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Analysis Methods
Transit Models
Each transit is fit using MCMC sampling via the emcee EnsembleSampler with two model options:
1. Trapezoidal Model
A geometric approximation suitable for rapid fitting:
- Fitted Parameters:
t_mid - Mid-transit time
depth - Transit depth
duration - Total transit duration T14
ingress_frac - Ingress duration fraction
baseline - Out-of-transit flux
2. Mandel-Agol Model
Physical transit model using the batman package (Mandel & Agol 2002):
- Limb Darkening: Quadratic law with coefficients (u₁, u₂) interpolated from Claret (2017) tables based on stellar Teff and log(g)
- Fitted Parameters:
t_mid - Mid-transit time
rp_rs - Planet-to-star radius ratio
a_rs - Semi-major axis in stellar radii
inc - Orbital inclination (degrees)
baseline - Out-of-transit flux
MCMC Configuration
- 32 walkers, 500 burn-in steps, 1500 production steps
- 48,000 total samples per transit
Phase-Folded Lightcurve
All TESS observations are phase-folded using the fitted ephemeris and binned into 200 phase bins for visualization.
Derived Properties
Properties derived from MCMC posterior distributions:
- Value: Mean of the posterior distribution
- Error: 1-sigma uncertainty (16th-84th percentile range / 2)
- Scatter: Standard deviation across all transits
O-C Analysis
Transit mid-times are compared against linear and quadratic ephemeris models:
- Linear: T(n) = T₀ + P × n
- Quadratic: T(n) = T₀ + P × n + ½(dP/dE) × n²
- Model Selection: Bayesian Information Criterion (BIC)
Lomb-Scargle Periodogram
TTV search using Astropy's LombScargle implementation:
- Frequency Grid: Uniformly spaced in frequency, from 1/(2×baseline) to 1/(2×P_orb)
- FAP Thresholds: Computed via bootstrap method (10%, 1%, 0.1%)
- Significance: Based on False Alarm Probability of peak power
Data Source
TESS SPOC Pipeline PDCSAP_FLUX (Pre-search Data Conditioning) from all available sectors per target. The "TESS Sectors" field lists all sector IDs included in the analysis.
Scientific Highlights Categories
Planets are flagged as "interesting" based on these criteria:
- O-C Excess Scatter: RMS of O-C residuals > 2× mean timing uncertainty (potential TTVs)
- Periodic TTVs: Lomb-Scargle peak with FAP < 1% (possible companion planets)
- Period Changes: Quadratic model preferred by BIC (orbital decay or dynamics)
- Depth Variations: Transit depth scatter > 2× error (starspots, variable limb darkening)
- Inclination Variations: Impact parameter changes (orbital precession)
- Ultra-Stable: 50+ transits with O-C RMS < 1 minute (precision ephemeris)
Earth Similarity Score
Composite score (0-100) based on:
- Planet Radius (50%): Closeness to 1.0 R⊕
- Stellar Temperature (30%): Closeness to Sun (5778 K)
- Orbital Period (20%): Longer periods score higher
Citation
@inproceedings{autottv2026scaling,
title={Scaling-up autonomous scientific discovery: TESS Transit Timing Catalog},
author={Shporer, Avi and Drori, Iddo},
booktitle={247th AAS Meeting},
year={2026}
}