def ln_priors(y):
""" Priors on the model parameters
Parameters
----------
y : ra, dec, M1, M2, A, ecc, v_k, theta, phi, ra_b, dec_b, t_b
Current HMXB location (ra, dec) and 10 model parameters
Returns
-------
lp : float
Natural log of the prior
"""
# M1, M2, A, v_k, theta, phi, ra_b, dec_b, t_b = y
ra, dec, M1, M2, A, ecc, v_k, theta, phi, ra_b, dec_b, t_b = y
lp = 0.0
# P(M1)
if M1 < c.min_mass or M1 > c.max_mass: return -np.inf
norm_const = (c.alpha+1.0) / (np.power(c.max_mass, c.alpha+1.0) - np.power(c.min_mass, c.alpha+1.0))
lp += np.log( norm_const * np.power(M1, c.alpha) )
# M1 must be massive enough to evolve off the MS by t_obs
if load_sse.func_sse_tmax(M1) > t_b: return -np.inf
# P(M2)
# Normalization is over full q in (0,1.0)
q = M2 / M1
if q < 0.3 or q > 1.0: return -np.inf
lp += np.log( (1.0 / M1 ) )
# P(ecc)
if ecc < 0.0 or ecc > 1.0: return -np.inf
lp += np.log(2.0 * ecc)
# P(A)
if A*(1.0-ecc) < c.min_A or A*(1.0+ecc) > c.max_A: return -np.inf
norm_const = np.log(c.max_A) - np.log(c.min_A)
lp += np.log( norm_const / A )
# A must avoid RLOF at ZAMS, by a factor of 2
r_1_roche = binary_evolve.func_Roche_radius(M1, M2, A*(1.0-ecc))
if 2.0 * load_sse.func_sse_r_ZAMS(M1) > r_1_roche: return -np.inf
# P(v_k)
if v_k < 0.0: return -np.inf
lp += np.log( maxwell.pdf(v_k, scale=c.v_k_sigma) )
# P(theta)
if theta <= 0.0 or theta >= np.pi: return -np.inf
lp += np.log(np.sin(theta) / 2.0)
# P(phi)
if phi < 0.0 or phi > np.pi: return -np.inf
lp += -np.log( np.pi )
# Get star formation history
sf_history.load_sf_history()
sfh = sf_history.get_SFH(ra_b, dec_b, t_b, sf_history.smc_coor, sf_history.smc_sfh)
if sfh <= 0.0: return -np.inf
# P(alpha, delta)
# From spherical geometric effect, we need to care about cos(declination)
lp += np.log(np.cos(c.deg_to_rad * dec_b) / 2.0)
##################################################################
# We add an additional prior that scales the RA and Dec by the
# area available to it, i.e. pi theta^2, where theta is the angle
# of the maximum projected separation over the distance.
#
# Still under construction
##################################################################
M1_b, M2_b, A_b = binary_evolve.func_MT_forward(M1, M2, A, ecc)
A_c, v_sys, ecc = binary_evolve.func_SN_forward(M1_b, M2_b, A_b, v_k, theta, phi)
if ecc < 0.0 or ecc > 1.0 or np.isnan(ecc): return -np.inf
# Ensure that we only get non-compact object companions
tobs_eff = binary_evolve.func_get_time(M1, M2, t_b)
M_tmp, M_dot_tmp, R_tmp, k_type = load_sse.func_get_sse_star(M2_b, tobs_eff)
if int(k_type) > 9: return -np.inf
# t_sn = (t_b - func_sse_tmax(M1)) * 1.0e6 * yr_to_sec # The time since the primary's core collapse
# theta_max = (v_sys * t_sn) / dist_LMC # Unitless
# area = np.pi * rad_to_dec(theta_max)**2
# lp += np.log(1.0 / area)
##################################################################
# Instead, let's estimate the number of stars formed within a cone
# around the observed position, over solid angle and time.
# Prior is in Msun/Myr/steradian
##################################################################
t_min = load_sse.func_sse_tmax(M1) * 1.0e6 * c.yr_to_sec
t_max = (load_sse.func_sse_tmax(M2_b) - binary_evolve.func_get_time(M1, M2, 0.0)) * 1.0e6 * c.yr_to_sec
if t_max-t_min < 0.0: return -np.inf
theta_C = (v_sys * (t_max - t_min)) / c.dist_SMC
stars_formed = get_stars_formed(ra, dec, t_min, t_max, v_sys, c.dist_SMC)
if stars_formed == 0.0: return -np.inf
volume_cone = (np.pi/3.0 * theta_C**2 * (t_max - t_min) / c.yr_to_sec / 1.0e6)
lp += np.log(sfh / stars_formed / volume_cone)
##################################################################
# # P(t_b | alpha, delta)
# sfh_normalization = 1.0e-6
# lp += np.log(sfh_normalization * sfh)
# Add a prior so that the post-MT secondary is within the correct bounds
M2_c = M1 + M2 - load_sse.func_sse_he_mass(M1)
if M2_c > c.max_mass or M2_c < c.min_mass: return -np.inf
# Add a prior so the effective time remains bounded
t_eff_obs = binary_evolve.func_get_time(M1, M2, t_b)
if t_eff_obs < 0.0: return -np.inf
if t_b * 1.0e6 * c.yr_to_sec < t_min: return -np.inf
if t_b * 1.0e6 * c.yr_to_sec > t_max: return -np.inf
return lp
def ln_priors_population(y):
""" Priors on the model parameters
Parameters
----------
y : M1, M2, A, ecc, v_k, theta, phi, ra_b, dec_b, t_b
10 model parameters
Returns
-------
lp : float
Natural log of the prior
"""
M1, M2, A, ecc, v_k, theta, phi, ra_b, dec_b, t_b = y
lp = 0.0
# P(M1)
if M1 < c.min_mass or M1 > c.max_mass: return -np.inf
norm_const = (c.alpha+1.0) / (np.power(c.max_mass, c.alpha+1.0) - np.power(c.min_mass, c.alpha+1.0))
lp += np.log( norm_const * np.power(M1, c.alpha) )
# M1 must be massive enough to evolve off the MS by t_obs
if load_sse.func_sse_tmax(M1) > t_b: return -np.inf
# P(M2)
# Normalization is over full q in (0,1.0)
q = M2 / M1
if q < 0.3 or q > 1.0: return -np.inf
lp += np.log( (1.0 / M1 ) )
# P(ecc)
if ecc < 0.0 or ecc > 1.0: return -np.inf
lp += np.log(2.0 * ecc)
# P(A)
if A*(1.0-ecc) < c.min_A or A*(1.0+ecc) > c.max_A: return -np.inf
norm_const = np.log(c.max_A) - np.log(c.min_A)
lp += np.log( norm_const / A )
# A must avoid RLOF at ZAMS, by a factor of 2
r_1_roche = binary_evolve.func_Roche_radius(M1, M2, A*(1.0-ecc))
if 2.0 * load_sse.func_sse_r_ZAMS(M1) > r_1_roche: return -np.inf
# P(v_k)
if v_k < 0.0: return -np.inf
lp += np.log( maxwell.pdf(v_k, scale=c.v_k_sigma) )
# P(theta)
if theta <= 0.0 or theta >= np.pi: return -np.inf
lp += np.log(np.sin(theta) / 2.0)
# P(phi)
if phi < 0.0 or phi > np.pi: return -np.inf
lp += -np.log( np.pi )
# Get star formation history
sfh = sf_history.get_SFH(ra_b, dec_b, t_b, sf_history.smc_coor, sf_history.smc_sfh)
if sfh <= 0.0: return -np.inf
lp += np.log(sfh)
# P(alpha, delta)
# From spherical geometric effect, scale by cos(declination)
lp += np.log(np.cos(c.deg_to_rad*dec_b) / 2.0)
M1_b, M2_b, A_b = binary_evolve.func_MT_forward(M1, M2, A, ecc)
A_c, v_sys, ecc = binary_evolve.func_SN_forward(M1_b, M2_b, A_b, v_k, theta, phi)
if ecc < 0.0 or ecc > 1.0 or np.isnan(ecc): return -np.inf
# Ensure that we only get non-compact object companions
tobs_eff = binary_evolve.func_get_time(M1, M2, t_b)
M_tmp, M_dot_tmp, R_tmp, k_type = load_sse.func_get_sse_star(M2_b, tobs_eff)
if int(k_type) > 9: return -np.inf
# Add a prior so that the post-MT secondary is within the correct bounds
M2_c = M1 + M2 - load_sse.func_sse_he_mass(M1)
if M2_c > c.max_mass or M2_c < c.min_mass: return -np.inf
# Add a prior so the effective time remains bounded
t_eff_obs = binary_evolve.func_get_time(M1, M2, t_b)
if t_eff_obs < 0.0: return -np.inf
t_max = (load_sse.func_sse_tmax(M2_b) - binary_evolve.func_get_time(M1, M2, 0.0))
if t_b > t_max: return -np.inf
return lp
