Understanding eccentric temperate giants: an in-depth study of the architecture and stellar obliquity of the TOI-2134 system
Pith reviewed 2026-07-02 05:21 UTC · model grok-4.3
The pith
New TESS and RV data confirm TOI-2134 planets and detect 59-degree obliquity for the outer one
A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.
Core claim
The authors confirm an inner planet with mass 9.37±0.54 Earth masses, radius 2.735±0.068 Earth radii, and a near-circular 9.229198-day orbit, plus an outer planet with mass 58.3±1.9 Earth masses, radius 7.35±0.18 Earth radii, 95.85284-day period, and eccentricity 0.31. They report a 59±31 degree obliquity for the outer planet at 4.7-sigma significance and attribute the long-term radial-velocity trend to a stellar magnetic cycle.
What carries the argument
Joint modeling of multi-sector TESS photometry and multi-instrument radial velocities, together with Rossiter-McLaughlin observations to measure stellar obliquity.
If this is right
- The refined eccentricity removes prior degeneracies for dynamical stability analyses of the pair.
- The measured obliquity for the outer planet constrains possible past scattering or migration pathways.
- The updated masses and radii permit direct calculation of bulk densities for interior models.
- The system architecture assessment identifies which additional planets could still hide in the data.
Where Pith is reading between the lines
- If the obliquity is primordial rather than excited, it would favor in-situ formation or disk-driven migration over high-eccentricity channels for this temperate giant.
- Longer radial-velocity baselines could test whether the trend is truly cyclic or contains an additional planetary signal.
- Detection of similar misalignments in other eccentric sub-Saturn systems would suggest a common pathway for generating obliquity in multi-planet architectures.
Load-bearing premise
The long-term radial velocity trend arises from a stellar magnetic cycle rather than an additional unseen companion.
What would settle it
Independent photometry or activity indicators that correlate with the radial-velocity trend, or a failure to recover the Rossiter-McLaughlin signal for the outer planet in new observations.
Figures
read the original abstract
We revisit the TOI-2134 planetary system with three new high-cadence TESS sectors and 98 more spectra. This new analysis confirms the two orbiting planets by simultaneously modelling a total of eight sectors of corrected TESS photometry and 280 HARPS-N and SOPHIE radial velocities: an inner mini-Neptune in a near-circular $9.229198\pm0.000003$ days orbit, and an outer temperate sub-Saturn orbiting with a $95.852840\pm0.000042$ days period and eccentricity of $0.31\pm0.01$. The masses and radii of the planets were computed to be $9.37\pm0.54$ Me and $2.735\pm0.068$ Re for planet b, and $58.3\pm1.9$ Me and $7.35\pm0.18$ Re for planet c. The new data not only improves the detection significance and precisions on the planetary orbits, but also breaks the original multimodality in the eccentricity solution for the outer planet. We also detect a long-term trend in the radial velocity data, which we attribute to a stellar magnetic cycle. We investigate the spin-orbit alignment of the system via observations of the Rossiter-McLaughlin effect for TOI-2134~b with EXPRES and TOI-2134~c with PARAS-2. No RM effect was detected for planet b, but we find a 4.7$\sigma$ detection of a $59\pm31^{\circ}$ obliquity for planet c. Finally, we examine the architecture of the system, assess its completeness, investigate the planetary interior, and their suitability for follow-up atmospheric analysis.
Editorial analysis
A structured set of objections, weighed in public.
Referee Report
Summary. The manuscript reports new TESS photometry (eight sectors) and 280 radial velocities from HARPS-N, SOPHIE, EXPRES, and PARAS-2 for the TOI-2134 system. It confirms an inner mini-Neptune (planet b: P=9.229198±0.000003 d, near-circular) and outer temperate sub-Saturn (planet c: P=95.852840±0.000042 d, e=0.31±0.01), derives masses 9.37±0.54 M⊕ and 58.3±1.9 M⊕ with radii 2.735±0.068 R⊕ and 7.35±0.18 R⊕, breaks the prior eccentricity multimodality for c, attributes a long-term RV trend to a stellar magnetic cycle, and reports a 4.7σ RM detection of 59±31° obliquity for planet c while assessing system architecture and atmospheric follow-up potential.
Significance. If the two-planet solution and obliquity measurement hold, the work supplies one of the best-characterized temperate sub-Saturns with a measured spin-orbit angle, directly constraining migration and dynamical history models. The improved eccentricity constraint and RM result add to the small sample of obliquity measurements for planets beyond the hot-Jupiter regime.
major comments (1)
- [Abstract and RV modeling section] Abstract and radial-velocity modeling section: the long-term RV trend is attributed to a stellar magnetic cycle, yet no correlation analysis with activity indicators (log R'HK, S-index) or contemporaneous photometry is described. This assumption is load-bearing for the claim of exactly two planets, as an unmodeled long-period companion would alter the two-Keplerian solution, the eccentricity posterior, and the RM obliquity interpretation.
Simulated Author's Rebuttal
We thank the referee for their careful reading of the manuscript and for highlighting this important point regarding the long-term RV trend. We address the comment below and will revise the manuscript to strengthen the supporting analysis.
read point-by-point responses
-
Referee: [Abstract and RV modeling section] Abstract and radial-velocity modeling section: the long-term RV trend is attributed to a stellar magnetic cycle, yet no correlation analysis with activity indicators (log R'HK, S-index) or contemporaneous photometry is described. This assumption is load-bearing for the claim of exactly two planets, as an unmodeled long-period companion would alter the two-Keplerian solution, the eccentricity posterior, and the RM obliquity interpretation.
Authors: We agree that the current manuscript does not present a quantitative correlation analysis between the long-term RV trend and stellar activity indicators. In the revised manuscript we will add this analysis in the RV modeling section, including Spearman rank correlations (and associated p-values) between the RV residuals after subtracting the two-planet model and the log R'HK and S-index values measured from the HARPS-N and SOPHIE spectra. We will also examine any available contemporaneous photometry from TESS or ground-based surveys for photometric activity proxies. If the correlations are significant and consistent with a magnetic-cycle timescale, this will directly support the attribution; if not, we will discuss the implications for possible additional companions. The two-planet solution itself remains anchored by the eight-sector TESS photometry and the clear Keplerian signals, but we acknowledge that a more robust treatment of the trend is needed to fully secure the eccentricity and obliquity results. revision: yes
Circularity Check
No significant circularity detected; central results are direct model fits to new external observations
full rationale
The paper's derivation chain consists of simultaneous modeling of eight TESS sectors and 280 new+archival RVs from HARPS-N, SOPHIE, EXPRES, and PARAS-2 to extract orbital elements, masses, radii, and the RM obliquity for planet c. These quantities are obtained by fitting Keplerian models plus a trend term directly to the fresh data; no step reduces a claimed prediction back to a previously fitted parameter by construction, nor does any load-bearing premise rest on a self-citation chain. The attribution of the long-term RV trend to a magnetic cycle is an interpretive choice rather than a mathematical reduction, and the eccentricity multimodality breaking is a direct consequence of the added observations. The analysis is therefore self-contained against external benchmarks.
Axiom & Free-Parameter Ledger
free parameters (1)
- orbital periods, eccentricities, masses, radii
axioms (2)
- domain assumption Standard Keplerian orbit model and limb-darkening assumptions hold for the RM effect analysis
- domain assumption Long-term RV trend originates from stellar magnetic cycle rather than additional body
Reference graph
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