def find_and_mask_transits(time,
flux,
flux_err,
periods,
durations,
nplanets=1):
"""
Iteratively find and mask transits in the flattened light curve.
Args:
time (array): The time array.
flux (array): The flux array. You'll get the best results
if this is flattened.
flux_err (array): The array of flux uncertainties.
periods (array): The array of periods to search over for BLS.
For example, periods = np.linspace(0.5, 20, 10)
durations (array): The array of durations to search over for BLS.
For example, durations = np.linspace(0.05, 0.2, 10)
nplanets (Optional[int]): The number of planets you'd like to search for.
This function will interatively find and remove nplanets. Default is 1.
Returns:
transit_masks (list): a list of masks that correspond to the in
transit points of each light curve. To mask out transits do
time[~transit_masks[index]], etc.
"""
cum_transit = np.ones(len(time), dtype=bool)
_time, _flux, _flux_err = time * 1, flux * 1, flux_err * 1
t0s, durs, porbs = [np.zeros(nplanets) for i in range(3)]
transit_masks = []
for i in range(nplanets):
bls = BoxLeastSquares(t=_time, y=_flux, dy=_flux_err)
bls.power(periods, durations)
print("periods")
periods = bls.autoperiod(durations,
minimum_n_transit=3,
frequency_factor=5.0)
print("results")
results = bls.autopower(durations, frequency_factor=5.0)
# Find the period of the peak
print("find_period")
period = results.period[np.argmax(results.power)]
print("extract")
# Extract the parameters of the best-fit model
index = np.argmax(results.power)
porbs[i] = results.period[index]
t0s[i] = results.transit_time[index]
durs[i] = results.duration[index]
# # Plot the periodogram
# fig, ax = plt.subplots(1, 1, figsize=(10, 5))
# ax.plot(results.period, results.power, "k", lw=0.5)
# ax.set_xlim(results.period.min(), results.period.max())
# ax.set_xlabel("period [days]")
# ax.set_ylabel("log likelihood")
# # Highlight the harmonics of the peak period
# ax.axvline(period, alpha=0.4, lw=4)
# for n in range(2, 10):
# ax.axvline(n*period, alpha=0.4, lw=1, linestyle="dashed")
# ax.axvline(period / n, alpha=0.4, lw=1, linestyle="dashed")
# plt.show()
# plt.plot(_time, _flux, ".")
# plt.xlim(1355, 1360)
print("mask")
in_transit = bls.transit_mask(_time, porbs[i], 2 * durs[i], t0s[i])
transit_masks.append(in_transit)
_time, _flux, _flux_err = _time[~in_transit], _flux[~in_transit], \
_flux_err[~in_transit]
return transit_masks, t0s, durs, porbs
def tess_lightcurves(filename, TIC):
import numpy as np
from astropy.io import fits
import matplotlib.pyplot as plt
tpf_url = str(filename)
with fits.open(tpf_url) as hdus:
tpf = hdus[1].data
tpf_hdr = hdus[1].header
tpf_mask = hdus[2].data
time = tpf["TIME"]
flux = tpf["FLUX"]
m = np.any(np.isfinite(flux), axis=(1, 2)) & (tpf["QUALITY"] == 0)
time = np.ascontiguousarray(time[m] - np.min(time[m]), dtype=np.float64)
flux = np.ascontiguousarray(flux[m], dtype=np.float64)
mean_img = np.median(flux, axis=0)
plt.imshow(mean_img.T, cmap="gray_r")
plt.title("TESS image of Pi Men")
plt.xticks([])
plt.yticks([])
from scipy.signal import savgol_filter
# Sort the pixels by median brightness
order = np.argsort(mean_img.flatten())[::-1]
# A function to estimate the windowed scatter in a lightcurve
def estimate_scatter_with_mask(mask):
f = np.sum(flux[:, mask], axis=-1)
smooth = savgol_filter(f, 1001, polyorder=5)
return 1e6 * np.sqrt(np.median((f / smooth - 1)**2))
# Loop over pixels ordered by brightness and add them one-by-one
# to the aperture
masks, scatters = [], []
for i in range(10, 100):
msk = np.zeros_like(tpf_mask, dtype=bool)
msk[np.unravel_index(order[:i], mean_img.shape)] = True
scatter = estimate_scatter_with_mask(msk)
masks.append(msk)
scatters.append(scatter)
# Choose the aperture that minimizes the scatter
pix_mask = masks[np.argmin(scatters)]
# Plot the selected aperture
plt.imshow(mean_img.T, cmap="gray_r")
plt.imshow(pix_mask.T, cmap="Reds", alpha=0.3)
plt.title("TIC" + str(TIC) + ": selected aperture ")
plt.xticks([])
plt.yticks([])
# plt.savefig('/Users/Admin/Documents/Research_Lisa/TESS/plots/'+str(TIC)+'_aperture.pdf')
plt.close()
plt.figure(figsize=(10, 5))
sap_flux = np.sum(flux[:, pix_mask], axis=-1)
sap_flux = (sap_flux / np.median(sap_flux) - 1) * 1e3
plt.plot(time, sap_flux, "k")
plt.xlabel("time [days]")
plt.ylabel("relative flux [ppt]")
plt.title("TIC" + str(TIC) + ": raw light curve")
plt.xlim(time.min(), time.max())
# plt.savefig('/Users/Admin/Documents/Research_Lisa/TESS/plots/'+str(TIC)+'_raw_lc.pdf')
plt.close()
# Build the first order PLD basis
X_pld = np.reshape(flux[:, pix_mask], (len(flux), -1))
X_pld = X_pld / np.sum(flux[:, pix_mask], axis=-1)[:, None]
# Build the second order PLD basis and run PCA to reduce the number of dimensions
X2_pld = np.reshape(X_pld[:, None, :] * X_pld[:, :, None], (len(flux), -1))
U, _, _ = np.linalg.svd(X2_pld, full_matrices=False)
X2_pld = U[:, :X_pld.shape[1]]
# Construct the design matrix and fit for the PLD model
X_pld = np.concatenate((np.ones((len(flux), 1)), X_pld, X2_pld), axis=-1)
XTX = np.dot(X_pld.T, X_pld)
w_pld = np.linalg.solve(XTX, np.dot(X_pld.T, sap_flux))
pld_flux = np.dot(X_pld, w_pld)
# Plot the de-trended light curve
plt.figure(figsize=(10, 5))
plt.plot(time, sap_flux - pld_flux, "k")
plt.xlabel("time [days]")
plt.ylabel("de-trended flux [ppt]")
plt.title("TIC" + str(TIC) + ": initial de-trended light curve")
plt.xlim(time.min(), time.max())
# plt.savefig('/Users/Admin/Documents/Research_Lisa/TESS/plots/'+str(TIC)+'_detrend_lc.pdf')
plt.close()
from astropy.stats import BoxLeastSquares
period_grid = np.exp(np.linspace(np.log(1), np.log(15), 50000))
bls = BoxLeastSquares(time, sap_flux - pld_flux)
bls_power = bls.power(period_grid, 0.1, oversample=20)
# Save the highest peak as the planet candidate
index = np.argmax(bls_power.power)
bls_period = bls_power.period[index]
bls_t0 = bls_power.transit_time[index]
bls_depth = bls_power.depth[index]
transit_mask = bls.transit_mask(time, bls_period, 0.2, bls_t0)
fig, axes = plt.subplots(2, 1, figsize=(10, 10))
# Plot the periodogram
ax = axes[0]
ax.axvline(np.log10(bls_period), color="C1", lw=5, alpha=0.8)
ax.plot(np.log10(bls_power.period), bls_power.power, "k")
ax.annotate("period = {0:.4f} d".format(bls_period), (0, 1),
xycoords="axes fraction",
xytext=(5, -5),
textcoords="offset points",
va="top",
ha="left",
fontsize=12)
ax.set_ylabel("bls power")
ax.set_yticks([])
ax.set_xlim(np.log10(period_grid.min()), np.log10(period_grid.max()))
ax.set_xlabel("log10(period)")
# Plot the folded transit
ax = axes[1]
x_fold = (time - bls_t0 + 0.5 * bls_period) % bls_period - 0.5 * bls_period
m = np.abs(x_fold) < 0.4
ax.plot(x_fold[m], sap_flux[m] - pld_flux[m], ".k")
# Overplot the phase binned light curve
bins = np.linspace(-0.41, 0.41, 32)
denom, _ = np.histogram(x_fold, bins)
num, _ = np.histogram(x_fold, bins, weights=sap_flux - pld_flux)
denom[num == 0] = 1.0
ax.plot(0.5 * (bins[1:] + bins[:-1]), num / denom, color="C1")
ax.set_xlim(-0.3, 0.3)
ax.set_ylabel("de-trended flux [ppt]")
ax.set_xlabel("time since transit")
plt.title("TIC" + str(TIC))
plt.savefig('/Users/Admin/Documents/Research_Lisa/TESS/plots/' + str(TIC) +
'_period_detrend_lc.pdf')
plt.close()
m = ~transit_mask
XTX = np.dot(X_pld[m].T, X_pld[m])
w_pld = np.linalg.solve(XTX, np.dot(X_pld[m].T, sap_flux[m]))
pld_flux = np.dot(X_pld, w_pld)
x = np.ascontiguousarray(time, dtype=np.float64)
y = np.ascontiguousarray(sap_flux - pld_flux, dtype=np.float64)
plt.figure(figsize=(10, 5))
plt.plot(time, y, "k")
plt.xlabel("time [days]")
plt.ylabel("de-trended flux [ppt]")
plt.title("TIC" + str(TIC) + ": final de-trended light curve")
plt.xlim(time.min(), time.max())
# plt.savefig('/Users/Admin/Documents/Research_Lisa/TESS/plots/'+str(TIC)+'_detrend_lc_final.pdf')
plt.close()
plt.figure(figsize=(10, 5))
x_fold = (x - bls_t0 + 0.5 * bls_period) % bls_period - 0.5 * bls_period
m = np.abs(x_fold) < 0.3
plt.plot(x_fold[m], pld_flux[m], ".k", ms=4)
bins = np.linspace(-0.5, 0.5, 60)
denom, _ = np.histogram(x_fold, bins)
num, _ = np.histogram(x_fold, bins, weights=pld_flux)
denom[num == 0] = 1.0
plt.plot(0.5 * (bins[1:] + bins[:-1]), num / denom, color="C1", lw=2)
plt.xlim(-0.2, 0.2)
plt.title("TIC" + str(TIC))
plt.xlabel("time since transit")
plt.ylabel("PLD model flux")
# plt.savefig('/Users/Admin/Documents/Research_Lisa/TESS/plots/'+str(TIC)+'_PLD_model.pdf')
plt.close()