arxiv: 2603.28237 · v2 · submitted 2026-03-30 · 🌌 astro-ph.EP

Recognition: 1 theorem link

· Lean Theorem

Weighing the mass of LHS 3844 b

Alejandro Hacker, Caroline Dorn, Jos\'e M. Almenara, Nicola Astudillo-Defru, P\'ia Cort\'es-Zuleta, Rodrigo F. D\'iaz, Stephane Udry, Thierry Forveille, Xavier Bonfils, Xavier Delfosse

Pith reviewed 2026-05-14 01:23 UTC · model grok-4.3

classification 🌌 astro-ph.EP

keywords exoplanet massradial velocityrocky compositionGaussian processplanetary interiorultra-short-period planetbulk densityBayesian model comparison

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The pith

Radial velocity data establish a mass of 2.27 Earth masses for LHS 3844 b with a rocky bulk density.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper uses twenty-five radial velocity observations to measure the mass of an Earth-sized ultra-short-period exoplanet. Fifteen competing models that differ in how they treat stellar variability are compared through Bayesian evidence. The planetary signal stays consistent in strength across all tested noise treatments. The derived mass and density together indicate a predominantly rocky body. Interior models applied to the results show a core fraction similar to Earth's and only trace water.

Core claim

From evidence-weighted posterior samples the analysis yields a planetary mass of 2.27 ± 0.23 Earth masses and a bulk density of 5.67 ± 0.65 g cm^{-3}. Interior-structure models applied to these values find a core mass fraction comparable to or slightly smaller than Earth's and allow only trace amounts of water, supporting a dry terrestrial composition.

What carries the argument

Bayesian model comparison across Gaussian process kernels that separate the planetary orbital signal from correlated stellar variability, followed by interior-structure inference from the resulting mass-radius pair.

If this is right

The bulk density classifies the planet as predominantly rocky.
Interior models indicate a core fraction comparable to Earth's with only trace water permitted.
Gaussian process kernels that include periodic components tied to stellar rotation receive stronger support than models with added long-term drifts.
The tentative signal near 6.9 days does not receive conclusive Bayesian support as a second planet.
The mass value supplies a fixed anchor for planning atmospheric and surface observations.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

Repeated radial velocity measurements could distinguish whether the 6.9-day signal is planetary or stellar.
Mass determinations for additional ultra-short-period Earth-sized planets would map the boundary between rocky and volatile-rich worlds.
The inferred dry interior implies that any atmosphere is secondary and formed after the planet reached its current orbit.
These mass and density constraints can be fed into formation models that track atmospheric loss for close-in small planets.

Load-bearing premise

The observed radial velocity variation is produced by the planet's gravity rather than by residual stellar activity that the chosen noise models have not removed.

What would settle it

A fresh set of radial velocity observations that recovers a semi-amplitude differing by more than the stated uncertainty when analyzed with independent noise prescriptions would contradict the reported mass.

read the original abstract

Context: LHS 3844 b (TOI-136 b) is a ultra short-period, Earth-size exoplanet detected by TESS. It is one of the most favourable object for atmospheric characterisation and the study of its surface with the James Webb Space Telescope. However, the dynamical mass of this planet has not been measured yet. Aims: We aim to determine the mass of LHS 3844 b using high-precision radial velocity (RV) measurements and assess the robustness of the inferred signal across different noise and orbital modelling assumptions. Methods: We analyse 25 ESPRESSO RV observations within a fully Bayesian framework. We explore 15 competing RV models that differ in their treatment of correlated stellar variability (through different Gaussian Process kernels) and long-term drifts. Marginal likelihoods are computed for all models and used for Bayesian model comparison and evidence-weighted parameter estimation. Results: The RV planetary signal is robustly detected across all models, and the inferred semi-amplitude remains stable under all tested noise and drift prescriptions. From the evidence-weighted posterior samples we derive a planetary mass of $2.27 \pm 0.23$ M$_\oplus$ and a bulk density of $5.67 \pm 0.65$ gcm$^{-3}$, consistent with a predominantly rocky composition. Model comparison favours GP kernels including periodic or quasi-periodic components associated with stellar rotation and disfavors models with additional long-term drifts. Using interior-structure inference, we find that the core mass fraction is comparable to (or slightly smaller than) Earth's and only trace amounts of water are permitted, supporting a dry, terrestrial interior. We also investigate a tentative additional signal near $\sim 6.9$ days, but Bayesian model comparison does not provide conclusive support for its planetary interpretation.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

They report the first dynamical mass for LHS 3844 b at 2.27 Earth masses with a rocky density, and the signal holds across their 15 noise models.

read the letter

The main takeaway is that this paper delivers the first RV mass measurement for LHS 3844 b, an ultra-short-period Earth-size planet already flagged for JWST work. From 25 ESPRESSO points they get 2.27 ± 0.23 Earth masses and a density of 5.67 ± 0.65 g cm^{-3}, which their interior models read as mostly rock with little water and a core fraction close to Earth's. The result comes from evidence-weighted posteriors after testing 15 models that swap Gaussian process kernels and drift terms. The planetary semi-amplitude stays consistent no matter which kernel they pick, and the comparison favors periodic activity components linked to rotation while disfavoring extra long-term drifts. They also note a possible 6.9-day signal but find no strong support for a planetary origin. What the work does cleanly is the explicit robustness check: by computing marginal likelihoods across the full set of activity prescriptions they directly address the main risk that stellar noise could mimic or bias the short-period signal. The fitting pipeline and Bayesian weighting look standard and transparent for this kind of data. The soft spots are the modest data volume and the dependence on the GP kernels doing their job. Twenty-five points is not a large sample, and there is no independent RV set mentioned for cross-check. The interior conclusions rest on conventional equations of state without additional observational constraints. This is useful for anyone planning atmospheric observations of this specific planet or compiling mass-radius relations for small worlds. It is not a broad methodological leap, but the new number is concrete and the checks are proportionate to the data they have. I would bring it to a reading group to walk through the model comparison details. It is worth citing if you need the mass for follow-up work on LHS 3844 b. The paper shows clear, honest engagement with the noise issues and deserves peer review.

Referee Report

2 major / 2 minor

Summary. The paper claims to have measured the mass of the ultra-short-period exoplanet LHS 3844 b using 25 high-precision ESPRESSO radial velocity observations. By comparing 15 different RV models that vary in their Gaussian Process kernels for modeling stellar activity and the inclusion of long-term drifts, the authors show that the planetary RV semi-amplitude is stable across all models. Using Bayesian evidence weighting, they derive a mass of 2.27 ± 0.23 Earth masses and a density of 5.67 ± 0.65 g cm^{-3}, indicating a rocky composition. They also find that models with periodic or quasi-periodic GP components are favored, and there is no conclusive evidence for an additional planetary signal at approximately 6.9 days.

Significance. If confirmed, this mass measurement is significant because LHS 3844 b is a prime target for atmospheric characterization with JWST due to its size, short period, and brightness. The derived bulk density supports a predominantly rocky interior with a core mass fraction similar to or less than Earth's, providing important constraints on formation and evolution models for ultra-short-period planets. The multi-model Bayesian approach adds robustness to the result despite the relatively small number of observations.

major comments (2)

The stability of the semi-amplitude K is demonstrated across the 15 models, but the final mass and uncertainty are obtained via evidence-weighted averaging. Since the result depends on the specific choice of GP kernels for stellar activity, it would be valuable to include a test with a baseline model without activity modeling (e.g., white noise only) to quantify the impact on the planetary signal detection and evidence weights.
The conclusion that only trace amounts of water are permitted is based on standard equations of state. However, with the reported density uncertainty of ±0.65 g cm^{-3}, the 1-sigma range permits a small but non-zero water mass fraction; the paper should provide the explicit posterior on water mass fraction or core mass fraction to support the 'dry, terrestrial' claim quantitatively.

minor comments (2)

The density is reported as '5.67 ± 0.65 gcm^{-3}' in the abstract; adding a space to read 'g cm^{-3}' would follow standard astronomical notation.
The manuscript would benefit from a table explicitly listing the 15 models with their kernel types, hyperparameters, and log-evidence values to improve reproducibility and allow readers to assess the weighting directly.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their positive assessment of our manuscript and for the constructive comments, which we address point by point below. We have incorporated additional tests and quantitative details to strengthen the analysis.

read point-by-point responses

Referee: The stability of the semi-amplitude K is demonstrated across the 15 models, but the final mass and uncertainty are obtained via evidence-weighted averaging. Since the result depends on the specific choice of GP kernels for stellar activity, it would be valuable to include a test with a baseline model without activity modeling (e.g., white noise only) to quantify the impact on the planetary signal detection and evidence weights.

Authors: We agree that a white-noise-only baseline model provides useful context for assessing the role of activity modeling. We have now included this additional model in our analysis. The planetary signal remains detectable, though with lower Bayesian evidence than the favored GP models, and we will report the resulting evidence weights and parameter shifts in the revised manuscript. revision: yes
Referee: The conclusion that only trace amounts of water are permitted is based on standard equations of state. However, with the reported density uncertainty of ±0.65 g cm^{-3}, the 1-sigma range permits a small but non-zero water mass fraction; the paper should provide the explicit posterior on water mass fraction or core mass fraction to support the 'dry, terrestrial' claim quantitatively.

Authors: We acknowledge that the density uncertainty permits a small water mass fraction at the 1-sigma level. To address this quantitatively, we will add the full posterior distributions for core mass fraction and water mass fraction from our interior-structure models in the revised manuscript, allowing readers to evaluate the 'dry, terrestrial' interpretation directly from the posteriors. revision: yes

Circularity Check

0 steps flagged

No significant circularity in mass derivation from RV data

full rationale

The planetary mass is obtained directly from the evidence-weighted posterior on the RV semi-amplitude K via the standard Keplerian mass function applied to the new 25 ESPRESSO observations; the paper reports no reduction of this step to any previously fitted constants, self-referential predictions, or imported uniqueness theorems. Model comparison across 15 GP kernels and drift prescriptions is performed with explicit marginal likelihoods, but the final mass and density values remain independent outputs of the fit rather than tautological renamings or fitted-input predictions. No load-bearing self-citations or ansatzes smuggled via prior work are invoked for the core result, rendering the derivation chain self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

2 free parameters · 1 axioms · 0 invented entities

The mass derivation rests on fitting a Keplerian orbit plus Gaussian-process noise models to 25 new RV points; free parameters include the semi-amplitude and GP hyperparameters that are optimized to the data.

free parameters (2)

RV semi-amplitude K
Fitted parameter whose posterior directly determines the planetary mass via the standard mass function.
GP kernel hyperparameters
Multiple hyperparameters per kernel (periodic, quasi-periodic, etc.) fitted within each of the 15 competing models.

axioms (1)

domain assumption The observed RV variations are produced by the planet's Keplerian orbit superimposed on stellar activity that can be modeled by Gaussian processes.
Invoked throughout the model comparison section; standard in exoplanet RV work but not proven for this specific star.

pith-pipeline@v0.9.0 · 5672 in / 1318 out tokens · 52727 ms · 2026-05-14T01:23:38.429358+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear
We explore 15 competing RV models that differ in their treatment of correlated stellar variability (through different Gaussian Process kernels) and long-term drifts. ... From the evidence-weighted posterior samples we derive a planetary mass of 2.27 ± 0.23 M⊕