simple example code: binary_population_synthesis.pyΒΆ

(Source code, png, hires.png, pdf)

../../_images/binary_population_synthesis.png
"""
Generates a grid of binaries with different, primary mass, mass ratio
and separation and evolves these over time.
"""
from __future__ import print_function

from amuse.units import units
from amuse.units import quantities
from amuse import datamodel
from amuse.community.seba.interface import SeBa
from amuse.community.bse.interface import BSE

from matplotlib import pyplot

import numpy
import time

USE_VECTOR_OPERATIONS = True

def multidimensional_meshgrid(*arrays):
    """
    Utitility function to create a multidimensional grid based
    on a list of arrays. Each array defines a
    range in one dimension.
    """
    reversed_quantities = tuple(reversed(arrays))
    lengths = map(len, reversed_quantities)
    dim = len(reversed_quantities)

    size = 1
    for length in lengths:
        size *= length

    result = []
    for i, quantity in enumerate(reversed_quantities):
        shape = numpy.ones(dim)
        shape[i] = lengths[i]
        if quantities.is_quantity(quantity):
            array = quantity.value_in(quantity.unit)
        else:
            array = quantity
        array = array.reshape(shape)
        for j, length in enumerate(lengths):
            if j != i:
                array = array.repeat(length, axis=j)


        if quantities.is_quantity(quantity):
            result.append(quantity.unit.new_quantity(array))
        else:
            result.append(array)

    return tuple(result[::-1])

def create_binary(stars, binaries, primary_mass, mass_ratio, separation, eccentricity):
    """
    creates a single binary, the constituent stars will be accumulated
    in the stars partice set, the binary will be added to the binaries
    particle set.
    """
    primary_star = datamodel.Particle()
    primary_star.mass = primary_mass

    # we add the particle to the stars set
    # and we get a reference to the particle in the stars set
    # back
    # we want to use that star in constructing the
    # binary, so that the binaries all refer to
    # the stars in the "stars set"
    primary_star = stars.add_particle(primary_star)

    secondary_star = datamodel.Particle()
    secondary_star.mass = primary_mass * mass_ratio
    secondary_star = stars.add_particle(secondary_star)

    binary = datamodel.Particle()
    binary.eccentricity = eccentricity
    binary.semi_major_axis = separation
    binary.child1 = primary_star
    binary.child2 = secondary_star

    binaries.add_particle(binary)


def generate_initial_population_grid(
    min_mass, max_mass, number_of_mass_bins,
    min_ratio, max_ratio, number_of_ratio_bins,
    min_separation, max_separation, number_of_separation_bins,
    min_eccentricity, max_eccentricity, number_of_eccentricity_bins
):
    """
    creates a set of binaries and a set of stars, the grid
    will be divided in equal parts amongst all dimensions (primary mass,
    ratio and separation), the total number of binaries will
    be the product of all bins.
    """

    # quantities.linspace takes care of the units,
    # but is otherwhise equal to numpy.arange
    primary_masses  = quantities.linspace(min_mass, max_mass, number_of_mass_bins)
    mass_ratios = quantities.linspace(min_ratio, max_ratio, number_of_ratio_bins)
    separations = quantities.linspace(min_separation, max_separation, number_of_separation_bins)
    eccentricities = quantities.linspace(min_eccentricity, max_eccentricity, number_of_eccentricity_bins)

    # We can create the binaries individualy (with nested for loops to
    # go through each dimension) or at once with vector operations.
    # As vector operations are handled by numpy (in C) these are
    # much faster (default in this script).
    if USE_VECTOR_OPERATIONS is True:
        grid = multidimensional_meshgrid(primary_masses, mass_ratios, separations, eccentricities)

        all_primary_masses = grid[0].flatten()
        all_mass_ratios    = grid[1].flatten()
        all_separations    = grid[2].flatten()
        all_eccentricities = grid[3].flatten()

        primary_stars   = datamodel.Particles(mass=all_primary_masses)
        secondary_stars = datamodel.Particles(mass=all_primary_masses * all_mass_ratios)

        stars = datamodel.Particles()
        primary_stars   = stars.add_particles(primary_stars)
        secondary_stars = stars.add_particles(secondary_stars)

        binaries = datamodel.Particles(
            semi_major_axis = all_separations,
            eccentricity    = all_eccentricities
        )
        binaries.child1 = list(primary_stars)
        binaries.child2 = list(secondary_stars)
    else:
        for primary_mass in primary_masses:
            for mass_ratio in mass_ratios:
                for separation in separations:
                    for eccentricity in eccentricities :
                        create_binary(
                            stars,
                            binaries,
                            primary_mass,
                            mass_ratio,
                            separation,
                            eccentricity
                        )

    return binaries, stars

def evolve_population(binaries, stars, end_time, time_step):
    code = SeBa()

    # add the stars first, as the binaries will
    # refer to them
    code.particles.add_particles(stars)
    code.binaries.add_particles(binaries)


    channel_from_code_to_model_for_binaries = code.binaries.new_channel_to(binaries)
    channel_from_code_to_model_for_stars = code.particles.new_channel_to(stars)

    #we evolve in steps of timestep, just to get some feedback
    print("start evolving...")
    time = 0.0 * end_time
    while time < end_time:
        time += time_step
        code.evolve_model(time)
        print("evolved to time: ", time.as_quantity_in(units.Myr))

    channel_from_code_to_model_for_stars.copy()
    channel_from_code_to_model_for_binaries.copy()

def make_hr_diagram(binaries):
    pyplot.figure(figsize = (8,8))
    pyplot.title('Binary population', fontsize=12)
    separation = binaries.semi_major_axis.value_in(units.RSun)
    eccentricity = binaries.eccentricity
    pyplot.hexbin(
        separation,
        eccentricity,
        gridsize = 40,
        bins = 'log',
        extent = (0, 100, 0.0, 0.9)
    )
    pyplot.xlabel('semi major axis (AU)')
    pyplot.ylabel('eccentricity')
    pyplot.show()


if __name__ == "__main__":
    print("generating a binary population...")

    binaries, stars = generate_initial_population_grid(
        0.5 | units.MSun, 1.5 | units.MSun, 3, #mass range
        0.9, 0.9, 1,                           #mass ratios range
        10 | units.RSun, 100 | units.RSun, 120,    #semi major axis range
        0.0 , 1.0, 120                          #eccentricity range
    )

    print("generated a population of", len(binaries), "binaries")

    evolve_population(binaries, stars,  1 | units.Gyr, 250 | units.Myr)

    make_hr_diagram(binaries)

Keywords: python, amuse, astrophysics, matplotlib, pylab, example, codex (see how-to-search-examples)

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