def evolve_model(end_time, double_star, stars):
time = 0 | units.yr
dt = 0.5 * end_time / 1000. * 2
converter = nbody_system.nbody_to_si(double_star.mass,
double_star.semimajor_axis)
stars2 = stars.copy()
gravity = Hermite(converter)
gravity.particles.add_particle(stars)
to_stars = gravity.particles.new_channel_to(stars)
from_stars = stars.new_channel_to(gravity.particles)
gravity2 = Hermite(converter)
gravity2.particles.add_particle(stars2)
to_stars2 = gravity2.particles.new_channel_to(stars2)
from_stars2 = stars2.new_channel_to(gravity2.particles)
period = (2 * numpy.pi *
(double_star.semimajor_axis * double_star.semimajor_axis *
double_star.semimajor_axis /
(constants.G * double_star.mass)).sqrt())
print("Period =", period.as_string_in(units.yr))
print("Mass loss timestep =", dt)
print("Steps per period: = {:1.2f}".format(period / dt))
a_an = [] | units.au
e_an = []
atemp = double_star.semimajor_axis
etemp = double_star.eccentricity
a = [] | units.au
e = []
ome = []
a2 = [] | units.au
e2 = []
ome2 = []
m1 = [] | units.MSun
m2 = [] | units.MSun
t = [] | units.yr
while time < end_time:
time += dt
gravity.evolve_model(time)
gravity2.evolve_model(time)
to_stars.copy()
to_stars2.copy()
dmdtloss = mass_loss_rate(stars.mass)
dmdtacc = dmdt_acc(dmdtloss)
orbital_elements = orbital_elements_from_binary(stars, G=constants.G)
orbital_elements2 = orbital_elements_from_binary(stars2, G=constants.G)
# etemp = orbital_elements[3]
# atemp = orbital_elements[2]
dadt = dadt_masschange(atemp, stars.mass, dmdtloss + dmdtacc)
dedt = dedt_masschange(etemp, stars.mass, dmdtloss + dmdtacc)
dadt += dadt_momentumchange(atemp, etemp, stars.mass, dmdtacc)
dedt += dedt_momentumchange(etemp, stars.mass, dmdtacc)
h = (constants.G * stars.mass.sum() * atemp * (1 - etemp * etemp))**0.5
dhdt = dhdt_momentumchange(h, stars.mass, dmdtacc)
atemp = atemp + dadt * dt
etemp = etemp + dedt * dt
a_an.append(atemp)
e_an.append(etemp)
kick_from_accretion(stars, dmdtacc, dt)
dhdt_dadt_to_kick(stars2, dhdt, dadt, dmdtloss + dmdtacc, dt)
stars.mass += (dmdtloss + dmdtacc) * dt
stars2.mass += (dmdtloss + dmdtacc) * dt
from_stars.copy()
from_stars2.copy()
a.append(orbital_elements[2])
e.append(orbital_elements[3])
ome.append(orbital_elements[7])
a2.append(orbital_elements2[2])
e2.append(orbital_elements2[3])
ome2.append(orbital_elements2[7])
m1.append(stars[0].mass)
m2.append(stars[1].mass)
t.append(time)
print("time=", time.in_(units.yr), "a=", a[-1].in_(units.RSun), "e=",
e[-1], "m=", stars.mass.in_(units.MSun), "end=\r")
gravity.stop()
gravity2.stop()
from matplotlib import pyplot
pyplot.rc('text', usetex=True)
pyplot.rcParams.update({'font.size': 16})
fig, axis = pyplot.subplots(nrows=2, ncols=2, sharex=True, figsize=(13, 6))
axis[0][0].plot(t.value_in(units.yr),
a.value_in(units.RSun),
label="nbody (direct)",
lw=2)
axis[0][0].plot(t.value_in(units.yr),
a2.value_in(units.RSun),
label="nbody (heuristic)",
lw=2,
ls="--")
axis[0][0].plot(t.value_in(units.yr),
a_an.value_in(units.RSun),
label="analytic",
lw=2,
ls="-.")
axis[0][0].set_ylabel("a [$R_\odot$]")
axis[0][0].legend()
axis[0][1].plot(t.value_in(units.yr),
m1.value_in(units.MSun),
label="m1",
lw=2,
c="tab:red")
axis[0][1].plot(t.value_in(units.yr),
m2.value_in(units.MSun),
label="m2",
lw=2,
c="tab:cyan")
axis[0][1].set_ylabel("M [$M_\odot$]")
axis[0][1].legend()
axis[1][1].plot(t.value_in(units.yr), e, lw=2)
axis[1][1].plot(t.value_in(units.yr), e2, lw=2, ls="--")
axis[1][1].plot(t.value_in(units.yr), e_an, lw=2, ls="-.")
axis[1][1].set_ylabel("e")
axis[1][0].plot(t.value_in(units.yr), ome, lw=2, label="nbody (direct)")
axis[1][0].plot(t.value_in(units.yr),
ome2,
lw=2,
ls="--",
label="nbody (heuristic)")
axis[1][0].set_ylabel("$\omega$ [degrees]")
axis[1][1].set_xlabel("time [yr]")
axis[1][0].set_xlabel("time [yr]")
pyplot.tight_layout()
pyplot.subplots_adjust(hspace=0, top=0.93, bottom=0.1)
pyplot.suptitle("mloss+macc+momentum change, same model")
pyplot.savefig("comparisons.png")
pyplot.show()
def evolve_model(end_time, double_star, stars):
time = 0 | units.yr
dt = 0.5 * end_time / 1000.
converter = nbody_system.nbody_to_si(double_star.mass,
double_star.semimajor_axis)
gravity = Hermite(converter)
gravity.particles.add_particle(stars)
to_stars = gravity.particles.new_channel_to(stars)
from_stars = stars.new_channel_to(gravity.particles)
a_an = [] | units.au
e_an = []
# dt_an = dt/1000.
atemp = double_star.semimajor_axis
etemp = double_star.eccentricity
print(atemp)
a = [] | units.au
e = []
m = [] | units.MSun
t = [] | units.yr
while time < end_time:
# ana_time = time
# ana_time_end = time + dt
# while ana_time < ana_time_end:
# dmdt_ana = -1*mass_loss_rate(stars.mass)
# print(atemp)
# dadt = dadt_massloss(atemp, stars.mass, dmdt_ana)
# dedt = dedt_massloss(etemp, stars.mass, dmdt_ana)
# atemp = dadt*dt
# etemp = dedt*dt
# ana_time += dt_an
time += dt
gravity.evolve_model(time)
to_stars.copy()
dmdt = mass_loss_rate(stars.mass)
dadt = dadt_massloss(atemp, stars.mass, dmdt)
dedt = dedt_massloss(etemp, stars.mass, dmdt)
atemp = atemp + dadt * dt
etemp = etemp + dedt * dt
a_an.append(atemp)
e_an.append(etemp)
stars.mass -= dmdt * dt
from_stars.copy()
orbital_elements = orbital_elements_from_binary(stars, G=constants.G)
a.append(orbital_elements[2])
e.append(orbital_elements[3])
m.append(stars.mass.sum())
t.append(time)
print("time=", time.in_(units.yr), "a=", a[-1].in_(units.RSun), "e=",
e[-1], "m=", stars.mass.in_(units.MSun))
gravity.stop()
from matplotlib import pyplot
fig, axis = pyplot.subplots(nrows=2, ncols=2, sharex=True)
axis[0][0].scatter(t.value_in(units.yr), a.value_in(units.RSun))
axis[0][0].scatter(t.value_in(units.yr), a_an.value_in(units.RSun))
axis[0][0].set_ylabel("a [$R_\odot$]")
axis[0][1].scatter(t.value_in(units.yr), m.value_in(units.MSun))
axis[0][1].set_ylabel("M [$M_\odot$]")
axis[1][1].scatter(t.value_in(units.yr), e)
axis[1][1].scatter(t.value_in(units.yr), e_an)
axis[1][1].set_ylabel("e")
axis[1][1].set_xlabel("time [yr]")
axis[1][0].set_xlabel("time [yr]")
pyplot.show()
pyplot.savefig("mloss.png")
def kick(self, dt):
kinetic_energy_before = self.particles.kinetic_energy()
dmdt = mass_loss_rate(self.particles.mass)
self.particles.mass -= dmdt*dt
kinetic_energy_after = self.particles.kinetic_energy()
return kinetic_energy_after - kinetic_energy_before
def evolve_model(end_time, double_star, stars):
time = 0 | units.yr
dt = 0.5 * end_time / 1000. * 2
converter = nbody_system.nbody_to_si(double_star.mass,
double_star.semimajor_axis)
gravity = Hermite(converter)
gravity.particles.add_particle(stars)
to_stars = gravity.particles.new_channel_to(stars)
from_stars = stars.new_channel_to(gravity.particles)
period = (2 * numpy.pi *
(double_star.semimajor_axis * double_star.semimajor_axis *
double_star.semimajor_axis /
(constants.G * double_star.mass)).sqrt())
print("Period =", period.as_string_in(units.yr))
print("Mass loss timestep =", dt)
print("Steps per period: = {:1.2f}".format(period / dt))
E_an = [] | (units.km / units.s)**2
h_an = [] | units.km**2 / units.s
Etemp = -double_star.mass * constants.G / (2 * double_star.semimajor_axis)
htemp = (double_star.mass * constants.G * double_star.semimajor_axis *
(1 - double_star.eccentricity * double_star.eccentricity))**0.5
E_num = [] | (units.km / units.s)**2
h_num = [] | units.km**2 / units.s
m1 = [] | units.MSun
m2 = [] | units.MSun
t = [] | units.yr
t_an = [] | units.yr
dt_an = period * 2.5
time_an = 0 | units.yr
while time < end_time:
time += dt
gravity.evolve_model(time)
to_stars.copy()
dmdtloss = mass_loss_rate(stars.mass)
dmdtacc = dmdt_acc(dmdtloss)
orbital_elements = orbital_elements_from_binary(stars, G=constants.G)
h = h_from_stars(stars)
E = E_from_stars(stars)
if time > time_an:
#atemp = orbital_elements[2]
#htemp = h
E_an.append(Etemp)
h_an.append(htemp)
t_an.append(time)
dEdt = dEdt_momentum_secular(htemp, Etemp, stars.mass, dmdtacc)
dhdt = dhdt_momentum_secular(htemp, stars.mass, dmdtacc)
Etemp = Etemp + dEdt * dt_an
htemp = htemp + dhdt * dt_an
E_an.append(Etemp)
h_an.append(htemp)
t_an.append(time + dt_an)
time_an += dt_an
kick_from_accretion(stars, dmdtacc, dt)
#stars.mass += (dmdtloss + dmdtacc) * dt
#stars2.mass += (dmdtloss + dmdtacc) * dt
from_stars.copy()
h_num.append(h)
E_num.append(E)
m1.append(stars[0].mass)
m2.append(stars[1].mass)
t.append(time)
print("time=",
time.in_(units.yr),
"h=",
h.in_(units.km**2 / units.s),
"E=",
E.in_((units.km / units.s)**2),
"m=",
stars.mass.in_(units.MSun),
end="\r")
gravity.stop()
from matplotlib import pyplot
pyplot.rc('text', usetex=True)
pyplot.rcParams.update({'font.size': 16})
fig, axis = pyplot.subplots(nrows=2, ncols=2, sharex=True, figsize=(13, 6))
axis[0][0].plot(t.value_in(units.yr),
E_num.value_in((units.km / units.s)**2),
label="nbody (direct)",
lw=2)
axis[0][0].plot(t_an.value_in(units.yr),
E_an.value_in((units.km / units.s)**2),
label="analytic",
lw=2,
ls="-.")
axis[0][0].set_ylabel("E [km/s]")
axis[0][0].legend()
axis[0][1].plot(t.value_in(units.yr),
m1.value_in(units.MSun),
label="m1",
lw=2,
c="tab:red")
axis[0][1].plot(t.value_in(units.yr),
m2.value_in(units.MSun),
label="m2",
lw=2,
c="tab:cyan")
axis[0][1].set_ylabel("M [$M_\odot$]")
axis[0][1].legend()
axis[1][1].plot(t.value_in(units.yr),
h_num.value_in(units.km**2 / units.s),
lw=2)
axis[1][1].plot(t_an.value_in(units.yr),
h_an.value_in(units.km**2 / units.s),
lw=2,
ls="-.")
axis[1][1].set_ylabel("h [km$^2$/s]")
#axis[1][0].plot(t.value_in(units.yr), ome, lw=2, label="nbody (direct)")
#axis[1][0].set_ylabel("$\omega$ [degrees]")
axis[1][1].set_xlabel("time [yr]")
axis[1][0].set_xlabel("time [yr]")
pyplot.tight_layout()
pyplot.subplots_adjust(hspace=0, top=0.93, bottom=0.1)
pyplot.suptitle("mloss+macc+momentum change, same model")
pyplot.savefig("debug.png")
pyplot.show()
def evolve_model(end_time, double_star, stars):
time = 0 | units.yr
dt = 0.5*end_time/1000.
converter = nbody_system.nbody_to_si(double_star.mass,
double_star.semimajor_axis)
gravity = Hermite(converter)
gravity.particles.add_particle(stars)
to_stars = gravity.particles.new_channel_to(stars)
from_stars = stars.new_channel_to(gravity.particles)
period = (
2*numpy.pi
* (
double_star.semimajor_axis*double_star.semimajor_axis*double_star.semimajor_axis
/ (constants.G*double_star.mass)
).sqrt()
)
print("Period =", period.as_string_in(units.yr))
print("Mass loss timestep =", dt)
print("Steps per period: = {:1.2f}".format(period/dt))
a_an = [] | units.au
e_an = []
atemp = double_star.semimajor_axis
etemp = double_star.eccentricity
print(atemp)
a = [] | units.au
e = []
m = [] | units.MSun
t = [] | units.yr
while time<end_time:
time += dt
gravity.evolve_model(time)
to_stars.copy()
dmdt = mass_loss_rate(stars.mass)
dadt = dadt_masschange(atemp, stars.mass, dmdt)
dedt = dedt_masschange(etemp, stars.mass, dmdt)
atemp = atemp + dadt*dt
etemp = etemp + dedt*dt
a_an.append(atemp)
e_an.append(etemp)
stars.mass += dmdt * dt
from_stars.copy()
orbital_elements = orbital_elements_from_binary(stars,
G=constants.G)
a.append(orbital_elements[2])
e.append(orbital_elements[3])
m.append(stars.mass.sum())
t.append(time)
print("time=", time.in_(units.yr),
"a=", a[-1].in_(units.RSun),
"e=", e[-1],
"m=", stars.mass.in_(units.MSun), end="\r")
gravity.stop()
from matplotlib import pyplot
fig, axis = pyplot.subplots(nrows=2, ncols=2, sharex=True)
axis[0][0].plot(t.value_in(units.yr), a.value_in(units.RSun), label="nbody")
axis[0][0].plot(t.value_in(units.yr), a_an.value_in(units.RSun), label="analytic")
axis[0][0].set_ylabel("a [$R_\odot$]")
axis[0][0].legend()
axis[0][1].plot(t.value_in(units.yr), m.value_in(units.MSun))
axis[0][1].set_ylabel("M [$M_\odot$]")
axis[1][1].plot(t.value_in(units.yr), e)
axis[1][1].plot(t.value_in(units.yr), e_an)
axis[1][1].set_ylabel("e")
axis[1][1].set_xlabel("time [yr]")
axis[1][0].set_xlabel("time [yr]")
pyplot.savefig("mloss.png")
pyplot.show()