attempt to model the effects of multiple moons in the system, which also would have increased the complexity of our simulations.

Given the current data, another caveat is that we do not know with certainty what the true nature of HIP 41378 f is. Through- out our analysis, we assumed that the planet has a mass and radius consistent with observations (Santerne et al. 2019) and tidal properties similar to a Jovian planet. However, if in reality the planet is more similar to Neptune and it possesses a circumplanetary ring system (e.g., Akinsanmi et al. 2020; Piro & Vissapragada 2020), this could change the tidal response of the planet and therefore affect the orbital stability of moons.

Moreover, self-consistent modeling of any moon-ring interactions is beyond the scope of this work but would be an interesting subject of future simulations. Akinsanmi et al. (2020) showed that observations of HIP 41378 f are consistent with a planet of radius $R_p = 3.7$ $R_⊕$ ($\rho_p = 1.4$ g cm$^{-3}$), with opaque rings extending from 1.05 to 2.6 $R_⊕$. If the rings disperse out to the Roche radius, it follows that the density of the ring material would be $\rho_r = 1.08$ g cm$^{-3}$. In this case, assuming that the ring particles have a typical radius of about 100 cm, the total mass of the rings would be approximately $10^{19}$ kg (see Equation (4) of Piro 2018b), roughly the observed mass of Saturn's rings (Iess et al. 2019). Hence, in reality, gravitational interactions between the rings and the moon may affect their long-term stability (e.g., Nakajima et al. 2020). On a similar note, we did not attempt to model the combined observable effects of moons and rings (e.g., Ohno & Fortney 2022).

Finally, throughout our analysis, we assumed that moons are a natural outcome of planet formation, and we only considered the stability of moons once they reached a tidally locked state with planet f. That is, we did not attempt to treat exomoon formation and evolution in a self-consistent manner, and we remained agnostic to the specific formation pathway of our simulated moons.

To assess the observability of an exomoon, we chose to model transit observations because these are likely the most promising for a long-period transiting planet like HIP 41378 f. We note that aside from photodynamical transit searches for exomoons such as HEK (Kipping et al. 2012) and the future Transiting Exosatellites, Moons, and Planets in Orion (TEMPO) survey (Limbach et al. 2023), several other methods of detecting exomoons have been proposed. For example, the orbital sampling effect (OSE) technique (Heller 2014), which leverages many transit observations to achieve robust statistics, can be used to infer the size, orbital separation, and mass of transiting exomoons from a phase-folded light curve of about a dozen transits (Hippke 2015; Heller et al. 2016). However, this is not currently feasible for HIP 41378 f because the planet's long orbital period and transit duration make it difficult to acquire the necessary large number of observations.

Other novel approaches, including direct imaging and Doppler spectroscopy (Peters & Turner 2013; Agol et al. 2015; Vanderburg et al. 2018), radio emission from satellite-hosting exoplanets (Noyola et al. 2014, 2016; Narang et al. 2023), and combined planet-moon thermal phase curves (Forgan 2017), may also be fruitful probes of exomoons with future technologies. But again, HIP 41378 f is not an optimal target for such studies. The semimajor axis of planet f is too small for current direct imaging technology, with a sky-projected angular separation of ~13 mas, and uncertainties in

the other planet masses and orbits preclude a radial velocity exomoon search. Moreover, uncertainty regarding the nature of planet f makes radio emission studies challenging, and the cool equilibrium temperature of planet f ($T_{eq} = 294$ K) is not sufficient to produce an appreciable thermal phase curve.

Nonetheless, as our ability to measure exoplanets continues to improve in the future, exomoons may indeed become a more important source of uncertainty (in addition to transit light source variability, stellar spectrum noise, etc.). Further into the future, we may even be able to robustly confirm detections of exomoons and constrain the properties of their atmospheres with state-of-the-art observational facilities such as ground-based ELTs and next-generation space missions like the Habitable Worlds Observatory (HWO). For example, the Ancillary Science Case A-19 for the Large UV/Optical/ Infrared Surveyor (LUVOIR) suggests spectroastrometry (i.e., measuring the astrometric shift that occurs between wavelengths with flux dominated by the exoplanet and wavelengths dominated by the exomoon) as a possible exomoon detection strategy with a 12 m class space telescope (The LUVOIR Team 2019). With contrast $>10^{-9}$ and relative astrometric precision between wavelength bands of ~0.1 mas, such an observatory could in principle detect an Earth-size exomoon orbiting a 1 au Jupiter-size planet at 10 pc (The LUVOIR Team 2019). Not only would this be a revolutionary discovery in itself, but it would also open the possibility of using exomoons as a way of studying planet formation and evolution, and even provide a potential new avenue for searching for signs of life beyond the solar system.

## Acknowledgments

The authors thank Kristo Ment for helpful discussions regarding quadtree algorithms. This paper makes use of observations from the NASA/ESA Hubble Space Telescope, obtained at the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., under NASA contract NAS 526555. These observations are associated with HST-GO program 16267 (PI: Dressing), and the analysis was supported by grant HST-GO-16267. This work was supported by the Programme National de Planétologie (PNP) of CNRS-INSU co-funded by CNES. This work was supported by FCT—Fundação para a Ciência e a Tecnologia through national funds and by FEDER through COMPETE2020—Programa Operacional Competitividade e Internacionalização by these grants: UIDB/04434/2020; UIDP/04434/2020, 2022.06962.PTDC. This research has also been partly funded by the Spanish State Research Agency (AEI) Project No. PID2019-107061GB-C61. A.C.C. acknowledges support from STFC consolidated grant numbers ST/R000824/1 and ST/V000861/1, and UKSA grant No. ST/R003203/1. C.K.H. acknowledges support from the National Science Foundation Graduate Research Fellowship Program under grant No. DGE 2146752. J.K. acknowledges financial support from Imperial College London through an Imperial College Research Fellowship grant. J.L.-B. acknowledges support from the Ramón y Cajal program (RYC2021-031640-I) supported by the MCIN/AEI/10.13039/501100011033 and the European Union “Next-GenerationEU”/PRTR as well as partial financial support received from “la Caixa” Foundation (ID 100010434) and the European Unions Horizon 2020 research and innovation program No. 847648, with fellowship code LCF/BQ/PI20/11760023. N.C.S. acknowledges funding from the European Union (ERC,
FIERCE, 101052347). Views and opinions expressed are however those of the author(s) only and do not necessarily reflect those of the European Union or the European Research Council. Neither the European Union nor the granting authority can be held responsible for them. S.G.S. acknowledges the support from FCT through Investigador FCT contract No. CEECIND/00826/2018 and POPH/FSE (EC). P.J. W. acknowledges support from the UK Science and Technology Facilities Council (STFC) under consolidated grant ST/ T000406/1.

Facilities: HST (WFC3), K2.

Software: Astropy (Astropy Collaboration et al. 2013, 2018), AstroQTpy (Harada 2023), EqTide (Barnes 2017), ExoTiC-LD (Wakeford & Grant 2022), IPython (Perez & Granger 2007), Matplotlib (Hunter 2007), NumPy (van der Walt et al. 2011; Harris et al. 2020), Pandora (Hippke & Heller 2022), PLATON (Zhang et al. 2019, 2020), Rebound (Rein & Liu 2012; Rein & Spiegel 2015), UltraNest (Buchner 2021).

## Appendix A
### Benchmark Three-body Simulation

While in the main text we describe our N-body simulations for exploring how the semimajor axis and inclination of the satellite and the presence of planet e affect the system's stability, here we describe the set of initial simulations that were used to test our N-body code.

We benchmarked our code by following the general procedure outlined by Domingos et al. (2006) and Rosario-Franco et al. (2020). We set up our grid of simulations using a quadtree data structure implemented in astrQTpy (Harada 2023), which we described in more detail in Section 2.1.1. We constrained the initial eccentricity, $e_f$, of planet f between 0.0 and 0.5, and the initial semimajor axis, $a_s$, of the satellite between 0.25 to $0.55R_H$, where $R_H$ is the Hill radius defined in Equation (1) ($R_H \approx 0.03$ au $\approx 76R_p$). These limits were chosen in order to explore the parameter space encompassing the stability limit determined by Rosario-Franco et al. (2020). Note however that the measured eccentricity of planet f is actually constrained to $e_f = 0.004^{+0.009}_{-0.003}$ (Santerne et al. 2019), as stated in the main text. As in Section 2.1.1, the planet and satellite were initialized with co-planar orbits, with the longitudes of the ascending node and arguments of pericenter set to zero

($\Omega = \omega = 0^\circ$), and the mean anomaly of the planet set to zero ($M_f = 0^\circ$).

We proceeded by dividing the parameter space evenly into a $4 \times 4$ grid and running 25 independent N-body simulations in each grid cell with ($e_f, a_s$) and the satellite mean anomaly, $M_s$, drawn from uniform distributions. We calculated the fraction of stable systems, $f_{\text{stab}}$, in each cell as the fraction of simulations (out of 25) which satisfied the stability criteria defined in the main text over a timescale of $10^5$ yr. We then continued splitting each grid cell in the quadtree into four equal child cells and computing more N-body simulations, following the procedure described in Section 2.1.1. Figure 7 shows the final stability grid generated by our simulations, where $f_{\text{stab}}$ is quantified by color. Regions where $0 < f_{\text{stab}} < 1$ are considered quasi-stable, while regions where $f_{\text{stab}} = 1$ (0) are absolutely stable (unstable) over $10^5$ yr.

Our results were qualitatively similar to Rosario-Franco et al. (2020) and quantitatively consistent in terms of the stability boundary for low-eccentricity orbits (i.e., the largest value of $a_s$ for a given $e_f$ where $f_{\text{stab}} = 1$). Rosario-Franco et al. (2020) modeled the stability boundary as

$$a_{\text{crit}} = c_1(1 - c_2e_f), \qquad (\text{A1})$$

where $a_{\text{crit}}$ is implicitly in terms of the fraction of the Hill radius, $c_1$ is the stability limit for circular orbits, and $c_2$ is a slope parameter.

From their N-body simulations, the authors determined that $c_1 = 0.4061 \pm 0.0028$ and $c_2 = 1.1257 \pm 0.0273$. Their stability limit is shown in Figure 7 plotted over our stability. Our results are in good agreement for low eccentricities, with our stability limit for circular orbits being $a_{\text{crit}} \approx 0.41R_H$. However, we note that our simulations tend to predict a slightly higher stability limit as eccentricity increases (for $e_f \gtrsim 0.15$). This discrepancy at higher eccentricities is likely due to our different choice of planetary semimajor axis; we assumed a semimajor axis of 1.37 au for HIP 41378 f, whereas Rosario-Franco et al. (2020) assumed an orbital separation of 1 au in their simulations. Because our simulated planet and its moon are farther away from the host star, the system tends to be more stable against gravitational perturbations.
FIERCE, 101052347). Views and opinions expressed are however those of the author(s) only and do not necessarily reflect those of the European Union or the European Research Council. Neither the European Union nor the granting authority can be held responsible for them. S.G.S. acknowledges the support from FCT through Investigador FCT contract No. CEECIND/00826/2018 and POPH/FSE (EC). P.J. W. acknowledges support from the UK Science and Technology Facilities Council (STFC) under consolidated grant ST/ T000406/1.

Facilities: HST (WFC3), K2.

Software: Astropy (Astropy Collaboration et al. 2013, 2018), AstroQTpy (Harada 2023), EqTide (Barnes 2017), ExoTiC-LD (Wakeford & Grant 2022), IPython (Perez & Granger 2007), Matplotlib (Hunter 2007), NumPy (van der Walt et al. 2011; Harris et al. 2020), Pandora (Hippke & Heller 2022), PLATON (Zhang et al. 2019, 2020), Rebound (Rein & Liu 2012; Rein & Spiegel 2015), UltraNest (Buchner 2021).

## Appendix A
### Benchmark Three-body Simulation

While in the main text we describe our N-body simulations for exploring how the semimajor axis and inclination of the satellite and the presence of planet e affect the system's stability, here we describe the set of initial simulations that were used to test our N-body code.

We benchmarked our code by following the general procedure outlined by Domingos et al. (2006) and Rosario-Franco et al. (2020). We set up our grid of simulations using a quadtree data structure implemented in astrQTpy (Harada 2023), which we described in more detail in Section 2.1.1. We constrained the initial eccentricity, $e_f$, of planet f between 0.0 and 0.5, and the initial semimajor axis, $a_s$, of the satellite between 0.25 to $0.55R_H$, where $R_H$ is the Hill radius defined in Equation (1) ($R_H \approx 0.03$ au $\approx 76R_p$). These limits were chosen in order to explore the parameter space encompassing the stability limit determined by Rosario-Franco et al. (2020). Note however that the measured eccentricity of planet f is actually constrained to $e_f = 0.004^{+0.009}_{-0.003}$ (Santerne et al. 2019), as stated in the main text. As in Section 2.1.1, the planet and satellite were initialized with co-planar orbits, with the longitudes of the ascending node and arguments of pericenter set to zero

($\Omega = \omega = 0^\circ$), and the mean anomaly of the planet set to zero ($M_f = 0^\circ$).

We proceeded by dividing the parameter space evenly into a $4 \times 4$ grid and running 25 independent N-body simulations in each grid cell with ($e_f, a_s$) and the satellite mean anomaly, $M_s$, drawn from uniform distributions. We calculated the fraction of stable systems, $f_{\text{stab}}$, in each cell as the fraction of simulations (out of 25) which satisfied the stability criteria defined in the main text over a timescale of $10^5$ yr. We then continued splitting each grid cell in the quadtree into four equal child cells and computing more N-body simulations, following the procedure described in Section 2.1.1. Figure 7 shows the final stability grid generated by our simulations, where $f_{\text{stab}}$ is quantified by color. Regions where $0 < f_{\text{stab}} < 1$ are considered quasi-stable, while regions where $f_{\text{stab}} = 1$ (0) are absolutely stable (unstable) over $10^5$ yr.

Our results were qualitatively similar to Rosario-Franco et al. (2020) and quantitatively consistent in terms of the stability boundary for low-eccentricity orbits (i.e., the largest value of $a_s$ for a given $e_f$ where $f_{\text{stab}} = 1$). Rosario-Franco et al. (2020) modeled the stability boundary as

$$a_{\text{crit}} = c_1(1 - c_2e_f), \qquad (A1)$$

where $a_{\text{crit}}$ is implicitly in terms of the fraction of the Hill radius, $c_1$ is the stability limit for circular orbits, and $c_2$ is a slope parameter.

From their N-body simulations, the authors determined that $c_1 = 0.4061 \pm 0.0028$ and $c_2 = 1.1257 \pm 0.0273$. Their stability limit is shown in Figure 7 plotted over our stability. Our results are in good agreement for low eccentricities, with our stability limit for circular orbits being $a_{\text{crit}} \approx 0.41R_H$. However, we note that our simulations tend to predict a slightly higher stability limit as eccentricity increases (for $e_f \gtrsim 0.15$). This discrepancy at higher eccentricities is likely due to our different choice of planetary semimajor axis; we assumed a semimajor axis of 1.37 au for HIP 41378 f, whereas Rosario-Franco et al. (2020) assumed an orbital separation of 1 au in their simulations. Because our simulated planet and its moon are farther away from the host star, the system tends to be more stable against gravitational perturbations.
<figure><img src="image_9.png" /><figcaption>**Figure 7.** Three-body orbital stability map for a system consisting of HIP 41378, planet f, and planet f's satellite, as a function of planetary eccentricity, *e*<sub>f</sub>, and satellite semimajor, axis *a*<sub>s</sub> (expressed in terms of the Hill radius, *R*<sub>H</sub>). The color of each grid cell corresponds to the fraction *f*<sub>stab</sub> of 25 simulations within each cell (indicated by the black points) that survive over 10<sup>5</sup> yr. The stability limit determined by Rosario-Franco et al. (2020), shown as the dashed line, indicated good agreement with our simulations at low eccentricities.</figcaption></figure>

**Appendix B**
**Additional Figures**

Here we present additional figures that supplement the main text. Figure 8 shows the posterior distributions derived from our nested sampling analysis of the HST white light curve shown in Figure 5—maximum likelihood values from the posteriors were used to compute the planet-only model therein.

Figure 9 shows additional observations of HIP 41378 f from K2 Campaigns 5 and 18, along with simulated data of a single transit event from the upcoming PLATO mission. The posterior distributions derived from nested sampling analyses of the K2 light curves are shown in Figure 10, which were used to calculate the maximum likelihood of planet-only transit models.
<figure><img src="image_11.png" /><figcaption>**Figure 7.** Three-body orbital stability map for a system consisting of HIP 41378, planet f, and planet f's satellite, as a function of planetary eccentricity, *e*<sub>f</sub>, and satellite semimajor, axis *a*<sub>s</sub> (expressed in terms of the Hill radius, *R*<sub>H</sub>). The color of each grid cell corresponds to the fraction *f*<sub>stab</sub> of 25 simulations within each cell (indicated by the black points) that survive over 10<sup>5</sup> yr. The stability limit determined by Rosario-Franco et al. (2020), shown as the dashed line, indicated good agreement with our simulations at low eccentricities.</figcaption></figure>

**Appendix B**
**Additional Figures**

Here we present additional figures that supplement the main text. Figure 8 shows the posterior distributions derived from our nested sampling analysis of the HST white light curve shown in Figure 5—maximum likelihood values from the posteriors were used to compute the planet-only model therein.

Figure 9 shows additional observations of HIP 41378 f from K2 Campaigns 5 and 18, along with simulated data of a single transit event from the upcoming PLATO mission. The posterior distributions derived from nested sampling analyses of the K2 light curves are shown in Figure 10, which were used to calculate the maximum likelihood of planet-only transit models.
<figure><img src="image_10.png" /><figcaption>**Figure 8.** HST white light curve posterior distributions for the planet-only model shown in Figure 5.</figcaption></figure>
<figure><img src="image_12.png" /><figcaption>**Figure 8.** HST white light curve posterior distributions for the planet-only model shown in Figure 5.</figcaption></figure>
<figure><img src="image_11.png" /><figcaption>**Figure 9.** Top: K2 transit light curve for HIP 41378 f from Campaigns 5 (blue points) with best-fit planet-only model (red dashed line). As in Figure 5, additional models with injected signals from a 0.53 R<sub>⊕</sub> moon and an Earth-size moon are shown by the black solid line and dashed-dotted line. The inset panel shows a zoomed-in view near mid-transit, demonstrating that the effects of moons are below the noise level of the data. Note that the 15 ppm difference in mid-transit flux between the moon-free and 0.53 R<sub>⊕</sub> moon cases is slightly greater in the K2 bandpass than the HST bandpass (Figure 5) due to differences in the stellar limb-darkening coefficients. Middle: Same as the top panel, but with data from K2 Campaign 18. Short-cadence data are shown by the transparent points, while the opaque points have been binned to match the long-cadence data. Bottom: Simulated 10 minute cadence PLATO data for a single transit of HIP 41378 f assuming the presence of no moon (red points) and an Earth-size moon (black points). The underlying *Pandora* models for each case are shown by the lines with corresponding colors, and a zoomed-in view near mid-transit is shown in the inset panel.</figcaption></figure>
<figure><img src="image_13.png" /><figcaption>**Figure 9.** Top: K2 transit light curve for HIP 41378 f from Campaigns 5 (blue points) with best-fit planet-only model (red dashed line). As in Figure 5, additional models with injected signals from a 0.53 R<sub>⊕</sub> moon and an Earth-size moon are shown by the black solid line and dashed-dotted line. The inset panel shows a zoomed-in view near mid-transit, demonstrating that the effects of moons are below the noise level of the data. Note that the 15 ppm difference in mid-transit flux between the moon-free and 0.53 R<sub>⊕</sub> moon cases is slightly greater in the K2 bandpass than the HST bandpass (Figure 5) due to differences in the stellar limb-darkening coefficients. Middle: Same as the top panel, but with data from K2 Campaign 18. Short-cadence data are shown by the transparent points, while the opaque points have been binned to match the long-cadence data. Bottom: Simulated 10 minute cadence PLATO data for a single transit of HIP 41378 f assuming the presence of no moon (red points) and an Earth-size moon (black points). The underlying *Pandora* models for each case are shown by the lines with corresponding colors, and a zoomed-in view near mid-transit is shown in the inset panel.</figcaption></figure>
<figure><img src="image_12.png" /><figcaption>**Figure 10.** (a) K2 C5 light curve posterior distributions for the planet-only model shown in the top panel of Figure 9. (b) K2 C18 light curve posterior distributions for the planet-only model shown in the middle panel of Figure 9.</figcaption></figure>

## ORCID iDs

Caleb K. Harada https://orcid.org/0000-0001-5737-1687

Courtney D. Dressing https://orcid.org/0000-0001-8189-0233

Munazza K. Alam https://orcid.org/0000-0003-4157-832X

James Kirk https://orcid.org/0000-0002-4207-6615

Mercedes López-Morales https://orcid.org/0000-0003-3204-8183

Kazumasa Ohno https://orcid.org/0000-0003-3290-6758

Babatunde Akinsanmi https://orcid.org/0000-0001-6519-1598

Susana C. C. Barros https://orcid.org/0000-0003-2434-3625

Lars A. Buchhave https://orcid.org/0000-0003-1605-5666

A. Collier Cameron https://orcid.org/0000-0002-8863-7828

Fei Dai https://orcid.org/0000-0002-8958-0683

Peter Gao https://orcid.org/0000-0002-8518-9601

Steven Giacalone https://orcid.org/0000-0002-8965-3969

Salomé Grouffal https://orcid.org/0000-0002-2805-5869

Jorge Lillo-Box https://orcid.org/0000-0003-3742-1987

Andrew W. Mayo https://orcid.org/0000-0002-7216-2135

Annelies Mortier https://orcid.org/0000-0001-7254-4363

Alexandre Santerne https://orcid.org/0000-0002-3586-1316

Nuno C. Santos https://orcid.org/0000-0003-4422-2919

Sérgio G. Sousa https://orcid.org/0000-0001-9047-2965

Emma V. Turtelboom https://orcid.org/0000-0002-1845-2617

Andrew Vanderburg https://orcid.org/0000-0001-7246-5438

Peter J. Wheatley https://orcid.org/0000-0003-1452-2240

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<figure><img src="image_14.png" /><figcaption>**Figure 10.** (a) K2 C5 light curve posterior distributions for the planet-only model shown in the top panel of Figure 9. (b) K2 C18 light curve posterior distributions for the planet-only model shown in the middle panel of Figure 9.</figcaption></figure>

## ORCID iDs

Caleb K. Harada https://orcid.org/0000-0001-5737-1687

Courtney D. Dressing https://orcid.org/0000-0001-8189-0233

Munazza K. Alam https://orcid.org/0000-0003-4157-832X

James Kirk https://orcid.org/0000-0002-4207-6615

Mercedes López-Morales https://orcid.org/0000-0003-3204-8183

Kazumasa Ohno https://orcid.org/0000-0003-3290-6758

Babatunde Akinsanmi https://orcid.org/0000-0001-6519-1598

Susana C. C. Barros https://orcid.org/0000-0003-2434-3625

Lars A. Buchhave https://orcid.org/0000-0003-1605-5666

A. Collier Cameron https://orcid.org/0000-0002-8863-7828

Fei Dai https://orcid.org/0000-0002-8958-0683

Peter Gao https://orcid.org/0000-0002-8518-9601

Steven Giacalone https://orcid.org/0000-0002-8965-3969

Salomé Grouffal https://orcid.org/0000-0002-2805-5869

Jorge Lillo-Box https://orcid.org/0000-0003-3742-1987

Andrew W. Mayo https://orcid.org/0000-0002-7216-2135

Annelies Mortier https://orcid.org/0000-0001-7254-4363

Alexandre Santerne https://orcid.org/0000-0002-3586-1316

Nuno C. Santos https://orcid.org/0000-0003-4422-2919

Sérgio G. Sousa https://orcid.org/0000-0001-9047-2965

Emma V. Turtelboom https://orcid.org/0000-0002-1845-2617

Andrew Vanderburg https://orcid.org/0000-0001-7246-5438

Peter J. Wheatley https://orcid.org/0000-0003-1452-2240

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Akinsanmi, B., Barros, S. C. C., Santos, N. C., et al. 2019, A&A, 621, A117

Akinsanmi, B., Santos, N. C., Faria, J. P., et al. 2020, A&A, 635, L8

Alam, M. K., Kirk, J., Dressing, C. D., et al. 2022, ApJL, 927, L5

Alvarado-Montes, J. A., Zuluaga, J. I., & Sucerquia, M. 2017, MNRAS, 471, 3019

Astropy Collaboration, Price-Whelan, A. M., Sipőcz, B. M., et al. 2018, AJ, 156, 123

Astropy Collaboration, Robitaille, T. P., Tollerud, E. J., et al. 2013, A&A, 558, A33

Barnes, J. W., & O'Brien, D. P. 2002, ApJ, 575, 1087

Barnes, R. 2017, CeMDA, 129, 509

Barros, S. C. C., Akinsanmi, B., Boué, G., et al. 2022, A&A, 657, A52

Becker, J. C., Vanderburg, A., Rodriguez, J. E., et al. 2019, AJ, 157, 19

Belkovski, M., Becker, J., Howe, A., Malsky, I., & Batygin, K. 2022, AJ, 163, 277

Berardo, D., Crossfield, I. J. M., Werner, M., et al. 2019, AJ, 157, 185

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

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