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arxiv: 2604.15035 · v2 · submitted 2026-04-16 · 🌌 astro-ph.EP

Recognition: unknown

The multi-planet system TOI-5624: Four transiting sub-Neptunes with an outer companion revealed by transit-timing variations

A. Bonfanti , D. Gandolfi , P. Leonardi , H. P. Osborn , L. M. Serrano , G. H\'ebrard , N. Billot , A. Bekkelien
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G. Olofsson C. Broeg D. Nardiello S. G. Sousa T. G. Wilson A. C. M. Correia C. Pezzotti A. Brandeker L. Fossati M. Gillon M. Stalport B. Akinsanmi Y. Alibert R. Alonso J. Asquier T. B\'arczy D. Barrado S. C. C. Barros W. Baumjohann W. Benz L. Borsato A. Castro Gonz\'alez A. Collier Cameron Sz. Csizmadia P. E. Cubillos M. B. Davies M. Deleuil X. Delfosse A. Deline O. D. S. Demangeon B.-O. Demory A. Derekas F. Destriez B. Edwards D. Ehrenreich A. Erikson A. Fortier M. Fridlund K. Gazeas M. G\"udel M. N. G\"unther N. Hara N. Heidari A. Heitzmann Ch. Helling K. G. Isaak T. Keller L. L. Kiss D. Kitzmann J. Korth G. Lacedelli K. W. F. Lam J. Laskar A. Lecavelier des Etangs A. Leleu M. Lendl D. Magrin P. F. L. Maxted M. Mecina B. Mer\'in C. Mordasini V. Nascimbeni R. Ottensamer I. Pagano E. Pall\'e G. Peter D. Piazza G. Piotto D. Pollacco D. Queloz R. Ragazzoni N. Rando H. Rauer I. Ribas N. C. Santos G. Scandariato D. S\'egransan A. E. Simon A. M. S. Smith S. Sulis Gy. M. Szab\'o S. Udry S. Ulmer-Moll V. Van Grootel J. Venturini F. Verrecchia E. Villaver N. A. Walton S. Wolf D. Wolter T. Zingales
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Pith reviewed 2026-05-10 09:57 UTC · model grok-4.3

classification 🌌 astro-ph.EP
keywords multi-planet systemstransit timing variationssub-Neptunesradial velocitiesTESSCHEOPSdynamical modelingexoplanet masses
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The pith

Four transiting sub-Neptunes orbit TOI-5624 while their timing variations reveal a fifth non-transiting companion.

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

The paper reports the detection of four planets transiting a G7 V star 100 pc away, with radii between 2.3 and 3.6 Earth radii and masses between 4.8 and 9.4 Earth masses derived from combined TESS, CHEOPS photometry and HARPS-N plus SOPHIE radial velocities. The outermost transiting planet exhibits clear transit timing variations that a dynamical N-body model attributes to gravitational tugging by an unseen outer body. Radial velocities independently show a Keplerian signal near the 2:1 period ratio with the outermost transiter, allowing the authors to assign a minimum mass of 13 Earth masses to this fifth planet. The radius measurements reach better than 1.7 percent precision, a level previously achieved for systems with more than four planets only in TRAPPIST-1.

Core claim

We present the discovery of four transiting sub-Neptunes with radii of R_b=2.314±0.035 R_⊕, R_c=2.474±0.042 R_⊕, R_d=3.584_{-0.050}^{+0.051} R_⊕, and R_e=3.247_{-0.043}^{+0.042} R_⊕ and masses of M_b=9.4±1.4 M_⊕, M_c=4.8±1.9 M_⊕, M_d=4.9±2.2 M_⊕, and M_e=8.9_{-3.0}^{+2.9} M_⊕. Photometric analysis shows significant TTVs on the outermost transiting planet TOI-5624 e. A robust Keplerian signal appears in the RV data close to the 2:1 commensurability with planet e; N-body integration of the equations of motion simultaneously fitted to transit times and detrended RVs identifies this signal as a non-transiting companion TOI-5624 f whose minimum mass is M_f sin i_f=13.0±3.7 M_⊕ and which accounts

What carries the argument

The N-body dynamical integration that simultaneously solves the equations of motion while fitting observed transit times and detrended radial velocities, thereby linking the TTV pattern of planet e to the outer companion at the 2:1 period ratio.

If this is right

  • Additional photometry will sample the full TTV modulation cycle and yield tighter dynamical mass constraints for all planets.
  • The system joins the small set of multi-planet systems in which radii are known to <1.7 percent and at least three masses exceed 3-sigma significance.
  • The 2:1 period ratio between planets e and f provides a concrete test case for resonant or near-resonant dynamics in compact sub-Neptune systems.

Where Pith is reading between the lines

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

  • Systems already known to host multiple transiting planets can be re-examined with combined TTV and RV data to uncover additional non-transiting members.
  • The sub-Neptune radii and measured masses supply concrete targets for transmission spectroscopy that could reveal atmospheric scale heights or compositions.
  • Long-term stability simulations of the five-planet configuration could test whether the observed periods remain stable over Gyr timescales without additional damping.

Load-bearing premise

The radial-velocity signal near twice the orbital period of planet e is produced by a real planetary companion rather than by stellar activity, an instrumental artifact, or an alias.

What would settle it

A longer radial-velocity baseline in which the ~43-day signal disappears, weakens below 3 sigma, or correlates tightly with stellar activity indicators such as the bisector span or log R'_HK would falsify the planetary interpretation of TOI-5624 f.

Figures

Figures reproduced from arXiv: 2604.15035 by A. Bekkelien, A. Bonfanti, A. Brandeker, A. Castro Gonz\'alez, 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, B. Akinsanmi, B. Edwards, B. Mer\'in, B.-O. Demory, C. Broeg, Ch. Helling, C. Mordasini, C. Pezzotti, D. Barrado, D. Ehrenreich, D. Gandolfi, D. Kitzmann, D. Magrin, D. Nardiello, D. Piazza, D. Pollacco, D. Queloz, D. S\'egransan, D. Wolter, E. Pall\'e, E. Villaver, F. Destriez, F. Verrecchia, G. H\'ebrard, G. Lacedelli, G. Olofsson, G. Peter, G. Piotto, G. Scandariato, Gy. M. Szab\'o, H. P. Osborn, H. Rauer, I. Pagano, I. Ribas, J. Asquier, J. Korth, J. Laskar, J. Venturini, K. Gazeas, K. G. Isaak, K. W. F. Lam, L. Borsato, L. Fossati, L. L. Kiss, L. M. Serrano, M. B. Davies, M. Deleuil, M. Fridlund, M. Gillon, M. G\"udel, M. Lendl, M. Mecina, M. N. G\"unther, M. Stalport, N. A. Walton, N. Billot, N. C. Santos, N. Hara, N. Heidari, N. Rando, O. D. S. Demangeon, P. E. Cubillos, P. F. L. Maxted, P. Leonardi, R. Alonso, R. Ottensamer, R. Ragazzoni, S. C. C. Barros, S. G. Sousa, S. Sulis, S. Udry, S. Ulmer-Moll, S. Wolf, Sz. Csizmadia, T. B\'arczy, T. G. Wilson, T. Keller, T. Zingales, V. Nascimbeni, V. Van Grootel, W. Baumjohann, W. Benz, X. Delfosse, Y. Alibert.

Figure 1
Figure 1. Figure 1: TTVs with respect to linear ephemerides for TOI-5624 b, [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: 5.2. Searching for a fifth transiting planet We looked for the putative fifth planet both in the available TESS data and in the RV time series. The only transit-like signal we could detect in the photometry is in Sector 22 at the epoch TExoFOP = 2 458 924.4 BJD, which appears on the ExoFOP web￾Article number, page 4 [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 2
Figure 2. Figure 2: Folded and detrendend LCs of planets b to e (top to bottom) as observed by CHEOPS (left) and TESS (right). Blue dots are [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Detrended RV time series folded according to the period of TOI-5624 b (top-left), TOI-5624 c (top-right), TOI-5624 d (middle￾left), TOI-5624 e (middle-right), and TOI-5624 f (bottom-left) after re￾moving the Keplerian signals of the other planets as inferred from the MCMCI analysis. The marker colour distinguishes the two different in￾struments (light blue for HARPS-N and orange for SOPHIE), while the red … view at source ↗
Figure 4
Figure 4. Figure 4: O−C diagrams of TOI-5624 d (top) & e (bottom) along with the residuals (res) with respect to the best-fit model when assuming the five-planet configuration. The best-fit TRADES model is shown as a black line, while the shaded areas display the 1σ, 2σ, and 3σ confidence intervals. which further confirms an increased evidence for the five-planet configuration. While the five-planet model reproduces the over￾… view at source ↗
read the original abstract

Following the 2022 alert of a TESS object of interest transiting TOI-5624 (a G7 V star $\sim$100 pc away), a CHEOPS campaign in 2023 detected four planetary signals at $P_b\approx3.4$, $P_c\approx7.9$, $P_d\approx13.7$, and $P_e\approx21.5$ days, later confirmed by additional TESS and CHEOPS photometry in 2024-2025. After analysing the TESS & CHEOPS photometric data, we extracted and modelled the HARPS-N & SOPHIE RV time series using two independent methodologies both within an MCMC framework. We further integrated the N-body equations of motion, while simultaneously fitting the transit times and the detrended RVs, to dynamically characterise the system. We present the discovery of four transiting sub-Neptunes with radii of $R_b=2.314\pm0.035 R_{\oplus}$, $R_c=2.474\pm0.042 R_{\oplus}$, $R_d=3.584_{-0.050}^{+0.051} R_{\oplus}$, and $R_e=3.247_{-0.043}^{+0.042} R_{\oplus}$ and masses of $M_b=9.4\pm1.4 M_{\oplus}$, $M_c=4.8\pm1.9 M_{\oplus}$, $M_d=4.9\pm2.2 M_{\oplus}$, and $M_e=8.9_{-3.0}^{+2.9} M_{\oplus}$. Our photometric analysis reveals that the outermost transiting planet TOI-5624 e shows significant TTVs. We find a robust Keplerian signal in the RV time series close to the 2:1 period commensurability with TOI-5624 e, which explains the TTV pattern exhibited by TOI-5624 e according to our dynamical analysis. We label this non-transiting planet as TOI-5624 f and find its minimum mass to be $M_f\sin{i_f}=13.0\pm3.7 M_{\oplus}$. Among the known systems hosting more than four planets, the remarkable precision with which the radii have been measured (<1.7%) and the firm assessment (>3$\sigma$) of the mass for at least three planets has been previously reached only for TRAPPIST-1. Additional photometric observations will enable a better sample of the TTV modulation and a more robust dynamical determination of the masses.

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.

Referee Report

2 major / 2 minor

Summary. The manuscript reports the discovery of a five-planet system around the G7 V star TOI-5624 (~100 pc). Four transiting sub-Neptunes (b, c, d, e) with periods ~3.4, 7.9, 13.7, and 21.5 days are characterized using TESS and CHEOPS photometry, yielding radii R_b=2.314±0.035 R_⊕, R_c=2.474±0.042 R_⊕, R_d=3.584_{-0.050}^{+0.051} R_⊕, R_e=3.247_{-0.043}^{+0.042} R_⊕. Masses are derived from joint MCMC modeling of HARPS-N and SOPHIE RVs (two independent pipelines) combined with N-body integrations that simultaneously fit observed transit times and detrended RVs. A non-transiting outer companion f is identified from a ~43-day Keplerian RV signal near 2:1 commensurability with e; this signal is used in the dynamical model to explain the significant TTVs observed on planet e, with M_f sin i_f = 13.0±3.7 M_⊕. The work emphasizes the high radius precision (<1.7%) and >3σ masses for at least three planets, comparable to TRAPPIST-1.

Significance. If the reported architecture holds, the system provides a high-precision benchmark for compact multi-planet systems, with radii measured to better than 1.7% and dynamical masses enabling composition and formation studies. Strengths include the use of two independent RV pipelines, multiple instruments and epochs for consistency checks, and the simultaneous N-body fit to TTVs and RVs rather than sequential post-hoc modeling. This approach reduces circularity in the TTV explanation. The result would add to the small sample of systems with >4 planets having both precise radii and masses, supporting statistical studies of sub-Neptune populations.

major comments (2)
  1. [RV analysis section] RV analysis section: The ~43-day signal is stated to be 'robust' and to explain the TTVs on planet e via the N-body model, but no explicit false-alarm probability, window-function alias test against the combined HARPS-N+SOPHIE sampling, or correlation analysis with activity indicators (e.g., bisector span or log R'_HK) is reported. This is load-bearing for the central claim because the five-planet architecture and the dynamical masses (particularly the marginal values for c and d) rest on interpreting this signal as planetary f rather than an alias, activity, or artifact; if the signal is non-planetary, the TTV pattern on e remains unexplained by the model.
  2. [Dynamical modeling and mass results] Dynamical modeling and mass results: Planets c and d have masses M_c=4.8±1.9 M_⊕ (~2.5σ) and M_d=4.9±2.2 M_⊕ (~2.2σ). While the abstract notes firm >3σ assessment for at least three planets, the N-body integration simultaneously fitting TTVs and RVs may be sensitive to these low-significance values; the manuscript should clarify whether these are treated as detections or upper limits and test the stability of the reported architecture when c and d masses are set to zero or their 1σ upper bounds.
minor comments (2)
  1. [Abstract] The abstract gives approximate periods; cross-reference to the exact fitted values and uncertainties in Table 1 or §3 would improve clarity.
  2. [Figures] Figure showing the RV periodogram or TTV residuals could include explicit marking of the 43-day peak, its aliases, and the window function for easier reader assessment.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful and constructive review of our manuscript. We appreciate the positive assessment of the system's significance as a high-precision benchmark and the strengths noted in our multi-instrument RV analysis and simultaneous N-body modeling. We address each major comment below and outline the revisions we will incorporate to strengthen the presentation.

read point-by-point responses

  1. Referee: [RV analysis section] The ~43-day signal is stated to be 'robust' and to explain the TTVs on planet e via the N-body model, but no explicit false-alarm probability, window-function alias test against the combined HARPS-N+SOPHIE sampling, or correlation analysis with activity indicators (e.g., bisector span or log R'_HK) is reported. This is load-bearing for the central claim because the five-planet architecture and the dynamical masses (particularly the marginal values for c and d) rest on interpreting this signal as planetary f rather than an alias, activity, or artifact; if the signal is non-planetary, the TTV pattern on e remains unexplained by the model.

    Authors: We agree that explicit statistical validation of the ~43-day RV signal would strengthen the manuscript. In the revised version, we will add the false-alarm probability derived from bootstrap resampling of the combined HARPS-N and SOPHIE data, window-function alias tests to exclude sampling-induced artifacts, and correlation analyses with activity indicators including the bisector span and log R'_HK. These tests will be presented in the RV analysis section. The simultaneous N-body fit already provides independent dynamical support by reproducing the observed TTVs on planet e, reducing reliance on the RV signal in isolation. revision: yes

  2. Referee: [Dynamical modeling and mass results] Planets c and d have masses M_c=4.8±1.9 M_⊕ (~2.5σ) and M_d=4.9±2.2 M_⊕ (~2.2σ). While the abstract notes firm >3σ assessment for at least three planets, the N-body integration simultaneously fitting TTVs and RVs may be sensitive to these low-significance values; the manuscript should clarify whether these are treated as detections or upper limits and test the stability of the reported architecture when c and d masses are set to zero or their 1σ upper bounds.

    Authors: We note that the abstract already specifies a firm >3σ mass assessment for at least three planets (b, e, and f), with the reported values for c and d reflecting their lower significance (~2.5σ and ~2.2σ). In the revision, we will explicitly clarify in the text, tables, and abstract that M_c and M_d are measured values with uncertainties but are not claimed as >3σ detections. We will also add N-body stability tests setting M_c and M_d to zero and to their 1σ upper bounds, confirming that the overall architecture remains stable under these conditions. The joint TTV-RV modeling provides dynamical constraints on all planets through interactions, even at marginal significance. revision: yes

Circularity Check

0 steps flagged

No significant circularity; central results are independent fits to photometric and RV datasets with dynamical consistency check

full rationale

The paper derives planetary radii and periods directly from TESS/CHEOPS transit photometry, extracts TTVs from the same photometry, and fits masses via MCMC on independent HARPS-N/SOPHIE RV time series. The N-body integration simultaneously fits observed transit times (photometric) and detrended RVs to confirm that the detected ~43-day Keplerian RV signal near 2:1 with planet e accounts for the TTV pattern on e. This is a cross-validation between independent observables rather than a self-definitional loop or a fitted parameter renamed as a prediction. No self-citations, ansatzes, or uniqueness theorems are invoked in the provided derivation chain to force the architecture. The minimum mass for f and the dynamical masses are outputs of the joint model constrained by the data, not inputs.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

The analysis rests on standard Keplerian orbit assumptions and N-body dynamics; masses and periods are fitted parameters from the data.

free parameters (2)
  • planetary masses and orbital elements
    Fitted via MCMC to RV curves and TTVs; specific values listed in abstract.
  • system inclination and eccentricity parameters
    Assumed or fitted within the dynamical model to match observed transit times.
axioms (2)
  • standard math Planets follow Newtonian N-body dynamics with no additional forces
    Invoked in the simultaneous fit of transit times and RVs.
  • domain assumption RV signal near 2:1 with planet e originates from a planetary companion
    Used to label the signal as planet f and explain TTVs.

pith-pipeline@v0.9.0 · 6367 in / 1525 out tokens · 35614 ms · 2026-05-10T09:57:52.731073+00:00 · methodology

discussion (0)

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Works this paper leans on

122 extracted references · 2 canonical work pages

  1. [1]

    & Deck, K

    Agol, E. & Deck, K. 2016, The Astrophysical Journal, 818, 177

    2016

  2. [2]

    L., et al

    Agol , E., Dorn , C., Grimm , S. L., et al. 2021, , 2, 1

    2021

  3. [3]

    & Fabrycky , D

    Agol , E. & Fabrycky , D. C. 2018, in Handbook of Exoplanets, ed. H. J. Deeg & J. A. Belmonte (Cambridge University Press), 7

    2018

  4. [4]

    2005, , 359, 567

    Agol , E., Steffen , J., Sari , R., & Clarkson , W. 2005, , 359, 567

    2005

  5. [5]

    2013, , 558, A109

    Alibert , Y., Carron , F., Fortier , A., et al. 2013, , 558, A109

    2013

  6. [6]

    R., Smith , A

    Anderson , D. R., Smith , A. M. S., Lanotte , A. A., et al. 2011, , 416, 2108

    2011

  7. [7]

    & Butler , R

    Anglada-Escud \'e , G. & Butler , R. P. 2012, , 200, 15

    2012

  8. [8]

    Armitage , P. J. 2024, arXiv e-prints, arXiv:2412.11064

    work page arXiv 2024

  9. [9]

    1996, , 119, 373

    Baranne , A., Queloz , D., Mayor , M., et al. 1996, , 119, 373

    1996

  10. [10]

    M., & Zicher , N

    Barrag \'a n , O., Aigrain , S., Rajpaul , V. M., & Zicher , N. 2022, , 509, 866

    2022

  11. [11]

    2019, , 482, 1017

    Barrag \'a n , O., Gandolfi , D., & Antoniciello , G. 2019, , 482, 1017

    2019

  12. [12]

    2021, Experimental Astronomy, 51, 109

    Benz , W., Broeg , C., Fortier , A., et al. 2021, Experimental Astronomy, 51, 109

    2021

  13. [13]

    Blackwell , D. E. & Shallis , M. J. 1977, , 180, 177

    1977

  14. [14]

    C., et al

    Boisse , I., Eggenberger , A., Santos , N. C., et al. 2010, , 523, A88

    2010

  15. [15]

    2025, , 693, A90

    Bonfanti , A., Amateis , I., Gandolfi , D., et al. 2025, , 693, A90

    2025

  16. [16]

    J., et al

    Bonfanti , A., Delrez , L., Hooton , M. J., et al. 2021, , 646, A157

    2021

  17. [17]

    A., et al

    Bonfanti , A., Gandolfi , D., Egger , J. A., et al. 2023, , 671, L8

    2023

  18. [18]

    & Gillon , M

    Bonfanti , A. & Gillon , M. 2020, , 635, A6

    2020

  19. [19]

    2016, , 585, A5

    Bonfanti , A., Ortolani , S., & Nascimbeni , V. 2016, , 585, A5

    2016

  20. [20]

    2015, , 575, A18

    Bonfanti , A., Ortolani , S., Piotto , G., & Nascimbeni , V. 2015, , 575, A18

    2015

  21. [21]

    2024, , 689, A52

    Borsato , L., Degen , D., Leleu , A., et al. 2024, , 689, A52

    2024

  22. [22]

    2019, , 484, 3233

    Borsato , L., Malavolta , L., Piotto , G., et al. 2019, , 484, 3233

    2019

  23. [23]

    2014, , 571, A38

    Borsato , L., Marzari , F., Nascimbeni , V., et al. 2014, , 571, A38

    2014

  24. [24]

    2021, , 506, 3810

    Borsato , L., Piotto , G., Gandolfi , D., et al. 2021, , 506, 3810

    2021

  25. [25]

    J., Koch , D., Basri , G., et al

    Borucki , W. J., Koch , D., Basri , G., et al. 2010, Science, 327, 977

    2010

  26. [26]

    F., H \'e brard , G., et al

    Bouchy , F., D \' az , R. F., H \'e brard , G., et al. 2013, , 549, A49

    2013

  27. [27]

    2009, , 505, 853

    Bouchy , F., H \'e brard , G., Udry , S., et al. 2009, , 505, 853

    2009

  28. [28]

    & Kurucz , R

    Castelli , F. & Kurucz , R. L. 2003, in IAU Symposium, Vol. 210, Modelling of Stellar Atmospheres, ed. N. Piskunov , W. W. Weiss , & D. F. Gray , A20

    2003

  29. [29]

    Correia , A. C. M., Couetdic , J., Laskar , J., et al. 2010, , 511, A21

    2010

  30. [30]

    Correia , A. C. M., Delisle , J.-B., & Laskar , J. 2018, in Handbook of Exoplanets, ed. H. J. Deeg & J. A. Belmonte ( Springer International Publishing AG, part of Springer Nature ), 12

    2018

  31. [31]

    Correia , A. C. M., Udry , S., Mayor , M., et al. 2005, , 440, 751

    2005

  32. [32]

    2012, in Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, Vol

    Cosentino , R., Lovis , C., Pepe , F., et al. 2012, in Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, Vol. 8446, Ground-based and Airborne Instrumentation for Astronomy IV, ed. I. S. McLean , S. K. Ramsay , & H. Takami , 84461V

    2012

  33. [33]

    Deck , K. M. & Agol , E. 2015, , 802, 116

    2015

  34. [34]

    A., Osborn , H

    Egger , J. A., Osborn , H. P., Kubyshkina , D., et al. 2024, , 688, A223

    2024

  35. [35]

    & Jord \'a n , A

    Espinoza , N. & Jord \'a n , A. 2015, , 450, 1879

    2015

  36. [36]

    2018, in American Astronomical Society Meeting Abstracts, Vol

    Fausnaugh , M., Huang , X., Glidden , A., Guerrero , N., & TESS Science Office . 2018, in American Astronomical Society Meeting Abstracts, Vol. 231, American Astronomical Society Meeting Abstracts \#231, 439.09

    2018

  37. [37]

    2017, , 154, 220

    Foreman-Mackey , D., Agol , E., Ambikasaran , S., & Angus , R. 2017, , 154, 220

    2017

  38. [38]

    W., Lang , D., & Goodman , J

    Foreman-Mackey , D., Hogg , D. W., Lang , D., & Goodman , J. 2013, , 125, 306

    2013

  39. [39]

    Fortier , A., Alibert , Y., Carron , F., Benz , W., & Dittkrist , K. M. 2013, , 549, A44

    2013

  40. [40]

    E., Broeg , C., et al

    Fortier , A., Simon , A. E., Broeg , C., et al. 2024, , 687, A302

    2024

  41. [41]

    Gaia Collaboration , Vallenari , A., Brown , A. G. A., et al. 2023, , 674, A1

    2023

  42. [42]

    & Rubin , D

    Gelman , A. & Rubin , D. B. 1992, Statistical Science, 7, 457

    1992

  43. [43]

    Geweke, J. F. 1991, Evaluating the accuracy of sampling-based approaches to the calculation of posterior moments , Staff Report 148, Federal Reserve Bank of Minneapolis

    1991

  44. [44]

    & Tremaine , S

    Goldreich , P. & Tremaine , S. 1980, , 241, 425

    1980

  45. [45]

    & Weare, J

    Goodman, J. & Weare, J. 2010, Communications in Applied Mathematics and Computational Science, 5, 65

    2010

  46. [46]

    & Lithwick , Y

    Hadden , S. & Lithwick , Y. 2017, , 154, 5

    2017

  47. [47]

    2024, , 681, A96

    Haldemann , J., Dorn , C., Venturini , J., Alibert , Y., & Benz , W. 2024, , 681, A96

    2024

  48. [48]

    Hatzes , A. P. 2019, The Doppler Method for the Detection of Exoplanets , 2514-3433 (IOP Publishing)

    2019

  49. [49]

    C., et al

    Heidari , N., Boisse , I., Hara , N. C., et al. 2024, , 681, A55

    2024

  50. [50]

    2025, , 694, A36

    Heidari , N., H \'e brard , G., Martioli , E., et al. 2025, , 694, A36

    2025

  51. [51]

    J., Soderblom , D

    Henry , T. J., Soderblom , D. R., Donahue , R. A., & Baliunas , S. L. 1996, , 111, 439

    1996

  52. [52]

    & Heller , R

    Hippke , M. & Heller , R. 2019, , 623, A39

    2019

  53. [53]

    2020, , 639, A35

    Hojjatpanah , S., Oshagh , M., Figueira , P., et al. 2020, , 639, A35

    2020

  54. [54]

    W., Sinukoff , E., Blunt , S., et al

    Howard , A. W., Sinukoff , E., Blunt , S., et al. 2025, , 278, 52

    2025

  55. [55]

    2020, , 635, A24

    Hoyer , S., Guterman , P., Demangeon , O., et al. 2020, , 635, A24

    2020

  56. [56]

    M., Twicken , J

    Jenkins , J. M., Twicken , J. D., McCauliff , S., et al. 2016, in Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, Vol. 9913, Software and Cyberinfrastructure for Astronomy IV, ed. G. Chiozzi & J. C. Guzman , 99133E

    2016

  57. [57]

    2019, , 622, A202

    Johansen , A., Ida , S., & Brasser , R. 2019, , 622, A202

    2019

  58. [58]

    Kass , R. E. & Raftery , A. E. 1995, Journal of the American Statistical Association, 90, 773

    1995

  59. [59]

    M., Woitke , P., & Dominik , C

    Khorshid , N., Min , M., D \'e sert , J. M., Woitke , P., & Dominik , C. 2022, , 667, A147

    2022

  60. [60]

    Kipping , D. M. 2008, , 389, 1383

    2008

  61. [61]

    Kurucz , R. L. 1993 a , SYNTHE spectrum synthesis programs and line data (Astrophysics Source Code Library)

    1993

  62. [62]

    Kurucz , R. L. 1993 b , SYNTHE spectrum synthesis programs and line data (Astrophysics Source Code Library)

    1993

  63. [63]

    1990, , 88, 266

    Laskar , J. 1990, , 88, 266

    1990

  64. [64]

    1993, Physica D Nonlinear Phenomena, 67, 257

    Laskar , J. 1993, Physica D Nonlinear Phenomena, 67, 257

    1993

  65. [65]

    Lee , M. H. & Peale , S. J. 2002, arXiv e-prints [ [arXiv] 0209176 ]

    2002

  66. [66]

    C., et al

    Leleu , A., Alibert , Y., Hara , N. C., et al. 2021, , 649, A26

    2021

  67. [67]

    2024, , 688, A211

    Leleu , A., Delisle , J.-B., Delrez , L., et al. 2024, , 688, A211

    2024

  68. [68]

    B., Udry , S., et al

    Leleu , A., Delisle , J. B., Udry , S., et al. 2023, , 669, A117

    2023

  69. [69]

    2025, , 702, A211

    Leonardi , P., Borsato , L., Pagliaro , L., et al. 2025, , 702, A211

    2025

  70. [70]

    2021, , 649, A4

    Lindegren , L., Bastian , U., Biermann , M., et al. 2021, , 649, A4

    2021

  71. [71]

    2012, , 761, 122

    Lithwick , Y., Xie , J., & Wu , Y. 2012, , 761, 122

    2012

  72. [72]

    & Pepe , F

    Lovis , C. & Pepe , F. 2007, , 468, 1115

    2007

  73. [73]

    P., Leleu , A., et al

    Luque , R., Osborn , H. P., Leleu , A., et al. 2023, , 623, 932

    2023

  74. [74]

    1995, , 110, 420

    Malhotra , R. 1995, , 110, 420

    1995

  75. [75]

    Mandell , A. M. 2011, Planetary Migration (Berlin, Heidelberg: Springer Berlin Heidelberg), 1275--1278

    2011

  76. [76]

    2017, , 835, 77

    Marigo , P., Girardi , L., Bressan , A., et al. 2017, , 835, 77

    2017

  77. [77]

    C., He , M

    Millholland , S. C., He , M. Y., Ford , E. B., et al. 2021, , 162, 166

    2021

  78. [78]

    2023, , 670, A68

    Mishra , L., Alibert , Y., Udry , S., & Mordasini , C. 2023, , 670, A68

    2023

  79. [79]

    Munavar Hussain , M. J. & Kunimoto , M. 2025, , 169, 91

    2025

  80. [80]

    Murray , C. D. & Dermott , S. F. 1999, Solar System Dynamics ( Publisher: Cambridge University Press )

    1999

Showing first 80 references.