University Astrophysics & Python for Astronomy Tutoring

Task. Fold a light curve on a known period and measure the transit depth. Here we simulate one TESS-like sector so the answer is known in advance: a 5000 ppm transit every 3.2 days, with 1000 ppm of white noise.

import numpy as np

# Simulated light curve: 27 days of 2-minute cadence, like one TESS sector
rng = np.random.default_rng(42)
t = np.arange(0, 27, 2 / 1440)                    # time [days]
P, t0, dur, depth = 3.2, 1.1, 0.12, 0.0050        # period, mid-transit, duration [d], depth
flux = 1 + rng.normal(0, 0.001, t.size)           # 1000 ppm white noise
phase = (t - t0 + 0.5 * P) % P - 0.5 * P          # days from the nearest mid-transit
flux[np.abs(phase) < dur / 2] -= depth            # box-shaped transit

# Fold on the known period and compare in-transit with out-of-transit flux
in_tr = np.abs(phase) < dur / 4                   # central half of the transit
out_tr = np.abs(phase) > dur                      # well away from the transit
measured = flux[out_tr].mean() - flux[in_tr].mean()
err = np.std(flux[out_tr]) / np.sqrt(in_tr.sum())

print(f"depth = {measured * 1e6:.0f} ± {err * 1e6:.0f} ppm")
print(f"Rp/R* = {np.sqrt(measured):.4f}")

Output:

depth = 4934 ± 51 ppm
Rp/R* = 0.0702

Reading the result. The measured depth agrees with the injected 5000 ppm to within about 1.3 standard errors. Since $\delta \approx (R_p/R_\star)^2$, a Sun-like host would make this planet about $0.0702 \times 109 \approx 7.7$ Earth radii. With real data you would first remove stellar variability and instrumental trends, and fit a limb-darkened transit model instead of a box.