box-least-squares

Box Least Squares (BLS) Periodogram

The Box Least Squares (BLS) periodogram is a statistical tool for detecting transiting exoplanets and eclipsing binaries in photometric time series data. BLS models a transit as a periodic upside-down top hat (box shape) and finds the period, duration, depth, and reference time that best fit the data.

Overview

BLS is built into Astropy and provides an alternative to Transit Least Squares (TLS). Both search for transits, but with different implementations and performance characteristics.

Key parameters BLS searches for:

• Period (orbital period)
• Duration (transit duration)
• Depth (how much flux drops during transit)
• Reference time (mid-transit time of first transit)

Installation

BLS is part of Astropy:

pip install astropy

Basic Usage

import numpy as np
import astropy.units as u
from astropy.timeseries import BoxLeastSquares

# Prepare data
# time, flux, and flux_err should be numpy arrays or Quantities
t = time * u.day  # Add units if not already present
y = flux
dy = flux_err  # Optional but recommended

# Create BLS object
model = BoxLeastSquares(t, y, dy=dy)

# Automatic period search with specified duration
duration = 0.2 * u.day  # Expected transit duration
periodogram = model.autopower(duration)

# Extract results
best_period = periodogram.period[np.argmax(periodogram.power)]
print(f"Best period: {best_period:.5f}")

Using autopower vs power

autopower: Automatic Period Grid

Recommended for initial searches. Automatically determines appropriate period grid:

# Specify duration (or multiple durations)
duration = 0.2 * u.day
periodogram = model.autopower(duration)

# Or search multiple durations
durations = [0.1, 0.15, 0.2, 0.25] * u.day
periodogram = model.autopower(durations)

power: Custom Period Grid

For more control over the search:

# Define custom period grid
periods = np.linspace(2.0, 10.0, 1000) * u.day
duration = 0.2 * u.day

periodogram = model.power(periods, duration)