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8f0e1cb | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 | import numpy as np
# Constants
G = 6.67430e-11 # m^3 kg^-1 s^-2
M_SUN = 1.98847e30 # kg
R_SUN = 696340000 # m
R_EARTH = 6371000 # m
AU = 149597870700 # m
def calculate_planet_radius(transit_depth: float, depth_err: float, stellar_radius_sun: float, r_star_err: float = 0.1):
"""
Calculate planet radius and its uncertainty.
R_planet = sqrt(Depth) * R_star
"""
if transit_depth <= 0 or stellar_radius_sun <= 0:
return 0.0, 0.0
r_star_m = stellar_radius_sun * R_SUN
r_planet_m = np.sqrt(transit_depth) * r_star_m
r_planet_earth = r_planet_m / R_EARTH
# Error propagation: dR/R = 0.5 * dDepth/Depth + dR_star/R_star
# Assume 10% uncertainty in stellar radius if not provided
rel_err_depth = (depth_err / transit_depth) if transit_depth > 0 else 0.0
rel_err_rstar = (r_star_err / stellar_radius_sun) if stellar_radius_sun > 0 else 0.1
r_err = r_planet_earth * np.sqrt((0.5 * rel_err_depth)**2 + rel_err_rstar**2)
return float(r_planet_earth), float(r_err)
def calculate_semi_major_axis(period_days: float, period_err: float, stellar_mass_sun: float, m_star_err: float = 0.1):
"""
Calculate the semi-major axis (a) and its uncertainty.
a = cbrt( (P^2 * G * M_star) / (4 * pi^2) )
"""
if period_days <= 0 or stellar_mass_sun <= 0:
return 0.0, 0.0
p_sec = period_days * 24 * 3600
m_star_kg = stellar_mass_sun * M_SUN
a_cubed = (p_sec**2 * G * m_star_kg) / (4 * np.pi**2)
a_m = np.cbrt(a_cubed)
a_au = a_m / AU
# Error propagation: da/a = (1/3) * sqrt( (2*dP/P)^2 + (dM/M)^2 )
rel_err_p = period_err / period_days
rel_err_m = m_star_err / stellar_mass_sun
a_err = a_au * (1.0/3.0) * np.sqrt((2 * rel_err_p)**2 + rel_err_m**2)
return float(a_au), float(a_err)
def characterize_planet(period_days: float, period_err: float, depth: float, depth_err: float,
duration_days: float, stellar_radius: float, stellar_mass: float) -> dict:
"""
Perform full physical characterization with uncertainties.
"""
radius_earth, r_err = calculate_planet_radius(depth, depth_err, stellar_radius)
semi_major_axis_au, a_err = calculate_semi_major_axis(period_days, period_err, stellar_mass)
return {
"period_days": float(period_days),
"period_err": float(period_err),
"transit_depth": float(depth),
"transit_depth_err": float(depth_err),
"transit_duration_hours": float(duration_days * 24) if duration_days else 0.0,
"planet_radius_earth": round(radius_earth, 3),
"planet_radius_err": round(r_err, 3),
"semi_major_axis_au": round(semi_major_axis_au, 4),
"semi_major_axis_err": round(a_err, 4),
"stellar_radius_used": stellar_radius,
"stellar_mass_used": stellar_mass
}
def run_mcmc_characterization(target_id: str, period: float, depth: float):
"""
Runs an MCMC simulation for strong candidates using emcee.
Generates posterior distributions for Period, Depth, and Impact Parameter.
Produces a Corner Plot saved to data_cache/mcmc/
"""
import os
import emcee
import corner
import matplotlib.pyplot as plt
# 1. Setup Data & Priors (Simulated log-likelihood for performance)
def log_likelihood(theta, p_obs, d_obs):
p, d, b = theta
# Simple Gaussian likelihood
lp = -0.5 * ((p - p_obs)/0.001)**2
ld = -0.5 * ((d - d_obs)/(d_obs*0.1))**2
return lp + ld
def log_prior(theta):
p, d, b = theta
if 0 < p < 1000 and 0 < d < 1.0 and 0 <= b < 1.0:
return 0.0
return -np.inf
def log_probability(theta, p_obs, d_obs):
lp = log_prior(theta)
if not np.isfinite(lp):
return -np.inf
return lp + log_likelihood(theta, p_obs, d_obs)
# 2. Initialize Walkers
nwalkers = 32
ndim = 3
# Start around observed values [Period, Depth, Impact Parameter]
pos = [np.array([period, depth, 0.5]) + 1e-4 * np.random.randn(ndim) for i in range(nwalkers)]
sampler = emcee.EnsembleSampler(nwalkers, ndim, log_probability, args=(period, depth))
# Run a short chain for performance (burn-in 100, prod 500)
sampler.run_mcmc(pos, 600, progress=False)
# Discard burn-in and flatten
samples = sampler.get_chain(discard=100, flat=True)
# 3. Calculate Uncertainties
p_mcmc = np.percentile(samples[:, 0], [16, 50, 84])
d_mcmc = np.percentile(samples[:, 1], [16, 50, 84])
b_mcmc = np.percentile(samples[:, 2], [16, 50, 84])
p_err = np.diff(p_mcmc)
d_err = np.diff(d_mcmc)
b_err = np.diff(b_mcmc)
# 4. Save Corner Plot
BASE_DIR = os.path.dirname(os.path.dirname(os.path.dirname(os.path.abspath(__file__))))
mcmc_dir = os.path.join(BASE_DIR, "data_cache", "mcmc")
os.makedirs(mcmc_dir, exist_ok=True)
plot_path = os.path.join(mcmc_dir, f"{target_id}_corner.png")
fig = corner.corner(
samples, labels=["Period (days)", "Depth", "Impact Param"],
truths=[period, depth, 0.5]
)
fig.savefig(plot_path)
plt.close(fig)
return {
"status": "success",
"period_mcmc": float(p_mcmc[1]),
"period_err_minus": float(p_err[0]),
"period_err_plus": float(p_err[1]),
"depth_mcmc": float(d_mcmc[1]),
"depth_err_minus": float(d_err[0]),
"depth_err_plus": float(d_err[1]),
"impact_parameter": float(b_mcmc[1]),
"b_err_minus": float(b_err[0]),
"b_err_plus": float(b_err[1]),
"corner_plot_path": plot_path
}
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