Circumbinary Planet Architectures

Circumbinary planets occupy a uniquely challenging region of parameter space that makes them intrinsically difficult to detect with standard transit-search techniques. Unlike planets orbiting single stars, circumbinary planets must remain dynamically stable within the time-varying gravitational potential of a binary system. This requirement imposes a sharp inner stability limit on planetary orbits, forcing stable circumbinary planets to reside at longer orbital periods, typically several times the binary period.

As shown in Figure 1, the known circumbinary planet population occupies a distinct region of orbital period–radius space when compared to the broader single-star exoplanet population. While small planets (roughly Earth–to–Neptune sized) dominate the single-star population, there is a striking absence of small circumbinary planets, despite their prevalence elsewhere. This demographic discrepancy is unexpected, as there is no clear theoretical reason to expect planet formation in circumbinary disks to strongly suppress the production of small planets. Instead, the observed deficit is widely interpreted as a detection bias, driven by the architectures of circumbinary systems rather than by intrinsic differences in planet formation.

Figure 1. Orbital period–radius distribution of known circumbinary planets (blue points: Kepler CBPs, pink points: TESS CBPs) compared to the single-star exoplanet population (black points). Circumbinary planets cluster at longer orbital periods and exhibit a notable absence of small planets relative to single-star systems, motivating dedicated searches for this missing population with the STANLEY pipeline.

Beyond their preferentially long orbital periods and correspondingly small number of observable transits, circumbinary planets present an additional challenge at the level of the photometric signal itself. As illustrated in Figure 2, circumbinary transits are fundamentally non-periodic. The orbital motion of the two stars about their barycenter induces strong gravitational perturbations that cause individual planetary transits to occur early or late relative to a linear ephemeris (transit timing variations; TTVs) and to exhibit significantly variable durations (transit duration variations; TDVs). Consecutive transits can differ by hours to days in timing, and their shapes and durations change depending on the instantaneous geometry of the stellar orbits.

Figure 2. Schematic illustration of transit timing variations (TTVs; left) and transit duration variations (TDVs; right) in circumbinary planet systems. The motion of the binary stars about their barycenter causes individual planetary transits to occur early or late relative to a linear ephemeris and to exhibit variable durations. These effects erase strict periodicity and fixed transit shapes in photometric data, severely reducing the sensitivity of conventional single-star transit search algorithms.

These effects violate the core assumptions of conventional single-star transit-search algorithms, which rely on strictly periodic signals with fixed durations and shapes. As a result, the sensitivity of standard pipelines to circumbinary planets, especially small planets near the detection threshold, is severely reduced.

Motivated by this apparent missing population and the intrinsically pathological nature of circumbinary transit signals, STANLEY was developed to systematically search for small circumbinary planets that are likely being missed by traditional methods. By coupling robust eclipsing-binary characterization with dynamically informed, variable-timing and variable-duration transit searches, STANLEY remains sensitive to precisely the class of signals that evade conventional pipelines. To date, STANLEY serves as the primary automated framework for conducting large-scale searches for small circumbinary planets in space-based photometric data, enabling both targeted discoveries and demographic studies of this unexplored population.

For a detailed description of the original Kepler-based implementation of the STANLEY pipeline and its application to the known circumbinary planet sample, see:

Martin & Fabrycky (2021), “Searching for Small Circumbinary Planets I. The STANLEY Automated Algorithm and No New Planets in Existing Systems” https://arxiv.org/abs/2101.03186

STANLEY Pipeline

STANLEY is a research pipeline for detecting, modeling, and analyzing eclipsing binaries and potential circumbinary planets (CBPs) in space-based photometric data. It was originally developed for the Kepler CBP sample and has since been extended to large-scale searches in TESS light curves. In circumbinary systems, planetary transits do not occur at regular intervals and transit durations vary significantly due to the orbital motion of both stars around the barycenter. As a result, conventional single-star transit search algorithms perform poorly. STANLEY implements methods specifically optimized for the variable-timing and variable-duration transit signatures unique to circumbinary planets.

Core Capabilities

Detrending

• Iterative cosine (COFIAM-like) filtering
• TESS-specific quadratic baseline removal
• Variable-duration biweight filters
• Outlier / flare / kink removal
• Optional ellipsoidal and reflection trend modeling

Binary Modeling & Validation

• Robust eclipse identification
• Multi-stage BLS period and harmonic validation
• Extraction of binary parameters (P, e, omega, eclipse depths and widths)

Secondary Eclipse Vetting

• Geometric feasibility tests
• Inclination / eccentricity constraints

Transit Timing Variation Search

• N-body forward modeling via REBOUND
• Variable-duration transit stacking matched to dynamically predicted timing signatures

Scalable Execution

• Fully HPC-compatible (SLURM)
• Each module (detrending, search, analysis) may run independently or as a unified pipeline
• Interpolative potential for less computational load

Scientific Context

STANLEY was first validated on the Kepler circumbinary-planet sample, where it successfully recovered all known CBPs including Kepler-47 b/c/d, searched for additional planets using variable-duration stacked transit detection, and demonstrated sensitivity to planets smaller than roughly three Earth radii in about half the systems. The current version extends the pipeline to TESS, enabling large-scale searches of low-mass eclipsing binaries and supporting demographic studies of small circumbinary planets.

Repository Structure and Data Requirements

This repository contains only the core source code (stanley_cbp/). All static catalogs needed at runtime are packaged inside:

stanley_cbp/Databases/

For standard local or Jupyter-based usage, users do not need to download any external data or set any environment variables.

Instead, when running the pipeline (typically from the Tutorials/ folder), STANLEY automatically creates and manages a local runtime workspace containing:

• LightCurves/
• PlanetSearchOutput/
• UserGeneratedData/

This workspace is created relative to the working directory and requires no manual configuration.

Runtime workspace (HPC / cluster use)

For large-scale or cluster-based runs, users may optionally define a runtime workspace via an environment variable:

export STANLEY_RUN_ROOT="/path/to/your/STANLEY/Runs"

When STANLEY_RUN_ROOT is set, all runtime products (light curves, diagnostics, and search outputs) are written under this directory instead of the local working directory. This is recommended for HPC environments where scratch space, quotas, or shared filesystems are involved.

If STANLEY_RUN_ROOT is not set, STANLEY falls back to the default local behavior described above.

Installation

Install from PyPI: pip install stanley_cbp

Or install from a locally built wheel: pip install dist/stanley_cbp-0.1.X-py3-none-any.whl

Environment setup (recommended)

For reproducible installations, this repository provides two Conda environment files:

environment.yml — for local machines and Jupyter-based workflows

clusterEnvironment.yml — for HPC or cluster environments

Users can create and activate an environment using either file, for example:

conda env create -f environment.yml conda activate stanley_env

or, for cluster usage:

conda env create -f clusterEnvironment.yml conda activate stanley_env

Once the environment is active, install STANLEY using one of the methods above.

Using STANLEY in Python

Example workflow:

Import:
from stanley_cbp import runDetrendingModule, Stanley_FindPlanets, runAnalysisModule

Detrending example:
result_det = runDetrendingModule(SystemName="TIC260128333", DetrendingName="DemoDetrend", UseSavedData=0)

Search example:
Stanley_FindPlanets(SearchName="DemoSearch", SystemName="TIC260128333", DetrendingName="DemoDetrend", totalSectors=1, currentSector=1)

Analysis example:
analysis_out = runAnalysisModule(searchName="DemoSearch", systemName="TIC260128333", totalSectors=1)

Tutorials

A Tutorials/ directory is provided with example Jupyter notebooks.
These notebooks assume:

• a local stanley_cbp installation,
• that the directory where the notebook is run will automatically function as the runtime workspace,
• and that STANLEY will generate all required folders (LightCurves/, PlanetSearchOutput/, UserGeneratedData/) as needed.

The tutorials demonstrate detrending, running the CBP search, interpreting outputs, and generating diagnostic figures.

Licensing

This package is released under the MIT License.