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Bayesian analysis of Gaia epoch astrometry and radial velocities with kima

This paper introduces and validates two new models within the open-source software kima for performing Bayesian analysis of Gaia epoch astrometry and radial velocity data to detect and characterize exoplanets, binary stars, and black holes.

Original authors: Thomas A. Baycroft, João P. Faria, Jean-Baptiste Delisle

Published 2026-06-24

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CC BY 4.0

Original authors: Thomas A. Baycroft, João P. Faria, Jean-Baptiste Delisle

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine the Gaia space telescope as a cosmic camera that has been taking billions of snapshots of the stars over many years. In late 2026, it will release a massive album of these snapshots, called "epoch astrometry." This data is so rich that scientists expect to find tens of thousands of new planets, binary stars, and even black holes. However, looking at this mountain of data is like trying to find a specific needle in a haystack while the haystack is shaking.

This paper introduces a new, open-source tool called kima (specifically updated for Gaia) that acts like a super-smart detective to solve these cosmic puzzles. Here is how it works, broken down into simple concepts:

1. The Detective's Toolkit: Two New Models

The authors added two new "detective modes" to the kima software:

The Solo Detective (GAIAmodel): This looks only at the Gaia snapshots. It tries to figure out if a star is wobbling because it has a planet, or if it's just wobbling due to other reasons.
The Team Detective (RVGAIAmodel): This is the ultimate investigator. It combines the Gaia snapshots with radial velocity data (which measures how fast a star is moving toward or away from us). By combining these two clues, the detective can figure out the 3D shape of the orbit and the true mass of the planet, rather than just guessing.

2. How It Solves the Puzzle: The "Nested Sampling"

Instead of guessing and checking one by one, kima uses a method called diffusive nested sampling.

The Analogy: Imagine you are trying to find the highest peak in a foggy mountain range. A normal search might get stuck in a small hill. Kima, however, sends out a swarm of explorers who can float through the fog, jump between valleys, and map the entire landscape at once.
The Magic Trick: This method allows kima to decide how many planets are in the system automatically. It doesn't just ask, "Is there one planet?" It asks, "Is there zero? One? Two? Three?" and picks the answer that best fits the data without forcing a conclusion.

3. The "Scan-Angle" Ghost

One of the biggest challenges with Gaia data is a "ghost signal."

The Problem: Sometimes, a star looks like it's wobbling in a perfect orbit, but it's actually an optical illusion caused by the telescope's scanning pattern (like a strobe light making a spinning fan look like it's moving backward). This is called a scan-angle dependent signal.
The Solution: The paper shows that kima can act like a lie detector. It can compare two stories: "Story A: This is a real planet orbiting a star." vs. "Story B: This is just a glitch in the telescope's scanning pattern."
The Result: In some cases, kima successfully identified that a signal was a "ghost" (a false alarm caused by a binary star system) rather than a real planet. However, the authors admit that sometimes the ghost and the real planet look so similar that even the best detective needs more clues (like high-resolution imaging) to be sure.

4. Testing the Detective

The authors tested their new tools in two ways:

The Simulation Lab: They created fake data with known planets (some easy to find, some very hard) and ran kima through it. The detective found the planets and measured their orbits correctly, matching the "truth" they had planted.
The Real Crime Scene: They applied the tool to Gaia BH3, a real system containing a black hole. The results matched what other top-tier tools found, proving that kima is ready for the real deal.

5. The "What-If" Limits (Compatibility Limits)

Finally, the paper explains how kima can tell you what isn't there.

The Analogy: If you listen to a quiet room and don't hear a mouse, you can't say for sure a mouse isn't there. But you can say, "If a mouse were this big, I would have heard it."
The Application: kima calculates "compatibility limits." It tells astronomers: "We didn't find a planet here, but if there were a planet of this size and this distance, we definitely would have seen it." This helps scientists understand the limits of their search.

Summary

In short, this paper presents kima as a powerful, flexible, and open-source tool designed to handle the massive amount of data coming from the Gaia telescope. It helps astronomers distinguish between real planets and optical illusions, combine different types of data for better accuracy, and clearly state what they have found—and what they haven't—using a robust statistical approach.

Technical Summary: Bayesian Analysis of Gaia Epoch Astrometry and Radial Velocities with kima

Problem and Context
The upcoming fourth data release (DR4) from the Gaia space telescope, expected in December 2026, will provide individual epoch astrometry for approximately two billion sources. This dataset promises the detection of tens of thousands of new exoplanets, as well as 3D orbital constraints for binary stars and black holes. However, analyzing this volume of data requires dedicated tools capable of handling complex orbital fitting, model comparison, and the simultaneous processing of astrometric and radial velocity (RV) data. Existing tools such as kepmodel, BINARYS, and Octofitter can fit Gaia epoch astrometry, but they lack the specific capabilities for efficient trans-dimensional sampling and robust Bayesian model comparison inherent to the kima codebase.

Methodology
The authors extend the open-source orbit-fitting code kima (originally developed for RV analysis) by implementing two new models:

GAIAmodel: Designed to analyze Gaia epoch astrometry alone. It models the along-scan position ( $w$ ) as a sum of a baseline single-star model (5 parameters: position offsets, proper motion, parallax), optional acceleration terms (7 or 9 parameters), scan-angle dependent signals (harmonics of the scan angle $\psi$ ), and Keplerian orbital components.
RVGAIAmodel: Combines the GAIAmodel with radial velocity data. It links the RV semi-amplitude ( $K$ ) and the photocenter semi-major axis ( $a$ ) through a physical relation, sharing orbital parameters (period, eccentricity, argument of pericenter, etc.) between the two datasets while allowing independent jitter and trend parameters.

Both models utilize the diffusive nested sampling algorithm (via the DNEST4 package) to explore the parameter space. A key feature is that the number of Keplerian signals ( $N_p$ ) is treated as a free parameter, enabling efficient Bayesian model comparison (calculating evidences) and parameter estimation within a single run. The models support both Thiele-Innes and geometric parameterizations, with the latter being preferred for RVGAIAmodel to handle inclination degeneracies.

Key Contributions

Software Implementation: The addition of bespoke models to kima for analyzing Gaia epoch astrometry, either standalone or jointly with RVs.
Scan-Angle Signal Discrimination: The inclusion of a specific model to account for scan-angle dependent signals (using 3rd, 5th, and 7th harmonics), allowing for the distinction between true Keplerian orbits and artifacts caused by marginally resolved binaries.
Compatibility Limits: A demonstration of how kima can generate "compatibility limits" (a Bayesian equivalent to detection limits) directly from posterior samples of non-detected signals, applicable to both simulated and real data.

Results
The authors tested the models on simulated data (derived from real Gaia residuals with injected signals) and real data from the Gaia BH3 system:

Validation: The models successfully recovered injected planetary signals (high and low signal-to-noise, long and short periods) with posterior distributions consistent with true values. Results were consistent with those obtained using kepmodel.
Model Comparison: In tests involving a known scan-angle dependent signal (Target 4), the model with scan-angle harmonics was decisively favored over a Keplerian model (Bayes Factor $\approx 640$ ). Conversely, for a low-S/N Keplerian (Target 6), the Keplerian model was favored over scan-angle models. However, for a high-S/N Keplerian (Target 5), the scan-angle model was slightly favored, illustrating that distinguishing these signals is not always definitive without follow-up.
Parameterization: Comparisons between Thiele-Innes and geometric parameterizations showed consistent posterior distributions but noted that the choice of parameterization affects the Bayes Factor due to the "Occam factor" (prior-posterior volume ratio).
Real Data Application: The models were applied to Gaia BH3. The authors noted that for very high signal-to-noise ratios ( $S/N \gtrsim 3000$ ), the "Known-Object" mode with narrower priors is recommended over blind searches to ensure the nested sampler can locate the sharp likelihood peak.
Compatibility Limits: The study generated compatibility limits for period vs. mass. The results showed expected shapes, including a minimum around the data's time-span, and highlighted potential degeneracies where partially covered orbits or multiple signals can mimic single Keplerian solutions.

Significance
The paper claims that kima provides an efficient, open-source tool for the analysis of Gaia epoch astrometry that is unique in its ability to simultaneously fit any number of Keplerians and perform rigorous model comparison in a single run. The authors assert that the tool is validated for analyzing Gaia data, capable of distinguishing true orbits from scan-angle artifacts in specific cases, and suitable for calculating occurrence rates and compatibility limits. The work positions kima as a critical tool for the upcoming analysis of Gaia DR4, particularly for studies requiring the joint analysis of astrometry and radial velocities.