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examples.py
executable file
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examples.py
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"""
Some examples illustrating the usage of SecularMultiple
Adrian Hamers, March 2020
"""
import numpy as np
import numpy.random as randomf
import argparse
import time
from secularmultiple import SecularMultiple,Particle,Tools
try:
from matplotlib import pyplot
HAS_MATPLOTLIB = True
except ImportError:
HAS_MATPLOTLIB = False
def add_bool_arg(parser, name, default=False,help=None):
group = parser.add_mutually_exclusive_group(required=False)
group.add_argument('--' + name, dest=name, action='store_true',help="Enable %s"%help)
group.add_argument('--no-' + name, dest=name, action='store_false',help="Disable %s"%help)
parser.set_defaults(**{name:default})
def parse_arguments():
parser = argparse.ArgumentParser(formatter_class=argparse.ArgumentDefaultsHelpFormatter)
parser.add_argument("--e", type=int, dest="example", default=1, help="Example number")
### boolean arguments ###
add_bool_arg(parser, 'verbose', default=True, help="Verbose terminal output")
add_bool_arg(parser, 'plot', default=True, help="Make plots")
add_bool_arg(parser, 'show', default=True, help="Show plots")
args = parser.parse_args()
return args
class examples():
def example1(self,args):
"""
Example of a three-planet system with tides in the innermost planet
System parameters taken from http://adsabs.harvard.edu/abs/2011ApJ...735..109W
Units used in SecularMultiple:
length -- AU
time -- yr
mass -- MSun
"""
code = SecularMultiple() ### initialize the code
CONST_G = code.CONST_G ### extract physical constants from the code
CONST_C = code.CONST_C
CONST_R_SUN = code.CONST_R_SUN
RJup = 0.1027922358015816*CONST_R_SUN
MJup = 0.0009546386983890755
day = 1.0/365.25
second = day/(24.0*3600.0)
N=4
m0 = 1.0
m1 = 0.5*MJup
m2 = MJup
m3 = 1.5*MJup
a1 = 1.0
a2 = 6.0
a3 = 16.0
e1 = 0.066
e2 = 0.188
e3 = 0.334
i1 = 4.5*np.pi/180.0
i2 = 19.9*np.pi/180.0
i3 = 7.9*np.pi/180.0
AP1 = np.pi
AP2 = 0.38*np.pi
AP3 = np.pi
LAN1 = 0.01
LAN2 = np.pi
LAN3 = 0.01
R0 = 1.0*CONST_R_SUN
R1 = 1.0*RJup
R2 = 1.0*RJup
R3 = 1.0*RJup
masses = [m0,m1,m2,m3]
radii = [R0,R1,R2,R3]
semimajor_axes = [a1,a2,a3]
eccentricities = [e1,e2,e3]
inclinations = [i1,i2,i3]
APs = [AP1,AP2,AP3]
LANs = [LAN1,LAN2,LAN3]
particles = Tools.create_nested_multiple(N, masses,semimajor_axes,eccentricities,inclinations,APs,LANs,radii=radii)
orbits = [x for x in particles if x.is_binary==True]
N_orbits = len(orbits)
particles[1].spin_vec_x = 0.0
particles[1].spin_vec_y = 0.0
particles[1].spin_vec_z = 4.0e-2/day
k_L = 0.38
k_AM = k_L/2.0
rg = 0.25
tau = 0.66*second
T = R1**3/(CONST_G*m1*tau)
t_V = 3.0*(1.0 + 1.0/k_L)*T
particles[0].include_tidal_friction_terms = False
particles[1].tides_method = 1
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
orbits[0].include_1PN_terms = False ### do not include 1PN terms here
code.add_particles(particles)
primary = code.particles[0]
code.enable_tides = True
code.enable_root_finding = True
a_AU_print = [[] for x in range(N_orbits)]
e_print = [[] for x in range(N_orbits)]
INCL_print = [[] for x in range(N_orbits)]
rel_INCL_print = [[] for x in range(N_orbits)]
t_print = []
t = 0.0
Nsteps = 2000
tend = 3.0e8
dt = tend/float(Nsteps)
import time
start = time.time()
while t<=tend:
code.evolve_model(t)
t+=dt
if args.verbose==True:
print('t/Myr',t*1e-6,'es',[o.e for o in orbits])
for i in range(N_orbits):
rel_INCL_print[i].append(orbits[i].INCL_parent)
a_AU_print[i].append(orbits[i].a)
e_print[i].append(orbits[i].e)
INCL_print[i].append(orbits[i].INCL)
t_print.append(t)
if args.verbose==True:
print('wall time',time.time()-start)
t_print = np.array(t_print)
for i in range(N_orbits):
INCL_print[i] = np.array(INCL_print[i])
rel_INCL_print[i] = np.array(rel_INCL_print[i])
e_print[i] = np.array(e_print[i])
a_AU_print[i] = np.array(a_AU_print[i])
if HAS_MATPLOTLIB==True and args.plot==True:
fig=pyplot.figure(figsize=(8,8))
plot1=fig.add_subplot(2,1,1,yscale="log")
plot2=fig.add_subplot(2,1,2,yscale="linear")
colors=['k','r','g']
for i in range(N_orbits):
color=colors[i]
plot1.plot(1.0e-6*t_print,a_AU_print[i],color=color)
plot1.plot(1.0e-6*t_print,a_AU_print[i]*(1.0-e_print[i]),color=color)
plot1.plot(1.0e-6*t_print,a_AU_print[i]*(1.0+e_print[i]),color=color)
plot2.plot(1.0e-6*t_print,INCL_print[i]*180.0/np.pi,color=color)
plot1.set_xlabel("$t/\mathrm{Myr}$")
plot2.set_xlabel("$t/\mathrm{Myr}$")
plot1.set_ylabel("$r_i/\mathrm{AU}$")
plot2.set_ylabel("$\mathrm{incl}_i/\mathrm{deg}$")
fig.savefig("example1.pdf")
if args.show==True:
pyplot.show()
def example2(self,args):
"""
Lidov-Kozai problem of a planet around a star around a supermassive black hole.
Includes perturbations from other stars in the form of vector resonant relaxation (VRR)
"""
code = SecularMultiple() ### initialize the code
CONST_G = code.CONST_G ### extract physical constants from the code
CONST_C = code.CONST_C
CONST_R_SUN = code.CONST_R_SUN
RJup = 0.1027922358015816*CONST_R_SUN
MJup = 0.0009546386983890755
day = 1.0/365.25
second = day/(24.0*3600.0)
meter = 1.0/1.496e+11
### Input parameters ###
m1 = 1.0
m2 = MJup
m3 = 4.0e6
a1 = 1.0e-1
a2 = 1.0e4
e1 = 0.01
e2 = 0.1
i1 = 4.5*np.pi/180.0
i2 = 19.9*np.pi/180.0
AP1 = np.pi
AP2 = 0.38*np.pi
LAN1 = 0.01
LAN2 = np.pi
R1 = 1.0*CONST_R_SUN
R2 = 1.0*RJup
R3 = CONST_G*m3/(CONST_C**2)
m_star = 1.0
gamma = 3.0/2.0
VRR_model = 3
### Simulation parameters ###
VRR_include_mass_precession = True
include_inner_1PN_terms = True
include_outer_1PN_terms = True
### Process parameters ###
P1 = 2.0*np.pi*np.sqrt(a1**3/(CONST_G*(m1+m2)))
P2 = 2.0*np.pi*np.sqrt(a2**3/(CONST_G*(m1+m2+m3)))
masses = [m1,m2,m3]
radii = [R1,R2,R3]
semimajor_axes = [a1,a2]
eccentricities = [e1,e2]
inclinations = [i1,i2]
APs = [AP1,AP2]
LANs = [LAN1,LAN2]
N = len(masses)
particles = Tools.create_nested_multiple(N, masses,semimajor_axes,eccentricities,inclinations,APs,LANs,radii=radii)
orbits = [x for x in particles if x.is_binary==True]
N_orbits = len(orbits)
inner_orbit = orbits[0]
outer_orbit = orbits[1]
c1 = 4.8
c2 = -2.9
log10_sigma_h_km_s = (np.log10(m3) - c2)/c1
sigma_h_km_s = pow(10.0,log10_sigma_h_km_s)
sigma_h = 1.0e3*sigma_h_km_s*meter/second
if args.verbose==True:
print('sigma_h_km_s',sigma_h_km_s,'sigma_h',sigma_h)
# K_12 = K_12_function(gamma)
# K_32 = K_32_function(gamma)
# C_NRR = ((3.0*numpy.pi)/(64.0))*1.0/( K_12 - (1.0/5.0)*K_32 + (5.0*numpy.pi/8.0)*(1.0/(2.0*gamma-1.0)) )
r_h = CONST_G*m3*(1.0/(sigma_h**2*(1.0+gamma)))*(1.0 + (1.0 + gamma)/(gamma - 1.0))
r_0 = r_h
n_0 = (2.0*m3/m_star)*((3.0-gamma)/(4.0*np.pi*r_h**3))
r = a2
rho_star = compute_rho_star_r(r,gamma,n_0,r_0,m_star)
n_star = compute_n_star_r(r,gamma,n_0,r_0,m_star)
M_star = compute_M_star_r(r,gamma,n_0,r_0,m_star)
N_star = compute_N_star_r(r,gamma,n_0,r_0,m_star)
sigma_r = compute_sigma_r(r,gamma,n_0,r_0,m_star,m3,CONST_G)
if args.verbose==True:
print('n_star',n_star,'M_star',M_star,'N_star',N_star,'sigma_r',sigma_r)
LK_timescale = (P2**2/P1)*((m1+m2+m3)/m3)*pow(1.0-e2**2,3.0/2.0)
if args.verbose==True:
print('LK_timescale',LK_timescale)
VRR_mass_precession_timescale = (1.0/2.0)*pow(1.0-e2**2,-1.0/2.0)*(m3/M_star)*P2
VRR_mass_precession_rate = 1.0/VRR_mass_precession_timescale
VRR_timescale = (P2/2.0)*(m3/m_star)*1.0/np.sqrt(N_star)
#VRR_timescale *= 0.1
if args.verbose==True:
print('VRR_mass_precession_timescale',VRR_mass_precession_timescale,'VRR_timescale',VRR_timescale)
outer_orbit.VRR_include_mass_precession = VRR_include_mass_precession
outer_orbit.VRR_mass_precession_rate = VRR_mass_precession_rate
VRR_reorientation_timestep = np.sqrt(0.1)*VRR_timescale
if args.verbose==True:
print('VRR_reorientation_timestep',VRR_reorientation_timestep)
outer_orbit.VRR_model = VRR_model
reorientation_function(VRR_model,VRR_timescale,VRR_reorientation_timestep,outer_orbit)
v_bin = np.sqrt(CONST_G*(m1+m2)/a1)
q_sigma = (m1+m2)/m_star
log_Lambda = np.log( 3.0*((1.0 + 1.0/q_sigma)/(1.0 + 2.0/q_sigma))*sigma_r**2/v_bin**2 )
evaporation_timescale = np.sqrt( (1.0+q_sigma)/(2.0*np.pi*q_sigma) )*(m1+m2)*sigma_r/(8.0*np.sqrt(np.pi)*CONST_G*a1*m_star**2*n_star*log_Lambda)
if args.verbose==True:
print('evaporation_timescale',evaporation_timescale)
inner_orbit.include_1PN_terms = include_inner_1PN_terms
outer_orbit.include_1PN_terms = include_outer_1PN_terms
code.add_particles(particles)
primary = code.particles[0]
code.enable_tides = False
code.enable_root_finding = True
code.enable_VRR = True
a_AU_print = [[] for x in range(N_orbits)]
e_print = [[] for x in range(N_orbits)]
INCL_print = [[] for x in range(N_orbits)]
rel_INCL_print = [[] for x in range(N_orbits)]
t_print = []
t = 0.0
Nsteps = 1000
tend = evaporation_timescale
dt_fixed = tend/float(Nsteps)
t_next_reorientation = VRR_reorientation_timestep
import time
start = time.time()
while t<=tend:
dt = dt_fixed
if t+dt > t_next_reorientation:
dt = t_next_reorientation - t
t_next_reorientation += VRR_reorientation_timestep
reorientation_function(VRR_model,VRR_timescale,t_next_reorientation,outer_orbit)
t+=dt
code.evolve_model(t)
if args.verbose==True:
print('t',t,'es',[o.e for o in orbits],'Omegas',[o.LAN for o in orbits])
for i in range(N_orbits):
rel_INCL_print[i].append(orbits[i].INCL_parent)
a_AU_print[i].append(orbits[i].a)
e_print[i].append(orbits[i].e)
INCL_print[i].append(orbits[i].INCL)
t_print.append(t)
if args.verbose==True:
print('wall time',time.time()-start)
t_print = np.array(t_print)
for i in range(N_orbits):
INCL_print[i] = np.array(INCL_print[i])
rel_INCL_print[i] = np.array(rel_INCL_print[i])
e_print[i] = np.array(e_print[i])
a_AU_print[i] = np.array(a_AU_print[i])
if HAS_MATPLOTLIB==True and args.plot==True:
fig=pyplot.figure(figsize=(8,8))
plot1=fig.add_subplot(2,1,1,yscale="log")
plot2=fig.add_subplot(2,1,2,yscale="linear")
colors=['k','r','g']
for i in range(N_orbits):
color=colors[i]
plot1.plot(1.0e-6*t_print,a_AU_print[i],color=color)
plot1.plot(1.0e-6*t_print,a_AU_print[i]*(1.0-e_print[i]),color=color)
plot1.plot(1.0e-6*t_print,a_AU_print[i]*(1.0+e_print[i]),color=color)
plot2.plot(1.0e-6*t_print,rel_INCL_print[i]*180.0/np.pi,color=color)
plot1.set_xlabel("$t/\mathrm{Myr}$")
plot2.set_xlabel("$t/\mathrm{Myr}$")
plot1.set_ylabel("$r_i/\mathrm{AU}$")
plot2.set_ylabel("$\mathrm{incl}_\mathrm{rel}/\mathrm{deg}$")
fig.savefig("example2.pdf")
pyplot.show()
def example3(self,args):
m1=1.0
m2=1.0e-6
m3=1.0
e1=0
e2=0.4
a1=1.0
a2=10.0
i1=0.2
i2=65.0*np.pi/180.0
AP1=0
AP2=0
LAN1=0
LAN2=0
do_nbody=True
particles = Tools.create_nested_multiple(3, [m1,m2,m3],[a1,a2],[e1,e2],[i1,i2],[AP1,AP2],[LAN1,LAN2])
bodies = [x for x in particles if x.is_binary==False]
binaries = [x for x in particles if x.is_binary==True]
N_binaries = len(binaries)
N_bodies = len(bodies)
code = SecularMultiple()
code.add_particles(particles)
CONST_G = code.CONST_G
P1=2.0*np.pi*np.sqrt(a1**3/(CONST_G*(m1+m2)))
P2=2.0*np.pi*np.sqrt(a2**3/(CONST_G*(m1+m2+m3)))
P_LK12 = (P2**2/P1)*((m1+m2+m3)/m3)*pow(1.0-e2**2,3.0/2.0)
if args.verbose==True:
print("Ps",P1*1e-6,P2*1e-6)
print("P_LKs",P_LK12*1e-6)
N = 5000
tend = 1.e4
integration_methods = [[0,0],[0,1]]
#integration_methods = [0,0,0]
KS_use_V = [[True,True],[True,True]]
#KS_use_V = [True,True,False]
terms = [[False,True,True,True,True,True],[False,True,True,True,True,True]]
import time
data_arrays = []
for index_combination,integration_method in enumerate(integration_methods):
if args.verbose==True:
print("index_combination",index_combination)
particles = Tools.create_nested_multiple(3, [m1,m2,m3],[a1,a2],[e1,e2],[i1,i2],[AP1,AP2],[LAN1,LAN2])
bodies = [x for x in particles if x.is_binary==False]
binaries = [x for x in particles if x.is_binary==True]
binaries[0].integration_method = integration_methods[index_combination][0]
binaries[1].integration_method = integration_methods[index_combination][1]
binaries[0].KS_use_perturbing_potential = KS_use_V[index_combination][0]
binaries[1].KS_use_perturbing_potential = KS_use_V[index_combination][1]
code = SecularMultiple()
code.add_particles(particles)
code.enable_root_finding = True
binaries[0].check_for_physical_collision_or_orbit_crossing=True
bodies[0].radius=1.0e-5
bodies[1].radius=1.0e-5
code.include_double_averaging_corrections = terms[index_combination][0]
code.include_quadrupole_order_terms = terms[index_combination][1]
code.include_octupole_order_binary_pair_terms = terms[index_combination][2]
code.include_octupole_order_binary_triplet_terms = terms[index_combination][3]
code.include_hexadecupole_order_binary_pair_terms = terms[index_combination][4]
code.include_dotriacontupole_order_binary_pair_terms = terms[index_combination][5]
if args.verbose==True:
print("Integration methods ",[x.integration_method for x in binaries],"KS_V",[x.KS_use_perturbing_potential for x in binaries],"terms",code.include_double_averaging_corrections,code.include_quadrupole_order_terms,code.include_octupole_order_binary_pair_terms,code.include_octupole_order_binary_triplet_terms,code.include_hexadecupole_order_binary_pair_terms,code.include_dotriacontupole_order_binary_pair_terms)
a_print = [[] for x in range(N_binaries)]
e_print = [[] for x in range(N_binaries)]
i_print = [[] for x in range(N_binaries)]
rel_INCL_print = [[] for x in range(N_binaries)]
t_print = []
start = time.time()
t = 0.0
dt = tend/float(N)
while t<tend:
t+=dt
code.evolve_model(t)
if args.verbose==True:
print('t',t,'es',[o.e for o in binaries])
for i in range(N_binaries):
a_print[i].append([binaries[i].a])
e_print[i].append([binaries[i].e])
i_print[i].append(binaries[i].INCL)
rel_INCL_print[i].append(binaries[i].INCL_parent)
t_print.append(t)
wall_time = time.time()-start
code.reset()
t_print = np.array(t_print)
for i in range(N_binaries):
a_print[i] = np.array(a_print[i])
e_print[i] = np.array(e_print[i])
i_print[i] = np.array(i_print[i])
data = {'t_print':t_print,'a_print':a_print,'e_print':e_print,'i_print':i_print,'wall_time':wall_time,'integration_methods':integration_methods[index_combination],'KS_use_perturbing_potential':KS_use_V[index_combination],'terms':terms[index_combination]}
data_arrays.append(data)
if HAS_MATPLOTLIB==True and args.plot==True:
linestyles=['solid','dotted','dashed','-.']
linewidth=2.0
fig=pyplot.figure(figsize=(8,8))
plot1=fig.add_subplot(2,1,1,yscale="linear")
plot2=fig.add_subplot(2,1,2,yscale="log")
linewidths=[1.5,2.5,1.5]
colors =['k','tab:red','tab:orange']
for index_combination,data in enumerate(data_arrays):
linewidth=linewidths[index_combination]
linestyle=linestyles[index_combination]
N_binaries = len(data["a_print"])
color=colors[index_combination]
if index_combination==0:
label = "$\mathrm{Double\,averaged; \,WT=%s\,s}$"%round(data["wall_time"],1)
elif index_combination==1:
label = "$\mathrm{Single\,averaged; \,WT=%s\,s}$"%round(data["wall_time"],1)
for i in range(N_binaries):
if i!=0:
label=""
label_nb=""
plot1.plot(1.0e-6*data["t_print"],data["i_print"][i]*180.0/np.pi,color=color,linestyle=linestyle,linewidth=linewidth)
plot2.plot(1.0e-6*data["t_print"],1.0-data["e_print"][i],color=color,linestyle=linestyle,linewidth=linewidth,label=label)
fontsize=18
labelsize=18
plot1.set_ylabel("$i_\mathrm{}\,(\mathrm{deg})$",fontsize=fontsize)
plot2.set_ylabel("$1-e$",fontsize=fontsize)
plot2.set_xlabel("$t/\mathrm{Myr}$",fontsize=fontsize)
plots=[plot1,plot2]
for plot in plots:
plot.tick_params(axis='both', which ='major', labelsize = labelsize,bottom=True, top=True, left=True, right=True)
plot2.set_ylim(5e-4,1.1e0)
plot1.set_xticklabels([])
ticks=plot1.get_yticks()
plot1.set_yticks(ticks[2::])
handles,labels = plot2.get_legend_handles_labels()
plot2.legend(handles,labels,loc="lower left",fontsize=0.8*fontsize)
fig.subplots_adjust(hspace=0.0,wspace=0.0)
fig.savefig("example3.pdf")
if args.show==True:
pyplot.show()
### Functions below are used for example 2 ###
def reorientation_function(VRR_model,VRR_timescale,next_reorientation_time,orbit):
print('='*50)
print('reorientation_function')
theta = 2.0*np.pi*randomf.random() - np.pi
phi = 2.0*np.pi*randomf.random()
r_hat_vec = np.array([np.sin(theta)*np.cos(phi),np.sin(theta)*np.sin(phi),np.cos(theta)])
if VRR_model == 1:
Omega = 1.0/VRR_timescale
orbit.VRR_Omega_vec_x = r_hat_vec[0]*Omega
orbit.VRR_Omega_vec_y = r_hat_vec[1]*Omega
orbit.VRR_Omega_vec_z = r_hat_vec[2]*Omega
if VRR_model == 2:
raise RuntimeError('VRR model 2 not supported')
if VRR_model == 3:
mu = 0.0
sigma = (1.0/VRR_timescale)
orbit.VRR_eta_20_init = orbit.VRR_eta_20_final
orbit.VRR_eta_a_22_init = orbit.VRR_eta_a_22_final
orbit.VRR_eta_b_22_init = orbit.VRR_eta_b_22_final
orbit.VRR_eta_a_21_init = orbit.VRR_eta_a_21_final
orbit.VRR_eta_b_21_init = orbit.VRR_eta_b_21_final
orbit.VRR_eta_20_final = randomf.normal(mu,sigma)
orbit.VRR_eta_a_22_final = randomf.normal(mu,sigma)
orbit.VRR_eta_b_22_final = randomf.normal(mu,sigma)
orbit.VRR_eta_a_21_final = randomf.normal(mu,sigma)
orbit.VRR_eta_b_21_final = randomf.normal(mu,sigma)
orbit.VRR_initial_time = orbit.VRR_final_time
orbit.VRR_final_time = next_reorientation_time
def compute_M_star_r(r,gamma,n_0,r_0,m_star):
return 4.0*np.pi*(1.0/(3.0-gamma))*m_star*r_0**3*n_0*pow(r/r_0,3.0-gamma)
def compute_N_star_r(r,gamma,n_0,r_0,m_star):
return compute_M_star_r(r,gamma,n_0,r_0,m_star)/m_star
def compute_n_star_r(r,gamma,n_0,r_0,m_star):
return n_0*pow(r/r_0,-gamma)
def compute_rho_star_r(r,gamma,n_0,r_0,m_star):
return m_star*compute_n_star_r(r,gamma,n_0,r_0,m_star)
def compute_sigma_r(r,gamma,n_0,r_0,m_star,M_MBH,CONST_G):
return np.sqrt( CONST_G*M_MBH*(1.0/(r*(1.0+gamma)))*(1.0 + ((gamma+1.0)/(2.0*gamma-2.0))*compute_M_star_r(r,gamma,n_0,r_0,m_star)/M_MBH ) )
if __name__ == '__main__':
args = parse_arguments()
t=examples()
print( 'Running example number',args.example,'; verbose =',args.verbose,'plot =',args.plot)
function = getattr(t, 'example%s'%args.example)
function(args)