A Bayesian Search for Planet Engulfment Signatures in Solar Analogs

Technical Summary: A Bayesian Search for Planet Engulfment Signatures in Solar Analogs

Problem Statement
Planets can be driven into their host stars via tidal decay or dynamical instability, potentially leaving measurable chemical imprints on the stellar photosphere if the accreted material mixes into a shallow envelope. While previous abundance-based searches have successfully identified such signatures in co-natal binary systems (where one star serves as a chemically matched control), it remains unclear whether comparable signatures can be identified in the much larger population of non-co-natal field stars. Existing methods for single stars often rely on the correlation between elemental abundance and condensation temperature ($T_c$ slope) or volatile-to-refractory ratios. However, these approaches compress multi-element patterns into single numbers, potentially obscuring detailed structures and failing to distinguish planet engulfment from other astrophysical processes such as Galactic chemical evolution (GCE), atomic diffusion, or stochastic formation factors.

Methodology
The authors present a systematic Bayesian framework to model full abundance patterns in 113 solar twins and analogs, 45 of which host known or candidate planets or brown dwarfs. The dataset comprises high-precision, line-by-line differential abundance measurements for 19 elements (C through Zn) from two sources: the Bedell et al. (2018) sample and the Planets Around Solar Twins/Analogs (PASTA) survey.

The core methodology involves comparing three classes of models for each star's abundance vector (relative to the Sun or sample mean):

1. Null Models:
   • Flat Model ($F$): An element-independent offset plus intrinsic scatter, representing the hypothesis of no resolved structure.
   • Galactic Chemical Evolution (GCE): Two variants were tested: $G_{Bedell}$ (linear [X/Fe]-age relations) and $G_{GALAH}$ (a two-process model combining prompt and delayed enrichment).
2. Engulfment Model ($E$): Assumes well-mixed accreted material in the stellar convection zone. The model predicts abundance enhancements based on the engulfed mass ($M_p$) and the composition of the accreted material, tested against two compositions: Bulk Earth and CM chondrite.

The analysis utilizes a Gaussian likelihood including reported uncertainties and an intrinsic scatter parameter ($\sigma_{int}$). Bayesian evidence ($Z$) is calculated using the dynesty nested sampling algorithm. Model preference is quantified via the log Bayes factor ($\Delta \ln Z$). To establish robust detection thresholds and avoid fixed cutoffs, the authors performed parametric bootstrapping on 121 mock abundance vectors to determine the maximum $\Delta \ln Z$ expected under null hypotheses, corresponding to a false-positive probability of $\sim 1/1210$.

The fiducial analysis adopts the Sun as the baseline and uses [X/Fe] ratios to mitigate atomic diffusion signatures. A "mirror test" (reversing abundance differences) confirmed that the Sun-[X/Fe] setup is the only configuration where reversing the data significantly reduces the Bayes factors for engulfment, validating the Sun as a physically motivated baseline with no recent engulfment history.

Key Results
Under the fiducial Sun-[X/Fe] setup, the study identified three high-significance candidate stars whose abundance patterns strongly favor the planet engulfment model over GCE and flat alternatives:

• TOI-3342: Favors Bulk Earth composition; inferred engulfed mass of $16 \pm 4 \, M_{\oplus}$.
• HIP 101905: Favors Bulk Earth composition; inferred engulfed mass of $7.5 \pm 1.0 \, M_{\oplus}$.
• TOI-2426: Favors CM chondrite composition; inferred engulfed mass of $33^{+9}_{-7} \, M_{\oplus}$.

Additionally, HIP 30502 emerged as a candidate under the mean-[X/Fe] setup. The study also identified 14 "optimistic" candidates that outperform the flat model but may still be explained by GCE.

The raw detection rate of planet-engulfment signatures in this sample is approximately 2.7% (3/113). When separated by sample, the rate is 1.3% for the generic Bedell sample and higher for the PASTA planet-host sample, though the authors caution against over-interpreting this difference due to selection function and systematic variations between the datasets.

Significance and Claims
The paper claims to extend abundance-based engulfment searches beyond the binary-star context, providing a framework for probing star–planet co-evolution in single solar analogs. Key contributions include:

• Methodological Advancement: Demonstrating that template-based Bayesian modeling of full abundance patterns is superior to $T_c$ slope analysis. The authors show that large $T_c$ slopes are neither necessary nor sufficient conditions for matching an engulfment template, and that GCE models can mimic trends that would be misinterpreted by slope-only analyses.
• Detection Rate: Establishing a nominal detection rate of $\sim 1–3\%$ for planet-engulfment signatures among solar analogs, which is consistent with upper limits derived from binary studies but derived here for the field population.
• Candidate Identification: Providing specific, high-confidence candidates (TOI-3342, HIP 101905, TOI-2426) with inferred engulfed masses ranging from $\sim 7.5$ to $33 \, M_{\oplus}$, all well below the total solids in a minimum-mass solar nebula.

The authors maintain a modest stance, acknowledging that the detection rate is a raw estimate without sensitivity corrections and that other effects (e.g., planet formation processes, GCE, atomic diffusion) can introduce degenerate signatures. They emphasize that future work requires larger, homogeneous samples with well-characterized planetary architectures to precisely constrain engulfment rates and distinguish between competing physical origins.