def grid_black_hole_companion_population(N_per_axis):
P = np.logspace(0.5, 2, N_per_axis)
M_star = salpeter_imf(N_per_axis, 2.35, 0.1, 100)
M_bh = np.random.uniform(3, 5, N_per_axis)
v = np.array([M_bh, M_star])
M_1 = np.max(v, axis=0)
M_2 = np.min(v, axis=0)
cos_i = np.random.uniform(0, 1, N_per_axis)
i = np.arccos(cos_i)
params = np.array(list(itertools.product(P, M_1, M_2, i)))
P, M_1, M_2, i = params.T
# always assume the more massive one is the bh
f_1 = np.zeros(M_1.size)
f_2 = np.ones(M_1.size)
P = P << u.day
M_1 = M_1 << u.solMass
M_2 = M_2 << u.solMass
i = i << u.rad
args = (P, M_1, M_2, f_1, f_2, i)
return (args, None)
def grid_giant_main_sequence_binary_population(N_per_axis, N_simulation):
P = np.logspace(1, 7, N_per_axis)
q = np.linspace(0.1, 1, N_per_axis)
cos_i = np.linspace(0, 1, N_simulation)
i = np.arccos(cos_i)
#cos_i = np.array([1.0])
#i = np.arccos(cos_i)
M_1 = salpeter_imf(N_simulation, 2.35, 0.1, 100)
params = np.array(list(itertools.product(P, q, M_1, i)))
P, q, M_1, i = params.T
M_2 = q * M_1
# TODO: revisit this assumption?
f_1 = 1000 #
f_2 = 1
P = P << u.day
M_1 = M_1 << u.solMass
M_2 = M_2 << u.solMass
i = i << u.rad
args = (P, M_1, M_2, f_1, f_2, i)
return (args, None)
def draw_black_hole_companion_population(N):
P = 30 * np.ones(N) * u.day
M_1 = salpeter_imf(N, 2.35, 0.1, 100) * u.solMass
f_1 = 1.0 * np.ones(N)
M_2 = np.random.uniform(3, 5, N) * u.solMass
f_2 = 0.0 * np.ones(N)
q = M_2 / M_1
cos_i = np.random.uniform(0, 1, N)
i = np.arccos(cos_i) * u.rad
args = (P, M_1, M_2, f_1, f_2, i)
ylabel = r"$\textrm{detection efficiency of black hole companions}$"
return (args, ylabel)
def draw_main_sequence_binary_population(N):
# We are using the same Ps, qs, etc at each distance trial.
P = np.random.lognormal(5.03, 2.28, N) * u.day # Raghavan et al. (2010)
q = np.random.uniform(0.1, 1, N)
cos_i = np.random.uniform(0, 1, N)
i = np.arccos(cos_i) * u.rad
M_1 = salpeter_imf(N, 2.35, 0.1, 100) * u.solMass
M_2 = q * M_1
# Assume main-sequence systems.
f_1 = M_1.value**3.5
f_2 = M_2.value**3.5
args = (P, M_1, M_2, f_1, f_2, i)
ylabel = r"$\textrm{detection efficiency of main-sequence binary systems}$"
return (args, ylabel)
def draw_hot_jupiter_host_population(N):
M_1 = salpeter_imf(N, 2.35, 0.1, 100) * u.solMass
f_1 = 1.0 * np.ones(N)
M_2 = 10 * np.ones(N) * constants.M_jup.to(u.solMass)
f_2 = 0.0 * np.ones(N)
q = M_2 / M_1
cos_i = np.random.uniform(0, 1, N)
i = np.arccos(cos_i) * u.rad
P = np.random.uniform(5, 10, N) * u.day
args = (P, M_1, M_2, f_1, f_2, i)
ylabel = r"$\textrm{detection efficiency of hot jupiters}$"
return (args, ylabel)