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