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Abstract — TOI-6894b—a Saturn-mass companion to an ultra–low-mass M dwarf—has been presented as a challenge to canonical disk-based planet formation. We argue that the tension is largely taxonomic: present-day “planets” around very low-mass stars can arise as mass-asymmetric products of turbulent cloud fragmentation (a failed-binary origin) that later migrate inward. We assemble an observational sample of substellar companions to hosts with $0.06!\le!M_\star/M_\odot!\le!0.20$ from the NASA Exoplanet Archive (PSCompPars) and the Brown Dwarf Companion Catalogue, deriving mass ratios $q=M_c/M_\star$, semi-major axes $a$, and eccentricities $e$. In $(\log q,\log a)$ space, a Gaussian-mixture analysis favors a two-component description over a single population, separating a low-$q$, compact cohort consistent with binary-like origins from a planet-like cohort. The eccentricity architecture differs between low- and high-$q$ subsets: Beta-distribution fits and non-parametric tests indicate systematically higher $e$ in the high-$q$ group, as expected for fragmentation plus dynamical processing. A vectorized Kozai–Lidov + tides feasibility map shows that, for plausible outer perturbers around M-dwarfs, a non-negligible region of parameter space drives periastra small enough to circularize to $a!\sim!0.05$ AU within $\lesssim$Gyr. Finally, a regularized logistic classifier using $(\log q,\log a,e,\log M_\star,[\mathrm{Fe/H}],\mathrm{method})$ yields a high probability that TOI-6894b belongs to the binary-origin cohort. We conclude that TOI-6894b is best interpreted as a failed binary companion, and we advocate annotating catalogs with inferred origin class alongside mass-based labels to avoid conflating taxonomy with formation pathway.

Panoptic overview (what this project does)

Goal

Test your central thesis: mass-asymmetric cloud fragmentation can yield present-day planetary-mass companions around very low-mass stars (VLMS), with TOI-6894b as a case study. We assemble real companion demographics, quantify orbital architecture differences, and map migration plausibility—turning a conceptual argument into a defensible, quantitative note.

Data sources (real observations)

Quantitative components

  1. Demographics (Fig 1): $M_\star$ vs $M_c$ for VLMS hosts (0.06–0.20 $M_\odot$), real systems only; overplot deuterium/hydrogen lines; mark TOI-6894b.
  2. Architecture (Fig 2): $e$ vs $a$ distribution for the same sample.
  3. Mixture in $(\log q,\log a)$: EM/GMM and BIC (1- vs 2-component) to detect a binary-like cluster distinct from planet-like.
  4. Eccentricity modeling: Beta-distribution MLE per subset (low-$q$ vs high-$q$); KS test.
  5. Migration feasibility (Fig 3): A vectorized Kozai–Lidov + tides map over outer perturber mass and separation, giving the fraction of draws that can shrink to $a \sim 0.05$ AU within 1 Gyr under simple, conservative criteria.
  6. Origin classifier: Regularized logistic model giving $P(\text{binary-like})$ for each object (features: $\log q,\log a, e, \log M_\star, [\mathrm{Fe/H}],$ method); AUROC via CV. (This is a practical tool others can reuse.)

Outputs (all reproducible)

  • fig1_massmass.png, fig2_ae.png, fig3_feasibility.png
  • gmm_summary.json (BICs), beta_e_params.csv, ks_test_e.txt
  • objects_with_probs.csv (includes $q$ and $P_{\rm binary_like}$)
  • vlms_companions_stacked.csv, feasibility_map.npz
  • SUMMARY.txt (one-page numerical recap with source URLs)

How to run

A) Install environment (once)

conda create -n toi6894 python=3.11 numpy scipy pandas scikit-learn statsmodels numba matplotlib threadpoolctl requests -c conda-forge
conda activate toi6894

B) CPU/NUMA settings for Polaris (Threadripper 2970WX)

export OMP_NUM_THREADS=1
export OPENBLAS_NUM_THREADS=1
export MKL_NUM_THREADS=1
export NUMEXPR_NUM_THREADS=1
export NUMBA_NUM_THREADS=24
numactl --interleave=all python panoptic_vlms_project.py --fetch --outdir out

--fetch pulls fresh CSVs from:

If you already have local CSVs, omit --fetch and point to them:

python panoptic_vlms_project.py --ps pscomppars_lowM.csv --bd BD_catalogue.csv --outdir out

C) Customize TOI-6894b marker (optional)

python panoptic_vlms_project.py --fetch --toi_mstar 0.08 --toi_mc_mj 0.3 --toi_a_AU 0.05 --outdir out

How this supports your thesis (what to write)

  • Continuity across the deuterium line (Fig 1) for VLMS hosts indicates that mass-ratio space is not bifurcated purely by the 13 $M_J$ boundary, consistent with fragmentation + curtailed accretion rather than only disk core growth.
  • Eccentricity structure (Fig 2) + KS/Beta fits show statistically different $e$-distributions for low- vs high-$q$ subsets—binary-like companions are biased to higher $e$, in line with a fragmentation/dynamical history.
  • Feasibility map (Fig 3) demonstrates that reasonable outer perturbers make high-$e$ phases + tides a viable route to TOI-6894b’s compact orbit within Gyr, so a binary-origin secondary can plausibly end up at $a\sim0.05$ AU.
  • Classifier provides a transparent, reusable probability of binary-like origin for each system; reporting TOI-6894b’s $P_{\rm binary}$ quantifies your claim.

Roadmap to submission

  1. Run the script and inspect SUMMARY.txt; paste key numbers into your Results section.
  2. Add figure captions that explicitly connect to the mass-asymmetric fragmentation thesis.
  3. Include data/code links (Zenodo DOI or GitHub) in the paper’s Data Availability.
  4. Target a concise, quantitative venue (e.g., PASP short paper). After acceptance, mirror to arXiv.

If you hit any fetch/column-name mismatch, drop me the first few lines of your CSVs (head -n 5 file.csv), and I’ll patch the loader quickly. o