def get_component_binary_elements(comp1, comp2):
kep = Kepler(redirection = "none")
kep.initialize_code()
mass = comp1.mass + comp2.mass
pos = comp2.position - comp1.position
vel = comp2.velocity - comp1.velocity
kep.initialize_from_dyn(mass, pos[0], pos[1], pos[2],
vel[0], vel[1], vel[2])
a,e = kep.get_elements()
r = kep.get_separation()
E,J = kep.get_integrals() # per unit reduced mass, note
kep.stop()
return mass,a,e,r,E
def get_binary_elements(p):
comp1 = p.child1
comp2 = p.child2
kep = Kepler(redirection="none")
kep.initialize_code()
mass = comp1.mass + comp2.mass
pos = [comp2.x - comp1.x, comp2.y - comp1.y, comp2.z - comp1.z]
vel = [comp2.vx - comp1.vx, comp2.vy - comp1.vy, comp2.vz - comp1.vz]
kep.initialize_from_dyn(mass, pos[0], pos[1], pos[2], vel[0], vel[1],
vel[2])
a, e = kep.get_elements()
kep.stop()
return mass, a, e
def get_binary_elements(p):
comp1 = p.child1
comp2 = p.child2
kep = Kepler(redirection = "none")
kep.initialize_code()
mass = comp1.mass + comp2.mass
pos = [comp2.x-comp1.x, comp2.y-comp1.y, comp2.z-comp1.z]
vel = [comp2.vx-comp1.vx, comp2.vy-comp1.vy, comp2.vz-comp1.vz]
kep.initialize_from_dyn(mass, pos[0], pos[1], pos[2],
vel[0], vel[1], vel[2])
a,e = kep.get_elements()
kep.stop()
return mass,a,e
def get_component_binary_elements(comp1, comp2):
kep = Kepler(redirection="none")
kep.initialize_code()
mass = comp1.mass + comp2.mass
pos = comp2.position - comp1.position
vel = comp2.velocity - comp1.velocity
kep.initialize_from_dyn(mass, pos[0], pos[1], pos[2], vel[0], vel[1],
vel[2])
a, e = kep.get_elements()
r = kep.get_separation()
E, J = kep.get_integrals() # per unit reduced mass, note
kep.stop()
return mass, a, e, r, E
def run_kepler(mass, semi, ecc, time):
kep = Kepler(redirection='none')
kep.initialize_code()
kep.set_longitudinal_unit_vector(1.0, 1.0,
0.0)
kep.initialize_from_elements(mass, semi, ecc)
a,e = kep.get_elements()
p = kep.get_periastron()
print "elements:", a, e, p
kep.transform_to_time(time)
x,y,z = kep.get_separation_vector()
print "separation:", x,y,z
x,y,z = kep.get_longitudinal_unit_vector()
print "longitudinal:", x,y,z
pos = [1, 0, 0] | nbody_system.length
vel = [0, 0.5, 0] | nbody_system.speed
kep.initialize_from_dyn(mass, pos[0], pos[1], pos[2],
vel[0], vel[1], vel[2])
a,e = kep.get_elements()
p = kep.get_periastron()
print "elements:", a, e, p
kep.transform_to_time(time)
x,y,z = kep.get_separation_vector()
print "separation:", x,y,z
x,y,z = kep.get_velocity_vector()
print "velocity:", x,y,z
x,y,z = kep.get_longitudinal_unit_vector()
print "longitudinal:", x,y,z
kep.set_random(42)
kep.make_binary_scattering(0.5 | nbody_system.mass,
0.5,
0.5 | nbody_system.mass,
0.0 | nbody_system.speed,
0.0 | nbody_system.length,
1.e-6,
0)
kep.stop()
def update_orb_elem(host_star, planets, converter=None, kepler_worker=None):
if kepler_worker == None:
if converter == None:
tot_sys = Particles(particles=(host_star, planets))
converter = nbody_system.nbody_to_si(tot_sys.mass.sum(),
2 * host_star.radius)
kep_p = Kepler(unit_converter=converter, redirection='none')
kep_p.initialize_code()
else:
kep_p = kepler_worker
for planet in planets:
total_mass = host_star.mass + planet.mass
kep_pos = host_star.position - planet.position
kep_vel = host_star.velocity - planet.velocity
kep_p.initialize_from_dyn(total_mass, kep_pos[0], kep_pos[1],
kep_pos[2], kep_vel[0], kep_vel[1],
kep_vel[2])
planet.semimajor_axis, planet.eccentricity = kep_p.get_elements()
planet.period = kep_p.get_period()
planet.true_anomaly, planet.mean_anomaly = kep_p.get_angles()
if kepler_worker == None:
kep_p.stop()
def get_heirarchical_systems_from_set(bodies,
kepler_workers=None,
converter=None,
RelativePosition=False):
# Initialize Kepler
if kepler_workers == None:
if converter == None:
converter = nbody_system.nbody_to_si(
bodies.mass.sum(),
2 * np.max(bodies.radius.number) | bodies.radius.unit)
kep_p = Kepler(unit_converter=converter, redirection='none')
kep_p.initialize_code()
kep_s = Kepler(unit_converter=converter, redirection='none')
kep_s.initialize_code()
else:
kep_p = kepler_workers[0]
kep_s = kepler_workers[1]
# Seperate Out Planets and Stars from Bodies
stars, planets = util.get_stars(bodies), util.get_planets(bodies)
num_stars, num_planets = len(stars), len(planets)
# Initialize the Dictionary that Contains all Planetary Systems
systems = {}
# Initialize the List Used to Check Star IDs Against Already Classified Binaries
binary_ids = []
# Find Nearest Neighbors of the Set
closest_neighbours = stars.nearest_neighbour()
# Start Looping Through Stars to Find Bound Planets
for index, star in enumerate(stars):
# If the star is already in Binary_IDs, just go to the next star.
if star.id in binary_ids:
continue
# If not, Set the System ID and Set-up Data Structure.
system_id = star.id
current_system = systems.setdefault(system_id, Particles())
current_system.add_particle(star)
noStellarHierarchy = False
# If there is only one stars, there is obviously no stellar heirarchy in
# the encounter that is occuring.
if len(stars) == 1:
noStellarHierarchy = True
if not noStellarHierarchy:
# Check to see if the Nearest Neighbor is Mutual
star_neighbour_id = closest_neighbours[index].id
neighbour_neighbour_id = closest_neighbours[
stars.id == star_neighbour_id].id[0]
for other_star in (stars - star):
# Check to see if the two stars are bound.
kep_s.initialize_from_dyn(
star.mass + other_star.mass, star.x - other_star.x,
star.y - other_star.y, star.z - other_star.z,
star.vx - other_star.vx, star.vy - other_star.vy,
star.vz - other_star.vz)
a_s, e_s = kep_s.get_elements()
print(star.id, other_star.id, e_s)
# If they ARE NOT bound ...
if e_s >= 1.0:
noStellarHierarchy = True
# If they ARE bound ...
else:
# If the star is the star's neighbour's neighbour and visa-versa, then proceed.
print(star.id, other_star.id, star_neighbour_id,
neighbour_neighbour_id)
if star.id == neighbour_neighbour_id and other_star.id == star_neighbour_id:
noStellarHierarchy = False
print("Binary composed of Star", star.id, "and Star",
other_star.id, "has been detected!")
current_system.add_particle(other_star)
binary_ids.append(star.id)
binary_ids.append(other_star.id)
else:
print(
"!!! Alert: Bound Stars are not closest neighbours ..."
)
print("!!! Current Star:", star.id, "| Other Star:",
other_star.id)
print("!!! CS's Neighbour:", star_neighbour_id, \
"| CS's Neighbour's Neighbour:", neighbour_neighbour_id)
checked_planet_ids = []
for KeyID in systems.keys():
current_system = systems[KeyID]
sys_stars = util.get_stars(current_system)
noStellarHierarchy = False
# If there is only one stars, there is obviously no stellar heirarchy in
# the encounter that is occuring.
if len(sys_stars) == 1:
noStellarHierarchy = True
for planet in planets:
if planet.id in checked_planet_ids:
continue
star = sys_stars[sys_stars.id == KeyID][0]
total_mass = star.mass + planet.mass
kep_pos = star.position - planet.position
kep_vel = star.velocity - planet.velocity
kep_p.initialize_from_dyn(total_mass, kep_pos[0], kep_pos[1],
kep_pos[2], kep_vel[0], kep_vel[1],
kep_vel[2])
a_p, e_p = kep_p.get_elements()
P_p = kep_p.get_period()
Ta_p, Ma_p = kep_p.get_angles()
host_star_id = star.id
if e_p < 1.0:
# Check to See if The Planetary System is tied to a Stellar Binary
# Note: Things get complicated if it is ...
if noStellarHierarchy:
# Get Additional Information on Orbit
planet.semimajor_axis = a_p
planet.eccentricity = e_p
planet.period = P_p
planet.true_anomaly = Ta_p
planet.mean_anomaly = Ma_p
planet.host_star = star.id
# Add the Planet to the System Set
current_system.add_particle(planet)
else:
# Handling for Planetary Systems in Stellar Heirarchical Structures
# Note: We check to see which other star in the current systems
# have a better boundness with the planet and choose that
# as the new host star.
for other_star in sys_stars - star:
total_mass = other_star.mass + planet.mass
kep_pos = other_star.position - planet.position
kep_vel = other_star.velocity - planet.velocity
kep_p.initialize_from_dyn(total_mass, kep_pos[0],
kep_pos[1], kep_pos[2],
kep_vel[0], kep_vel[1],
kep_vel[2])
a_p2, e_p2 = kep_p.get_elements()
# Check to see if the planet is more bound to 'star' or
# 'other_star'. If its more bound to 'other_star',
# set the attributes to the more bound object. This will
# replace *_p with the better values with each loop.
if e_p2 < e_p:
a_p = a_p2
e_p = e_p2
P_p = kep_p.get_period()
Ta_p, Ma_p = kep_p.get_angles()
host_star_id = other_star.id
planet.semimajor_axis = a_p
planet.eccentricity = e_p
planet.period = P_p
planet.true_anomaly = Ta_p
planet.mean_anomaly = Ma_p
planet.host_star = host_star_id
# Add the Planet to the System Set
current_system.add_particle(planet)
checked_planet_ids.append(planet.id)
elif not noStellarHierarchy:
# Handling for Planetary Systems in Stellar Heirarchical Structures
# Note: We check to see which other star in the current systems
# have a better boundness with the planet and choose that
# as the new host star.
for other_star in sys_stars - star:
total_mass = other_star.mass + planet.mass
kep_pos = other_star.position - planet.position
kep_vel = other_star.velocity - planet.velocity
kep_p.initialize_from_dyn(total_mass, kep_pos[0],
kep_pos[1], kep_pos[2],
kep_vel[0], kep_vel[1],
kep_vel[2])
a_p2, e_p2 = kep_p.get_elements()
# Check to see if the planet is more bound to 'star' or
# 'other_star'. If its more bound to 'other_star',
# set the attributes to the more bound object. This will
# replace *_p with the better values with each loop.
if e_p2 < e_p:
a_p = a_p2
e_p = e_p2
P_p = kep_p.get_period()
Ta_p, Ma_p = kep_p.get_angles()
host_star_id = other_star.id
planet.semimajor_axis = a_p
planet.eccentricity = e_p
planet.period = P_p
planet.true_anomaly = Ta_p
planet.mean_anomaly = Ma_p
planet.host_star = host_star_id
# Add the Planet to the System Set
current_system.add_particle(planet)
else:
print(
"!!! Alert: Planet is not bound nor is it bound to any other star."
)
if kepler_workers == None:
kep_p.stop()
kep_s.stop()
return systems
def get_planetary_systems_from_set(bodies,
converter=None,
RelativePosition=False):
# Initialize Kepler
if converter == None:
converter = nbody_system.nbody_to_si(
bodies.mass.sum(),
2 * np.max(bodies.radius.number) | bodies.radius.unit)
kep_p = Kepler(unit_converter=converter, redirection='none')
kep_p.initialize_code()
kep_s = Kepler(unit_converter=converter, redirection='none')
kep_s.initialize_code()
# Seperate Out Planets and Stars from Bodies
stars, planets = util.get_stars(bodies), util.get_planets(bodies)
num_stars, num_planets = len(stars), len(planets)
# Initialize the Dictionary that Contains all Planetary Systems
systems = {}
# Start Looping Through Stars to Find Bound Planets
for star in stars:
system_id = star.id
#star.semimajor_axis, star.eccentricity, star.period, star.true_anomaly, star.mean_anomaly, star.kep_energy, star.angular_momentum = \
# None, None, None, None, None, None, None
current_system = systems.setdefault(system_id, Particles())
current_system.add_particle(star)
for planet in planets:
total_mass = star.mass + planet.mass
kep_pos = star.position - planet.position
kep_vel = star.velocity - planet.velocity
kep_p.initialize_from_dyn(total_mass, kep_pos[0], kep_pos[1],
kep_pos[2], kep_vel[0], kep_vel[1],
kep_vel[2])
a_p, e_p = kep_p.get_elements()
if e_p < 1.0:
# Check to See if The Stellar System is a Binary
# Note: Things get complicated if it is ...
noStellarHeirarchy = False
for other_star in (stars - star):
kep_s.initialize_from_dyn(
star.mass + other_star.mass, star.x - other_star.x,
star.y - other_star.y, star.z - other_star.z,
star.vx - other_star.vx, star.vy - other_star.vy,
star.vz - other_star.vz)
a_s, e_s = kep_s.get_elements()
r_apo = kep_s.get_apastron()
HillR = util.calc_HillRadius(a_s, e_s, other_star.mass,
star.mass)
if e_s >= 1.0 or HillR < r_apo:
noStellarHeirarchy = True
else:
noStellarHeirarchy = False
if noStellarHeirarchy:
# Get Additional Information on Orbit
planet.semimajor_axis = a_p
planet.eccentricity = e_p
planet.period = kep_p.get_period()
planet.true_anomaly, planet.mean_anomaly = kep_p.get_angles(
)
#planet.kep_energy, planet.angular_momentum = kep_p.get_integrals()
# Add the Planet to the System Set
current_system.add_particle(planet)
else:
# Handling for Planetary Systems in Stellar Heirarchical Structures
# Note: This is empty for now, maybe consider doing it by the heaviest bound stellar object as the primary.
pass
else:
continue
kep_p.stop()
kep_s.stop()
return systems
def compress_binary_components(comp1, comp2, scale):
# Compress the two-body system consisting of comp1 and comp2 to
# lie within distance scale of one another.
pos1 = comp1.position
pos2 = comp2.position
sep12 = ((pos2-pos1)**2).sum()
if sep12 > scale*scale:
print '\ncompressing components', int(comp1.id.number), \
'and', int(comp2.id.number), 'to separation', scale.number
sys.stdout.flush()
mass1 = comp1.mass
mass2 = comp2.mass
total_mass = mass1 + mass2
vel1 = comp1.velocity
vel2 = comp2.velocity
cmpos = (mass1*pos1+mass2*pos2)/total_mass
cmvel = (mass1*vel1+mass2*vel2)/total_mass
# For now, create and delete a temporary kepler
# process to handle the transformation. Obviously
# more efficient to define a single kepler at the
# start of the calculation and reuse it.
kep = Kepler(redirection = "none")
kep.initialize_code()
mass = comp1.mass + comp2.mass
rel_pos = pos2 - pos1
rel_vel = vel2 - vel1
kep.initialize_from_dyn(mass,
rel_pos[0], rel_pos[1], rel_pos[2],
rel_vel[0], rel_vel[1], rel_vel[2])
M,th = kep.get_angles()
a,e = kep.get_elements()
if e < 1:
peri = a*(1-e)
apo = a*(1+e)
else:
peri = a*(e-1)
apo = 2*a # OK - used ony to reset scale
limit = peri + 0.01*(apo-peri)
if scale < limit: scale = limit
if M < 0:
# print 'approaching'
kep.advance_to_periastron()
kep.advance_to_radius(limit)
else:
# print 'receding'
if kep.get_separation() < scale:
kep.advance_to_radius(limit)
else:
kep.return_to_radius(scale)
# a,e = kep.get_elements()
# r = kep.get_separation()
# E,J = kep.get_integrals()
# print 'kepler: a,e,r =', a.number, e.number, r.number
# print 'E, J =', E, J
# Note: if periastron > scale, we are now just past periastron.
new_rel_pos = kep.get_separation_vector()
new_rel_vel = kep.get_velocity_vector()
kep.stop()
# Enew = 0
# r2 = 0
# for k in range(3):
# Enew += 0.5*(new_rel_vel[k].number)**2
# r2 += (new_rel_pos[k].number)**2
# rnew = math.sqrt(r2)
# Enew -= mass.number/r1
# print 'E, Enew, rnew =', E.number, E1, r1
# Problem: the vectors returned by kepler are lists,
# not numpy arrays, and it looks as though we can say
# comp1.position = pos, but not comp1.position[k] =
# xxx, as we'd like... Also, we don't know how to
# copy a numpy array with units... TODO
newpos1 = pos1 - pos1 # stupid trick to create zero vectors
newpos2 = pos2 - pos2 # with the proper form and units...
newvel1 = vel1 - vel1
newvel2 = vel2 - vel2
frac2 = mass2/total_mass
for k in range(3):
dxk = new_rel_pos[k]
dvk = new_rel_vel[k]
newpos1[k] = cmpos[k] - frac2*dxk
newpos2[k] = cmpos[k] + (1-frac2)*dxk
newvel1[k] = cmvel[k] - frac2*dvk
newvel2[k] = cmvel[k] + (1-frac2)*dvk
# Perform the changes to comp1 and comp2, and recursively
# transmit them to the (currently absolute) coordinates of
# all lower components.
offset_particle_tree(comp1, newpos1-pos1, newvel1-vel1)
offset_particle_tree(comp2, newpos2-pos2, newvel2-vel2)
def CutOrAdvance(enc_bodies, primary_sysID, converter=None):
bodies = enc_bodies.copy()
if converter==None:
converter = nbody_system.nbody_to_si(bodies.mass.sum(), 2 * np.max(bodies.radius.number) | bodies.radius.unit)
systems = stellar_systems.get_heirarchical_systems_from_set(bodies, converter=converter, RelativePosition=False)
# Deal with Possible Key Issues with Encounters with 3+ Star Particles Being Run More than Other Systems ...
if int(primary_sysID) not in systems.keys():
print "...: Error: Previously run binary system has been found! Not running this system ..."
print primary_sysID
print systems.keys()
print "---------------------------------"
return None
# As this function is pulling from Multiples, there should never be more or less than 2 "Root" Particles ...
if len(systems) != 2:
print "...: Error: Encounter has more roots than expected! Total Root Particles:", len(systems)
print bodies
print "---------------------------------"
return None
# Assign the Primary System to #1 and Perturbing System to #2
sys_1 = systems[int(primary_sysID)]
secondary_sysID = [key for key in systems.keys() if key!=int(primary_sysID)][0]
sys_2 = systems[secondary_sysID]
print 'All System Keys:', systems.keys()
print 'Primary System Key:', primary_sysID
print 'System 1 IDs:', sys_1.id
print 'System 2 IDs:', sys_2.id
# Calculate Useful Quantities
mass_ratio = sys_2.mass.sum()/sys_1.mass.sum()
total_mass = sys_1.mass.sum() + sys_2.mass.sum()
rel_pos = sys_1.center_of_mass() - sys_2.center_of_mass()
rel_vel = sys_1.center_of_mass_velocity() - sys_2.center_of_mass_velocity()
# Initialize Kepler Worker
kep = Kepler(unit_converter = converter, redirection = 'none')
kep.initialize_code()
kep.initialize_from_dyn(total_mass, rel_pos[0], rel_pos[1], rel_pos[2], rel_vel[0], rel_vel[1], rel_vel[2])
# Check to See if the Periastron is within the Ignore Distance for 10^3 Perturbation
p = kep.get_periastron()
ignore_distance = mass_ratio**(1./3.) * 600 | units.AU
if p > ignore_distance:
print "Encounter Ignored due to Periastron of", p.in_(units.AU), "and an IgnoreDistance of",ignore_distance
kep.stop()
print "---------------------------------"
return None
# Move the Particles to be Relative to their Respective Center of Mass
cm_sys_1, cm_sys_2 = sys_1.center_of_mass(), sys_2.center_of_mass()
cmv_sys_1, cmv_sys_2 = sys_1.center_of_mass_velocity(), sys_2.center_of_mass_velocity()
for particle in sys_1:
particle.position -= cm_sys_1
particle.velocity -= cmv_sys_1
for particle in sys_2:
particle.position -= cm_sys_2
particle.velocity -= cmv_sys_2
# Check to See if the Planets are Closer than the Ignore Distance
# Note: This shouldn't happen in the main code, but this prevents overshooting the periastron in debug mode.
if kep.get_separation() > ignore_distance:
kep.advance_to_radius(ignore_distance)
# Advance the Center of Masses to the Desired Distance in Reduced Mass Coordinates
x, y, z = kep.get_separation_vector()
rel_pos_f = rel_pos.copy()
rel_pos_f[0], rel_pos_f[1], rel_pos_f[2] = x, y, z
vx, vy, vz = kep.get_velocity_vector()
rel_vel_f = rel_vel.copy()
rel_vel_f[0], rel_vel_f[1], rel_vel_f[2] = vx, vy, vz
# Transform to Absolute Coordinates from Kepler Reduced Mass Coordinates
cm_pos_1, cm_pos_2 = sys_2.mass.sum() * rel_pos_f / total_mass, -sys_1.mass.sum() * rel_pos_f / total_mass
cm_vel_1, cm_vel_2 = sys_2.mass.sum() * rel_vel_f / total_mass, -sys_1.mass.sum() * rel_vel_f / total_mass
# Move the Particles to the New Postions of their Respective Center of Mass
for particle in sys_1:
particle.position += cm_pos_1
particle.velocity += cm_vel_1
for particle in sys_2:
particle.position += cm_pos_2
particle.velocity += cm_vel_2
# Stop Kepler and Return the Systems as a Particle Set
kep.stop()
# Collect the Collective Particle Set to be Returned Back
final_set = Particles()
final_set.add_particles(sys_1)
final_set.add_particles(sys_2)
print "---------------------------------"
return final_set
class StellarEncounterInHydrodynamics(object):
"""
Resolves collisions between stars by converting them to SPH models, let them
collide in an SPH code, and converting the resulting SPH particle distribution
back to a 1D stellar evolution model.
Requires a stellar evolution code to supply the internal structure of the
stars for the convert_stellar_model_to_SPH routine.
Requires a gravity code to set up the initial configuration. The stars in the
gravity code have typically already collided, so they are first "evolved" back
in time up to a certain separation, assuming Keplerian motion.
:argument number_of_particles: Total number of gas particles in the SPH simulation
:argument hydrodynamics: SPH code class for the simulation
:argument initial_separation: a factor relative to the sum of the radii (1 means in contact, default: 5)
"""
stellar_evolution_code_required = True
gravity_code_required = True
def __init__(
self,
number_of_particles,
hydrodynamics,
initial_separation = 5,
relax_sph_models = True,
verbose = False,
debug = False,
hydrodynamics_arguments = dict(),
hydrodynamics_parameters = dict(),
star_to_sph_arguments = dict(),
sph_to_star_arguments = dict(),
):
self.number_of_particles = number_of_particles
self.hydrodynamics = hydrodynamics
self.initial_separation = initial_separation
if not relax_sph_models:
self.relax = self.no_relax
self.verbose = verbose
self.debug = debug
self.hydrodynamics_arguments = hydrodynamics_arguments
self.hydrodynamics_parameters = hydrodynamics_parameters
self.star_to_sph_arguments = star_to_sph_arguments
self.sph_to_star_arguments = sph_to_star_arguments
self.dynamical_timescales_per_step = 1.0 # encounter_is_over check is performed at this interval
self.extra_steps_when_encounter_is_over = 3
self.continue_with_kepler = False
def handle_collision(self, primary, secondary, stellar_evolution_code=None, gravity_code=None):
particles = self.local_copy_of_particles(primary, secondary)
self.collect_required_attributes(particles, gravity_code, stellar_evolution_code)
self.backtrack_particles(particles)
gas_particles = self.convert_stars(particles, stellar_evolution_code)
self.simulate_collision(gas_particles)
self.models = [convert_SPH_to_stellar_model(group, **self.sph_to_star_arguments) for group in self.groups_after_encounter]
return self.new_particles_with_internal_structure_from_models()
def new_particles_with_internal_structure_from_models(self):
def get_internal_structure(set, particle=None):
return self.models[(set.key == particle.key).nonzero()[0]]
result = Particles(len(self.models))
result.add_function_attribute("get_internal_structure", None, get_internal_structure)
result.mass = [model.dmass.sum().as_quantity_in(self.mass_unit) for model in self.models]
result.radius = [model.radius[-1].as_quantity_in(self.radius_unit) for model in self.models]
result.position = (self.original_center_of_mass + self.stars_after_encounter.position).as_quantity_in(self.position_unit)
result.velocity = (self.original_center_of_mass_velocity + self.stars_after_encounter.velocity).as_quantity_in(self.velocity_unit)
return result
def local_copy_of_particles(self, primary, secondary):
particles = Particles(0)
particles.add_particle(primary)
particles.add_particle(secondary)
return particles
def collect_required_attributes(self, particles, gravity_code, stellar_evolution_code):
# Collect the required attributes and copy to the particles in memory
required_attributes = set(["mass", "x","y","z", "vx","vy","vz", "radius"])
required_attributes -= set(particles.get_attribute_names_defined_in_store())
for code in [stellar_evolution_code, gravity_code]:
attrs_in_code = required_attributes & set(code.particles.get_attribute_names_defined_in_store())
if len(attrs_in_code) > 0:
code.particles.copy_values_of_attributes_to(list(attrs_in_code), particles)
required_attributes -= attrs_in_code
self.mass_unit = particles.mass.unit
self.radius_unit = particles.radius.unit
self.position_unit = particles.position.unit
self.velocity_unit = particles.velocity.unit
self.dynamical_timescale = numpy.pi * (particles.radius.sum()**3 / (8 * constants.G * particles.total_mass())).sqrt()
def start_kepler(self, mass_unit, length_unit):
unit_converter = nbody_system.nbody_to_si(mass_unit, length_unit)
self.kepler = Kepler(unit_converter, redirection = "none" if self.debug else "null")
self.kepler.initialize_code()
def initialize_binary_in_kepler(self, star_a, star_b):
self.kepler.initialize_from_dyn(
star_a.mass + star_b.mass,
star_a.x - star_b.x, star_a.y - star_b.y, star_a.z - star_b.z,
star_a.vx-star_b.vx, star_a.vy-star_b.vy, star_a.vz-star_b.vz
)
return self.kepler
def backtrack_particles(self, particles):
self.original_center_of_mass = particles.center_of_mass()
self.original_center_of_mass_velocity = particles.center_of_mass_velocity()
initial_separation = self.initial_separation * particles.radius.sum()
if self.verbose:
print "Particles at collision:"
print particles
print "Backtrack particles to initial separation", initial_separation.as_string_in(units.RSun)
self.start_kepler(particles.total_mass(), initial_separation)
kepler = self.initialize_binary_in_kepler(particles[0], particles[1])
kepler.return_to_radius(initial_separation)
self.begin_time = kepler.get_time()
particles[1].position = kepler.get_separation_vector()
particles[1].velocity = kepler.get_velocity_vector()
kepler.advance_to_periastron()
self.begin_time -= kepler.get_time()
particles[0].position = [0, 0, 0] | units.m
particles[0].velocity = [0, 0, 0] | units.m / units.s
particles.move_to_center()
if self.verbose:
print "Backtracking particles done. Initial conditions:"
print particles
def convert_stars(self, particles, stellar_evolution_code):
n_particles = self.divide_number_of_particles(particles)
se_colliders = particles.get_intersecting_subset_in(stellar_evolution_code.particles)
if self.verbose:
print "Converting stars of {0} to SPH models of {1} particles, respectively.".format(particles.mass, n_particles)
sph_models = (
self.relax(convert_stellar_model_to_SPH(se_colliders[0], n_particles[0], **self.star_to_sph_arguments)),
self.relax(convert_stellar_model_to_SPH(se_colliders[1], n_particles[1], **self.star_to_sph_arguments))
)
gas_particles = Particles()
for particle, sph_model in zip(particles, sph_models):
sph_model.position += particle.position
sph_model.velocity += particle.velocity
gas_particles.add_particles(sph_model)
if self.verbose:
print "Converting stars to SPH particles done"
if self.debug:
print gas_particles
return gas_particles
def divide_number_of_particles(self, particles):
n1 = int(0.5 + self.number_of_particles * particles[0].mass / particles.total_mass())
return (n1, self.number_of_particles - n1)
def relax(self, sph_model):
if self.debug:
monitor = dict(time=[]|units.day, kinetic=[]|units.J, potential=[]|units.J, thermal=[]|units.J)
gas_particles = sph_model.gas_particles
hydro = self.new_hydrodynamics(gas_particles)
hydro.parameters.artificial_viscosity_alpha = 0.0 # Viscous damping doesn't seem to be very important, but turned off just in case...
channel_from_hydro = hydro.gas_particles.new_channel_to(gas_particles)
channel_to_hydro = gas_particles.new_channel_to(hydro.gas_particles)
dynamical_timescale = numpy.pi * (gas_particles.total_radius()**3 / (8 * constants.G * gas_particles.total_mass())).sqrt()
t_end_in_t_dyn = 2.5 # Relax for this many dynamical timescales
n_steps = 100
velocity_damp_factor = 1.0 - (2.0*numpy.pi*t_end_in_t_dyn)/n_steps # Critical damping
if self.verbose:
print "Relaxing SPH model with {0} for {1} ({2} dynamical timescales).".format(
self.hydrodynamics.__name__,
(t_end_in_t_dyn*dynamical_timescale).as_string_in(units.day),
t_end_in_t_dyn)
for i_step, time in enumerate(t_end_in_t_dyn*dynamical_timescale * numpy.linspace(1.0/n_steps, 1.0, n_steps)):
hydro.evolve_model(time)
channel_from_hydro.copy_attributes(["mass","x","y","z","vx","vy","vz","u"])
gas_particles.position -= gas_particles.center_of_mass()
gas_particles.velocity = velocity_damp_factor * (gas_particles.velocity - gas_particles.center_of_mass_velocity())
channel_to_hydro.copy_attributes(["x","y","z","vx","vy","vz"])
if self.debug:
K, U, Q = hydro.kinetic_energy, hydro.potential_energy, hydro.thermal_energy
print "t, K, U, Q:", time, K, U, Q
monitor["time"].append(time)
monitor["kinetic"].append(K)
monitor["potential"].append(U)
monitor["thermal"].append(Q)
hydro.stop()
if self.debug:
energy_evolution_plot(monitor["time"], monitor["kinetic"], monitor["potential"], monitor["thermal"])
return gas_particles
def no_relax(self, sph_model):
return sph_model.gas_particles
def new_hop(self, particles):
converter = nbody_system.nbody_to_si(particles.total_mass(), 1.0 | units.RSun)
if self.debug:
print "Output of Hop is redirected to hop_out.log"
options = dict(redirection="file", redirect_file="hop_out.log")
else:
options = dict()
hop = Hop(unit_converter=converter, **options)
hop.parameters.number_of_neighbors_for_hop = 100
hop.parameters.saddle_density_threshold_factor = 0.8
hop.parameters.relative_saddle_density_threshold = True
return hop
def new_hydrodynamics(self, gas_particles):
unit_converter = nbody_system.nbody_to_si(gas_particles.total_mass(), self.dynamical_timescale)
hydro = self.hydrodynamics(unit_converter, **self.hydrodynamics_arguments)
hydro.initialize_code()
for par, value in self.hydrodynamics_parameters.iteritems():
setattr(hydro.parameters, par, value)
hydro.commit_parameters()
hydro.gas_particles.add_particles(gas_particles)
hydro.commit_particles()
return hydro
def simulate_collision(self, gas_particles):
self.hop = self.new_hop(gas_particles)
hydro = self.new_hydrodynamics(gas_particles)
channel = hydro.gas_particles.new_channel_to(gas_particles)
if self.verbose:
print "Simulating collision with {0} from {1} to {2}.".format(
self.hydrodynamics.__name__,
self.begin_time.as_string_in(units.day),
(self.dynamical_timescales_per_step * self.dynamical_timescale).as_string_in(units.day))
hydro.evolve_model(self.dynamical_timescales_per_step * self.dynamical_timescale - self.begin_time)
channel.copy_attributes(["x","y","z","vx","vy","vz","pressure","density","u"])
extra_steps_counter = 0
while True:
if self.encounter_is_over(gas_particles):
extra_steps_counter += 1
if extra_steps_counter > self.extra_steps_when_encounter_is_over:
print "Encounter is over and finished extra steps."
break
else:
print "Encounter is over. Now performing step {0} out of {1} extra steps".format(
extra_steps_counter, self.extra_steps_when_encounter_is_over)
else:
extra_steps_counter = 0
print "Continuing to {0}.".format((hydro.model_time + self.next_dt + self.begin_time).as_string_in(units.day))
if self.continue_with_kepler:
self.evolve_with_kepler(hydro)
hydro.evolve_model(hydro.model_time + self.next_dt)
channel.copy_attributes(["x","y","z","vx","vy","vz","pressure","density","u"])
hydro.stop()
self.hop.stop()
self.kepler.stop()
def encounter_is_over(self, gas_particles):
self.next_dt = self.dynamical_timescales_per_step * self.dynamical_timescale
groups = self.group_bound_particles(gas_particles)
stars = self.convert_groups_to_stars(groups)
self.groups_after_encounter = groups
self.stars_after_encounter = stars
if len(stars) > 1:
# Should do full check for stable binaries, triple, multiples, two escapers,
# escaping star + binary, etc.
# For now we only check whether the two most massive groups will (re)collide
a, b = stars.sorted_by_attribute("mass")[-2:]
if self.debug: print "System consists of {0} groups. The two most massive are: {1} and {2}.".format(len(stars), a.mass.as_string_in(units.MSun), b.mass.as_string_in(units.MSun))
if self.binary_will_collide(a, b):
return False
if self.verbose:
print "Encounter is over, {0} stars after encounter.".format(len(groups))
return True
def group_bound_particles(self, gas_particles):
groups, lost = self.analyze_particle_distribution(gas_particles)
while len(lost) > 0:
if self.debug:
group_plot(groups, lost)
previous_number_of_lost_particles = len(lost)
groups, lost = self.select_bound_particles(groups, lost)
if len(lost) == previous_number_of_lost_particles:
break
return groups
def convert_groups_to_stars(self, groups):
stars = Particles(len(groups))
for star, group in zip(stars, groups):
star.mass = group.total_mass()
star.position = group.center_of_mass()
star.velocity = group.center_of_mass_velocity()
star.radius = group.LagrangianRadii(mf=[0.9], cm=star.position)[0][0]
return stars
def analyze_particle_distribution(self, gas_particles):
if self.verbose:
print "Analyzing particle distribution using Hop"
if "density" in gas_particles.get_attribute_names_defined_in_store():
if self.debug: print "Using the original particles' density"
self.hop.parameters.outer_density_threshold = 0.5 * gas_particles.density.mean()
self.hop.particles.add_particles(gas_particles)
gas_particles.copy_values_of_attribute_to("density", self.hop.particles)
else:
if self.debug: print "Using Hop to calculate the density"
self.hop.particles.add_particles(gas_particles)
self.hop.calculate_densities()
self.hop.parameters.outer_density_threshold = 0.5 * self.hop.particles.density.mean()
self.hop.do_hop()
result = []
for group in self.hop.groups():
result.append(group.get_intersecting_subset_in(gas_particles))
lost = self.hop.no_group().get_intersecting_subset_in(gas_particles)
self.hop.particles.remove_particles(self.hop.particles)
return result, lost
def select_bound_particles(self, groups, lost):
specific_total_energy_relative_to_group = [] | (units.m / units.s)**2
for group in groups:
group_mass = group.total_mass()
group_com = group.center_of_mass()
group_com_velocity = group.center_of_mass_velocity()
specific_total_energy_relative_to_group.append(
(lost.velocity - group_com_velocity).lengths_squared() + lost.u -
constants.G * group_mass / (lost.position - group_com).lengths())
index_minimum = specific_total_energy_relative_to_group.argmin(axis=0)
bound=lost[:0]
for i, group in enumerate(groups):
bound_to_group = lost[numpy.logical_and(
index_minimum == i,
specific_total_energy_relative_to_group[i] < 0 | (units.m / units.s)**2
)]
bound += bound_to_group
groups[i] = group + bound_to_group
return groups, lost - bound
def binary_will_collide(self, a, b):
self.continue_with_kepler = False
if self.verbose:
print "Using Kepler to check whether the two stars will (re)collide."
kepler = self.initialize_binary_in_kepler(a, b)
true_anomaly = kepler.get_angles()[1]
eccentricity = kepler.get_elements()[1]
if true_anomaly > 0.0 and eccentricity >= 1.0:
if self.verbose:
print "Stars are on hyperbolic/parabolic orbits and moving away from each other, interaction is over."
return False
periastron = kepler.get_periastron()
will_collide = periastron < a.radius + b.radius
if self.verbose:
print "Stars {0} collide. Distance at periastron: {1}, sum of radii: {2}".format(
"will" if will_collide else "won't",
periastron.as_string_in(units.RSun), (a.radius + b.radius).as_string_in(units.RSun))
if will_collide:
# 1) check whether the stars are still relaxing: less than ~3 t_dyn passed since last moment of contact --> relax
# 2) check whether the stars are already within 'initial_separation', else skip (dtmax?)
kepler.advance_to_periastron()
self.next_dt = kepler.get_time() + self.dynamical_timescales_per_step * self.dynamical_timescale
if self.debug:
print "Time to collision: {0}, next_dt: {1}".format(
kepler.get_time().as_string_in(units.day), self.next_dt.as_string_in(units.day))
if kepler.get_time() > 3 * self.dynamical_timescale and kepler.get_apastron() > 2.0 * self.initial_separation * (a.radius + b.radius):
# evolve for 3 * self.dynamical_timescale and skip the rest until ~initial_separation
kepler.return_to_apastron()
kepler.return_to_radius(a.radius + b.radius)
if -kepler.get_time() > 2.9 * self.dynamical_timescale: # If ~3 t_dyn have passed since the end of the collision
if self.verbose: print "~3 t_dyn have passed since the end of the collision -> skip to next collision"
self.continue_with_kepler = True
kepler.advance_to_apastron()
kepler.advance_to_radius(2.0 * self.initial_separation * (a.radius + b.radius))
self.skip_to_relative_position_velocity = (kepler.get_separation_vector(), kepler.get_velocity_vector())
self.begin_time = kepler.get_time()
kepler.advance_to_periastron()
self.next_dt = self.dynamical_timescales_per_step * self.dynamical_timescale + kepler.get_time() - self.begin_time
else:
self.next_dt = 3 * self.dynamical_timescale + kepler.get_time()
return will_collide
def evolve_with_kepler(self, hydro):
if self.verbose: print "evolve_with_kepler"
indices_two_most_massive = self.stars_after_encounter.mass.argsort()[-2:]
groups = [self.groups_after_encounter[i] for i in indices_two_most_massive]
old_particles = self.stars_after_encounter[indices_two_most_massive]
new_particles = Particles(2)
new_particles.mass = old_particles.mass
new_particles[0].position, new_particles[0].velocity = self.skip_to_relative_position_velocity
new_particles.move_to_center()
for group, old_particle, new_particle in zip(groups, old_particles, new_particles):
in_hydro = group.get_intersecting_subset_in(hydro.gas_particles)
if self.verbose: print in_hydro.center_of_mass().as_quantity_in(units.RSun), old_particle.position.as_quantity_in(units.RSun), new_particle.position.as_quantity_in(units.RSun)
in_hydro.position += new_particle.position - old_particle.position
in_hydro.velocity += new_particle.velocity - old_particle.velocity
def compress_binary_components(comp1, comp2, scale):
# Compress the two-body system consisting of comp1 and comp2 to
# lie within distance scale of one another.
pos1 = comp1.position
pos2 = comp2.position
sep12 = ((pos2 - pos1)**2).sum()
if sep12 > scale * scale:
print('\ncompressing components', int(comp1.id.number), \
'and', int(comp2.id.number), 'to separation', scale.number)
sys.stdout.flush()
mass1 = comp1.mass
mass2 = comp2.mass
total_mass = mass1 + mass2
vel1 = comp1.velocity
vel2 = comp2.velocity
cmpos = (mass1 * pos1 + mass2 * pos2) / total_mass
cmvel = (mass1 * vel1 + mass2 * vel2) / total_mass
# For now, create and delete a temporary kepler
# process to handle the transformation. Obviously
# more efficient to define a single kepler at the
# start of the calculation and reuse it.
kep = Kepler(redirection="none")
kep.initialize_code()
mass = comp1.mass + comp2.mass
rel_pos = pos2 - pos1
rel_vel = vel2 - vel1
kep.initialize_from_dyn(mass, rel_pos[0], rel_pos[1], rel_pos[2],
rel_vel[0], rel_vel[1], rel_vel[2])
M, th = kep.get_angles()
a, e = kep.get_elements()
if e < 1:
peri = a * (1 - e)
apo = a * (1 + e)
else:
peri = a * (e - 1)
apo = 2 * a # OK - used ony to reset scale
limit = peri + 0.01 * (apo - peri)
if scale < limit: scale = limit
if M < 0:
# print 'approaching'
kep.advance_to_periastron()
kep.advance_to_radius(limit)
else:
# print 'receding'
if kep.get_separation() < scale:
kep.advance_to_radius(limit)
else:
kep.return_to_radius(scale)
# a,e = kep.get_elements()
# r = kep.get_separation()
# E,J = kep.get_integrals()
# print 'kepler: a,e,r =', a.number, e.number, r.number
# print 'E, J =', E, J
# Note: if periastron > scale, we are now just past periastron.
new_rel_pos = kep.get_separation_vector()
new_rel_vel = kep.get_velocity_vector()
kep.stop()
# Enew = 0
# r2 = 0
# for k in range(3):
# Enew += 0.5*(new_rel_vel[k].number)**2
# r2 += (new_rel_pos[k].number)**2
# rnew = math.sqrt(r2)
# Enew -= mass.number/r1
# print 'E, Enew, rnew =', E.number, E1, r1
# Problem: the vectors returned by kepler are lists,
# not numpy arrays, and it looks as though we can say
# comp1.position = pos, but not comp1.position[k] =
# xxx, as we'd like... Also, we don't know how to
# copy a numpy array with units... TODO
newpos1 = pos1 - pos1 # stupid trick to create zero vectors
newpos2 = pos2 - pos2 # with the proper form and units...
newvel1 = vel1 - vel1
newvel2 = vel2 - vel2
frac2 = mass2 / total_mass
for k in range(3):
dxk = new_rel_pos[k]
dvk = new_rel_vel[k]
newpos1[k] = cmpos[k] - frac2 * dxk
newpos2[k] = cmpos[k] + (1 - frac2) * dxk
newvel1[k] = cmvel[k] - frac2 * dvk
newvel2[k] = cmvel[k] + (1 - frac2) * dvk
# Perform the changes to comp1 and comp2, and recursively
# transmit them to the (currently absolute) coordinates of
# all lower components.
offset_particle_tree(comp1, newpos1 - pos1, newvel1 - vel1)
offset_particle_tree(comp2, newpos2 - pos2, newvel2 - vel2)
class StellarEncounterInHydrodynamics(object):
"""
Resolves collisions between stars by converting them to SPH models, let them
collide in an SPH code, and converting the resulting SPH particle distribution
back to a 1D stellar evolution model.
Requires a stellar evolution code to supply the internal structure of the
stars for the convert_stellar_model_to_SPH routine.
Requires a gravity code to set up the initial configuration. The stars in the
gravity code have typically already collided, so they are first "evolved" back
in time up to a certain separation, assuming Keplerian motion.
:argument number_of_particles: Total number of gas particles in the SPH simulation
:argument hydrodynamics: SPH code class for the simulation
:argument initial_separation: a factor relative to the sum of the radii (1 means in contact, default: 5)
"""
stellar_evolution_code_required = True
gravity_code_required = True
def __init__(
self,
number_of_particles,
hydrodynamics,
initial_separation=5,
relax_sph_models=True,
verbose=False,
debug=False,
hydrodynamics_arguments=dict(),
hydrodynamics_parameters=dict(),
star_to_sph_arguments=dict(),
sph_to_star_arguments=dict(),
):
self.number_of_particles = number_of_particles
self.hydrodynamics = hydrodynamics
self.initial_separation = initial_separation
if not relax_sph_models:
self.relax = self.no_relax
self.verbose = verbose
self.debug = debug
self.hydrodynamics_arguments = hydrodynamics_arguments
self.hydrodynamics_parameters = hydrodynamics_parameters
self.star_to_sph_arguments = star_to_sph_arguments
self.sph_to_star_arguments = sph_to_star_arguments
self.dynamical_timescales_per_step = 1.0 # encounter_is_over check is performed at this interval
self.extra_steps_when_encounter_is_over = 3
self.continue_with_kepler = False
def handle_collision(self,
primary,
secondary,
stellar_evolution_code=None,
gravity_code=None):
particles = self.local_copy_of_particles(primary, secondary)
self.collect_required_attributes(particles, gravity_code,
stellar_evolution_code)
self.backtrack_particles(particles)
gas_particles = self.convert_stars(particles, stellar_evolution_code)
self.simulate_collision(gas_particles)
self.models = [
convert_SPH_to_stellar_model(group, **self.sph_to_star_arguments)
for group in self.groups_after_encounter
]
return self.new_particles_with_internal_structure_from_models()
def new_particles_with_internal_structure_from_models(self):
def get_internal_structure(set, particle=None):
return self.models[(set.key == particle.key).nonzero()[0]]
result = Particles(len(self.models))
result.add_function_attribute("get_internal_structure", None,
get_internal_structure)
result.mass = [
model.dmass.sum().as_quantity_in(self.mass_unit)
for model in self.models
]
result.radius = [
model.radius[-1].as_quantity_in(self.radius_unit)
for model in self.models
]
result.position = (self.original_center_of_mass +
self.stars_after_encounter.position).as_quantity_in(
self.position_unit)
result.velocity = (self.original_center_of_mass_velocity +
self.stars_after_encounter.velocity).as_quantity_in(
self.velocity_unit)
return result
def local_copy_of_particles(self, primary, secondary):
particles = Particles(0)
particles.add_particle(primary)
particles.add_particle(secondary)
return particles
def collect_required_attributes(self, particles, gravity_code,
stellar_evolution_code):
# Collect the required attributes and copy to the particles in memory
required_attributes = set(
["mass", "x", "y", "z", "vx", "vy", "vz", "radius"])
required_attributes -= set(
particles.get_attribute_names_defined_in_store())
for code in [stellar_evolution_code, gravity_code]:
attrs_in_code = required_attributes & set(
code.particles.get_attribute_names_defined_in_store())
if len(attrs_in_code) > 0:
code.particles.copy_values_of_attributes_to(
list(attrs_in_code), particles)
required_attributes -= attrs_in_code
self.mass_unit = particles.mass.unit
self.radius_unit = particles.radius.unit
self.position_unit = particles.position.unit
self.velocity_unit = particles.velocity.unit
self.dynamical_timescale = numpy.pi * (
particles.radius.sum()**3 /
(8 * constants.G * particles.total_mass())).sqrt()
def start_kepler(self, mass_unit, length_unit):
unit_converter = nbody_system.nbody_to_si(mass_unit, length_unit)
self.kepler = Kepler(unit_converter,
redirection="none" if self.debug else "null")
self.kepler.initialize_code()
def initialize_binary_in_kepler(self, star_a, star_b):
self.kepler.initialize_from_dyn(
star_a.mass + star_b.mass, star_a.x - star_b.x,
star_a.y - star_b.y, star_a.z - star_b.z, star_a.vx - star_b.vx,
star_a.vy - star_b.vy, star_a.vz - star_b.vz)
return self.kepler
def backtrack_particles(self, particles):
self.original_center_of_mass = particles.center_of_mass()
self.original_center_of_mass_velocity = particles.center_of_mass_velocity(
)
initial_separation = self.initial_separation * particles.radius.sum()
if self.verbose:
print "Particles at collision:"
print particles
print "Backtrack particles to initial separation", initial_separation.as_string_in(
units.RSun)
self.start_kepler(particles.total_mass(), initial_separation)
kepler = self.initialize_binary_in_kepler(particles[0], particles[1])
kepler.return_to_radius(initial_separation)
self.begin_time = kepler.get_time()
particles[1].position = kepler.get_separation_vector()
particles[1].velocity = kepler.get_velocity_vector()
kepler.advance_to_periastron()
self.begin_time -= kepler.get_time()
particles[0].position = [0, 0, 0] | units.m
particles[0].velocity = [0, 0, 0] | units.m / units.s
particles.move_to_center()
if self.verbose:
print "Backtracking particles done. Initial conditions:"
print particles
def convert_stars(self, particles, stellar_evolution_code):
n_particles = self.divide_number_of_particles(particles)
se_colliders = particles.get_intersecting_subset_in(
stellar_evolution_code.particles)
if self.verbose:
print "Converting stars of {0} to SPH models of {1} particles, respectively.".format(
particles.mass, n_particles)
sph_models = (self.relax(
convert_stellar_model_to_SPH(se_colliders[0], n_particles[0],
**self.star_to_sph_arguments)),
self.relax(
convert_stellar_model_to_SPH(
se_colliders[1], n_particles[1],
**self.star_to_sph_arguments)))
gas_particles = Particles()
for particle, sph_model in zip(particles, sph_models):
sph_model.position += particle.position
sph_model.velocity += particle.velocity
gas_particles.add_particles(sph_model)
if self.verbose:
print "Converting stars to SPH particles done"
if self.debug:
print gas_particles
return gas_particles
def divide_number_of_particles(self, particles):
n1 = int(0.5 + self.number_of_particles * particles[0].mass /
particles.total_mass())
return (n1, self.number_of_particles - n1)
def relax(self, sph_model):
if self.debug:
monitor = dict(time=[] | units.day,
kinetic=[] | units.J,
potential=[] | units.J,
thermal=[] | units.J)
gas_particles = sph_model.gas_particles
hydro = self.new_hydrodynamics(gas_particles)
hydro.parameters.artificial_viscosity_alpha = 0.0 # Viscous damping doesn't seem to be very important, but turned off just in case...
channel_from_hydro = hydro.gas_particles.new_channel_to(gas_particles)
channel_to_hydro = gas_particles.new_channel_to(hydro.gas_particles)
dynamical_timescale = numpy.pi * (
gas_particles.total_radius()**3 /
(8 * constants.G * gas_particles.total_mass())).sqrt()
t_end_in_t_dyn = 2.5 # Relax for this many dynamical timescales
n_steps = 100
velocity_damp_factor = 1.0 - (
2.0 * numpy.pi * t_end_in_t_dyn) / n_steps # Critical damping
if self.verbose:
print "Relaxing SPH model with {0} for {1} ({2} dynamical timescales).".format(
self.hydrodynamics.__name__,
(t_end_in_t_dyn * dynamical_timescale).as_string_in(units.day),
t_end_in_t_dyn)
for i_step, time in enumerate(
t_end_in_t_dyn * dynamical_timescale *
numpy.linspace(1.0 / n_steps, 1.0, n_steps)):
hydro.evolve_model(time)
channel_from_hydro.copy_attributes(
["mass", "x", "y", "z", "vx", "vy", "vz", "u"])
gas_particles.position -= gas_particles.center_of_mass()
gas_particles.velocity = velocity_damp_factor * (
gas_particles.velocity -
gas_particles.center_of_mass_velocity())
channel_to_hydro.copy_attributes(["x", "y", "z", "vx", "vy", "vz"])
if self.debug:
K, U, Q = hydro.kinetic_energy, hydro.potential_energy, hydro.thermal_energy
print "t, K, U, Q:", time, K, U, Q
monitor["time"].append(time)
monitor["kinetic"].append(K)
monitor["potential"].append(U)
monitor["thermal"].append(Q)
hydro.stop()
if self.debug:
energy_evolution_plot(monitor["time"], monitor["kinetic"],
monitor["potential"], monitor["thermal"])
return gas_particles
def no_relax(self, sph_model):
return sph_model.gas_particles
def new_hop(self, particles):
converter = nbody_system.nbody_to_si(particles.total_mass(),
1.0 | units.RSun)
if self.debug:
print "Output of Hop is redirected to hop_out.log"
options = dict(redirection="file", redirect_file="hop_out.log")
else:
options = dict()
hop = Hop(unit_converter=converter, **options)
hop.parameters.number_of_neighbors_for_hop = 100
hop.parameters.saddle_density_threshold_factor = 0.8
hop.parameters.relative_saddle_density_threshold = True
return hop
def new_hydrodynamics(self, gas_particles):
unit_converter = nbody_system.nbody_to_si(gas_particles.total_mass(),
self.dynamical_timescale)
hydro = self.hydrodynamics(unit_converter,
**self.hydrodynamics_arguments)
hydro.initialize_code()
for par, value in self.hydrodynamics_parameters.iteritems():
setattr(hydro.parameters, par, value)
hydro.commit_parameters()
hydro.gas_particles.add_particles(gas_particles)
hydro.commit_particles()
return hydro
def simulate_collision(self, gas_particles):
self.hop = self.new_hop(gas_particles)
hydro = self.new_hydrodynamics(gas_particles)
channel = hydro.gas_particles.new_channel_to(gas_particles)
if self.verbose:
print "Simulating collision with {0} from {1} to {2}.".format(
self.hydrodynamics.__name__,
self.begin_time.as_string_in(units.day),
(self.dynamical_timescales_per_step *
self.dynamical_timescale).as_string_in(units.day))
hydro.evolve_model(self.dynamical_timescales_per_step *
self.dynamical_timescale - self.begin_time)
channel.copy_attributes(
["x", "y", "z", "vx", "vy", "vz", "pressure", "density", "u"])
extra_steps_counter = 0
while True:
if self.encounter_is_over(gas_particles):
extra_steps_counter += 1
if extra_steps_counter > self.extra_steps_when_encounter_is_over:
print "Encounter is over and finished extra steps."
break
else:
print "Encounter is over. Now performing step {0} out of {1} extra steps".format(
extra_steps_counter,
self.extra_steps_when_encounter_is_over)
else:
extra_steps_counter = 0
print "Continuing to {0}.".format(
(hydro.model_time + self.next_dt +
self.begin_time).as_string_in(units.day))
if self.continue_with_kepler:
self.evolve_with_kepler(hydro)
hydro.evolve_model(hydro.model_time + self.next_dt)
channel.copy_attributes(
["x", "y", "z", "vx", "vy", "vz", "pressure", "density", "u"])
hydro.stop()
self.hop.stop()
self.kepler.stop()
def encounter_is_over(self, gas_particles):
self.next_dt = self.dynamical_timescales_per_step * self.dynamical_timescale
groups = self.group_bound_particles(gas_particles)
stars = self.convert_groups_to_stars(groups)
self.groups_after_encounter = groups
self.stars_after_encounter = stars
if len(stars) > 1:
# Should do full check for stable binaries, triple, multiples, two escapers,
# escaping star + binary, etc.
# For now we only check whether the two most massive groups will (re)collide
a, b = stars.sorted_by_attribute("mass")[-2:]
if self.debug:
print "System consists of {0} groups. The two most massive are: {1} and {2}.".format(
len(stars), a.mass.as_string_in(units.MSun),
b.mass.as_string_in(units.MSun))
if self.binary_will_collide(a, b):
return False
if self.verbose:
print "Encounter is over, {0} stars after encounter.".format(
len(groups))
return True
def group_bound_particles(self, gas_particles):
groups, lost = self.analyze_particle_distribution(gas_particles)
while len(lost) > 0:
if self.debug:
group_plot(groups, lost)
previous_number_of_lost_particles = len(lost)
groups, lost = self.select_bound_particles(groups, lost)
if len(lost) == previous_number_of_lost_particles:
break
return groups
def convert_groups_to_stars(self, groups):
stars = Particles(len(groups))
for star, group in zip(stars, groups):
star.mass = group.total_mass()
star.position = group.center_of_mass()
star.velocity = group.center_of_mass_velocity()
star.radius = group.LagrangianRadii(mf=[0.9],
cm=star.position)[0][0]
return stars
def analyze_particle_distribution(self, gas_particles):
if self.verbose:
print "Analyzing particle distribution using Hop"
if "density" in gas_particles.get_attribute_names_defined_in_store():
if self.debug: print "Using the original particles' density"
self.hop.parameters.outer_density_threshold = 0.5 * gas_particles.density.mean(
)
self.hop.particles.add_particles(gas_particles)
gas_particles.copy_values_of_attribute_to("density",
self.hop.particles)
else:
if self.debug: print "Using Hop to calculate the density"
self.hop.particles.add_particles(gas_particles)
self.hop.calculate_densities()
self.hop.parameters.outer_density_threshold = 0.5 * self.hop.particles.density.mean(
)
self.hop.do_hop()
result = []
for group in self.hop.groups():
result.append(group.get_intersecting_subset_in(gas_particles))
lost = self.hop.no_group().get_intersecting_subset_in(gas_particles)
self.hop.particles.remove_particles(self.hop.particles)
return result, lost
def select_bound_particles(self, groups, lost):
specific_total_energy_relative_to_group = [] | (units.m / units.s)**2
for group in groups:
group_mass = group.total_mass()
group_com = group.center_of_mass()
group_com_velocity = group.center_of_mass_velocity()
specific_total_energy_relative_to_group.append(
(lost.velocity - group_com_velocity).lengths_squared() +
lost.u - constants.G * group_mass /
(lost.position - group_com).lengths())
index_minimum = specific_total_energy_relative_to_group.argmin(axis=0)
bound = lost[:0]
for i, group in enumerate(groups):
bound_to_group = lost[numpy.logical_and(
index_minimum == i,
specific_total_energy_relative_to_group[i] < 0 |
(units.m / units.s)**2)]
bound += bound_to_group
groups[i] = group + bound_to_group
return groups, lost - bound
def binary_will_collide(self, a, b):
self.continue_with_kepler = False
if self.verbose:
print "Using Kepler to check whether the two stars will (re)collide."
kepler = self.initialize_binary_in_kepler(a, b)
true_anomaly = kepler.get_angles()[1]
eccentricity = kepler.get_elements()[1]
if true_anomaly > 0.0 and eccentricity >= 1.0:
if self.verbose:
print "Stars are on hyperbolic/parabolic orbits and moving away from each other, interaction is over."
return False
periastron = kepler.get_periastron()
will_collide = periastron < a.radius + b.radius
if self.verbose:
print "Stars {0} collide. Distance at periastron: {1}, sum of radii: {2}".format(
"will" if will_collide else "won't",
periastron.as_string_in(units.RSun),
(a.radius + b.radius).as_string_in(units.RSun))
if will_collide:
# 1) check whether the stars are still relaxing: less than ~3 t_dyn passed since last moment of contact --> relax
# 2) check whether the stars are already within 'initial_separation', else skip (dtmax?)
kepler.advance_to_periastron()
self.next_dt = kepler.get_time(
) + self.dynamical_timescales_per_step * self.dynamical_timescale
if self.debug:
print "Time to collision: {0}, next_dt: {1}".format(
kepler.get_time().as_string_in(units.day),
self.next_dt.as_string_in(units.day))
if kepler.get_time(
) > 3 * self.dynamical_timescale and kepler.get_apastron(
) > 2.0 * self.initial_separation * (a.radius + b.radius):
# evolve for 3 * self.dynamical_timescale and skip the rest until ~initial_separation
kepler.return_to_apastron()
kepler.return_to_radius(a.radius + b.radius)
if -kepler.get_time(
) > 2.9 * self.dynamical_timescale: # If ~3 t_dyn have passed since the end of the collision
if self.verbose:
print "~3 t_dyn have passed since the end of the collision -> skip to next collision"
self.continue_with_kepler = True
kepler.advance_to_apastron()
kepler.advance_to_radius(2.0 * self.initial_separation *
(a.radius + b.radius))
self.skip_to_relative_position_velocity = (
kepler.get_separation_vector(),
kepler.get_velocity_vector())
self.begin_time = kepler.get_time()
kepler.advance_to_periastron()
self.next_dt = self.dynamical_timescales_per_step * self.dynamical_timescale + kepler.get_time(
) - self.begin_time
else:
self.next_dt = 3 * self.dynamical_timescale + kepler.get_time(
)
return will_collide
def evolve_with_kepler(self, hydro):
if self.verbose: print "evolve_with_kepler"
indices_two_most_massive = self.stars_after_encounter.mass.argsort(
)[-2:]
groups = [
self.groups_after_encounter[i] for i in indices_two_most_massive
]
old_particles = self.stars_after_encounter[indices_two_most_massive]
new_particles = Particles(2)
new_particles.mass = old_particles.mass
new_particles[0].position, new_particles[
0].velocity = self.skip_to_relative_position_velocity
new_particles.move_to_center()
for group, old_particle, new_particle in zip(groups, old_particles,
new_particles):
in_hydro = group.get_intersecting_subset_in(hydro.gas_particles)
if self.verbose:
print in_hydro.center_of_mass().as_quantity_in(
units.RSun), old_particle.position.as_quantity_in(
units.RSun), new_particle.position.as_quantity_in(
units.RSun)
in_hydro.position += new_particle.position - old_particle.position
in_hydro.velocity += new_particle.velocity - old_particle.velocity
