TRICERATOPS+ Pipeline for Exoplanet Validation

• TRICERATOPS+ is a Bayesian pipeline that integrates multi-band photometry, high-resolution imaging, and astrophysical scenario modeling to statistically validate transiting exoplanet candidates.
• It employs modular data ingestion, advanced detrending, and hierarchical Bayesian model comparison to compute false positive and nearby false positive probabilities.
• The pipeline improves upon previous methods by explicitly modeling contaminant scenarios and combining diverse observational constraints to robustly validate planets in crowded stellar fields.

TRICERATOPS+ is a Bayesian pipeline designed for the vetting and statistical validation of transiting exoplanet candidates, particularly those discovered by the Transiting Exoplanet Survey Satellite (TESS). Distinguished by its explicit modeling of both resolved and unresolved contaminating sources and its fully modular architecture, TRICERATOPS+ integrates multi-bandpass photometry, high-resolution imaging constraints, and extensive astrophysical scenario modeling to output false positive probabilities (FPP) and nearby false positive probabilities (NFPP), thereby enabling robust exoplanet validation in complex stellar environments (Barrientos et al., 4 Aug 2025, Greklek-McKeon et al., 10 Dec 2025, Giacalone et al., 2020).

1. Data Ingestion, Preprocessing, and Multi-Color Integration

TRICERATOPS+ operates on a diverse set of observational inputs:

• TESS PDCSAP light curves (2-min/10-min cadence), processed per sector and aperture specification.
• Ground-based photometry in one or more near-IR/optical bandpasses (e.g., J, g, r, i, z), phase-folded to the candidate periodicity.
• High-resolution imaging contrast curves (speckle, AO), resolving nearby sources and imposing constraints on allowable companion brightness as a function of separation.
• Stellar parameters and neighbor catalogs, consolidated from TIC, Gaia, and TRILEGAL simulations.

Preprocessing removes stellar/instrumental trends (via polynomial or GP detrending), phase-folds the photometry, and jointly fits transit models to each bandpass, yielding period $P$, epoch $t_0$, scaled semi-major axis $a/R_\star$, impact parameter $b$, and band-specific radius ratios $R_p/R_\star(\lambda)$. Limb-darkening coefficients are fixed per bandpass based on ExoTiC-LD. Detrending and normalization for individual ground transits employ comparison-star weights, sky background, PSF width, and airmass terms, selected by Bayesian Information Criterion (Greklek-McKeon et al., 10 Dec 2025).

2. Astrophysical Scenario Generation and Prior Construction

The pipeline generates an exhaustive set of astrophysical hypotheses (scenarios) for each candidate:

• STP: planet transiting the target star.
• PC / STP₂: planet transiting an unresolved (bound) companion.
• BEB/FEB: background/foreground eclipsing binaries, with periods at detected P or P/2.
• HTEB/SEB: hierarchical triples containing an unresolved eclipsing binary.
• Diluted background/foreground scenarios drawing from TRILEGAL-based synthetic stellar populations.

For each scenario, synthetic populations and dilution factors are derived using mass–luminosity splines, Galactic stellar densities, binary star statistics (including mass-ratio distributions and frequency), and enforced consistency with measured contrast curve limits. Scenarios are discarded if derived undiluted depths $\delta_s = \delta_{\mathrm{obs}}/X_s$ exceed physical plausibility ($\delta_s > 1$) (Giacalone et al., 2020).

3. Bayesian Model Comparison and Likelihood Computation

TRICERATOPS+ utilizes hierarchical Bayesian model comparison via importance sampling:

• For each scenario $s$ and parameter vector $\theta_s$ drawn from $P(\theta_s|s)$, the code computes synthetic light curves $M_b(t; \theta_s)$ for all bandpasses $b$.
• The per-bandpass likelihood is

$$\mathcal L_b(D_b | \theta_s) = \prod_{j=1}^{N_b} \frac{1}{\sqrt{2\pi}\sigma_{b,j}} \exp\left[-\frac{1}{2}\left(\frac{D_{b,j} - M_b(t_{b,j}; \theta_s)}{\sigma_{b,j}}\right)^2\right]$$

• The joint likelihood across bandpasses:

$$\mathcal L(D | \theta_s) = \prod_b \mathcal L_b(D_b | \theta_s)$$

• Each scenario is assigned a weight

$$w_s \propto P(s) \int P(\theta_s|s) \mathcal L(D | \theta_s) \, d\theta_s$$

where $P(s)$ encapsulates scenario priors derived from occurrence rates, field binary statistics, and prior exclusion by contrast curves (Greklek-McKeon et al., 10 Dec 2025, Barrientos et al., 4 Aug 2025).

4. False-Positive Probability (FPP) and Nearby FPP (NFPP) Calculation

Scenario weights are aggregated as follows:

• $W_{\mathrm{PL}} = \sum_{s \in \text{planet}} w_s$
• $W_{\mathrm{FP}} = \sum_{s \in \text{FP}} w_s$
• $$W_{\mathrm{NFP}} = \sum_{s \in \text{nearby FP}} w_s$$

Resulting probabilities are defined as

• False-Positive Probability (FPP):

$$\mathrm{FPP} = \frac{W_{\mathrm{FP}}}{W_{\mathrm{PL}} + W_{\mathrm{FP}}}$$

• Nearby False-Positive Probability (NFPP):

$$\mathrm{NFPP} = \frac{W_{\mathrm{NFP}}}{W_{\mathrm{PL}} + W_{\mathrm{FP}}}$$

Both FPP and NFPP are reported as medians over 10–20 Monte Carlo iterations, with 68% credible intervals (Barrientos et al., 4 Aug 2025, Greklek-McKeon et al., 10 Dec 2025).

Table: FPP/NFPP Disposition Criteria

FPP	NFPP	Disposition
$<$1.5%	$<$0.1%	Validated Planet
1.5–50%	$<$0.1%	Possible Planet
$>$70% or $>$10%	—	False Positive

5. High-Resolution Imaging Constraints

Contrast curves derived from high-resolution imaging (e.g., Gemini/'Alopeke speckle) define the allowed brightness and separation of unresolved companions. For each scenario requiring a companion within the aperture, those parameter draws that exceed the contrast-limited $\Delta m$ at a given angular separation are assigned zero prior weight, thereby excluding large sections of false-positive parameter space. Ground-based multi-band photometry in combination with contrast curves is critical for reducing both FPP and NFPP, particularly in systems with blended or closely separated sources (Greklek-McKeon et al., 10 Dec 2025, Barrientos et al., 4 Aug 2025).

6. Improvements over Original TRICERATOPS and Pipeline Implementation

Key TRICERATOPS+ enhancements over the original TRICERATOPS (Giacalone et al., 2020) include:

• Multi-bandpass fitting with simultaneous TESS and ground-based photometry (Greklek-McKeon et al., 10 Dec 2025, Barrientos et al., 4 Aug 2025).
• Wavelength-dependent dilution and limb-darkening [Ciardi+2015 corrections, ExoTiC-LD].
• Explicit modeling of the “planet around companion” (PC) scenario.
• Modular likelihood aggregation across instruments.
• Automatic ingestion and enforcement of contrast-curve and flux-ratio priors.
• Enhanced statistical convergence assessment, with MCMC convergence monitored (e.g., $\hat{R} < 1.1$ for critical parameters) (Barrientos et al., 4 Aug 2025).

The pipeline is implemented in Python (open-source, with public GitHub repository), leveraging packages such as AstroPy, batman, lightkurve, and TRILEGAL, and supports command-line use as well as outputting scenario-by-scenario probabilities, FPP/NFPP, and full transit/posterior parameter sets (Giacalone et al., 2020).

7. Validation Thresholds, Practical Impact, and Limitations

Statistical validation in TRICERATOPS+ follows the thresholds $\,\mathrm{FPP}<1.5\%$ and $\,\mathrm{NFPP}<0.1\%$ (Greklek-McKeon et al., 10 Dec 2025, Barrientos et al., 4 Aug 2025, Giacalone et al., 2020). In benchmarks on 68 known TOIs and large-scale application to 384 TESS objects of interest, TRICERATOPS+ demonstrated robust discrimination between bonafide exoplanets and astrophysical false positives, uniquely identifying contamination from both resolved and unresolved neighboring sources. Inclusion of high-S/N ground-based, multi-band transit data typically decreases FPP and can lead to statistical planet validation in cases where TESS photometry alone is ambiguous (Barrientos et al., 4 Aug 2025).

Key limitations include the reliance on accurate catalog stellar parameters, the need for high-quality contrast curves in relevant bandpasses, modeling assumptions of circular orbits, and the dependency on high S/N for ground-based transits. Chromatic noise and ambiguous companion color can increase uncertainty in NFPP estimation, particularly in the absence of full-band coverage. For candidates near validation thresholds, the recommended workflow prioritizes (1) high-resolution imaging to rule out FP parameter space, followed by (2) ground-based, multi-color photometry to further reduce residual FPP/NFPP (Barrientos et al., 4 Aug 2025, Giacalone et al., 2020).

A plausible implication is that TRICERATOPS+ enables statistical validation of small planets in compact, blended, or binary systems that would otherwise require resource-intensive radial velocity or high-contrast imaging confirmation. This expands the scope of transiting planet validation beyond that of previous tools by integrating comprehensive contaminant scenario modeling and multi-instrument likelihood treatment.