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REVIEW 2 major objections 4 minor 3 cited by

Four planets orbit a 12.5-billion-year-old thick-disk star, the paper shows.

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

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2026-08-04 18:05 UTC pith:UFXVYMXB

load-bearing objection Solid characterization paper: three new planets around an old thick-disk star, two with precisely measured masses and radii; the two RV-only planets are the main residual risk, but the evidence is strong. the 2 major comments →

arxiv 2509.10136 v1 pith:UFXVYMXB submitted 2025-09-12 astro-ph.EP astro-ph.SR

A four-planet system orbiting the old thick disk star TOI-1203

D. Gandolfi , A. Alnajjarine , L. M. Serrano , J. A. Egger , K. W. F. Lam , J. Cabrera , A. P. Hatzes , M. Fridlund
show 115 more authors
M. Garbaccio Gili T. G. Wilson W. D. Cochran A. Brandeker E. Goffo S. G. Sousa G. Nowak A. Heitzmann C. Hellier J. Venturini J. Livingston A. Bonfanti O. Barrag\'an V. Adibekyan E. Knudstrup Y. Alibert S. Grziwa C. Ziegler L. Fossati F. Murgas A. C. M. Correia S. H. Albrecht J. Laskar E. W. Guenther S. J.A.J. Salmon S. Redfield N. Billot H. J. Deeg L. Delrez L. Palethorpe V. Van Eylen F. Rodler J. Alarcon J. M. Jenkins J. D. Twicken A. W. Mann R. Alonso J. Asquier T. B\'arczy D. Barrado S. C. C. Barros W. Baumjohann W. Benz L. Borsato C. Broeg M. Buder P. Chaturvedi A. Collier Cameron Sz. Csizmadia P. E. Cubillos M. B. Davies M. Deleuil A. Deline O. D. S. Demangeon B.-O. Demory A. Derekas B. Edwards D. Ehrenreich A. Erikson A. Fortier K. Gazeas M. Gillon M. G\"udel M. N. G\"unther Ch. Helling K. G. Isaak L. L. Kiss J. Korth N. Law A. Lecavelier des Etangs A. Leleu M. Lendl P. Leonardi D. Magrin G. Mantovan L. Marafatto P. F. L. Maxted M. Mecina B. Mer\'in C. Mordasini V. Nascimbeni A. Nigioni G. Olofsson H. P. Osborn R. Ottensamer I. Pagano E. Pall\'e C. M. Persson G. Peter D. Piazza G. Piotto D. Pollacco D. Queloz R. Ragazzoni N. Rando H. Rauer I. Ribas G. R. Ricker N. C. Santos G. Scandariato S. Seager D. S\'egransan A. E. Simon A. M. S. Smith M. Stalport S. Sulis Gy. M. Szab\'o S. Udry S. Ulmer-Moll V. Van Grootel E. Villaver N. A. Walton J. N. Winn S. Wolf T. Zingales
This is my paper
classification astro-ph.EP astro-ph.SR
keywords four-planet systemsuper-Earthsub-Neptuneradial velocitytransit photometrythick diskstellar abundancesdynamical stability
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

The paper reports that the bright G3V star TOI-1203, a 12.5-billion-year-old, alpha-element-enhanced member of the galactic thick disk, hosts four planets: a transiting super-Earth on a 4.2-day orbit, a non-transiting super-Earth on a 13.1-day orbit, the previously known transiting sub-Neptune on a 25.5-day orbit (now with a measured mass), and a non-transiting eccentric Neptune-mass planet on a 204.6-day orbit. Masses and radii of the two transiting planets are measured to 8-9% precision, and dynamical integrations find configurations stable over billion-year timescales. If correct, this is one of the oldest known multi-planet systems, with implications for when rocky planets could form in the metal-poor early galaxy. The paper also identifies a ~615-day variation in the HARPS instrumental profile that leaves no detectable imprint on the radial velocities, a cautionary result for ultra-precise Doppler surveys.

Core claim

TOI-1203 is a four-planet system. The 25.5-day transiting sub-Neptune previously flagged by TESS is spectroscopically confirmed, with its mass determined (7.39±0.62 M⊕) and radius refined (2.918 R⊕). A new transiting super-Earth, TOI-1203 b, is confirmed by CHEOPS photometry with mass 3.51 M⊕ and radius 1.52 R⊕. Two additional Doppler signals at 13.1 and 204.6 days are attributed to planets with minimum masses 5.46 and 42.10 M⊕; the outer planet is eccentric (e=0.152). The host is an old (12.5 Gyr), metal-poor, alpha-enhanced thick-disk star. Stability maps show the system is stable for Gyr, sits near but not inside mean-motion resonances, and has the pericenters of c and d anti-aligned. A l

What carries the argument

The analysis rests on a joint Markov-chain Monte Carlo fit of TESS and CHEOPS transit light curves together with HARPS radial velocities modeled as four Keplerians, combined with iterative pre-whitening of GLS periodograms to isolate the Doppler signals. The long-period systematic in the HARPS line-profile FWHM is diagnosed by comparing the CCF FWHM against the FWHM of Th-Ar calibration lines, identifying a ~615-day instrumental profile variation. Dynamical stability is assessed with global frequency analysis maps and long symplectic integrations, and internal compositions are inferred from mass-radius modeling.

Load-bearing premise

The 13.1-day and 204.6-day radial-velocity signals are genuine planets, not artifacts of the pre-whitening procedure, stellar activity, or the ~615-day instrumental profile drift whose 230-day alias sits within the frequency resolution of the 204.6-day signal.

What would settle it

Two more years of high-precision radial velocities tracking the 204.6-day signal through at least two additional cycles: if it is not coherent as a single Keplerian, or if modeling the instrument-profile variation removes it, the planetary interpretation of TOI-1203 e collapses. A secondary check would be detecting transits of c or e, which the paper argues are unlikely but which would settle their geometry.

Watch this falsifier. Get emailed when new claim-graph text bears on it.

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If this is right

  • TOI-1203 b becomes one of the rare small planets whose mass and radius are both known to better than ~10%, placing it in the rocky/silicate regime of the mass-radius diagram.
  • The system straddles the radius valley, with a rocky super-Earth and a volatile-rich sub-Neptune orbiting the same old star, offering a test of how wide binaries and stellar age affect the valley's location.
  • The near-but-not-exact period commensurabilities (3:1, 2:1, 8:1) and the anti-aligned pericenters of c and d provide a benchmark for models of migration, tidal damping, and secular evolution in ancient systems.
  • The detected ~615-day instrumental profile variation, with no RV counterpart, shows that symmetric profile changes can hide in line-width diagnostics; monitoring IP shape is therefore essential for RV surveys aiming at 10 cm/s precision.

Where Pith is reading between the lines

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

  • If the 204.6-day signal is confirmed as a planet, TOI-1203 will be a reference for how early-galaxy rocky planets form, since the system assembled when the universe was about 1.3 Gyr old.
  • The stability analysis maps out stable niches between b and c and between d and e; additional RV monitoring could test whether those niches are empty or occupied by smaller companions.
  • The Th-Ar line-width diagnostic used here could be reapplied to archival HARPS data to flag long-period RV signals that coincide with instrument-profile variations, potentially reclassifying some published planet candidates.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

2 major / 4 minor

Summary. The paper reports the discovery and characterization of a four-planet system around the bright, old, metal-poor G3V star TOI-1203. Using 190 HARPS RVs, TESS and CHEOPS photometry, and a joint MCMC analysis, the authors confirm the previously known transiting sub-Neptune TOI-1203 d (P≈25.5 d, M=7.39±0.62 M⊕, R=2.918±0.045 R⊕), discover and confirm a transiting super-Earth TOI-1203 b (P≈4.16 d, M=3.51±0.33 M⊕, R=1.520±0.045 R⊕), and report two RV-only planets: TOI-1203 c (P≈13.08 d, M sin i=5.46±0.51 M⊕) and TOI-1203 e (P≈204.6 d, M sin i=42.10±1.8 M⊕, e=0.152±0.029). A stability analysis shows that configurations consistent with the data can be stable over Gyr timescales, and an interior-structure analysis of b and d is presented. The paper also identifies a ~615–630 d systematic in the HARPS CCF FWHM, traced to Th-Ar line widths, and attributes it to instrumental profile variations with no counterpart in the RVs.

Significance. If the detections hold, this is a valuable addition to the small sample of precisely characterized multi-planet systems around very old, α-enhanced thick-disk stars. The two transiting planets have masses and radii measured to better than ~10% and ~3%, respectively, placing them on the mass–radius diagram with clear compositional implications. The RV-only planets, especially the 13.1 d signal at K≈1.6 m/s, are the weakest link, and the paper would benefit from a correlated-noise robustness check. The HARPS instrumental-profile finding is an important cautionary result for precision-RV programs. Strengths include the large homogeneous HARPS dataset, the independent CHEOPS confirmation of TOI-1203 b, the use of ancillary activity indicators, the bootstrap FAP calculations, and the explicit forward stability and interior-structure checks that use the fitted parameters as inputs rather than as predictions.

major comments (2)
  1. [Sects. 4 and 9; Table B.2] The two RV-only signals (TOI-1203 c at 13.08 d with K_c=1.62±0.14 m/s, and TOI-1203 e at 204.6 d) are load-bearing for the four-planet claim. Their detection significance is established through pre-whitening with bootstrap FAPs that assume white noise, and the final fit models all noise with a single white jitter term (σ_HARPS=0.83±0.10 m/s). For a signal whose amplitude is only ~2× the jitter, unmodeled correlated noise could inflate the significance. I request a robustness check, e.g., a joint fit that includes a Gaussian-process or moving-average term for the RVs, or an injection-recovery test with red-noise residuals. This would materially increase confidence in planets c and e.
  2. [Sect. 9 and Sect. 5] The TESS Sector 36 transits of TOI-1203 b are excluded 'due to the lack of a detectable transit signal' in that sector. This is a post-hoc data selection that could bias the transit parameters and ephemeris if the non-detection is due to an unmodeled systematic rather than noise. Since CHEOPS confirms the transit near the same epoch, the exclusion likely does not affect the planet's existence, but the paper should quantify the consistency, e.g., by performing an injection-recovery test in Sector 36 or by modeling the Sector 36 data with a high-noise term.
minor comments (4)
  1. [Table B.2] The reported RV semi-amplitude for TOI-1203 d is listed as K_d=1.74±0.014 m/s. Given the values for the other planets and the mass uncertainty, the error bar is likely 0.14 m/s, not 0.014. Please check and correct.
  2. [Sect. 2] The text 'from 5 January to 2 March 2026, 2025.1' contains a stray '2025.1'; the intended date should be cleaned up.
  3. [Sect. 8.5] 'Adopting the LRS determination' should read 'LSR determination'.
  4. [Sect. 9] Typo: 'Markow chains' should be 'Markov chains'.

Circularity Check

0 steps flagged

No significant circularity found: the planet parameters are fitted directly to independent RV and photometric data, and the stability and interior-structure analyses are forward consistency checks using those fitted parameters as inputs.

full rationale

The paper's central claims are the detection and characterization of four planets around TOI-1203. These are derived by directly fitting a four-Keplerian RV model to HARPS radial velocities and transit models to TESS and CHEOPS photometry (Sect. 9), with no parameter that defines the result being set by the result itself. The two RV-only planets (c and e) are identified by periodogram analysis and pre-whitening (Sect. 4), and their significance is assessed via bootstrap FAPs against the data, not against any output of the final model. The transiting planets b and d are confirmed by independent photometry (CHEOPS and TESS). The stellar parameters (Teff, [Fe/H], [alpha/Fe], age) come from separate spectroscopic, photometric, and isochrone analyses; the thick-disk classification combines these with kinematic probabilities. The stability analysis (Sect. 10) takes the fitted orbital parameters as input and checks whether any dynamically stable configuration exists; it does not generate the orbital parameters. Likewise, the interior-structure analysis (Sect. 11) uses the measured masses and radii as inputs to a forward model. The only predictive step, estimating the radius of non-transiting planet c from a mass-radius relation (Otegi et al. 2020), is an externally calibrated empirical relation used to assess transit detectability, not to define the planet's existence. Self-citations (pyaneti, DST, plaNETic, BICEPS, PIPE, pycheops) are citations to published codes/methods, not to unverified uniqueness theorems or to the present result, and none is load-bearing in a way that reduces the argument to itself. The residual scientific risk (correlated noise affecting the 13.1 d signal) is a data-quality concern, not a circularity. I therefore find no circular step and assign a score of 0.

Axiom & Free-Parameter Ledger

2 free parameters · 4 axioms · 0 invented entities

The central claim rests on standard exoplanet detection assumptions: the RV and transit signals are planetary, and the stellar parameters are correct. No new physical entities are introduced. The main fitted parameters are the orbital elements themselves, which constitute the result rather than ad hoc inputs; the only auxiliary fitted parameters are the RV jitter and limb-darkening coefficients.

free parameters (2)
  • RV jitter sigma_HARPS = 0.83±0.10 m/s
    Added to the noise model to absorb excess RV scatter; affects significance of the small-amplitude Keplerian signals.
  • Limb-darkening coefficients q1 and q2 = TESS: q1=0.27±0.08, q2=0.22; CHEOPS: q1=0.45, q2=0.32
    Fitted with Gaussian priors from theoretical values; affect transit depth and radius estimates.
axioms (4)
  • domain assumption The Doppler signals at 4.2, 13.1, and 204.6 d are Keplerian reflex motion from planets, not stellar activity or instrumental artifacts.
    Supported by FAP<0.1%, pre-whitening, and absence of counterparts in log R'HK, BIS, and FWHM periodograms (Sects. 4 and 9), but not directly proven for non-transiting planets c and e.
  • domain assumption The detected transit signals (25.5 d and 4.2 d) are caused by planets transiting TOI-1203 and not by a blended eclipsing binary.
    SOAR speckle imaging rules out companions within 3 arcsec (Sect. 7); TESS centroid tests and CHEOPS follow-up support this (Sects. 2 and 6).
  • domain assumption Stellar parameters (T_eff=5737 K, [Fe/H]=-0.39, R*=1.179 R_sun, M*=0.886 M_sun, age=12.5 Gyr) derived from spectroscopy, photometry, and isochrones are accurate.
    Used in the joint fit to convert RV semi-amplitudes and transit depths into masses and radii (Sects. 8 and 9); independent SME analysis agrees.
  • domain assumption The 613-629 day signal in HARPS CCF FWHM and Th-Ar line widths is instrumental and does not affect the RVs.
    Argued in Sect. 4 from the lack of an RV counterpart and the correspondence with Th-Ar line FWHM, but the physical mechanism is not identified.

pith-pipeline@v1.3.0-alltime-deepseek · 43010 in / 13414 out tokens · 132191 ms · 2026-08-04T18:05:36.343886+00:00 · methodology

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Cite this review

Pith. "Pith review of A four-planet system orbiting the old thick disk star TOI-1203." pith.science (2026). https://pith.science/paper/UFXVYMXB

@misc{pith2026250910136,
  author       = {Pith},
  title        = {Pith review of: A four-planet system orbiting the old thick disk star TOI-1203},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/UFXVYMXB}},
  note         = {Machine review of arXiv:2509.10136}
}
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read the original abstract

TOI-1203 is a bright (V=8.6) G3 V star known to host a transiting warm sub-Neptune on a 25.5 d orbit. Here we report on an intensive high-precision radial velocity and photometric follow-up campaign carried out with the HARPS spectrograph and the CHEOPS space telescope. We found that TOI-1203 has an enhancement of $\alpha$ elements relative to iron of [$\alpha$/Fe]=$0.21\pm0.04$. With an age of $\sim$12.5 Gyr, TOI-1203 belongs to the old, $\alpha$-element enhanced stellar population of the galactic thick disk. We spectroscopically confirmed the planetary nature of the 25.5 d sub-Neptune TOI-1203 d, measured its mass ($M_{d}=7.39\pm0.62~M_{\oplus}$) and refined its radius ($R_{d}=2.918_{-0.045}^{+0.046}~R_{\oplus}$). We discovered the presence of an additional transiting super-Earth on a 4.2 d orbit (TOI-1203 b) with a mass of $M_{b}=3.51_{-0.32}^{+0.33}~M_{\oplus}$ and a radius of $R_{b}=1.520_{-0.046}^{+0.045}~R_{\oplus}$. We also revealed the presence of two additional low-mass planets at 13.1 d and 204.6 d (TOI-1203 c and e), with minimum masses of $5.46_{-0.50}^{+0.51}~M_{\oplus}$ and $42.10_{-1.78}^{+1.83}~M_{\oplus}$. We found that the outer planet TOI-1203 e lies on an eccentric orbit with $e_{e}=0.152\pm0.029$. We performed a stability analysis of the system confirming that there are configurations consistent with the observed parameters that are dynamically stable over billion-year timescales. While analyzing the HARPS time series, we discovered that the FWHM of the HARPS cross-correlation function shows a significant long-period signal ($\sim$615 d) that has no counterpart in the radial velocity data or in the remaining HARPS ancillary time series. We significantly detected the same signal in the FWHM of the Th-Ar calibration lines used to compute the nightly wavelength solution, and attributed this systematic effect to a long-term variation of the HARPS instrumental profile.

Figures

Figures reproduced from arXiv: 2509.10136 by A. Alnajjarine, A. Bonfanti, A. Brandeker, A. C. M. Correia, A. Collier Cameron, A. Deline, A. Derekas, A. Erikson, A. E. Simon, A. Fortier, A. Heitzmann, A. Lecavelier des Etangs, A. Leleu, A. M. S. Smith, A. Nigioni, A. P. Hatzes, A. W. Mann, B. Edwards, B. Mer\'in, B.-O. Demory, C. Broeg, C. Hellier, Ch. Helling, C. Mordasini, C. M. Persson, C. Ziegler, D. Barrado, D. Ehrenreich, D. Gandolfi, D. Magrin, D. Piazza, D. Pollacco, D. Queloz, D. S\'egransan, E. Goffo, E. Knudstrup, E. Pall\'e, E. Villaver, E. W. Guenther, F. Murgas, F. Rodler, G. Mantovan, G. Nowak, G. Olofsson, G. Peter, G. Piotto, G. R. Ricker, G. Scandariato, Gy. M. Szab\'o, H. J. Deeg, H. P. Osborn, H. Rauer, I. Pagano, I. Ribas, J. A. Egger, J. Alarcon, J. Asquier, J. Cabrera, J. D. Twicken, J. Korth, J. Laskar, J. Livingston, J. M. Jenkins, J. N. Winn, J. Venturini, K. Gazeas, K. G. Isaak, K. W. F. Lam, L. Borsato, L. Delrez, L. Fossati, L. L. Kiss, L. Marafatto, L. M. Serrano, L. Palethorpe, M. B. Davies, M. Buder, M. Deleuil, M. Fridlund, M. Garbaccio Gili, M. Gillon, M. G\"udel, M. Lendl, M. Mecina, M. N. G\"unther, M. Stalport, N. A. Walton, N. Billot, N. C. Santos, N. Law, N. Rando, O. Barrag\'an, O. D. S. Demangeon, P. Chaturvedi, P. E. Cubillos, P. F. L. Maxted, P. Leonardi, R. Alonso, R. Ottensamer, R. Ragazzoni, S. C. C. Barros, S. Grziwa, S. G. Sousa, S. H. Albrecht, S. J.A.J. Salmon, S. Redfield, S. Seager, S. Sulis, S. Udry, S. Ulmer-Moll, S. Wolf, Sz. Csizmadia, T. B\'arczy, T. G. Wilson, T. Zingales, V. Adibekyan, V. Nascimbeni, V. Van Eylen, V. Van Grootel, W. Baumjohann, W. Benz, W. D. Cochran, Y. Alibert.

Figure 1
Figure 1. Figure 1: TESS Sector 9 (upper panel), Sector 10 (second panel), Sector 36 (third panel), Sector 63 (fourth panel), and Sector 90 (lower panel) PDC-SAP light curves of TOI-1203. The 120-second data points are displayed as light gray circles, along with the out-of-transit Gaussian process model overplotted in red. The resulting detrended light curves are depicted as blue circles. The transit mid-times of TOI-1203 b a… view at source ↗
Figure 2
Figure 2. Figure 2: Generalized Lomb-Scargle periodograms of the TOI-1203’s HARPS TERRA RVs (upper panel) and of the RV residuals after subtracting the Doppler reflex motion(s) induced by TOI-1203 e (second panel), TOI-1203 e and d (third panel), TOI-1203 e, d, and b (fourth panel), TOI-1203 e, d, b, and c (bottom panel). The dashed horizontal red lines mark the 0.1 % false alarm probability (FAP) as computed using the bootst… view at source ↗
Figure 3
Figure 3. Figure 3: Frequency analysis of the activity indicator and line profile diagnostics of TOI-1203 extracted from the HARPS spectra. Top: Generalized Lomb-Scargle periodograms of: (1) the Ca ii H & K lines activity indicator log R′ HK (upper panel); (2) the bisector inverse slope (BIS) of the HARPS CCF (second panel); (3) the full width at half maximum (FWHM) of the HARPS CCF (lower panel). The dashed horizontal red li… view at source ↗
Figure 4
Figure 4. Figure 4: Upper panel: Generalized Lomb-Scargle periodogram of the intensity-weighted average of the FWHM of the Th-Ar spectral lines. The GLS power of the FAP at 0.1 % is marked with a dashed horizontal red line. The dominant signal is found at 0.00159 d−1 (∼629 d). The dashed vertical blue line marks the position of the significant signal at f1 ≈ 0.00163 d−1 (∼613 d) seen in the periodogram of the FWHM of the HARP… view at source ↗
Figure 5
Figure 5. Figure 5: TESS Sector 90 PDC-SAP light curve of TOI-1203. The 120 s data points are displayed with light gray circles, along with the 30-minute binned photometry (black circles). The mid-time of the expected transit of TOI-1203 e, as predicted from the orbital period and reference time of inferior conjunction listed in Table B.2, is marked with a light blue triangle, whereas the transit mid-times of TOI-1203 b and d… view at source ↗
Figure 6
Figure 6. Figure 6: Contrast curve computed from the high-resolution speckle ob￾servations in Cousins I-band on the 4.1 m Southern Astrophysical Re￾search telescope. The inset shows the speckle autocorrelation function centered on the target star. No bright companions are detected within 3′′ of TOI-1203 in this observation. 8. Stellar parameters 8.1. Photospheric parameters and chemical abundances We co-added the individual H… view at source ↗
Figure 7
Figure 7. Figure 7: Folded transit light curves of TOI-1203 b (left panel) and TOI-1203 d (right panel). The TESS (top) and CHEOPS (bottom) data points are plotted with gray circles. The 20-minute binned photometry is displayed as green and red circles for TESS and CHEOPS, respectively. The thick black lines mark the transit models derived from the medians of the marginalized posterior distributions of the transit parameters … view at source ↗
Figure 8
Figure 8. Figure 8: Upper panel: HARPS TERRA RV time series. The thick black line marks the Keplerian model derived from the medians of the marginalized posterior distributions of the RV parameters (Table B.2). Lower panels: Phase-folded RV curve of TOI-1203 b (middle left), c (middle right), d (bottom left), and e (bottom right) and Keplerian model (thick black line). The error bars include the RV jitter contribution in gray… view at source ↗
Figure 9
Figure 9. Figure 9: Stability analysis of the TOI-1203 system in the orbital period-eccentricity domain: planet b (top left), c (top right), d (bottom left), and e (bottom right). For fixed initial conditions, the phase space of the system is explored by varying the orbital period Pi and eccentricity ei of each planet independently. For each initial condition, the system is integrated over 40 kyr, and a stability criterion is… view at source ↗
Figure 10
Figure 10. Figure 10: Evolution of the angle ϖc−ϖd in the TOI-1203 system, starting with the orbital solution listed in Tables B.2 and B.3. 0 0 0 0 0 0   000 00 00 [PITH_FULL_IMAGE:figures/full_fig_p014_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: displays the evolution of the eccentricities and in￾clinations with respect to the invariant plane of the planets over 50 kyr. The inner three planets exhibit considerable variations 0 0 0 0 0 0  00  0 0 0 00 ϖ [PITH_FULL_IMAGE:figures/full_fig_p014_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: Secular evolution of the impact parameter b for TOI-1203 b (blue) and TOI-1203 d (green), starting with the orbital solution listed in Tables B.2 and B.3. 10.2. Resonant chain A three-planet MMR occurs when there exist integers k1, k2, and k3 such that k1n1 + k2n2 + k3n3 = 0, where n1, n2, and n3 are the mean motions of the planets. The resonance is classified accord￾ing to the sum | k1 + k2 + k3 |, which… view at source ↗
Figure 13
Figure 13. Figure 13: Stability analysis of the TOI-1203 system in the (P12, P23) plane, where P12 = Pc/Pb and P23 = Pc/Pd. For fixed initial condi￾tions, the phase space is explored by varying the period ratios of the inner three planets, while all other parameters are kept at their nom￾inal values. As in [PITH_FULL_IMAGE:figures/full_fig_p015_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: Stability analysis of the TOI-1203 system in the (Ω, i) plane for planets c and e, where Ω and i represent the longitude of ascend￾ing node and inclination of each planet, respectively. For each planet, the phase space is explored by varying these two parameters, while keeping all other orbital elements fixed at their nominal values. As in Figs. 9 and 13, the color scale corresponds to the decimal logarit… view at source ↗
Figure 15
Figure 15. Figure 15: Possible location of an additional fifth planet in the TOI-1203 system. The stability of an Earth-size planet (K = 0.1 m s−1 ) is analyzed for various semimajor axes vs. eccentricity. All the angles of the additional fifth planet are set to 0◦ , except for the inclination (90◦ ). As in Figs. 9, 13, and 14 the color scale corresponds to the decimal logarithm of the stability index D. The red zones correspo… view at source ↗
Figure 16
Figure 16. Figure 16: Posterior distributions for the inferred internal structure of TOI-1203 b. Shown are the mass fractions of the inner core (wcore), mantle (wmantle), and envelope (wenvelope), as well as the mass fraction of hydrogen and helium in the volatile layer (1 − Zenvelope), where Zenvelope refers to the mass fraction of water in the envelope. The distributions were generated with a prior assuming a water-rich comp… view at source ↗
Figure 17
Figure 17. Figure 17: Same as [PITH_FULL_IMAGE:figures/full_fig_p018_17.png] view at source ↗
Figure 18
Figure 18. Figure 18: Mass-radius diagram for small planets (1 ≤ Rp ≤ 3.5 R⊕, 1 ≤ Mp < 10 M⊕) with mass and radius determinations better than 10 %, as retrieved from the Transiting Extrasolar Planet Catalogue (TEPCat, Southworth 2011, as of July 2025). TOI-1203 b and d are highlighted with red circles. The solid and dashed curves are BICEPS theoretical models (Haldemann et al. 2024) for planets with a Mercury-like com￾position… view at source ↗

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