Constraining the Presence of Companion Planets in Hot Jupiter Planetary System Using TTV Observation from TESS

Zixin Zhang School of Physics and Astronomy, Sun Yat-sen University, Zhuhai 519082, China CSST Science Center for the Guangdong-HongKong-Macau Great Bay Area, Sun Yat-sen University, Zhuhai 519082, China Wenqin Wang School of Physics and Astronomy, Sun Yat-sen University, Zhuhai 519082, China CSST Science Center for the Guangdong-HongKong-Macau Great Bay Area, Sun Yat-sen University, Zhuhai 519082, China Xinyue Ma School of Physics and Astronomy, Sun Yat-sen University, Zhuhai 519082, China CSST Science Center for the Guangdong-HongKong-Macau Great Bay Area, Sun Yat-sen University, Zhuhai 519082, China Zhangliang Chen School of Physics and Astronomy, Sun Yat-sen University, Zhuhai 519082, China CSST Science Center for the Guangdong-HongKong-Macau Great Bay Area, Sun Yat-sen University, Zhuhai 519082, China Yonghao Wang Hainan University, China Cong Yu School of Physics and Astronomy, Sun Yat-sen University, Zhuhai 519082, China CSST Science Center for the Guangdong-HongKong-Macau Great Bay Area, Sun Yat-sen University, Zhuhai 519082, China Shangfei Liu School of Physics and Astronomy, Sun Yat-sen University, Zhuhai 519082, China CSST Science Center for the Guangdong-HongKong-Macau Great Bay Area, Sun Yat-sen University, Zhuhai 519082, China Yang Gao School of Physics and Astronomy, Sun Yat-sen University, Zhuhai 519082, China CSST Science Center for the Guangdong-HongKong-Macau Great Bay Area, Sun Yat-sen University, Zhuhai 519082, China Baitian Tang School of Physics and Astronomy, Sun Yat-sen University, Zhuhai 519082, China CSST Science Center for the Guangdong-HongKong-Macau Great Bay Area, Sun Yat-sen University, Zhuhai 519082, China Bo Ma School of Physics and Astronomy, Sun Yat-sen University, Zhuhai 519082, China CSST Science Center for the Guangdong-HongKong-Macau Great Bay Area, Sun Yat-sen University, Zhuhai 519082, China Bo Ma [email protected]

Abstract

The presence of another planetary companion in a transiting exoplanet system can impact its transit light curve, leading to sinusoidal transit timing variations (TTV). By utilizing both $\chi^{2}$ and RMS analysis, we have combined the TESS observation data with an N-body simulation to investigate the existence of an additional planet in the system and put a limit on its mass. We have developed CMAT, an efficient and user-friendly tool for fitting transit light curves and calculating TTV with a theoretical period, based on which we can give a limit on its hidden companion’s mass. We use 260 hot Jupiter systems from the complete TESS data set to demonstrate the use of CMAT. Our findings indicate that, for most systems, the upper mass limit of a companion planet can be restricted to several Jupiter masses. This constraint becomes stronger near resonance orbits, such as the 1:2, 2:1, 3:1, and 4:1 mean motion resonance, where the limit is reduced to several Earth masses. These findings align with previous studies suggesting that a lack of companion planets with resonance in hot Jupiter systems could potentially support the high eccentricity migration theory. Additionally, we observed that the choice between $\chi^{2}$ or root mean square (RMS) method does not significantly affect the upper limit on companion mass; however, $\chi^{2}$ analysis may result in weaker restrictions but is statistically more robust compared to RMS analysis in most cases.

Hot Jupiter – Exoplanet – Transit – Transit Timing

^†^†facilities: TESS^†^†software: PyTransit, CMAT, REBOUND, Astroquery

1 Introduction

Hot Jupiters are exoplanets akin to Jupiter in mass and size but distinct due to their short orbital periods of less than 10 days, orbiting very close to their host stars (Dawson & Johnson, 2018). The large sizes and short orbital periods make them the most easily studied targets using the transit technique. Despite being the first type of exoplanet discovered orbiting a sun-like star (Mayor & Queloz, 1995), the origin of hot Jupiters remains a mystery. Several competing theories attempt to explain their formation: in-situ formation (Batygin et al., 2016; Dawson & Johnson, 2018), disk migration (Goldreich & Tremaine, 1980; Lin & Papaloizou, 1986; Lin et al., 1996; Ward, 1997; Kley & Nelson, 2012) and high-eccentricity migration (Fa & Eb, 1996; Trilling et al., 1998; Wu & Murray, 2003).

In the high-eccentricity migration scenario, a cold Jupiter is launched to eccentric orbits through dynamical interactions with other planets/stars, followed by tidal friction that can shrink and circularize its orbit over a long period. Since this process is usually dynamically hot, hot Jupiters formed through this channel are likely isolated without any resonant companion planets. Therefore, the presence of a nearby planetary companion has long been considered evidence against the high eccentricity migration theory. Recent research, however, has observed some hot Jupiters with nearby companions, challenging the high eccentricity migration theory (Zhu & Dong, 2021; Wu et al., 2023).

In multi-planet systems, mutual gravitational perturbations can alter the times of transit. Thus, transit timing variations (TTVs) are a powerful tool for characterizing planets in multi-planet systems (Holman & Murray, 2005; Agol et al., 2005; Lithwick et al., 2012). For example, it has been used for measuring masses and eccentricities of planets (Hadden & Lithwick, 2014, 2016, 2017). This is because the TTV amplitude is directly proportional to the perturber’s mass (Lithwick et al., 2012), and the TTV period and phase are related to the perturber’s orbital eccentricity. Because of the well-known degeneracy between mass and eccentricity, TTVs alone cannot accurately determine the companion planet’s mass. Nevertheless, the phases and amplitudes of TTVs can be used to establish upper limits on the masses of companion planetary candidates (Xie, 2013; Wang et al., 2021).

Launched in 2018, the Transiting Exoplanet Survey Satellite (TESS, Ricker et al., 2014) succeeded the Kepler space telescope, aiming to enhance our knowledge of exoplanets through the transit method. TESS’s wide field of view and high photometric accuracy make it particularly effective for studying hot Jupiters. It can survey nearly the entire sky and detect subtle brightness changes as low as 20 parts per million (ppm) for a magnitude 12 star with a 2-minute exposure. These capabilities make TESS an excellent tool for detecting hot Jupiters, significantly advancing exoplanetary research. Studying TTVs of a large sample of hot Jupiters using TESS data can put additional constraints on the hot Jupiter’s nearby companion planet and its formation channel. The short orbital periods and large radii of hot Jupiters make them ideal targets for TTV analysis. With accurate TTV measurements from TESS, we can constrain the presence of nearby companions and potentially shed light on the formation of hot Jupiters.

Here in this paper, we employ TTV analysis and numerical three-body simulations to constrain the presence of additional planets around 260 hot Jupiters using TESS observation data. This approach allows us to establish the upper mass limit of potential companion planets and provides insight into whether the hot Jupiter is situated in an isolated system. Our research builds upon the foundational work of Wang et al. (2018a, 2021), who investigated Transit Timing Variations (TTVs) in 39 hot Jupiter systems. Utilizing 127 new transit light curves from two ground-based telescopes, they were able to impose significant constraints on the presence of nearby companions. Despite these contributions, the sample sizes in these studies remain relatively modest, and the constraints they impose on the masses of hidden companions are less stringent compared to this study. In this work, we also introduce CMAT(Zhang, 2024)¹¹1Available at https://github.com/troyzx/CMAT, a Python package developed to analyze TTVs and establish the upper mass limit of planetary companions orbiting hot Jupiters.

This paper is structured as follows. Section 2 provides an overview of the data used in this study. In Section 3, we outline our methodology for analyzing TTVs of hot Jupiters and determining the upper mass limits of their companion planets. Our results and findings are described in Section 4. Comparisons with previous studies and the broader implications for hot Jupiter formation are discussed in Section 5. A summary of our findings is provided in Section 6.

2 Data and Observation

The data for this study are taken from the TESS observations. We select transiting hot Jupiters observed by TESS based on the following criteria: an orbital period of less than 10 days and a mass greater than 0.3 $\mathrm{M_{J}}$ . This results in a sample of 260 hot Jupiter systems, the largest sample size used in such a study to date.

Refer to caption — Figure 1: Orbital periods and radii of 260 hot Jupiter systems, the majority of which have orbital periods between 2-6 days and radii between 0.8-1.6 Jupiter radii

The HJ system parameters, as shown in Figure 1, reveal that most hot Jupiters have a radius between 0.8 and 1.6 Jupiter radii and an orbital period ranging from 1 to 10 days. Further discussions on how the parameters of hot Jupiters can affect the mass of their companions can be found in Section 4. The properties of the host stars in our sample are presented in Figure 2. Most of the host stars have masses ranging from 0.8 to 2.0 solar masses, radii ranging from 0.6 to 3 solar radii, and effective temperatures in the range of 5000 to 8000 K.

We use Astroquery (Ginsburg et al., 2017) to retrieve the TESS data products for hot Jupiters generated by the SPOC pipeline (Jenkins et al., 2016a) from MAST (Brasseur & Donaldson, 2020; Team, 2021). To ensure that we can obtain high-precision measurements of TTV, we included only systems with a minimum of 3 transits covered by TESS observations. Furthermore, we obtained these systems’ parameters from the NASA Exoplanet Archive (Akeson et al., 2013), including stellar mass, planetary mass, and orbital period. Figure 3 displays the number of transits in the data we used from TESS observations for our sample of 260 hot Jupiter systems. While the majority of systems have fewer than 100 transits, some exceed this number, with one system having more than 200 transits, namely Qatar-10 b (Alsubai et al., 2019).

The presearch data conditioning simple aperture photometry (PDCSAP, Stumpe et al., 2012; Smith et al., 2012b; Stumpe et al., 2014) light curves from SPOC (Jenkins et al., 2016b) with 2 minute time sampling (“cadence”) are used in this analysis, where common instrumental systematics have been removed. To ensure the quality of the light curves, we also remove any outlier data points with a quality flag $>0$ . Subsequently, we normalized the light curves to account for the varying brightness levels of different stars. Following this, we used our CMAT tool to fit the transit light curves and calculate the mid-transit times of HJs, which will be detailed in the next section.

3 Method

In this section, we present our TTV analysis method. Initially, we evaluate the TTVs by determining the amplitude caused by the companion. Subsequently, precise transit times are calculated from the TESS time series data, and adjustments for TTV are made based on a linear fit of the transit times. A dynamic simulation of the system is conducted to replicate observations and generate simulated TTVs using the transit light curve of the hot Jupiter. Finally, we combine the observed and simulated TTVs ( $\mathrm{TTV}_{\mathrm{observed}}$ and $\mathrm{TTV}_{\mathrm{simulated}}$ ) using $\chi^{2}$ and RMS analysis to calculate an upper mass limit for the companion. Figure 4 illustrates the flowchart of our TTV analysis method.

3.1 TTV from Light-curve Analysis

We derive the transit mid-time data of hot Jupiters using TESS data and Pytransit, similar to our previous studies in Wang et al. (2024). Pytransit is a Python package designed to fit transit light curves (Parviainen, 2015). It employs the Mandel-Agol model to fit transit light curves and then uses differential evolution and the Markov Chain Monte Carlo (MCMC) method to optimize the fit for stellar and orbital parameters, namely transit midtime, orbital period, planet radius in the unit of star radius, stellar density, and impact factor. Figure 5 presents the corner plot derived from the MCMC fitting of WASP-142 b’s orbital parameters.

We adapted the Pytransit code to calculate precise transit times and periods for each transit. These values were then aggregated and fitted using a linear model to determine predicted transit times. TTVs were calculated by subtracting the actual transit times from the predicted transit times based on this linear model.

Figure 6 displays the cumulative probability distribution of RMS of TTV calculated from TESS observation data for our 260 hot Jupiter systems sample. The graph shows that all of them have an RMS of less than 150 seconds, with over 80% of the systems having an RMS of less than 50 seconds.

WASP-142 b, a hot Jupiter, has an orbital period of 2.05 days and a radius of 1.53 Jupiter radii. It orbits an F-type star, 1.33 times the mass of the Sun (Hellier et al., 2017). Figure 7 illustrates the TTV of WASP-142 b calculated by our method. The blue line represents the TTV obtained from two separate observation data sets, while the yellow line shows a zoomed-in view for each observation. The total RMS of all observations is 40 seconds, with individual observations having an RMS of 43 and 36 seconds respectively. The graph shows that there are two distinct data sets, and the RMS of each observation is close to one another, as well as the total RMS.

3.2 TTV from Dynamical simulation

We employ the rebound package (Rein & Liu, 2012; Rein & Spiegel, 2015) to simulate the TTV of a hot Jupiter when an additional companion planet is present in the planetary system. The orbit of the additional companion planet is set to be coplanar and circular. As discussed by Agol & Deck (2016), the coplanar and circular configuration induces smaller TTVs compared with non-coplanar or eccentric orbits. Therefore we can obtain a conservative estimate of the companion planets’ upper mass limits. We have explored the period ratio of an additional companion planet and hot Jupiter from 0.1 to 4.0. The companion planets’ masses are set to vary between 0.01 and $10^{5}$ Earth masses ( $\mathrm{M_{\oplus}}$ ). The simulation is carried out in a parameter space grid of 300 by 300, where the companion planet mass is in log space. We set the system integration time to match the duration of the TESS observation data for each HJ system. To encompass all possible coplanar and circular orbital configurations, we have varied the initial orbital phase difference between the HJ and the additional planet at the time of the first HJ transit recorded by TESS from 0 to $2\pi$ , using a phase step of $\pi/6$ .

Additionally, we also compute the Mean Exponential Growth factor of Nearby Orbits (MEGNO) (Cincotta et al., 2003) to assess the dynamical stability of the simulated planetary system, as depicted in Figure 8. The MEGNO value is a measure of chaos in a dynamical system, with $\langle Y\rangle$ converging to 2 indicating a stable system. We integrated each system for 10000 orbits to test the stability of the system.

3.3 Constraints on Additional Planets

The presence of an additional planet in the transiting hot Jupiter system can perturb the hot Jupiter and generate significant TTV. To constrain the mass of the additional companion planet, we have employed two different methods, the $\chi^{2}$ method, and the RMS method, to compare the simulated TTV dataset with the observed TTV dataset. We will proceed to describe the specifics of these two methods next.

The $\chi^{2}$ test is a statistical tool that assesses the fit of a model to a dataset. It utilizes the chi-squared distribution, which adds up the squares of independent standard normal random variables. The $\chi^{2}$ can be expressed as:

\displaystyle\chi^{2}=\sum_{i}\left(\frac{O_{i}-E_{i}}{\sigma_{i}}\right)^{2},

(1)

where $O_{i}$ and $\sigma_{i}$ represent the measured mid-transit time from observation and corresponding uncertainty from Section 3.1, and $E_{i}$ represent the simulated mid-transit time values as described in Section 3.2.

RMS is a statistical measure of the dispersion of a set of data from its mean. The RMS method has been widely used to analyze the TTV observation data of hot Jupiters in the past. For instance, HAT-P-25 b is a hot Jupiter discovered by Quinn et al. (2011). Wang et al. (2018a) have utilized the RMS approach to establish the maximum mass limit of HAT-P-25 b’s companion and have ruled out any hidden long-period perturber with $M_{p}>0.5,0.3,$ and $0.5\mathrm{M_{\oplus}}$ near the 1:2, 2:1, and 3:1 resonances. It is calculated by taking the square root of the mean of the squared TTV values. The RMS value of TTVs from TESS observation and numerical simulation can be calculated as:

	$\displaystyle RMS_{\rm obs}=\sqrt{\frac{1}{n}\sum_{i=1}^{n}O_{i}^{2}},$		(2)
	$\displaystyle RMS_{\rm sim}=\sqrt{\frac{1}{n}\sum_{i=1}^{n}E_{i}^{2}}.$		(3)

After obtaining the TTV data from both observations ( $O_{i}$ ) and simulations ( $E_{i}$ ), we calculated the RMS and $\chi^{2}$ value for each HJ system. The upper mass limit of any companion planet was then established by comparing the simulated TTV data with observed TTV data using either the RMS method or the $\chi^{2}$ method. For each period ratio, we reduced the potential companion’s mass until the RMS value from the simulation ( $RMS_{\rm sim}$ ) fell below the RMS value from the TESS observation ( $RMS_{\rm obs}$ ), or the $\chi^{2}$ value fell below the 3- $\sigma$ critical threshold. The result for WASP-142 b is illustrated in Figure 8 as an example. The red dashed line and white solid line indicate, respectively, the upper mass limit of a potential hidden companion around WASP-142 b as determined by $\chi^{2}$ and RMS analysis. The background color corresponds to MEGNO values calculated from the REBOUND simulations.

For seven HJ systems in our sample (HAT-P-59 b, KELT-8 b, KELT-24 b, WASP-62 b, WASP-160 B b, WASP-170 b, and XO-6 b), none of the simulated TTVs using a three-body model using parameters in our grid can match the observed TTV data. There are two possible explanations for this discrepancy. One is that we may have underestimated the measurement errors in the observational data, possibly due to unknown systematics. The other is that underlying physical processes in the HJ systems may be causing the observed TTVs to deviate from the predictions of a simple three-body model. As a result, we are unable to place meaningful constraints on the companion planets using the $\chi^{2}$ method for these seven systems (see also Figure 12), and we encourage further TTV follow-up studies of these seven systems.

3.4 CMAT

Here we introduce Companion MAss from Transit timing variation (CMAT), a Python package designed to calculate the TTV of hot Jupiter systems and establish the upper mass limit of their hidden planetary companions. We aim to provide a user-friendly tool for determining the upper mass limit of hidden planetary companions by analyzing high-precision lightcurve data. CMAT utilizes the MCMC method to accurately compute transit mid-times and TTVs based on input transit time series data. By evaluating $\chi^{2}$ and RMS values, it can identify the upper mass limit of any hidden planetary companion. The package can also automatically retrieve time series data from exo.MAST. To enhance its performance, we integrated multiprocessing into the package via the joblib package (Joblib Development Team, 2020). Multiprocessing significantly reduces the time required for the time-intensive computation of TTV. For instance, analyzing an observation of 100 transits takes approximately 2 minutes with 96 threads. We also plan to incorporate additional features in future updates.

For testing purposes, we used CMAT to analyze 32 sources from Wang et al. (2021). Our results align with their findings, demonstrating that CMAT is a dependable tool for analyzing TTV data and establishing the upper mass limit of concealed planetary companions.

4 Result

In this study, we have analyzed 260 hot Jupiter systems using our newly developed tool CMAT. Our findings indicate that for most systems, the upper mass limit of a hidden companion can be restricted to several Jupiter masses. This restriction becomes even stronger near resonance orbits such as 1:2, 2:1, 3:1, and 4:1, where we were able to limit the additional companion’s mass to just a few Earth masses.

Though some MMR or near-MMR systems have been discovered (Quinn et al., 2019), systematic searches by Lissauer et al. (2011) and Fabrycky et al. (2014) indicate that among the multiple planetary systems discovered, the vast majority are neither in nor near low-order mean-motion resonance systems. This aligns with our study’s findings, which show a sharp decrease in the upper mass of a companion planet near resonance, indicating a relatively low occurrence rate at these locations. These findings align with previous studies suggesting that a lack of companion planets with resonance in hot Jupiter systems could potentially support the high eccentricity migration theory. Additionally, we observed that the choice between $\chi^{2}$ or the RMS method does not significantly affect the upper limit on companion mass. However, $\chi^{2}$ analysis usually provides slightly weaker restrictions for the upper mass limit of companion planet compared to the RMS analysis but is statistically more robust.

We present the combined results for all our targets in Figure 9, which can be seen as a fold of Figure 8 for all 260 hot Jupiter systems. In Figure 8, each grid point’s color indicates the percentage of hot Jupiters in our sample that are capable of hiding companion planets with corresponding mass and period ratio. The solid lines on the plot indicate equal-percentage levels at around $10\%$ , $50\%$ , and $90\%$ , respectively. The left panel displays the statistical results from the $\chi^{2}$ method, and the right panel shows the results from the RMS method. Our results indicate that, for half of hot Jupiter systems in our sample, we can limit the mass of a hidden companion planet to just a few Earth masses near the 1:2 and 2:1 MMR. It is important to note that our dynamic simulation was based on a coplanar and circular hypothesis. This particular configuration results in smaller TTVs compared to non-coplanar or eccentric orbits, as discussed by Agol et al. (2005). Consequently, this approach yields a more conservative estimate of upper mass limits for the hidden companion planets. However, according to Xie et al. (2016), most multi-planet systems are coplanar and circular, aligning with our assumption.

We have found that specific systems in our sample, such as WASP-47 b, WASP-57 b, and WASP-60 b (see Figure 12), do not exhibit a significant reduction in the upper mass limit of a companion planet near resonance. This can be mainly attributed to the insufficient number of transits available for analysis for these targets, which results in a weaker constraint on the maximum mass of the potential companion planet. When more observation data are available in the future, we will be able to impose more stringent constraints on the mass of hidden companion planets in these systems.

We seek to find correlations between the upper mass limits of hidden companion planets with the HJ parameters in Figure 10. The primary planet’s orbital period ( $P$ ) and radius ( $R_{p}$ ) are divided into 15 $\times$ 5 bins, with logarithmic spacing for the orbital period. The color coding indicates the median maximum mass limit in Earth/Jupiter mass for the hidden companions near resonance ratios of 1:2, 2:1, and 3:1 (from top to bottom). We have calculated the Pearson correlation coefficients between the companion’s upper mass limits near the resonance ratios and the HJ’s radii and orbital periods. The results indicate that no significant correlation was found within the currently available dataset. However, there is a lack of HJs in the top-right corner bins of Figure 10, and future data in these bins could potentially alter the correlation results.

Our results provide valuable insights into the dynamics of hot Jupiter systems and their hidden companions, contributing to the ongoing debate on the origin of hot Jupiters.

5 Discussion

5.1 Comparison with Previous Studies

In this subsection, we compare our findings with those of previous studies utilizing TTV methods to investigate companion planets near hot Jupiter.

Holman et al. (2006) launched the Transit Light Curve (TLC) project to create a collection of precise transit photometry data. The goal is to improve system parameters and detect variations in transit times and light-curve shapes that could suggest the presence of extra planets (Chan et al., 2011; Fernandez et al., 2009; Holman et al., 2007a, b; Winn et al., 2007a, b, c, d, 2008b, 2008a, 2009a, 2009b). In one of the TLC series papers, Carter et al. (2011) used the TTV method on GJ 1214b to rule out the presence of a companion planet with a mass exceeding 0.004 and 0.01 $\mathrm{M_{\oplus}}$ near 1:2 and 2:1 resonances, respectively. Gibson et al. (2010) studied the TTV of HAT-P-3 b and established upper mass limits of 0.33 and 1.81 Earth masses for a hypothetical planetary companion in 1:2 and 2:1 resonances, respectively. By comparison, we have improved upon their constraint by taking upper mass limits down to 0.1 Earth masses at both resonance positions shown in Section 4. The exploration of Kepler data by Steffen et al. (2012) found no significant TTV signal of a nearby companion planet in 63 Kepler hot Jupiter systems. Nevertheless, a photometric analysis successfully excluded companions with masses ranging from about 2/3 to 5 times that of Earth.

The Transit Monitoring in the South project (TraMoS, Hoyer et al., 2012) did not detect any TTV RMS variations exceeding 1 minute over a span of 3 years for the hot Jupiter WASP-5 b, and ruled out the existence of planets with masses greater than 5 $\mathrm{M_{\oplus}}$ and 2 $\mathrm{M_{\oplus}}$ near the 1:2 and 2:1 resonances, respectively. Their subsequent study of WASP-4 b (Hoyer et al., 2013) excluded companions with masses exceeding 2.5 and 1.0 $\mathrm{M_{\oplus}}$ near the 1:2 and 2:1 resonances, respectively. Their most recent study of WASP-19 b (Cortés-Zuleta et al., 2020) ruled out companions with masses greater than 0.26 and 2.8 $\mathrm{M_{\oplus}}$ near the 1:2 and 2:1 resonances, respectively. Our study has narrowed down these limits in most cases, reaching as low as 0.39 $\mathrm{M_{\oplus}}$ and 1.35 $\mathrm{M_{\oplus}}$ near these resonances, except for the 2:1 resonance of WASP-19 b.

The TEMP project (Wang et al., 2018a) aims to study TTV signals of hot Jupiter systems using ground-based telescopes. Using data from ground-based telescopes, they have excluded companions with masses above 0.6 and 0.4 $\mathrm{M_{\oplus}}$ for HAT-P-29 b (Wang et al., 2018a), and 0.5 and 0.3 $\mathrm{M_{\oplus}}$ for HAT-P-25 b (Wang et al., 2018b) near the 1:2 and 2:1 resonances, respectively. Our study only narrows down this limit to tens of Earth masses near these resonances for both systems due to the small number of transits observed by the TESS mission. The TEMP team also investigated the HAT-P-33 b system (Wang et al., 2017), ruling out a perturber with a mass exceeding 0.6 and 0.3 $\mathrm{M_{\oplus}}$ near the 1:2 and 2:1 resonances, respectively. With an adequate number of transits, we have managed to refine this limit to as low as 0.16 and 1.09 $\mathrm{M_{\oplus}}$ near these resonances. In their most recent research, the TEMP team analyzed 39 hot Jupiter systems, excluding companions with masses greater than $0.39-5.0\ \mathrm{M_{\oplus}}$ and $0.69-6.75\ \mathrm{M_{\oplus}}$ near the 1:2 and 2:1 resonances (Wang et al., 2021). Our work has further enhanced this constraint by narrowing the lower end down to as small as 0.05 $\mathrm{M_{\oplus}}$ near these resonances.

In summary, our study has expanded the sample size compared to previous studies on Transit Timing Variations (TTV) of hot Jupiters and generally establishes lower upper mass limit values compared to prior research. With the largest sample size to date, our study enables us to provide the most robust and statistically significant assessment of the upper mass limit for hidden planetary companions in hot Jupiter systems.

5.2 Eccentricity and Inclination

Since multi-planet transiting systems usually have nearly circular orbits and small mutual inclinations, we have used coplanar approximation to put constraints on additional companion planets in the hot Jupiter system in Section 3.2. However, it is important to note that TTV signal can be signiﬁcantly ampliﬁed for hierarchical planetary systems with substantial orbital inclinations and/or for an eccentric transiting planet with the anti-aligned orbit of the planetary companion (Holman & Murray, 2005; Nesvorný, 2009; Agol & Deck, 2016; Kubiak et al., 2023). These studies indicate that our reliance on coplanar and circular assumptions may lead to an underestimation of the TTV effects induced by an eccentric and/or inclined hidden companion, consequently resulting in a more conservative upper mass limit estimate. If non-coplanar and eccentric orbits are adopted for the concealed companion planet in the hot Jupiter system, we anticipate a decrease in the upper mass limits depicted in Figure 9. In our future work, we plan to consider both inclination and eccentricity to explore the possibility of non-coplanar or non-circular-orbital companions.

5.3 HJs with Known Companion Planets

Several HJ systems in our sample have known companion planets, including WASP-47, WASP-84, and WASP-132 (Bryant & Bayliss, 2022; Maciejewski et al., 2023; Grieves et al., 2024). We show their results in Figure 11. We find all four known companion planets are sitting below the upper limits derived using simple three-body simulations presented in Section 3, which in part validates the effectiveness of our method. Thus, we have kept these three HJ systems in our group study presented in Figure 9 and Figure 10. However, we do want to note here that our study assumes a simple three-body model. And for systems like WASP-47, where there is one star and at least three known planets, our method does not necessarily apply. A four- or five-body model is required to put more precise constraints on additional unknown companion planets in these systems, which is beyond the scope of this work.

Among these three HJ systems, Becker et al. (2015) have detected a TTV variation of WASP-47 b with an amplitude of $0.63\pm 0.10$ mins and a period of $\sim 53$ days using data from the Kepler mission. Bryant & Bayliss (2022) and Nascimbeni et al. (2023) have studied the TTVs of WASP-47 b using TESS and CHEOPS data. Similar to the study by Bryant & Bayliss (2022), we can not confirm this variation using TESS data alone due to the larger timing noise (about 1 minute) and short time coverage (around 20 days).

5.4 Formation Theories of Hot Jupiters

We will discuss the implications of our results for the study of hot Jupiter formation theories in this section. Through the TTV analysis, hidden planetary companions of hot Jupiters can be detected or their existence ruled out. And the constraints become more stringent near resonance orbits. Thus, our findings can be used to constrain theoretical models used to generate hot Jupiter systems. Giant planets are more likely to form at larger separations, beyond the ice line of the star, where dust production is enhanced, before migrating inwards (Kokubo & Ida, 2002). Studying the existence and distribution of planetary companions in hot Jupiter systems can offer valuable insights into the migration mechanisms of these planets, which are a key aspect of their formation and evolution (Wu et al., 2023; Zink & Howard, 2023). Several popular migrating scenarios proposed by previous studies include high eccentricity migration and disk migration. In the high eccentricity migration scenario, planet-planet scattering (Fa & Eb, 1996; Chatterjee et al., 2008; Beaugé & Nesvorný, 2012), Kozai–Lidov effect (Wu & Murray, 2003; Naoz et al., 2012; Petrovich & Tremaine, 2016; Vick et al., 2019), and secular dynamics (Wu & Lithwick, 2011; Petrovich, 2015) have been invoked to circularize and shrink the orbits of hot Jupiters.

Resonance chains could be common, as giant planets may have captured terrestrial planets in such chains during migration. Multiple systems have been found in this type of resonance chain (Tinney et al., 2006), supporting the disk migration theory. If a hot Jupiter has migrated to its current position through high eccentricity migration, there should be no/few companions nearby (Mustill et al., 2015). Therefore, detecting a high percentage of hidden companions near the resonance orbits of hot Jupiters would favor the disk migration theory over the high eccentricity migration theory, or vice versa. Currently, several population synthesis studies have been carried out to study the formation of exoplanets (Mordasini et al., 2009a, b; Alibert et al., 2011; Mordasini et al., 2012; Emsenhuber et al., 2021a, b; Schlecker et al., 2021a; Burn et al., 2021; Schlecker et al., 2021b; Mishra et al., 2021). Results from similar population synthesis studies in the future for HJs can be used to directly compare with our statistical results.

Here, we propose two ways to utilize our findings for testing planetary formation models. The first one involves generating a synthetic population of hot Jupiters using a planetary population synthesis model. We then identify those with hidden companions in the vicinity of MMR. By comparing their mass distribution with our results, we can assess the feasibility of the HJ formation model. The second one also involves generating a synthetic population of hot Jupiters. We can then perform a statistical analysis of the synthetic population to obtain the percentages of hot Jupiters with companion planets above the three percentage lines shown in Figure 9. If any of the three percentages from the synthetic population is larger than the corresponding percentage (90 $\%$ , 50 $\%$ , or 10 $\%$ ) of the three solid lines, which means there are too many HJ systems with companion planets from theory than from observation, we can then infer that the formation model is inconsistent with observations.

A potential source of statistical bias arises from the fact that the discovery of hot Jupiters may favor systems with weak interactions, resulting in smaller transit timing variations (TTVs). Large TTVs might hinder the detection of hot Jupiters using detection algorithms such as the Box-fitting Least Squares (BLS) method. However, given the large transit depths of hot Jupiters, this bias is expected to be minimal. Future studies on TTVs of smaller planets should consider and adjust for this potential bias to ensure accuracy.

6 Summary and Conclusion

The study of hot Jupiters and their companion planets is an active research field in exoplanet science. Here we investigate the existence of additional planets in 260 hot Jupiter systems by analyzing transit timing variations observed by the TESS mission. The use of our newly developed CMAT tool, which combines observation data with numerical N-body simulations using $\chi^{2}$ and RMS analysis, has enabled us to provide more stringent constraints on the mass of the hidden companions than previous studies. This is particularly evident near resonance orbits, where we have been able to limit the companion planet mass to just a few Earth masses. These findings not only enhance our understanding of the dynamics of hot Jupiter systems but also provide valuable insights into the processes of planet formation and migration. The absence of resonant companion planets in hot Jupiter systems, as revealed by our study, lends support to the high eccentricity migration theory, contributing to the ongoing debate on the origin of hot Jupiters. We also note that $\chi^{2}$ analysis, while less restrictive, offers a statistically robust approach compared to RMS analysis.

Our work has pushed the boundaries of what is currently known about hot Jupiter systems and their hidden companions. With more high precision transit time data becoming available in the future, such as from PLAnetary Transits and Oscillation of stars mission (PLATO, Rauer et al., 2014), the China Space Station Telescope (CSST, Zhan, 2011), and the Earth 2.0 mission (ET, Ge et al., 2022), we expect more detailed measurements leading to better comprehension of planetary system formation and evolution within our galaxy as well as beyond it.

We plan to extend our TTV study from hot Jupiters to short-period transiting brown dwarfs (BDs) to further investigate the differences between the hot Jupiter and brown dwarf populations, as highlighted by researchers such as Grether & Lineweaver (2006) and Ma & Ge (2014). For instance, Bowler et al. (2020) argued that high-mass brown dwarfs predominantly form similarly to stellar binaries, based on a comparison of the mass-eccentricity distributions of brown dwarfs and giant planets. Since TTV studies can help reveal the dynamic properties of brown dwarf systems, we believe that expanding TTV analysis to transiting BDs can provide additional observational evidence for distinct formation mechanisms. Therefore, we encourage our colleagues to continue monitoring the transits of both hot Jupiters and transiting brown dwarfs to enhance our understanding of these celestial objects.

Acknowledgements

We express our gratitude to the TESS mission for its outstanding contribution to exoplanet science. The precise transit-time measurements from TESS were instrumental in our study of TTVs in hot Jupiters. We thank NSFC grants 12073092, 12103097, and 12103098, the National Key R $\&$ D Program of China (2020YFC2201400), as well as the science research grants from the China Manned Space Project (No. CMS-CSST2021-B09) for their financial support. Additionally, we appreciate the valuable assistance of the NASA Exoplanet Archive, which granted us access to a vast amount of observational data and resources that greatly aided our research efforts. We also thank open-source software developers for their contributions to the scientific community.

References

Addison et al. (2016) Addison, B. C., Tinney, C. G., Wright, D. J., & Bayliss, D. 2016, ApJ, 823, 29, doi: 10.3847/0004-637X/823/1/29
Agol & Deck (2016) Agol, E., & Deck, K. 2016, ApJ, 818, 177, doi: 10.3847/0004-637X/818/2/177
Agol et al. (2005) Agol, E., Steffen, J., Sari, R., & Clarkson, W. 2005, Monthly Notices of the Royal Astronomical Society, 359, 567, doi: 10.1111/j.1365-2966.2005.08922.x
Akeson et al. (2013) Akeson, R. L., Chen, X., Ciardi, D., et al. 2013, PASP, 125, 989, doi: 10.1086/672273
Alibert et al. (2011) Alibert, Y., Mordasini, C., & Benz, W. 2011, Astronomy & Astrophysics, 526, A63, doi: 10.1051/0004-6361/201014760
Almenara et al. (2022) Almenara, J. M., Hébrard, G., Díaz, R. F., et al. 2022, A&A, 663, A134, doi: 10.1051/0004-6361/202142964
Alonso et al. (2008) Alonso, R., Auvergne, M., Baglin, A., et al. 2008, A&A, 482, L21, doi: 10.1051/0004-6361:200809431
Alsubai et al. (2018) Alsubai, K., Tsvetanov, Z. I., Latham, D. W., et al. 2018, AJ, 155, 52, doi: 10.3847/1538-3881/aaa000
Alsubai et al. (2019) Alsubai, K., Tsvetanov, Z. I., Pyrzas, S., et al. 2019, The Astronomical Journal, 157, 224, doi: 10.3847/1538-3881/ab19bc
Alsubai et al. (2019a) Alsubai, K., Tsvetanov, Z. I., Latham, D. W., et al. 2019a, AJ, 157, 74, doi: 10.3847/1538-3881/aaf80a
Alsubai et al. (2019b) Alsubai, K., Tsvetanov, Z. I., Pyrzas, S., et al. 2019b, AJ, 157, 224, doi: 10.3847/1538-3881/ab19bc
Alsubai et al. (2011) Alsubai, K. A., Parley, N. R., Bramich, D. M., et al. 2011, MNRAS, 417, 709, doi: 10.1111/j.1365-2966.2011.19316.x
Anderson et al. (2011) Anderson, D. R., Collier Cameron, A., Hellier, C., et al. 2011, A&A, 531, A60, doi: 10.1051/0004-6361/201016208
Anderson et al. (2013) Anderson, D. R., Collier, C. A., Gillon, M., et al. 2013, VizieR Online Data Catalog: Three short-period, transiting exoplanets (Anderson+, 2012), VizieR On-line Data Catalog: J/MNRAS/422/1988. Originally published in: 2012MNRAS.422.1988A
Anderson et al. (2014) Anderson, D. R., Collier Cameron, A., Delrez, L., et al. 2014, MNRAS, 445, 1114, doi: 10.1093/mnras/stu1737
Anderson et al. (2015) Anderson, D. R., Collier Cameron, A., Hellier, C., et al. 2015, A&A, 575, A61, doi: 10.1051/0004-6361/201423591
Anderson et al. (2017) Anderson, D. R., Collier Cameron, A., Delrez, L., et al. 2017, A&A, 604, A110, doi: 10.1051/0004-6361/201730439
Bakos et al. (2009) Bakos, G. Á., Howard, A. W., Noyes, R. W., et al. 2009, ApJ, 707, 446, doi: 10.1088/0004-637X/707/1/446
Bakos et al. (2011) Bakos, G. Á., Hartman, J., Torres, G., et al. 2011, ApJ, 742, 116, doi: 10.1088/0004-637X/742/2/116
Bakos et al. (2012) Bakos, G. Á., Hartman, J. D., Torres, G., et al. 2012, AJ, 144, 19, doi: 10.1088/0004-6256/144/1/19
Bakos et al. (2020) Bakos, G. Á., Bayliss, D., Bento, J., et al. 2020, AJ, 159, 267, doi: 10.3847/1538-3881/ab8ad1
Bakos et al. (2021) Bakos, G. Á., Hartman, J. D., Bhatti, W., et al. 2021, AJ, 162, 7, doi: 10.3847/1538-3881/abf637
Barge et al. (2008) Barge, P., Baglin, A., Auvergne, M., et al. 2008, A&A, 482, L17, doi: 10.1051/0004-6361:200809353
Barkaoui et al. (2019) Barkaoui, K., Burdanov, A., Hellier, C., et al. 2019, AJ, 157, 43, doi: 10.3847/1538-3881/aaf422
Barros et al. (2012) Barros, S. C. C., Pollacco, D. L., Gibson, N. P., et al. 2012, MNRAS, 419, 1248, doi: 10.1111/j.1365-2966.2011.19784.x
Barros et al. (2016) Barros, S. C. C., Brown, D. J. A., Hébrard, G., et al. 2016, A&A, 593, A113, doi: 10.1051/0004-6361/201526517
Batygin et al. (2016) Batygin, K., Bodenheimer, P. H., & Laughlin, G. P. 2016, The Astrophysical Journal, 829, 114, doi: 10.3847/0004-637X/829/2/114
Bayliss et al. (2013) Bayliss, D., Zhou, G., Penev, K., et al. 2013, AJ, 146, 113, doi: 10.1088/0004-6256/146/5/113
Bayliss et al. (2018) Bayliss, D., Gillen, E., Eigmüller, P., et al. 2018, MNRAS, 475, 4467, doi: 10.1093/mnras/stx2778
Beaugé & Nesvorný (2012) Beaugé, C., & Nesvorný, D. 2012, The Astrophysical Journal, 751, 119, doi: 10.1088/0004-637X/751/2/119
Becker et al. (2015) Becker, J. C., Vanderburg, A., Adams, F. C., Rappaport, S. A., & Schwengeler, H. M. 2015, ApJ, 812, L18, doi: 10.1088/2041-8205/812/2/L18
Bento et al. (2017) Bento, J., Schmidt, B., Hartman, J. D., et al. 2017, MNRAS, 468, 835, doi: 10.1093/mnras/stx500
Bento et al. (2018) Bento, J., Hartman, J. D., Bakos, G. Á., et al. 2018, MNRAS, 477, 3406, doi: 10.1093/mnras/sty726
Bieryla et al. (2014) Bieryla, A., Hartman, J. D., Bakos, G. Á., et al. 2014, AJ, 147, 84, doi: 10.1088/0004-6256/147/4/84
Bieryla et al. (2015) Bieryla, A., Collins, K., Beatty, T. G., et al. 2015, AJ, 150, 12, doi: 10.1088/0004-6256/150/1/12
Boisse et al. (2013) Boisse, I., Hartman, J. D., Bakos, G. Á., et al. 2013, A&A, 558, A86, doi: 10.1051/0004-6361/201220993
Bouchy et al. (2010) Bouchy, F., Hebb, L., Skillen, I., et al. 2010, A&A, 519, A98, doi: 10.1051/0004-6361/201014817
Bourrier et al. (2020) Bourrier, V., Ehrenreich, D., Lendl, M., et al. 2020, A&A, 635, A205, doi: 10.1051/0004-6361/201936640
Bowler et al. (2020) Bowler, B. P., Blunt, S. C., & Nielsen, E. L. 2020, AJ, 159, 63, doi: 10.3847/1538-3881/ab5b11
Brahm et al. (2018) Brahm, R., Hartman, J. D., Jordán, A., et al. 2018, AJ, 155, 112, doi: 10.3847/1538-3881/aaa898
Brasseur & Donaldson (2020) Brasseur, C., & Donaldson, T. 2020, MAST APIs: Present to Future
Brown et al. (2012) Brown, D. J. A., Collier Cameron, A., Díaz, R. F., et al. 2012, ApJ, 760, 139, doi: 10.1088/0004-637X/760/2/139
Bryant & Bayliss (2022) Bryant, E. M., & Bayliss, D. 2022, AJ, 163, 197, doi: 10.3847/1538-3881/ac58ff
Buchhave et al. (2010) Buchhave, L. A., Bakos, G. Á., Hartman, J. D., et al. 2010, ApJ, 720, 1118, doi: 10.1088/0004-637X/720/2/1118
Buchhave et al. (2011) —. 2011, ApJ, 733, 116, doi: 10.1088/0004-637X/733/2/116
Burdanov et al. (2018) Burdanov, A., Benni, P., Sokov, E., et al. 2018, PASP, 130, 074401, doi: 10.1088/1538-3873/aabde2
Burke et al. (2008) Burke, C. J., McCullough, P. R., Valenti, J. A., et al. 2008, ApJ, 686, 1331, doi: 10.1086/591497
Burn et al. (2021) Burn, R., Schlecker, M., Mordasini, C., et al. 2021, Astronomy & Astrophysics, 656, A72, doi: 10.1051/0004-6361/202140390
Carter et al. (2011) Carter, J. A., Winn, J. N., Holman, M. J., et al. 2011, Astrophysical Journal, 730, 82, doi: 10.1088/0004-637X/730/2/82
Castro-González et al. (2022) Castro-González, A., Díez Alonso, E., Menéndez Blanco, J., et al. 2022, MNRAS, 509, 1075, doi: 10.1093/mnras/stab2669
Chakrabarty & Sengupta (2019) Chakrabarty, A., & Sengupta, S. 2019, AJ, 158, 39, doi: 10.3847/1538-3881/ab24dd
Chan et al. (2011) Chan, T., Ingemyr, M., Winn, J. N., et al. 2011, Astronomical Journal, 141, 179, doi: 10.1088/0004-6256/141/6/179
Chatterjee et al. (2008) Chatterjee, S., Ford, E. B., Matsumura, S., & Rasio, F. A. 2008, Astrophysical Journal, 686, 580, doi: 10.1086/590227
Christensen-Dalsgaard et al. (2010) Christensen-Dalsgaard, J., Kjeldsen, H., Brown, T. M., et al. 2010, ApJ, 713, L164, doi: 10.1088/2041-8205/713/2/L164
Ciceri et al. (2016) Ciceri, S., Mancini, L., Henning, T., et al. 2016, PASP, 128, 074401, doi: 10.1088/1538-3873/128/965/074401
Cincotta et al. (2003) Cincotta, P., Giordano, C., & Simó, C. 2003, Physica D-nonlinear Phenomena - PHYSICA D, 182, 151, doi: 10.1016/S0167-2789(03)00103-9
Collins et al. (2014) Collins, K. A., Eastman, J. D., Beatty, T. G., et al. 2014, AJ, 147, 39, doi: 10.1088/0004-6256/147/2/39
Cooke et al. (2020) Cooke, B. F., Pollacco, D., Almleaky, Y., et al. 2020, VizieR Online Data Catalog: Observation & radial velocity of WASP-150 & WASP-176 (Cooke+, 2020), VizieR On-line Data Catalog: J/AJ/159/255. Originally published in: 2020AJ….159..255C, doi: 10.26093/cds/vizier.51590255
Cortés-Zuleta et al. (2020) Cortés-Zuleta, P., Rojo, P., Wang, S., et al. 2020, Astronomy & Astrophysics, 636, A98, doi: 10.1051/0004-6361/201936279
Costes et al. (2020) Costes, J. C., Watson, C. A., Belardi, C., et al. 2020, MNRAS, 491, 2834, doi: 10.1093/mnras/stz3140
Crouzet et al. (2017) Crouzet, N., McCullough, P. R., Long, D., et al. 2017, AJ, 153, 94, doi: 10.3847/1538-3881/153/3/94
Crouzet et al. (2020) Crouzet, N., Healy, B. F., Hébrard, G., et al. 2020, AJ, 159, 44, doi: 10.3847/1538-3881/ab5b12
Dawson & Johnson (2018) Dawson, R. I., & Johnson, J. A. 2018, Annual Review of Astronomy and Astrophysics, 56, 175, doi: 10.1146/annurev-astro-081817-051853
de Val-Borro et al. (2016) de Val-Borro, M., Bakos, G. Á., Brahm, R., et al. 2016, AJ, 152, 161, doi: 10.3847/0004-6256/152/6/161
Delrez et al. (2014) Delrez, L., Van Grootel, V., Anderson, D. R., et al. 2014, VizieR Online Data Catalog: WASP-68b, WASP-73b, WASP-88b transits (Delrez+, 2014), VizieR On-line Data Catalog: J/A+A/563/A143. Originally published in: 2014A&A…563A.143D, doi: 10.26093/cds/vizier.35630143
Demangeon et al. (2018) Demangeon, O. D. S., Faedi, F., Hébrard, G., et al. 2018, A&A, 610, A63, doi: 10.1051/0004-6361/201731735
Dorval et al. (2020) Dorval, P., Talens, G. J. J., Otten, G. P. P. L., et al. 2020, A&A, 635, A60, doi: 10.1051/0004-6361/201935611
Emsenhuber et al. (2021a) Emsenhuber, A., Mordasini, C., Burn, R., et al. 2021a, Astronomy and Astrophysics, 656, A69, doi: 10.1051/0004-6361/202038553
Emsenhuber et al. (2021b) —. 2021b, Astronomy and Astrophysics, 656, A70, doi: 10.1051/0004-6361/202038863
Enoch et al. (2010) Enoch, B., Collier Cameron, A., Parley, N. R., & Hebb, L. 2010, A&A, 516, A33, doi: 10.1051/0004-6361/201014326
Enoch et al. (2011a) Enoch, B., Cameron, A. C., Anderson, D. R., et al. 2011a, MNRAS, 410, 1631, doi: 10.1111/j.1365-2966.2010.17550.x
Enoch et al. (2011b) Enoch, B., Anderson, D. R., Barros, S. C. C., et al. 2011b, AJ, 142, 86, doi: 10.1088/0004-6256/142/3/86
Espinoza et al. (2016) Espinoza, N., Bayliss, D., Hartman, J. D., et al. 2016, AJ, 152, 108, doi: 10.3847/0004-6256/152/4/108
Espinoza et al. (2019) Espinoza, N., Hartman, J. D., Bakos, G. Á., et al. 2019, AJ, 158, 63, doi: 10.3847/1538-3881/ab26bb
Fa & Eb (1996) Fa, R., & Eb, F. 1996, Science (New York, N.Y.), 274, doi: 10.1126/science.274.5289.954
Fabrycky et al. (2014) Fabrycky, D. C., Lissauer, J. J., Ragozzine, D., et al. 2014, The Astrophysical Journal, 790, 146, doi: 10.1088/0004-637X/790/2/146
Faedi et al. (2011) Faedi, F., Barros, S. C. C., Anderson, D. R., et al. 2011, A&A, 531, A40, doi: 10.1051/0004-6361/201116671
Faedi et al. (2013) Faedi, F., Pollacco, D., Barros, S. C. C., et al. 2013, A&A, 551, A73, doi: 10.1051/0004-6361/201220520
Fernandez et al. (2009) Fernandez, J. M., Holman, M. J., Winn, J. N., et al. 2009, The Astronomical Journal, 137, 4911, doi: 10.1088/0004-6256/137/6/4911
Gaudi et al. (2017) Gaudi, B. S., Stassun, K. G., Collins, K. A., et al. 2017, Nature, 546, 514, doi: 10.1038/nature22392
Ge et al. (2022) Ge, J., Zhang, H., Zang, W., et al. 2022, arXiv e-prints, arXiv:2206.06693, doi: 10.48550/arXiv.2206.06693
Gibson et al. (2010) Gibson, N. P., Pollacco, D. L., Barros, S., et al. 2010, Monthly Notices of the Royal Astronomical Society, 401, 1917, doi: 10.1111/j.1365-2966.2009.15770.x
Gillon et al. (2011) Gillon, M., Doyle, A. P., Lendl, M., et al. 2011, VizieR Online Data Catalog: WASP-50b photometry and radial velocities (Gillon+, 2011), VizieR On-line Data Catalog: J/A+A/533/A88. Originally published in: 2011A&A…533A..88G, doi: 10.26093/cds/vizier.35330088
Gillon et al. (2013) Gillon, M., Anderson, D. R., Collier-Cameron, A., et al. 2013, A&A, 552, A82, doi: 10.1051/0004-6361/201220561
Ginsburg et al. (2017) Ginsburg, A., Parikh, M., Woillez, J., et al. 2017, Astrophysics Source Code Library, ascl:1708.004
Goldreich & Tremaine (1980) Goldreich, P., & Tremaine, S. 1980, The Astrophysical Journal, 241, 425, doi: 10.1086/158356
Gómez Maqueo Chew et al. (2013) Gómez Maqueo Chew, Y., Faedi, F., Pollacco, D., et al. 2013, A&A, 559, A36, doi: 10.1051/0004-6361/201322314
Grether & Lineweaver (2006) Grether, D., & Lineweaver, C. H. 2006, ApJ, 640, 1051, doi: 10.1086/500161
Grieves et al. (2024) Grieves, N., Bouchy, F., Armstrong, D. J., et al. 2024, arXiv e-prints, arXiv:2406.15986, doi: 10.48550/arXiv.2406.15986
Günther et al. (2018) Günther, M. N., Queloz, D., Gillen, E., et al. 2018, MNRAS, 478, 4720, doi: 10.1093/mnras/sty1193
Hadden & Lithwick (2014) Hadden, S., & Lithwick, Y. 2014, The Astrophysical Journal, 787, 80, doi: 10.1088/0004-637X/787/1/80
Hadden & Lithwick (2016) —. 2016, The Astrophysical Journal, 828, 44, doi: 10.3847/0004-637X/828/1/44
Hadden & Lithwick (2017) —. 2017, The Astronomical Journal, 154, 5, doi: 10.3847/1538-3881/aa71ef
Hartman et al. (2011a) Hartman, J. D., Bakos, G. Á., Sato, B., et al. 2011a, ApJ, 726, 52, doi: 10.1088/0004-637X/726/1/52
Hartman et al. (2011b) Hartman, J. D., Bakos, G. Á., Torres, G., et al. 2011b, ApJ, 742, 59, doi: 10.1088/0004-637X/742/1/59
Hartman et al. (2012) Hartman, J. D., Bakos, G. Á., Béky, B., et al. 2012, AJ, 144, 139, doi: 10.1088/0004-6256/144/5/139
Hartman et al. (2014) Hartman, J. D., Bakos, G. Á., Torres, G., et al. 2014, AJ, 147, 128, doi: 10.1088/0004-6256/147/6/128
Hartman et al. (2015a) Hartman, J. D., Bhatti, W., Bakos, G. Á., et al. 2015a, AJ, 150, 168, doi: 10.1088/0004-6256/150/6/168
Hartman et al. (2015b) Hartman, J. D., Bayliss, D., Brahm, R., et al. 2015b, AJ, 149, 166, doi: 10.1088/0004-6256/149/5/166
Hartman et al. (2016) Hartman, J. D., Bakos, G. Á., Bhatti, W., et al. 2016, AJ, 152, 182, doi: 10.3847/0004-6256/152/6/182
Hartman et al. (2019) Hartman, J. D., Bakos, G. Á., Bayliss, D., et al. 2019, AJ, 157, 55, doi: 10.3847/1538-3881/aaf8b6
Hartman et al. (2020) Hartman, J. D., Jordán, A., Bayliss, D., et al. 2020, AJ, 159, 173, doi: 10.3847/1538-3881/ab7821
Hay et al. (2016) Hay, K. L., Collier-Cameron, A., Doyle, A. P., et al. 2016, MNRAS, 463, 3276, doi: 10.1093/mnras/stw2090
Hébrard et al. (2013) Hébrard, G., Collier Cameron, A., Brown, D. J. A., et al. 2013, A&A, 549, A134, doi: 10.1051/0004-6361/201220363
Hellier et al. (2011) Hellier, C., Anderson, D. R., Collier Cameron, A., et al. 2011, A&A, 535, L7, doi: 10.1051/0004-6361/201117081
Hellier et al. (2012) —. 2012, MNRAS, 426, 739, doi: 10.1111/j.1365-2966.2012.21780.x
Hellier et al. (2015) —. 2015, AJ, 150, 18, doi: 10.1088/0004-6256/150/1/18
Hellier et al. (2017) Hellier, C., Anderson, D. R., Collier Cameron, A., et al. 2017, Monthly Notices of the Royal Astronomical Society, 465, 3693, doi: 10.1093/mnras/stw3005
Hellier et al. (2017) Hellier, C., Anderson, D. R., Collier Cameron, A., et al. 2017, MNRAS, 465, 3693, doi: 10.1093/mnras/stw3005
Hellier et al. (2019a) Hellier, C., Anderson, D. R., Bouchy, F., et al. 2019a, MNRAS, 482, 1379, doi: 10.1093/mnras/sty2741
Hellier et al. (2019b) Hellier, C., Anderson, D. R., Barkaoui, K., et al. 2019b, MNRAS, 490, 1479, doi: 10.1093/mnras/stz2713
Henning et al. (2018) Henning, T., Mancini, L., Sarkis, P., et al. 2018, AJ, 155, 79, doi: 10.3847/1538-3881/aaa254
Holman & Murray (2005) Holman, M. J., & Murray, N. W. 2005, Science, 307, 1288, doi: 10.1126/science.1107822
Holman et al. (2006) Holman, M. J., Winn, J. N., Latham, D. W., et al. 2006, The Astrophysical Journal, 652, 1715, doi: 10.1086/508155
Holman et al. (2007a) Holman, M. J., Winn, J. N., Fuentes, C. I., et al. 2007a, The Astrophysical Journal, 655, 1103, doi: 10.1086/510342
Holman et al. (2007b) Holman, M. J., Winn, J. N., Latham, D. W., et al. 2007b, Astrophysical Journal, 664, 1185, doi: 10.1086/519077
Hord et al. (2022) Hord, B. J., Colón, K. D., Berger, T. A., et al. 2022, AJ, 164, 13, doi: 10.3847/1538-3881/ac6f57
Hoyer et al. (2012) Hoyer, S., Rojo, P., & López-Morales, M. 2012, The Astrophysical Journal, 748, 22, doi: 10.1088/0004-637X/748/1/22
Hoyer et al. (2013) Hoyer, S., López-Morales, M., Rojo, P., et al. 2013, Monthly Notices of the Royal Astronomical Society, 434, 46, doi: 10.1093/mnras/stt962
Huang et al. (2015) Huang, C. X., Hartman, J. D., Bakos, G. Á., et al. 2015, AJ, 150, 85, doi: 10.1088/0004-6256/150/3/85
Ikwut-Ukwa et al. (2020) Ikwut-Ukwa, M., Rodriguez, J. E., Bieryla, A., et al. 2020, AJ, 160, 209, doi: 10.3847/1538-3881/aba964
Jackson et al. (2023) Jackson, D. G., Watson, C. A., de Mooij, E. J. W., et al. 2023, MNRAS, 518, 4845, doi: 10.1093/mnras/stac3192
Jenkins et al. (2016a) Jenkins, J. M., Twicken, J. D., McCauliff, S., et al. 2016a, 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, doi: 10.1117/12.2233418
Jenkins et al. (2016b) Jenkins, J. M., Twicken, J. D., McCauliff, S., et al. 2016b, 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, doi: 10.1117/12.2233418
Joblib Development Team (2020) Joblib Development Team. 2020, Joblib: running Python functions as pipeline jobs. https://joblib.readthedocs.io/
Johns-Krull et al. (2008) Johns-Krull, C. M., McCullough, P. R., Burke, C. J., et al. 2008, ApJ, 677, 657, doi: 10.1086/528950
Johnson et al. (2011) Johnson, J. A., Winn, J. N., Bakos, G. Á., et al. 2011, ApJ, 735, 24, doi: 10.1088/0004-637X/735/1/24
Johnson et al. (2018) Johnson, M. C., Rodriguez, J. E., Zhou, G., et al. 2018, AJ, 155, 100, doi: 10.3847/1538-3881/aaa5af
Jordán et al. (2014) Jordán, A., Brahm, R., Bakos, G. Á., et al. 2014, AJ, 148, 29, doi: 10.1088/0004-6256/148/2/29
Juncher et al. (2015) Juncher, D., Buchhave, L. A., Hartman, J. D., et al. 2015, PASP, 127, 851, doi: 10.1086/682725
Kipping et al. (2010) Kipping, D. M., Bakos, G. Á., Hartman, J., et al. 2010, ApJ, 725, 2017, doi: 10.1088/0004-637X/725/2/2017
Kipping et al. (2011) Kipping, D. M., Hartman, J., Bakos, G. Á., et al. 2011, AJ, 142, 95, doi: 10.1088/0004-6256/142/3/95
Kley & Nelson (2012) Kley, W., & Nelson, R. 2012, Annual Review of Astronomy and Astrophysics, 50, 211, doi: 10.1146/annurev-astro-081811-125523
Kokubo & Ida (2002) Kokubo, E., & Ida, S. 2002, Astrophysical Journal, 581, 666, doi: 10.1086/344105
Kubiak et al. (2023) Kubiak, S., Vanderburg, A., Becker, J., et al. 2023, Monthly Notices of the Royal Astronomical Society, 521, 4679, doi: 10.1093/mnras/stad766
Lam et al. (2017) Lam, K. W. F., Faedi, F., Brown, D. J. A., et al. 2017, A&A, 599, A3, doi: 10.1051/0004-6361/201629403
Latham et al. (2009) Latham, D. W., Bakos, G. Á., Torres, G., et al. 2009, ApJ, 704, 1107, doi: 10.1088/0004-637X/704/2/1107
Lendl et al. (2012) Lendl, M., Anderson, D. R., Collier-Cameron, A., et al. 2012, A&A, 544, A72, doi: 10.1051/0004-6361/201219585
Lendl et al. (2019) Lendl, M., Anderson, D. R., Bonfanti, A., et al. 2019, MNRAS, 482, 301, doi: 10.1093/mnras/sty2667
Lin et al. (1996) Lin, D. N. C., Bodenheimer, P., & Richardson, D. C. 1996, Nature, 380, 606, doi: 10.1038/380606a0
Lin & Papaloizou (1986) Lin, D. N. C., & Papaloizou, J. 1986, The Astrophysical Journal, 309, 846, doi: 10.1086/164653
Lindor et al. (2021) Lindor, B. M., Hartman, J. D., Bakos, G. Á., et al. 2021, AJ, 161, 64, doi: 10.3847/1538-3881/abc700
Lissauer et al. (2011) Lissauer, J. J., Ragozzine, D., Fabrycky, D. C., et al. 2011, The Astrophysical Journal Supplement Series, 197, 8, doi: 10.1088/0067-0049/197/1/8
Lithwick et al. (2012) Lithwick, Y., Xie, J., & Wu, Y. 2012, The Astrophysical Journal, 761, 122, doi: 10.1088/0004-637X/761/2/122
Lund et al. (2017) Lund, M. B., Rodriguez, J. E., Zhou, G., et al. 2017, AJ, 154, 194, doi: 10.3847/1538-3881/aa8f95
Ma & Ge (2014) Ma, B., & Ge, J. 2014, MNRAS, 439, 2781, doi: 10.1093/mnras/stu134
Maciejewski et al. (2023) Maciejewski, G., Golonka, J., Łoboda, W., et al. 2023, MNRAS, 525, L43, doi: 10.1093/mnrasl/slad078
Mancini et al. (2015) Mancini, L., Hartman, J. D., Penev, K., et al. 2015, A&A, 580, A63, doi: 10.1051/0004-6361/201526069
Mancini et al. (2020) Mancini, L., Sarkis, P., Henning, T., et al. 2020, A&A, 633, A30, doi: 10.1051/0004-6361/201936532
Mandushev et al. (2011) Mandushev, G., Quinn, S. N., Buchhave, L. A., et al. 2011, ApJ, 741, 114, doi: 10.1088/0004-637X/741/2/114
Maxted et al. (2010) Maxted, P. F. L., Anderson, D. R., Gillon, M., et al. 2010, AJ, 140, 2007, doi: 10.1088/0004-6256/140/6/2007
Maxted et al. (2016) Maxted, P. F. L., Anderson, D. R., Collier Cameron, A., et al. 2016, A&A, 591, A55, doi: 10.1051/0004-6361/201628250
Mayor & Queloz (1995) Mayor, M., & Queloz, D. 1995, Nature, 378, 355, doi: 10.1038/378355a0
McLeod et al. (2017) McLeod, K. K., Rodriguez, J. E., Oelkers, R. J., et al. 2017, AJ, 153, 263, doi: 10.3847/1538-3881/aa6d5d
Mishra et al. (2021) Mishra, L., Alibert, Y., Leleu, A., et al. 2021, Astronomy & Astrophysics, 656, A74, doi: 10.1051/0004-6361/202140761
Mohler-Fischer et al. (2013) Mohler-Fischer, M., Mancini, L., Hartman, J. D., et al. 2013, A&A, 558, A55, doi: 10.1051/0004-6361/201321663
Mordasini et al. (2009a) Mordasini, C., Alibert, Y., & Benz, W. 2009a, Astronomy & Astrophysics, 501, 1139, doi: 10.1051/0004-6361/200810301
Mordasini et al. (2012) Mordasini, C., Alibert, Y., Benz, W., Klahr, H., & Henning, T. 2012, Astronomy & Astrophysics, 541, A97, doi: 10.1051/0004-6361/201117350
Mordasini et al. (2009b) Mordasini, C., Alibert, Y., Benz, W., & Naef, D. 2009b, Astronomy & Astrophysics, 501, 1161, doi: 10.1051/0004-6361/200810697
Mortier et al. (2013) Mortier, A., Santos, N. C., Sousa, S. G., et al. 2013, A&A, 558, A106, doi: 10.1051/0004-6361/201322240
Močnik et al. (2020) Močnik, T., Hellier, C., & Anderson, D. R. 2020, PASP, 132, 014401, doi: 10.1088/1538-3873/ab5598
Mustill et al. (2015) Mustill, A. J., Davies, M. B., & Johansen, A. 2015, The Astrophysical Journal, 808, 14, doi: 10.1088/0004-637X/808/1/14
Naoz et al. (2012) Naoz, S., Farr, W. M., & Rasio, F. A. 2012, Astrophysical Journal, 754, L36, doi: 10.1088/2041-8205/754/2/L36
Nascimbeni et al. (2023) Nascimbeni, V., Borsato, L., Zingales, T., et al. 2023, A&A, 673, A42, doi: 10.1051/0004-6361/202245486
Nesvorný (2009) Nesvorný, D. 2009, Astrophysical Journal, 701, 1116, doi: 10.1088/0004-637X/701/2/1116
Neveu-VanMalle et al. (2016) Neveu-VanMalle, M., Queloz, D., Anderson, D. R., et al. 2016, A&A, 586, A93, doi: 10.1051/0004-6361/201526965
Nielsen et al. (2019) Nielsen, L. D., Bouchy, F., Turner, O. D., et al. 2019, MNRAS, 489, 2478, doi: 10.1093/mnras/stz2351
Obermeier et al. (2020) Obermeier, C., Steuer, J., Kellermann, H., et al. 2020, A&A, 639, A130, doi: 10.1051/0004-6361/202037715
Oberst et al. (2017) Oberst, T. E., Rodriguez, J. E., Colón, K. D., et al. 2017, AJ, 153, 97, doi: 10.3847/1538-3881/153/3/97
Oliveira et al. (2019) Oliveira, J. M., Martioli, E., & Tucci-Maia, M. 2019, Research Notes of the American Astronomical Society, 3, 35, doi: 10.3847/2515-5172/ab06c7
Parviainen (2015) Parviainen, H. 2015, Monthly Notices of the Royal Astronomical Society, 450, 3233, doi: 10.1093/mnras/stv894
Pearson (2019) Pearson, K. A. 2019, AJ, 158, 243, doi: 10.3847/1538-3881/ab4e1c
Penev et al. (2013) Penev, K., Bakos, G. Á., Bayliss, D., et al. 2013, AJ, 145, 5, doi: 10.1088/0004-6256/145/1/5
Pepper et al. (2013) Pepper, J., Siverd, R. J., Beatty, T. G., et al. 2013, ApJ, 773, 64, doi: 10.1088/0004-637X/773/1/64
Petrovich (2015) Petrovich, C. 2015, Astrophysical Journal, 805, 75, doi: 10.1088/0004-637X/805/1/75
Petrovich & Tremaine (2016) Petrovich, C., & Tremaine, S. 2016, Astrophysical Journal, 829, 132, doi: 10.3847/0004-637X/829/2/132
Queloz et al. (2010) Queloz, D., Anderson, D. R., Collier Cameron, A., et al. 2010, A&A, 517, L1, doi: 10.1051/0004-6361/201014768
Quinn et al. (2011) Quinn, S. N., Bakos, G. Á., Hartman, J., et al. 2011, The Astrophysical Journal, 745, 80, doi: 10.1088/0004-637X/745/1/80
Quinn et al. (2012) Quinn, S. N., Bakos, G. Á., Hartman, J., et al. 2012, ApJ, 745, 80, doi: 10.1088/0004-637X/745/1/80
Quinn et al. (2019) Quinn, S. N., Becker, J. C., Rodriguez, J. E., et al. 2019, The Astronomical Journal, 158, 177, doi: 10.3847/1538-3881/ab3f2b
Rauer et al. (2014) Rauer, H., Catala, C., Aerts, C., et al. 2014, Experimental Astronomy, 38, 249
Raynard et al. (2018) Raynard, L., Goad, M. R., Gillen, E., et al. 2018, MNRAS, 481, 4960, doi: 10.1093/mnras/sty2581
Rein & Liu (2012) Rein, H., & Liu, S.-F. 2012, Astronomy & Astrophysics, 537, A128, doi: 10.1051/0004-6361/201118085
Rein & Spiegel (2015) Rein, H., & Spiegel, D. S. 2015, Monthly Notices of the Royal Astronomical Society, 446, 1424, doi: 10.1093/mnras/stu2164
Ricker et al. (2014) Ricker, G. R., Winn, J. N., Vanderspek, R., et al. 2014, Journal of Astronomical Telescopes, Instruments, and Systems, 1, 014003, doi: 10.1117/1.JATIS.1.1.014003
Rodriguez et al. (2019) Rodriguez, J. E., Eastman, J. D., Zhou, G., et al. 2019, AJ, 158, 197, doi: 10.3847/1538-3881/ab4136
Sarkis et al. (2018) Sarkis, P., Henning, T., Hartman, J. D., et al. 2018, AJ, 156, 216, doi: 10.3847/1538-3881/aade54
Sato et al. (2012) Sato, B., Hartman, J. D., Bakos, G. Á., et al. 2012, PASJ, 64, 97, doi: 10.1093/pasj/64.5.97
Schanche et al. (2020) Schanche, N., Hébrard, G., Collier Cameron, A., et al. 2020, MNRAS, 499, 428, doi: 10.1093/mnras/staa2848
Schlecker et al. (2021a) Schlecker, M., Mordasini, C., Emsenhuber, A., et al. 2021a, Astronomy & Astrophysics, 656, A71, doi: 10.1051/0004-6361/202038554
Schlecker et al. (2021b) Schlecker, M., Pham, D., Burn, R., et al. 2021b, Astronomy & Astrophysics, 656, A73, doi: 10.1051/0004-6361/202140551
Shporer et al. (2009) Shporer, A., Bakos, G. Á., Bouchy, F., et al. 2009, ApJ, 690, 1393, doi: 10.1088/0004-637X/690/2/1393
Simpson et al. (2011a) Simpson, E. K., Pollacco, D., Cameron, A. C., et al. 2011a, MNRAS, 414, 3023, doi: 10.1111/j.1365-2966.2011.18603.x
Simpson et al. (2011b) Simpson, E. K., Faedi, F., Barros, S. C. C., et al. 2011b, AJ, 141, 8, doi: 10.1088/0004-6256/141/1/8
Smalley et al. (2010) Smalley, B., Anderson, D. R., Collier Cameron, A., et al. 2010, A&A, 520, A56, doi: 10.1051/0004-6361/201014705
Smalley et al. (2011) —. 2011, A&A, 526, A130, doi: 10.1051/0004-6361/201015992
Smalley et al. (2012) Smalley, B., Anderson, D. R., Collier-Cameron, A., et al. 2012, A&A, 547, A61, doi: 10.1051/0004-6361/201219731
Smith (2015) Smith, A. M. S. 2015, Acta Astron., 65, 117, doi: 10.48550/arXiv.1412.0451
Smith et al. (2012a) Smith, A. M. S., Anderson, D. R., Collier Cameron, A., et al. 2012a, AJ, 143, 81, doi: 10.1088/0004-6256/143/4/81
Smith et al. (2013) Smith, A. M. S., Anderson, D. R., Bouchy, F., et al. 2013, A&A, 552, A120, doi: 10.1051/0004-6361/201220727
Smith et al. (2014) Smith, A. M. S., Anderson, D. R., Armstrong, D. J., et al. 2014, A&A, 570, A64, doi: 10.1051/0004-6361/201424752
Smith et al. (2012b) Smith, J. C., Stumpe, M. C., Van Cleve, J. E., et al. 2012b, PASP, 124, 1000, doi: 10.1086/667697
Sozzetti et al. (2009) Sozzetti, A., Torres, G., Charbonneau, D., et al. 2009, ApJ, 691, 1145, doi: 10.1088/0004-637X/691/2/1145
Spake et al. (2016) Spake, J. J., Brown, D. J. A., Doyle, A. P., et al. 2016, PASP, 128, 024401, doi: 10.1088/1538-3873/128/960/024401
Stassun et al. (2017) Stassun, K. G., Collins, K. A., & Gaudi, B. S. 2017, AJ, 153, 136, doi: 10.3847/1538-3881/aa5df3
Steffen et al. (2012) Steffen, J. H., Ragozzine, D., Fabrycky, D. C., et al. 2012, Proceedings of the National Academy of Sciences, 109, 7982, doi: 10.1073/pnas.1120970109
Street et al. (2010) Street, R. A., Simpson, E., Barros, S. C. C., et al. 2010, ApJ, 720, 337, doi: 10.1088/0004-637X/720/1/337
Stumpe et al. (2014) Stumpe, M. C., Smith, J. C., Catanzarite, J. H., et al. 2014, PASP, 126, 100, doi: 10.1086/674989
Stumpe et al. (2012) Stumpe, M. C., Smith, J. C., Van Cleve, J. E., et al. 2012, PASP, 124, 985, doi: 10.1086/667698
Team (2021) Team, M. 2021, TESS Light Curves - All Sectors, STScI/MAST, doi: 10.17909/T9-NMC8-F686
Temple et al. (2019) Temple, L. Y., Hellier, C., Almleaky, Y., et al. 2019, AJ, 157, 141, doi: 10.3847/1538-3881/ab095a
Tinney et al. (2006) Tinney, C. G., Butler, R. P., Marcy, G. W., et al. 2006, Astrophysical Journal, 647, 594, doi: 10.1086/503706
Torres et al. (2008a) Torres, G., Winn, J. N., & Holman, M. J. 2008a, ApJ, 677, 1324, doi: 10.1086/529429
Torres et al. (2008b) —. 2008b, ApJ, 677, 1324, doi: 10.1086/529429
Torres et al. (2010) Torres, G., Bakos, G. Á., Hartman, J., et al. 2010, ApJ, 715, 458, doi: 10.1088/0004-637X/715/1/458
Triaud et al. (2011) Triaud, A. H. M. J., Queloz, D., Hellier, C., et al. 2011, VizieR Online Data Catalog: WASP-23 photometric and radial velocity data (Triaud+, 2011), VizieR On-line Data Catalog: J/A+A/531/A24. Originally published in: 2011A&A…531A..24T, doi: 10.26093/cds/vizier.35310024
Triaud et al. (2013) Triaud, A. H. M. J., Anderson, D. R., Collier, C. A., et al. 2013, VizieR Online Data Catalog: WASP-80 photometric and radial velocity data (Triaud+, 2013), VizieR On-line Data Catalog: J/A+A/551/A80. Originally published in: 2013A&A…551A..80T, doi: 10.26093/cds/vizier.35510080
Triaud et al. (2017) Triaud, A. H. M. J., Neveu-VanMalle, M., Lendl, M., et al. 2017, MNRAS, 467, 1714, doi: 10.1093/mnras/stx154
Trilling et al. (1998) Trilling, D. E., Benz, W., Guillot, T., et al. 1998, The Astrophysical Journal, 500, 428, doi: 10.1086/305711
Turner et al. (2016) Turner, O. D., Anderson, D. R., Collier Cameron, A., et al. 2016, PASP, 128, 064401, doi: 10.1088/1538-3873/128/964/064401
Turner et al. (2019) Turner, O. D., Anderson, D. R., Barkaoui, K., et al. 2019, MNRAS, 485, 5790, doi: 10.1093/mnras/stz742
Vick et al. (2019) Vick, M., Lai, D., & Anderson, K. R. 2019, Monthly Notices of the Royal Astronomical Society, 484, 5645, doi: 10.1093/mnras/stz354
Vines et al. (2019) Vines, J. I., Jenkins, J. S., Acton, J. S., et al. 2019, MNRAS, 489, 4125, doi: 10.1093/mnras/stz2349
Wang et al. (2024) Wang, W., Zhang, Z., Chen, Z., et al. 2024, ApJS, 270, 14, doi: 10.3847/1538-4365/ad0847
Wang et al. (2018a) Wang, X.-Y., Wang, S., Hinse, T. C., et al. 2018a, Publications of the Astronomical Society of the Pacific, 130, 064401, doi: 10.1088/1538-3873/aab93e
Wang et al. (2018b) —. 2018b, Publications of the Astronomical Society of the Pacific, 130, 064401, doi: 10.1088/1538-3873/aab93e
Wang et al. (2021) Wang, X.-Y., Wang, Y.-H., Wang, S., et al. 2021, The Astrophysical Journal Supplement Series, 255, 15, doi: 10.3847/1538-4365/ac0835
Wang et al. (2017) Wang, Y.-H., Wang, S., Liu, H.-G., et al. 2017, The Astronomical Journal, 154, 49, doi: 10.3847/1538-3881/aa7519
Ward (1997) Ward, W. R. 1997, Icarus, 126, 261, doi: 10.1006/icar.1996.5647
West et al. (2016) West, R. G., Hellier, C., Almenara, J. M., et al. 2016, A&A, 585, A126, doi: 10.1051/0004-6361/201527276
Winn et al. (2009a) Winn, J. N., Holman, M. J., Carter, J. A., et al. 2009a, Astronomical Journal, 137, 3826, doi: 10.1088/0004-6256/137/4/3826
Winn et al. (2007a) Winn, J. N., Holman, M. J., & Fuentes, C. I. 2007a, The Astronomical Journal, 133, 11, doi: 10.1086/509658
Winn et al. (2007b) Winn, J. N., Holman, M. J., & Roussanova, A. 2007b, The Astrophysical Journal, 657, 1098, doi: 10.1086/510834
Winn et al. (2008a) Winn, J. N., Holman, M. J., Shporer, A., et al. 2008a, The Astronomical Journal, 136, 267, doi: 10.1088/0004-6256/136/1/267
Winn et al. (2007c) Winn, J. N., Holman, M. J., Henry, G. W., et al. 2007c, Astronomical Journal, 133, 1828, doi: 10.1086/512159
Winn et al. (2007d) Winn, J. N., Holman, M. J., Bakos, G. Á., et al. 2007d, Astronomical Journal, 134, 1707, doi: 10.1086/521599
Winn et al. (2008b) Winn, J. N., Holman, M. J., Torres, G., et al. 2008b, Astrophysical Journal, 683, 1076, doi: 10.1086/589737
Winn et al. (2009b) Winn, J. N., Holman, M. J., Henry, G. W., et al. 2009b, The Astrophysical Journal, 693, 794, doi: 10.1088/0004-637X/693/1/794
Wu et al. (2023) Wu, D.-H., Rice, M., & Wang, S. 2023, The Astronomical Journal, 165, 171, doi: 10.3847/1538-3881/acbf3f
Wu & Lithwick (2011) Wu, Y., & Lithwick, Y. 2011, Astrophysical Journal, 735, 109, doi: 10.1088/0004-637X/735/2/109
Wu & Murray (2003) Wu, Y., & Murray, N. 2003, The Astrophysical Journal, 589, 605, doi: 10.1086/374598
Xie (2013) Xie, J.-W. 2013, The Astrophysical Journal Supplement Series, 208, 22, doi: 10.1088/0067-0049/208/2/22
Xie et al. (2016) Xie, J.-W., Dong, S., Zhu, Z., et al. 2016, Proceedings of the National Academy of Science, 113, 11431, doi: 10.1073/pnas.1604692113
Zhan (2011) Zhan, H. 2011, Scientia Sinica Physica, Mechanica & Astronomica, 41, 1441, doi: 10.1360/132011-961
Zhang (2024) Zhang, Z. 2024, CMAT: Companion MAss from Ttv modeling, 0.1, Zenodo, doi: 10.5281/zenodo.13739647
Zhou et al. (2016) Zhou, G., Rodriguez, J. E., Collins, K. A., et al. 2016, AJ, 152, 136, doi: 10.3847/0004-6256/152/5/136
Zhou et al. (2017) Zhou, G., Bakos, G. Á., Hartman, J. D., et al. 2017, AJ, 153, 211, doi: 10.3847/1538-3881/aa674a
Zhou et al. (2019a) Zhou, G., Huang, C. X., Bakos, G. Á., et al. 2019a, AJ, 158, 141, doi: 10.3847/1538-3881/ab36b5
Zhou et al. (2019b) Zhou, G., Bakos, G. Á., Bayliss, D., et al. 2019b, AJ, 157, 31, doi: 10.3847/1538-3881/aaf1bb
Zhu & Dong (2021) Zhu, W., & Dong, S. 2021, Annual Review of Astronomy and Astrophysics, 59, 291, doi: 10.1146/annurev-astro-112420-020055
Zink & Howard (2023) Zink, J. K., & Howard, A. W. 2023, ApJ, 956, L29, doi: 10.3847/2041-8213/acfdab

Appendix A Result of Individual Target

In this appendix, we present the individual upper mass limit of hidden companions for 260 hot Jupiter systems. The upper mass limit is calculated using $\chi^{2}$ and RMS analysis. The results are shown in Figure 12.

\restartappendixnumbering

Appendix B Star and Hot Jupiter mass

In this appendix, we provide the masses of the host stars and hot Jupiters for 260 systems included in our research. \startlongtable

Table 1: The mass of the host star and the planet in the system. The mass of the star is in solar mass and the mass of the planet is in Jupiter mass. The references for the mass of the star and the planet are also provided.

Planet Name	$\mathrm{M_{\star}}\ \big{[}\mathrm{M_{\odot}}\big{]}$	$\mathrm{M_{\star}}$ Ref	$\mathrm{M_{p}}\ \big{[}\mathrm{M_{J}}\big{]}$	$\mathrm{M_{p}}$ Ref
CoRoT-1 b	0.95	Barge et al. (2008)	1.02979	Calculated from MSINI and I
CoRoT-2 b	0.97	Alonso et al. (2008)	3.27527	Calculated from MSINI and I
HAT-P-1 b	1.133	Torres et al. (2008a)	0.532369	Calculated from MSINI and I
HAT-P-2 b	1.308	Torres et al. (2008a)	8.87066	Calculated from MSINI and I
HAT-P-3 b	0.928	Torres et al. (2008a)	0.595712	Calculated from MSINI and I
HAT-P-4 b	1.248	Torres et al. (2008a)	0.671507	Calculated from MSINI and I
HAT-P-5 b	1.157	Torres et al. (2008a)	1.05561	Calculated from MSINI and I
HAT-P-6 b	1.29	Torres et al. (2008a)	1.05957	Calculated from MSINI and I
HAT-P-7 b	1.5	Christensen-Dalsgaard et al. (2010)	1.7916	Calculated from MSINI and I
HAT-P-8 b	1.28	Latham et al. (2009)	1.29336	Calculated from MSINI and I
HAT-P-9 b	1.28	Shporer et al. (2009)	0.776601	Calculated from MSINI and I
HAT-P-13 b	1.22	Bakos et al. (2009)	0.85708	Calculated from MSINI and I
HAT-P-14 b	1.386	Torres et al. (2010)	2.23603	Calculated from MSINI and I
HAT-P-16 b	1.218	Buchhave et al. (2010)	4.2025	Calculated from MSINI and I
HAT-P-19 b	0.842	Hartman et al. (2011a)	0.292273	Calculated from MSINI and I
HAT-P-20 b	0.756	Bakos et al. (2011)	7.28953	Calculated from MSINI and I
HAT-P-21 b	0.947	Bakos et al. (2011)	4.07833	Calculated from MSINI and I
HAT-P-22 b	0.916	Bakos et al. (2011)	2.15137	Calculated from MSINI and I
HAT-P-23 b	1.13	Bakos et al. (2011)	2.09606	Calculated from MSINI and I
HAT-P-24 b	1.191	Kipping et al. (2010)	0.685857	Calculated from MSINI and I
HAT-P-25 b	1.01	Quinn et al. (2012)	0.567181	Calculated from MSINI and I
HAT-P-27 b	0.92	Brown et al. (2012)	0.617485	Calculated from MSINI and I
HAT-P-28 b	1.025	Buchhave et al. (2011)	0.627833	Calculated from MSINI and I
HAT-P-29 b	1.207	Buchhave et al. (2011)	0.779004	Calculated from MSINI and I
HAT-P-30 b	1.242	Johnson et al. (2011)	0.711088	Calculated from MSINI and I
HAT-P-31 b	1.218	Kipping et al. (2011)	2.16904	Calculated from MSINI and I
HAT-P-32 b	1.16	Hartman et al. (2011b)	0.861516	Calculated from MSINI and I
HAT-P-33 b	1.375	Hartman et al. (2011b)	0.763256	Calculated from MSINI and I
HAT-P-34 b	1.392	Bakos et al. (2012)	3.334	Calculated from MSINI and I
HAT-P-35 b	1.236	Bakos et al. (2012)	1.05422	Calculated from MSINI and I
HAT-P-36 b	1.022	Bakos et al. (2012)	1.83923	Calculated from MSINI and I
HAT-P-37 b	0.929	Bakos et al. (2012)	1.17362	Calculated from MSINI and I
HAT-P-38 b	0.886	Sato et al. (2012)	0.267569	Calculated from MSINI and I
HAT-P-39 b	1.404	Hartman et al. (2012)	0.599196	Calculated from MSINI and I
HAT-P-40 b	1.512	Hartman et al. (2012)	0.6202	Calculated from MSINI and I
HAT-P-41 b	1.418	Hartman et al. (2012)	0.800254	Calculated from MSINI and I
HAT-P-42 b	1.18	Boisse et al. (2013)	1.044	Boisse et al. (2013)
HAT-P-43 b	1.03	Castro-González et al. (2022)	0.662	Boisse et al. (2013)
HAT-P-44 b	0.942	Hartman et al. (2014)	0.352	Hartman et al. (2014)
HAT-P-49 b	1.543	Bieryla et al. (2014)	1.72959	Calculated from MSINI and I
HAT-P-50 b	1.27	Hartman et al. (2015a)	1.35	Hartman et al. (2015a)
HAT-P-51 b	0.98	Hartman et al. (2015a)	0.309	Hartman et al. (2015a)
HAT-P-52 b	0.89	Hartman et al. (2015a)	0.818	Hartman et al. (2015a)
HAT-P-55 b	1.01	Juncher et al. (2015)	0.582	Juncher et al. (2015)
HAT-P-56 b	1.296	Huang et al. (2015)	2.18029	Calculated from MSINI and I
HAT-P-58 b	1.03	Bakos et al. (2021)	0.372	Bakos et al. (2021)
HAT-P-59 b	1.01	Bakos et al. (2021)	1.54	Bakos et al. (2021)
HAT-P-60 b	1.44	Bakos et al. (2021)	0.574	Bakos et al. (2021)
HAT-P-61 b	1.0	Bakos et al. (2021)	1.057	Bakos et al. (2021)
HAT-P-62 b	1.02	Bakos et al. (2021)	0.761	Bakos et al. (2021)
HAT-P-65 b	1.21	Hartman et al. (2016)	0.527	Hartman et al. (2016)
HAT-P-66 b	1.26	Hartman et al. (2016)	0.783	Hartman et al. (2016)
HAT-P-67 b	1.64	Zhou et al. (2017)	0.34	Zhou et al. (2017)
HAT-P-68 b	0.68	Lindor et al. (2021)	0.724	Lindor et al. (2021)
HAT-P-69 b	1.65	Zhou et al. (2019a)	3.58	Zhou et al. (2019a)
HAT-P-70 b	1.89	Zhou et al. (2019a)	6.78	Zhou et al. (2019a)
HATS-1 b	0.986	Penev et al. (2013)	1.86507	Calculated from MSINI and I
HATS-2 b	0.882	Mohler-Fischer et al. (2013)	1.34915	Calculated from MSINI and I
HATS-3 b	1.209	Bayliss et al. (2013)	1.0735	Calculated from MSINI and I
HATS-4 b	1.001	Jordán et al. (2014)	1.323	Jordán et al. (2014)
HATS-6 b	0.574	Hartman et al. (2015b)	0.319	Hartman et al. (2015b)
HATS-13 b	0.962	Mancini et al. (2015)	0.542398	Calculated from MSINI and I
HATS-16 b	0.97	Ciceri et al. (2016)	3.27	Ciceri et al. (2016)
HATS-18 b	1.04	Chakrabarty & Sengupta (2019)	1.9795	Chakrabarty & Sengupta (2019)
HATS-22 b	0.76	Bento et al. (2017)	2.74	Bento et al. (2017)
HATS-23 b	1.12	Bento et al. (2017)	1.47	Bento et al. (2017)
HATS-24 b	1.07	Oliveira et al. (2019)	2.26	Oliveira et al. (2019)
HATS-25 b	0.99	Espinoza et al. (2016)	0.613	Espinoza et al. (2016)
HATS-26 b	1.3	Espinoza et al. (2016)	0.65	Espinoza et al. (2016)
HATS-27 b	1.42	Espinoza et al. (2016)	0.53	Espinoza et al. (2016)
HATS-28 b	0.93	Espinoza et al. (2016)	0.672	Espinoza et al. (2016)
HATS-30 b	1.09	Espinoza et al. (2016)	0.706	Espinoza et al. (2016)
HATS-31 b	1.28	de Val-Borro et al. (2016)	0.88	de Val-Borro et al. (2016)
HATS-32 b	1.1	de Val-Borro et al. (2016)	0.92	de Val-Borro et al. (2016)
HATS-33 b	1.06	de Val-Borro et al. (2016)	1.192	de Val-Borro et al. (2016)
HATS-34 b	0.96	de Val-Borro et al. (2016)	0.941	de Val-Borro et al. (2016)
HATS-39 b	1.38	Bento et al. (2018)	0.63	Bento et al. (2018)
HATS-40 b	1.56	Bento et al. (2018)	1.59	Bento et al. (2018)
HATS-41 b	1.5	Bento et al. (2018)	9.7	Bento et al. (2018)
HATS-42 b	1.27	Bento et al. (2018)	1.88	Bento et al. (2018)
HATS-43 b	0.84	Brahm et al. (2018)	0.261	Brahm et al. (2018)
HATS-44 b	0.86	Brahm et al. (2018)	0.56	Brahm et al. (2018)
HATS-45 b	1.27	Brahm et al. (2018)	0.7	Brahm et al. (2018)
HATS-47 b	0.67	Hartman et al. (2020)	0.369	Hartman et al. (2020)
HATS-51 b	1.19	Henning et al. (2018)	0.768	Henning et al. (2018)
HATS-52 b	1.11	Henning et al. (2018)	2.24	Henning et al. (2018)
HATS-53 b	0.96	Henning et al. (2018)	0.595	Henning et al. (2018)
HATS-54 b	1.05	Jackson et al. (2023)	0.753	Jackson et al. (2023)
HATS-55 b	1.2	Espinoza et al. (2019)	0.921	Espinoza et al. (2019)
HATS-56 b	1.57	Espinoza et al. (2019)	0.602	Espinoza et al. (2019)
HATS-57 b	1.03	Espinoza et al. (2019)	3.147	Espinoza et al. (2019)
HATS-59 b	1.04	Sarkis et al. (2018)	0.806	Sarkis et al. (2018)
HATS-60 b	1.1	Hartman et al. (2019)	0.662	Hartman et al. (2019)
HATS-63 b	0.93	Hartman et al. (2019)	0.96	Hartman et al. (2019)
HATS-64 b	1.56	Hartman et al. (2019)	0.96	Hartman et al. (2019)
HATS-67 b	1.44	Hartman et al. (2019)	1.45	Hartman et al. (2019)
HATS-68 b	1.35	Hartman et al. (2019)	1.29	Hartman et al. (2019)
HATS-69 b	0.89	Hartman et al. (2019)	0.577	Hartman et al. (2019)
HATS-70 b	1.78	Zhou et al. (2019b)	12.9	Zhou et al. (2019b)
HATS-71 b	0.49	Bakos et al. (2020)	0.37	Bakos et al. (2020)
HD 189733 b	0.806	Torres et al. (2008b)	1.1436	Calculated from MSINI and I
K2-237 b	1.26	Ikwut-Ukwa et al. (2020)	1.363	Ikwut-Ukwa et al. (2020)
KELT-3 b	1.282	Pepper et al. (2013)	1.46164	Calculated from MSINI and I
KELT-6 b	1.085	Collins et al. (2014)	0.43122	Calculated from MSINI and I
KELT-7 b	1.535	Bieryla et al. (2015)	1.28	Bieryla et al. (2015)
KELT-8 b	0.81	Stassun et al. (2017)	0.66	Stassun et al. (2017)
KELT-9 b	2.52	Gaudi et al. (2017)	2.88	Gaudi et al. (2017)
KELT-15 b	2.06	Stassun et al. (2017)	1.31	Stassun et al. (2017)
KELT-16 b	1.21	Oberst et al. (2017)	2.75	Oberst et al. (2017)
KELT-17 b	1.64	Zhou et al. (2016)	1.31	Zhou et al. (2016)
KELT-18 b	1.52	McLeod et al. (2017)	1.18	McLeod et al. (2017)
KELT-20 b	1.76	Lund et al. (2017)	3.382	Lund et al. (2017)
KELT-21 b	1.46	Johnson et al. (2018)	3.91	Johnson et al. (2018)
KELT-24 b	1.46	Rodriguez et al. (2019)	5.18	Rodriguez et al. (2019)
KPS-1 b	0.89	Burdanov et al. (2018)	1.09	Burdanov et al. (2018)
MASCARA-4 b	1.75	Dorval et al. (2020)	3.1	Dorval et al. (2020)
NGTS-1 b	0.62	Bayliss et al. (2018)	0.812	Bayliss et al. (2018)
NGTS-2 b	1.64	Raynard et al. (2018)	0.74	Raynard et al. (2018)
NGTS-3 A b	1.02	Günther et al. (2018)	2.38	Günther et al. (2018)
NGTS-6 b	0.77	Vines et al. (2019)	1.339	Vines et al. (2019)
NGTS-9 b	1.34	Costes et al. (2020)	2.9	Costes et al. (2020)
OGLE-TR-113 b	0.779	Torres et al. (2008b)	1.26	Torres et al. (2008b)
Qatar-1 b	0.85	Alsubai et al. (2011)	1.08979	Calculated from MSINI and I
Qatar-6 b	0.82	Alsubai et al. (2018)	0.668	Alsubai et al. (2018)
Qatar-7 b	1.41	Alsubai et al. (2019a)	1.88	Alsubai et al. (2019a)
Qatar-8 b	1.03	Alsubai et al. (2019b)	0.371	Alsubai et al. (2019b)
Qatar-9 b	0.72	Alsubai et al. (2019b)	1.19	Alsubai et al. (2019b)
Qatar-10 b	1.16	Alsubai et al. (2019b)	0.736	Alsubai et al. (2019b)
TrES-1 b	0.878	Torres et al. (2008b)	0.752484	Calculated from MSINI and I
TrES-2 b	0.983	Torres et al. (2008b)	1.20071	Calculated from MSINI and I
TrES-3 b	0.915	Torres et al. (2008b)	1.91	Sozzetti et al. (2009)
TrES-4 b	1.394	Torres et al. (2008b)	0.925	Sozzetti et al. (2009)
TrES-5 b	0.893	Mandushev et al. (2011)	1.7781	Calculated from MSINI and I
WASP-1 b	1.2	Enoch et al. (2010)	0.918	Simpson et al. (2011a)
WASP-2 b	0.88	Enoch et al. (2010)	0.908659	Calculated from MSINI and I
WASP-3 b	1.22	Enoch et al. (2010)	2.01184	Calculated from MSINI and I
WASP-4 b	0.91	Enoch et al. (2010)	1.22311	Calculated from MSINI and I
WASP-5 b	1.01	Enoch et al. (2010)	1.62423	Calculated from MSINI and I
WASP-6 b	0.93	Enoch et al. (2010)	0.52136	Calculated from MSINI and I
WASP-7 b	1.2	Enoch et al. (2010)	0.919279	Calculated from MSINI and I
WASP-8 b	1.03	Queloz et al. (2010)	2.13797	Queloz et al. (2010)
WASP-10 b	0.79	Enoch et al. (2010)	3.19144	Calculated from MSINI and I
WASP-11 b	0.8	Enoch et al. (2010)	0.539755	Calculated from MSINI and I
WASP-12 b	1.28	Enoch et al. (2010)	1.36063	Calculated from MSINI and I
WASP-13 b	1.09	Barros et al. (2012)	0.473883	Calculated from MSINI and I
WASP-14 b	1.31	Enoch et al. (2010)	7.69234	Calculated from MSINI and I
WASP-15 b	1.18	Enoch et al. (2010)	0.542797	Calculated from MSINI and I
WASP-16 b	1.0	Enoch et al. (2010)	0.842294	Calculated from MSINI and I
WASP-17 b	1.19	Enoch et al. (2010)	0.508547	Calculated from MSINI and I
WASP-18 b	1.22	Enoch et al. (2010)	10.2006	Calculated from MSINI and I
WASP-19 b	0.93	Enoch et al. (2010)	1.13339	Calculated from MSINI and I
WASP-20 b	1.2	Anderson et al. (2015)	0.311	Anderson et al. (2015)
WASP-21 b	1.01	Bouchy et al. (2010)	0.300272	Calculated from MSINI and I
WASP-22 b	1.1	Maxted et al. (2010)	0.559059	Calculated from MSINI and I
WASP-23 b	0.78	Triaud et al. (2011)	0.872226	Calculated from MSINI and I
WASP-24 b	1.184	Street et al. (2010)	1.091	Calculated from MSINI and I
WASP-25 b	1.0	Enoch et al. (2011a)	0.57847	Calculated from MSINI and I
WASP-26 b	1.12	Smalley et al. (2010)	1.01746	Calculated from MSINI and I
WASP-31 b	1.165	Anderson et al. (2011)	0.479329	Calculated from MSINI and I
WASP-32 b	1.07	Brown et al. (2012)	3.45362	Calculated from MSINI and I
WASP-34 b	1.01	Smalley et al. (2011)	0.583354	Calculated from MSINI and I
WASP-35 b	1.07	Enoch et al. (2011b)	0.717098	Calculated from MSINI and I
WASP-36 b	1.02	Smith et al. (2012a)	2.26929	Calculated from MSINI and I
WASP-37 b	0.925	Simpson et al. (2011b)	1.79362	Calculated from MSINI and I
WASP-39 b	0.93	Faedi et al. (2011)	0.284338	Calculated from MSINI and I
WASP-41 b	0.93	Neveu-VanMalle et al. (2016)	0.939101	Calculated from MSINI and I
WASP-42 b	0.881	Lendl et al. (2012)	0.496968	Calculated from MSINI and I
WASP-43 b	0.58	Hellier et al. (2011)	1.77609	Calculated from MSINI and I
WASP-44 b	0.951	Anderson et al. (2013)	0.889836	Calculated from MSINI and I
WASP-45 b	0.909	Anderson et al. (2013)	1.00657	Calculated from MSINI and I
WASP-46 b	0.956	Anderson et al. (2013)	2.10232	Calculated from MSINI and I
WASP-47 b	1.02	Mortier et al. (2013)	1.12341	Calculated from MSINI and I
WASP-48 b	1.19	Enoch et al. (2011b)	0.984236	Calculated from MSINI and I
WASP-49 b	0.938	Lendl et al. (2012)	0.378231	Calculated from MSINI and I
WASP-50 b	0.892	Gillon et al. (2011)	1.47244	Calculated from MSINI and I
WASP-53 b	0.84	Triaud et al. (2017)	2.132	Triaud et al. (2017)
WASP-54 b	1.213	Faedi et al. (2013)	0.63273	Calculated from MSINI and I
WASP-56 b	1.107	Faedi et al. (2013)	0.605385	Calculated from MSINI and I
WASP-57 b	0.954	Faedi et al. (2013)	0.675887	Calculated from MSINI and I
WASP-58 b	0.94	Hébrard et al. (2013)	0.891379	Calculated from MSINI and I
WASP-59 b	0.719	Hébrard et al. (2013)	0.859095	Calculated from MSINI and I
WASP-60 b	1.078	Hébrard et al. (2013)	0.512143	Calculated from MSINI and I
WASP-61 b	1.22	Hellier et al. (2012)	2.05491	Calculated from MSINI and I
WASP-62 b	1.25	Hellier et al. (2012)	0.56227	Calculated from MSINI and I
WASP-63 b	1.32	Hellier et al. (2012)	0.378096	Calculated from MSINI and I
WASP-64 b	1.004	Gillon et al. (2013)	1.27137	Calculated from MSINI and I
WASP-65 b	0.93	Gómez Maqueo Chew et al. (2013)	1.55	Gómez Maqueo Chew et al. (2013)
WASP-66 b	1.3	Hellier et al. (2012)	2.31346	Calculated from MSINI and I
WASP-69 b	0.826	Anderson et al. (2014)	0.259543	Calculated from MSINI and I
WASP-71 b	1.572	Smith et al. (2013)	2.242	Smith et al. (2013)
WASP-72 b	1.327	Gillon et al. (2013)	1.40771	Calculated from MSINI and I
WASP-73 b	1.34	Delrez et al. (2014)	1.88059	Calculated from MSINI and I
WASP-78 b	1.33	Smalley et al. (2012)	0.883997	Calculated from MSINI and I
WASP-79 b	1.52	Smalley et al. (2012)	0.887514	Calculated from MSINI and I
WASP-80 b	0.58	Triaud et al. (2013)	0.551763	Calculated from MSINI and I
WASP-81 b	1.08	Triaud et al. (2017)	0.729	Triaud et al. (2017)
WASP-82 b	1.64	Smith (2015)	1.25	Smith (2015)
WASP-83 b	1.11	Hellier et al. (2015)	0.3	Hellier et al. (2015)
WASP-84 b	0.842	Anderson et al. (2014)	0.69431	Calculated from MSINI and I
WASP-87 b	1.2	Addison et al. (2016)	2.18	Addison et al. (2016)
WASP-90 b	1.55	West et al. (2016)	0.63	West et al. (2016)
WASP-91 b	0.84	Anderson et al. (2017)	1.34	Anderson et al. (2017)
WASP-92 b	1.19	Hay et al. (2016)	0.805	Hay et al. (2016)
WASP-93 b	1.33	Hay et al. (2016)	1.47	Hay et al. (2016)
WASP-104 b	1.076	Smith et al. (2014)	1.272	Smith et al. (2014)
WASP-105 b	0.89	Anderson et al. (2017)	1.8	Anderson et al. (2017)
WASP-106 b	1.092	Smith et al. (2014)	1.925	Smith et al. (2014)
WASP-113 b	1.32	Barros et al. (2016)	0.475	Barros et al. (2016)
WASP-118 b	1.32	Hay et al. (2016)	0.514	Hay et al. (2016)
WASP-119 b	1.02	Maxted et al. (2016)	1.23	Maxted et al. (2016)
WASP-120 b	1.39	Turner et al. (2016)	4.85	Turner et al. (2016)
WASP-121 b	1.36	Bourrier et al. (2020)	1.157	Bourrier et al. (2020)
WASP-123 b	1.17	Turner et al. (2016)	0.899	Turner et al. (2016)
WASP-124 b	1.07	Maxted et al. (2016)	0.6	Maxted et al. (2016)
WASP-126 b	1.12	Pearson (2019)	0.28411	Pearson (2019)
WASP-129 b	1.0	Maxted et al. (2016)	1.0	Maxted et al. (2016)
WASP-131 b	1.06	Hellier et al. (2017)	0.27	Hellier et al. (2017)
WASP-132 b	0.78	Hord et al. (2022)	0.41	Hord et al. (2022)
WASP-135 b	0.98	Spake et al. (2016)	1.90043	Calculated from MSINI and I
WASP-136 b	1.41	Lam et al. (2017)	1.51	Lam et al. (2017)
WASP-138 b	1.22	Lam et al. (2017)	1.22	Lam et al. (2017)
WASP-140 b	0.9	Hellier et al. (2017)	2.44	Hellier et al. (2017)
WASP-141 b	1.25	Hellier et al. (2017)	2.69	Hellier et al. (2017)
WASP-142 b	1.33	Hellier et al. (2017)	0.84	Hellier et al. (2017)
WASP-144 b	0.81	Hellier et al. (2019a)	0.44	Hellier et al. (2019a)
WASP-147 b	1.04	Lendl et al. (2019)	0.275	Lendl et al. (2019)
WASP-148 b	0.95	Almenara et al. (2022)	0.287	Almenara et al. (2022)
WASP-150 b	1.39	Cooke et al. (2020)	8.46	Cooke et al. (2020)
WASP-151 b	1.08	Močnik et al. (2020)	0.316	Močnik et al. (2020)
WASP-153 b	1.34	Demangeon et al. (2018)	0.39	Demangeon et al. (2018)
WASP-159 b	1.41	Hellier et al. (2019a)	0.55	Hellier et al. (2019a)
WASP-160 B b	0.87	Lendl et al. (2019)	0.278	Lendl et al. (2019)
WASP-161 b	1.39	Barkaoui et al. (2019)	2.49	Barkaoui et al. (2019)
WASP-162 b	0.95	Hellier et al. (2019a)	5.2	Hellier et al. (2019a)
WASP-164 b	0.95	Lendl et al. (2019)	2.13	Lendl et al. (2019)
WASP-165 b	1.25	Lendl et al. (2019)	0.658	Lendl et al. (2019)
WASP-168 b	1.08	Hellier et al. (2019a)	0.42	Hellier et al. (2019a)
WASP-169 b	1.34	Nielsen et al. (2019)	0.561	Nielsen et al. (2019)
WASP-170 b	0.93	Barkaoui et al. (2019)	1.6	Barkaoui et al. (2019)
WASP-171 b	1.17	Nielsen et al. (2019)	1.084	Nielsen et al. (2019)
WASP-172 b	1.49	Hellier et al. (2019a)	0.47	Hellier et al. (2019a)
WASP-174 b	1.24	Mancini et al. (2020)	0.33	Mancini et al. (2020)
WASP-175 b	1.21	Nielsen et al. (2019)	0.99	Nielsen et al. (2019)
WASP-176 b	1.34	Cooke et al. (2020)	0.855	Cooke et al. (2020)
WASP-178 b	2.07	Hellier et al. (2019b)	1.66	Hellier et al. (2019b)
WASP-181 b	1.04	Turner et al. (2019)	0.299	Turner et al. (2019)
WASP-183 b	0.78	Turner et al. (2019)	0.502	Turner et al. (2019)
WASP-184 b	1.23	Hellier et al. (2019b)	0.57	Hellier et al. (2019b)
WASP-186 b	1.22	Schanche et al. (2020)	4.22	Schanche et al. (2020)
WASP-187 b	1.54	Schanche et al. (2020)	0.8	Schanche et al. (2020)
WASP-190 b	1.35	Temple et al. (2019)	1.0	Temple et al. (2019)
WASP-192 b	1.09	Hellier et al. (2019b)	2.3	Hellier et al. (2019b)
Wendelstein-1 b	0.65	Obermeier et al. (2020)	0.592	Obermeier et al. (2020)
XO-1 b	1.027	Torres et al. (2008b)	0.918464	Calculated from MSINI and I
XO-2 b	0.974	Torres et al. (2008b)	0.566541	Calculated from MSINI and I
XO-3 b	1.41	Johns-Krull et al. (2008)	13.2849	Calculated from MSINI and I
XO-4 b	1.1	Stassun et al. (2017)	1.42	Stassun et al. (2017)
XO-5 b	1.0	Burke et al. (2008)	1.15251	Calculated from MSINI and I
XO-6 b	1.47	Crouzet et al. (2017)	4.4	Crouzet et al. (2017)
XO-7 b	1.41	Crouzet et al. (2020)	0.709	Crouzet et al. (2020)