SecularMultiple()
code.particles.add_particles(particles)
channel_from_particles_to_code = particles.new_channel_to(code.particles)
channel_from_code_to_particles = code.particles.new_channel_to(particles)
channel_from_particles_to_code.copy()
### set up some arrays for plotting ###
print_smas_AU = [[] for x in range(N_binaries)]
print_rps_AU = [[] for x in range(N_binaries)]
print_parent_is_deg = [[] for x in range(N_binaries)]
print_times_Myr = []
time = 0.0 | units.yr
output_time_step = end_time / float(N_output)
while time <= end_time:
time += output_time_step
code.evolve_model(time)
channel_from_code_to_particles.copy()
print '=' * 50
print 't/Myr', time.value_in(units.Myr)
print 'e', binaries.eccentricity
print 'i/deg', numpy.rad2deg(binaries.inclination)
print 'AP/deg', \
numpy.rad2deg(binaries.argument_of_pericenter)
print 'LAN/deg', \
numpy.rad2deg(binaries.longitude_of_ascending_node)
### write to output arrays ###
print_times_Myr.append(time.value_in(units.Myr))
for index_binary in range(N_binaries):
print_smas_AU[index_binary].append(
binaries[index_binary].semimajor_axis.value_in(units.AU))
print_rps_AU[index_binary].append(
binaries[index_binary].semimajor_axis.value_in(units.AU) *
(1.0 - binaries[index_binary].eccentricity))
print_parent_is_deg[index_binary].append(
numpy.rad2deg(
binaries[index_binary].inclination_relative_to_parent))
### compute the `canonical' maximum eccentricity/periapsis distance that applies in the quadrupole-order test-particle limit if the `outer' binary is replaced by a point mass ###
print inclination[0], inclination[2], longitude_of_ascending_node[
0], longitude_of_ascending_node[2]
i_AC_init = compute_mutual_inclination(inclination[0], inclination[2],
longitude_of_ascending_node[0],
longitude_of_ascending_node[2])
i_BC_init = compute_mutual_inclination(inclination[1], inclination[2],
longitude_of_ascending_node[1],
longitude_of_ascending_node[2])
canonical_rp_min_A_AU = (
semimajor_axis[0] *
(1.0 - numpy.sqrt(1.0 -
(5.0 / 3.0) * numpy.cos(i_AC_init)**2))).value_in(
units.AU)
canonical_rp_min_B_AU = (
semimajor_axis[1] *
(1.0 - numpy.sqrt(1.0 -
(5.0 / 3.0) * numpy.cos(i_BC_init)**2))).value_in(
units.AU)
data = print_times_Myr, print_smas_AU, print_rps_AU, print_parent_is_deg, canonical_rp_min_A_AU, canonical_rp_min_B_AU
return data
def test6(self):
"""
test precession due to rotation
"""
M = 1.0|units.MJupiter
R = 1.5|units.RJupiter
m_per = 1.0|units.MSun
a0 = 30.0 | units.AU
e0 = 0.999
P0 = 2.0*numpy.pi*numpy.sqrt(a0**3/(constants.G*(M+m_per)))
n0 = 2.0*numpy.pi/P0
aF = a0*(1.0-e0**2)
nF = numpy.sqrt( constants.G*(M+m_per)/(aF**3) )
particles = create_nested_multiple(2, [m_per, M], [a0], [e0], [1.0e-5], [1.0e-5], [1.0e-5])
binaries = particles[particles.is_binary]
particles[0].radius = 1.0 | units.RSun
particles[1].radius = R
particles[1].spin_vec_x = 0.0 | 1.0/units.day
particles[1].spin_vec_y = 0.0 | 1.0/units.day
Omega_PS0 = n0*(33.0/10.0)*pow(a0/aF,3.0/2.0)
particles[1].spin_vec_z = Omega_PS0
k_L = 0.51
k_AM = k_L/2.0
rg = 0.25
particles[1].tides_method = 1
particles[1].include_tidal_friction_terms = False
particles[1].include_tidal_bulges_precession_terms = False
particles[1].include_rotation_precession_terms = True
particles[1].minimum_eccentricity_for_tidal_precession = 1.0e-5
particles[1].tides_apsidal_motion_constant = k_AM
particles[1].tides_gyration_radius = rg
code = SecularMultiple(redirection='none')
code.particles.add_particles(particles)
channel_to_code = particles.new_channel_to(code.particles)
channel_from_code = code.particles.new_channel_to(particles)
channel_to_code.copy()
t = 0.0 | units.Myr
dt = 1.0e1 | units.Myr
tend = 1.0e2 | units.Myr
t_print_array = quantities.AdaptingVectorQuantity()
a_print_array = quantities.AdaptingVectorQuantity()
e_print_array = quantities.AdaptingVectorQuantity()
AP_print_array = quantities.AdaptingVectorQuantity()
Omega_vec = [particles[1].spin_vec_x,particles[1].spin_vec_y,particles[1].spin_vec_z]
Omega = numpy.sqrt(Omega_vec[0]**2 + Omega_vec[1]**2 + Omega_vec[2]**2)
print 'Omega/n',Omega/n0
g_dot_rot = n0*(1.0 + m_per/M)*k_AM*pow(R/a0,5.0)*(Omega/n0)**2/((1.0-e0**2)**2)
t_rot = 2.0*numpy.pi/g_dot_rot
print 't_rot/Myr',t_rot.value_in(units.Myr)
N=0
while (t<tend):
t+=dt
code.evolve_model(t)
print 'flag',code.flag,t,binaries[0].semimajor_axis,binaries[0].eccentricity
channel_from_code.copy()
t_print_array.append(t)
a_print_array.append(binaries[0].semimajor_axis)
e_print_array.append(binaries[0].eccentricity | units.none)
AP_print_array.append(binaries[0].argument_of_pericenter | units.none)
N+=1
if HAS_MATPLOTLIB == True:
fig = pyplot.figure(figsize=(16,10))
plot1 = fig.add_subplot(4,1,1)
plot2 = fig.add_subplot(4,1,2,yscale="log")
plot3 = fig.add_subplot(4,1,3,yscale="log")
plot4 = fig.add_subplot(4,1,4,yscale="log")
plot1.plot(t_print_array.value_in(units.Myr),AP_print_array.value_in(units.none), color='r')
points = numpy.linspace(0.0,tend.value_in(units.Myr),N)
AP = 0.01 +2.0*numpy.pi*points/(t_rot.value_in(units.Myr))
AP = (AP+numpy.pi)%(2.0*numpy.pi) - numpy.pi ### -pi < AP < pi
plot1.plot(points,AP,color='g')
plot2.plot(t_print_array.value_in(units.Myr),numpy.fabs( (AP - AP_print_array.value_in(units.none))/AP ), color='r')
plot3.plot(t_print_array.value_in(units.Myr),numpy.fabs((a0-a_print_array)/a0), color='r')
plot4.plot(t_print_array.value_in(units.Myr),numpy.fabs((e0-e_print_array)/e0), color='r')
fontsize = 15
plot1.set_ylabel("$\omega$",fontsize=fontsize)
plot2.set_ylabel("$|(\omega_p-\omega)/\omega_p|$",fontsize=fontsize)
plot3.set_ylabel("$|(a_0-a)/a_0|$",fontsize=fontsize)
plot4.set_ylabel("$|(e_0-e)/e_0|$",fontsize=fontsize)
pyplot.show()