Giant Planets: Good Neighbors for Habitable Worlds?

The discovery of planets of similar size to that of Earth has led to numerous interdisciplinary research activities about the potential habitability of other worlds (Cockell et al. 2016). Previous studies suggest that the presence of a giant planet in the same extrasolar planetary system can affect the gestation and evolution of potentially habitable planets in various ways. During the planetary system's formation, a giant planet can operate as a dynamical barrier that blocks the inward migration of protoplanetary cores (Izidoro et al. 2015). This is important for the gestation of habitable planets, since the absence of a giant planet allows super-Earths to migrate inward with the danger of strongly depleting the terrestrial planet forming zones of accretion material (Izidoro et al. 2014). Systems where hot Jupiters form in the outer parts of the disk and then migrate inward seem to be unfavorable places for habitable worlds. Yet, not only it is possible to have terrestrial planets in the habitable zones³ of such systems, but it is also likely that these planets have a substantial amount of liquid water owing to the formation and inward migration history of the giant planet (Fogg & Nelson 2007; Mandell et al. 2007). While the presence of a giant planet close to the habitable zone can mean dynamical chaos and instability for Earth analogs (Sándor et al. 2007), giant planets residing within the habitable zone can be hosts to habitable Trojan planets (Schwarz et al. 2005) or habitable exomoons (Heller et al. 2014), assuming that the latter were not removed through an evection resonance during the planetary migration phase (Spalding et al. 2016). Even after the planetary formation, phase giant planets continue to influence habitable conditions on terrestrial neighbors. Large impacts of minor bodies on terrestrial planets, for instance, may be decisive for the existence of liquid water and the evolution of life (Kring 2003; Dvorak et al. 2012), and the presence of giant planets can increase the impact flux of comets and other minor bodies on terrestrial planets and hence the delivery of life-enabling volatiles (Horner & Jones 2008, 2009; Horner et al. 2010; Grazier 2016). Once life has emerged, however, impacts of asteroids and comets can trigger mass extinction events (Davis et al. 1984; Kaiho & Oshima 2017). The sometimes contradictory nature of the aforementioned processes shows that the role giant planets play for habitable worlds is not clear-cut.

This work is concerned with yet another vital piece in the puzzle. For planets such as our Earth the incoming stellar radiation constitutes the main energy source that determines the global climate on long timescales (Kasting et al. 1993). Consequently, the quantity and spectral distribution of insolation defines where a terrestrial planet can host liquid water close to its surface, which is the prime condition for habitability. Planetary atmospheres can react strongly to changes in the incoming starlight, so that variations in some of the orbital elements or the obliquity of the planet constitute an important factor in assessing a planet's capacity to remain far from runaway states (Dressing et al. 2010; Spiegel et al. 2010; Bolmont et al. 2016). This is where giant planet "neighbors" enter the picture. The sheer presence of a giant planet in an exoplanetary system alters the orbit of a potentially habitable world over time. This effect may be very mild—a small change in the orbital elements of the terrestrial planet that results in spending some time outside the habitable insolation limits—or very dramatic, leading to an eventual escape of the terrestrial planet from the system. In our solar system, for instance, Earth's orbital eccentricity oscillates from 0 to 0.06 owing to the long-term perturbations of the other planets over a period of a few million years (Laskar et al. 2004). These so-called Milankovitch cycles have been linked to recent glaciation and interglacial periods (Horner & Jones 2011; Kaufmann & Juselius 2016). While Earth experiences such variations over long timescales, this may not be the case for other terrestrial planets in exoplanetary systems. The dynamical interactions of planets in the habitable zone with a more massive planet have been extensively studied in the past (e.g., Menou & Tabachnik 2003; Jones et al. 2005; Sándor et al. 2007; von Bloh et al. 2007; Dvorak et al. 2010; Kopparapu & Barnes 2010; Carrera et al. 2016; Agnew et al. 2017). Previous studies mainly focused on the orbital stability of the terrestrial planet assuming the habitable zone limits to be independent of the terrestrial planet's orbit. This assumption, however, is only valid for terrestrial planets on a circular, unperturbed orbit. In this work, we study the effects of the presence of a giant planet on the habitability of an additional Earth-like planet in a more self-consistent manner. By using analytical solutions for the evolution of a terrestrial planet under the gravitational perturbations of the giant planet, we are able to calculate the actual insolation received by a potentially habitable world. Having estimates of the insolation extrema and variability⁴ for any given system configuration at our disposal, we are able to determine more realistic habitable zone limits.

The practically circular orbit of Earth around the Sun and the relatively small variations in the luminosity of our star entail that we receive a near-constant amount of sunlight on a permanent basis. For similar systems consisting of a star and a terrestrial planet on a fixed circular orbit, the limits of the (classical) habitable zone (CHZ) read (Kasting et al. 1993)

$$\begin{eqnarray}&&{r}_{I}={\left(\displaystyle \frac{L}{{S}_{I}}\right)}^{\tfrac{1}{2}}\hspace{0.4cm}{\rm{and}}\qquad {r}_{O}={\left(\displaystyle \frac{L}{{S}_{O}}\right)}^{\tfrac{1}{2}},\end{eqnarray} \tag{ 1 }$$

where r is the distance of the planet to its host star in astronomical units, L is the host star's luminosity in solar luminosities, and S_I and S_O are "spectral weights" corresponding to the number of solar constants that trigger a runaway greenhouse process (subscript I) evaporating surface oceans, or a snowball state (subscript O) freezing oceans on a global scale. These spectral weights are functions of the effective temperature of the host star. As such they take the specific wavelength distribution of a star's light into account. They constitute the most popular way to estimate the reaction of a terrestrial planet's climate to the amount and spectral distribution of the incoming stellar radiation based on parameterization of globally averaged radiative-convective energy balance models (Kasting et al. 1993; Kopparapu et al. 2013, 2014). The latter provide "spectral weights" associated with the borders of the inner and outer edge of the habitable zone:

$$\begin{eqnarray}{S}_{I} & = & 1.107+1.332\cdot {10}^{-4}{T}_{c}+1.580\cdot {10}^{-8}{T}_{c}^{2}\\ & & -\,8.308\cdot {10}^{-12}{T}_{c}^{3}-1.931\cdot {10}^{-15}{T}_{c}^{4}\end{eqnarray} \tag{ 2 }$$

$$\begin{eqnarray}{S}_{O} & = & 0.356+6.171\cdot {10}^{-5}{T}_{c}+1.698\cdot {10}^{-9}{T}_{c}^{2}\\ & & -\,3.198\cdot {10}^{-12}{T}_{c}^{3}-5.575\cdot {10}^{-16}{T}_{c}^{4}.\end{eqnarray} \tag{ 3 }$$

${T}_{c}={T}_{\mathrm{eff}}/1\ K-5780$, with T_eff being the effective temperature of the star, while the value of 5780 used in the above fit formulae corresponds to the effective temperature T_⊙ of the Sun. Although the coefficients in Equations (2) and (3) refer to a planet of one Earth mass, they have also been evaluated for different terrestrial planet masses (Kopparapu et al. 2014). In order to calculate the habitable zone borders, the luminosity of the host star has to be known. In case stellar luminosities have not been observed directly, one can use stellar radii R and effective temperatures T_eff instead:

$$\begin{eqnarray*}&&\displaystyle \frac{L}{{L}_{\odot }}={\left(\displaystyle \frac{R}{{R}_{\odot }}\right)}^{2}{\left(\displaystyle \frac{{T}_{\mathrm{eff}}}{{T}_{\odot }}\right)}^{4},\end{eqnarray*}$$

where R_⊙ is the solar radius. The corresponding uncertainties are best determined via nonlinear estimators.

CHZ borders that are calculated from spectral weights are based on the implicit assumption that the energy flux arriving at the top of the atmosphere of a potentially habitable world remains constant on timescales long enough so that incoming radiation and outgoing radiation reach an equilibrium state. Stable climatic conditions on the planet are linked to such equilibrium states. The distance of a planet to its star and consequently the amount of light a planet receives depend on its orbit, however. Equations (1) for CHZ borders assume a constant amount of insolation. They are, therefore, valid for terrestrial planets on circular orbits only. The coexistence of a giant planet and a terrestrial planet in the same exoplanetary system necessitates a modification of this concept. Giant planets can alter the orbits of terrestrial planets in nontrivial, time-dependent fashion. This implies that insolation can vary substantially with time. For Earth-like planets on variable orbits, the minimum and maximum distances of the planet with respect to its host star determine the maximum and minimum insolation the planet experiences on its long-term orbit. Based on long-term radiative equilibrium calculations, the standard climate model (Kasting et al. 1993; Kopparapu et al. 2013, 2014) used to calculate habitable zone limits is not meant to resolve time-dependent variations in the amount of insolation.

How quickly an Earth-like planet's climate reacts and adapts to such a time-dependent forcing is not completely understood (Bolmont et al. 2016; Popp & Eggl 2017; Way & Georgakarakos 2017). We therefore consider three possible scenarios based on the concept of "climate inertia." Zero climate inertia means that the planet's climate reacts quasi-instantaneously to changes in insolation. This poses strict constraints on the apocenter and pericenter distances a planet can attain in order not to enter a runaway or a freeze-out state. Previous studies (Williams & Pollard 2002) suggest, however, that a planet's climate can buffer changes in insolation to some degree. This corresponds to a finite climate inertia. If the climate inertia tends toward infinity, any variation in insolation can be buffered as long as the insolation average over one orbital period stays within reasonable (habitable) limits.

4.1. Definitions

4.2. Calculating Dynamically Informed Habitable Zones

Quantifying the concept of climate inertia, dynamically informed habitable zones can deal with elliptic and variable orbits of terrestrial planets. They can be calculated in the following manner. The PHZ can be found by identifying the minimum and maximum distances to the host star along the time-dependent orbit. For a coplanar hierarchical system that is dynamically stable, changes in orbital semimajor axes are practically negligible, and hence the semimajor axes remain constant over long timescales (e.g., Harrington 1968). Then, the only relevant variable to change with time is e(t). The PHZ borders must not become time dependent themselves, however. We can solve this issue by searching for ${\max }_{t}\ e(t)={e}^{\max }$, the estimated maximum eccentricity that the terrestrial planet reaches during its orbital evolution. The corresponding minimum and maximum distances to the host star then read ${r}_{\min }=a(1-{e}^{\max })$ and ${r}_{\max }=a(1+{e}^{\max })$, where a is the terrestrial planet semimajor axis. Consequently, the inner and outer borders of the PHZ can be found by solving the equations

$$\begin{eqnarray}&&{S}_{I}=L{[a(1-{e}^{\max })]}^{-2},\qquad {S}_{O}=L{[a(1+{e}^{\max })]}^{-2},\end{eqnarray} \tag{ 4 }$$

with respect to a. In a coplanar setup, the solution of Equations (4) yields circles around the host star defining the edges of the PHZ. The gravitational influence of the giant planet on the orbit of the terrestrial world depends on the configuration of the system, so that the maximum eccentricity, although independent of time, is still a function of other system parameters, such as the terrestrial planet's and the giant planet's semimajor axes (a, a_g) and initial eccentricities (e₀, e_g), as well as the masses of the celestial bodies in the system: the stellar mass m_*, the giant planet mass m_g, and the terrestrial planet mass m. The inner and outer borders of the PHZ form an annulus around the host star spanning from ${a}_{{I}}({S}_{{I}},\,{a}_{{g}},\,{e}_{{\rm{0}}},\,{e}_{{g}},\,m,\,{m}_{{g}},\,m\ast )$ to ${a}_{{O}}({S}_{{O}},\,{a}_{{g}},\,{e}_{{\rm{0}}},\,{e}_{{g}},\,m,\,{m}_{{g}},m\ast )$. In most of the cases, Equations (4) cannot be transformed into an explicit expression for a, because e^max generally depends on a in a nontrivial manner. They need to be calculated using numerical techniques for implicit equations. The CHZ borders can serve as initial starting points for the corresponding algorithm. Only in the most simple cases can explicit expressions be found (see Appendix A.4).

In order to find the borders of the AHZ, where we assume that the planet has a very high climate inertia, we need to solve

$$\begin{eqnarray}&&\langle S\rangle ={S}_{I},\qquad \langle S\rangle ={S}_{O}\end{eqnarray} \tag{ 5 }$$

in terms of a, where S is the insolation (in units of solar constants) that the terrestrial planet receives. The averaged over time insolation that the terrestrial planet receives is

$$\begin{eqnarray}&&\langle S\rangle =\displaystyle \frac{1}{{P}_{s}}{\int }_{0}^{{P}_{s}}\displaystyle \frac{L}{{r}^{2}(t)}{dt},\end{eqnarray} \tag{ 6 }$$

where we average over P_s, the secular period of the terrestrial planet's orbit. Neglecting short-period and resonant terms, the planet's orbit evolution returns to its initial state after P_s. Hence, the average over one P_s becomes equivalent to the average over $t\to \infty$. For practical reasons, it is more convenient to transform the time average into averages over angular quantities (Arnold 1978). Equation (6) then becomes

$$\begin{eqnarray}\langle S\rangle & \approx & \displaystyle \frac{L}{4{\pi }^{2}}{\displaystyle \int }_{0}^{2\pi }{\displaystyle \int }_{0}^{2\pi }\displaystyle \frac{1}{{a}^{2}{(1-{e}^{2})}^{\tfrac{1}{2}}}{dfd}\phi \\ & \approx & \displaystyle \frac{L}{4{\pi }^{2}}{\displaystyle \int }_{0}^{2\pi }{\displaystyle \int }_{0}^{2\pi }\displaystyle \frac{1+(1/2){e}^{2}}{{a}^{2}}{dfd}\phi \\ & = & L\displaystyle \frac{1+(1/2)\langle {e}^{2}\rangle }{{a}^{2}},\end{eqnarray} \tag{ 7 }$$

where we have used Kepler's second law

$$\begin{eqnarray*}&&\displaystyle \frac{{dt}}{{r}^{2}(t)}=\displaystyle \frac{{df}}{{{na}}^{2}{(1-{e}^{2})}^{1/2}}.\end{eqnarray*}$$

Here, n is the mean motion of the terrestrial planet. Moreover, $\langle {e}^{2}\rangle$ is the averaged squared terrestrial planet eccentricity and $\phi =\nu t$, where $\nu =2\pi /{P}_{s}$ is the analytical estimate for the secular frequency of the motion of the terrestrial planet; see Appendix A.2. The first "approximately equal" sign in Equation (7) occurs owing to the fact that the two frequencies ${df}(t)/{dt}$ and ν are not independent. However, since the secular timescale is much longer than the orbital period of the terrestrial planet, we have made the assumption that $\nu \ll {df}(t)/{dt}$ so that we can consider the system to evolve independently on orbital and secular timescales. The second "approximately equal" sign in Equation (7) is used because we carry out a binomial expansion and we only keep the first term of that expansion in $\langle {e}^{2}\rangle$.

The above formula for $\langle S\rangle$ holds for the case of an initially zero planetary eccentricity. However, it is likely that terrestrial planets form on slightly elliptic orbits owing to the interaction between the giant planet and the primordial disk. More specifically, the initial eccentricity of the terrestrial planet's orbit is dampened toward the forced eccentricity injected by the giant planet (Mardling 2007). In that case the eccentricity remains constant and the averaged insolation reads

$$\begin{eqnarray*}\langle S\rangle & = & \displaystyle \frac{1}{{P}_{s}}{\displaystyle \int }_{0}^{{P}_{s}}\displaystyle \frac{L}{{r}^{2}(t)}{dt}=\displaystyle \frac{L}{2\pi }{\displaystyle \int }_{0}^{2\pi }\displaystyle \frac{1}{{a}^{2}{(1-{e}^{2})}^{\tfrac{1}{2}}}{df}\\ & = & \displaystyle \frac{L}{{a}^{2}{(1-{e}^{2})}^{\tfrac{1}{2}}}.\end{eqnarray*}$$

Finally, the EHZ corresponding to a planet with intermediate climate inertia can be found by solving

$$\begin{eqnarray}&&\langle S\rangle +\sigma ={S}_{I},\qquad \langle S\rangle -\sigma ={S}_{O}\end{eqnarray} \tag{ 8 }$$

in terms of a. Hence, in addition to the averaged over time insolation, we need to find the insolation variance σ.

Regarding the variance of the insolation, we know that

$$\begin{eqnarray*}&&{\sigma }^{2}=\langle {S}^{2}\rangle -\langle S{\rangle }^{2}.\end{eqnarray*}$$

For a terrestrial planet perturbed by a giant planet we have

$$\begin{eqnarray*}\langle {S}^{2}\rangle & = & \displaystyle \frac{1}{{P}_{s}}{\displaystyle \int }_{0}^{{P}_{s}}\displaystyle \frac{{L}^{2}}{{r}^{4}(t)}{dt}\approx \displaystyle \frac{{L}^{2}}{4{\pi }^{2}}{\displaystyle \int }_{0}^{2\pi }{\displaystyle \int }_{0}^{2\pi }\displaystyle \frac{{(1+e\cos f)}^{2}}{{a}^{4}{(1-{e}^{2})}^{\tfrac{5}{2}}}{dfd}\phi \\ & \approx & \displaystyle \frac{{L}^{2}}{4{\pi }^{2}}{\displaystyle \int }_{0}^{2\pi }{\displaystyle \int }_{0}^{2\pi }\displaystyle \frac{{(1+e\cos f)}^{2}(1+\tfrac{5}{2}{e}^{2})}{{a}^{4}}{dfd}\phi \\ & = & {L}^{2}\displaystyle \frac{1+3\langle {e}^{2}\rangle }{{a}^{4}},\end{eqnarray*}$$

and consequently

$$\begin{eqnarray*}&&{\sigma }^{2}={L}^{2}\displaystyle \frac{2\langle {e}^{2}\rangle -(1/4)\langle {e}^{2}{\rangle }^{2}}{{a}^{4}}\approx {L}^{2}\displaystyle \frac{2\langle {e}^{2}\rangle }{{a}^{4}}.\end{eqnarray*}$$

When e is constant, then

$$\begin{eqnarray*}\langle {S}^{2}\rangle & = & \displaystyle \frac{1}{{P}_{s}}{\displaystyle \int }_{0}^{{P}_{s}}\displaystyle \frac{{L}^{2}}{{r}^{4}(t)}{dt}=\displaystyle \frac{{L}^{2}}{2\pi }{\displaystyle \int }_{0}^{2\pi }\displaystyle \frac{{(1+e\cos f)}^{2}}{{a}^{4}{(1-{e}^{2})}^{\tfrac{5}{2}}}{df}\\ & = & \displaystyle \frac{{L}^{2}}{2{a}^{4}}\displaystyle \frac{2+{e}^{2}}{{(1-{e}^{2})}^{\tfrac{5}{2}}}\end{eqnarray*}$$

and consequently

$$\begin{eqnarray*}&&{\sigma }^{2}=\displaystyle \frac{{L}^{2}}{{a}^{4}}\left[\displaystyle \frac{1+(1/2){e}^{2}}{{(1-{e}^{2})}^{\tfrac{5}{2}}}-\displaystyle \frac{1}{(1-{e}^{2})}\right].\end{eqnarray*}$$

We should point out here that as a consequence of the way we have defined the PHZ and the EHZ, these two zones will always be narrower than the CHZ. From Equations (4) and (8) it can be seen that the inner border of either the PHZ or the EHZ will be located farther out than the inner edge of the CHZ, while the outer borders will be inside the outer edge of the CHZ. On the other hand, Equation (5) tell us that both borders of the AHZ will be shifted away from the star. This implies that it is possible in certain cases to have an AHZ that is wider than the CHZ.

In all the above calculations the stellar radii, luminosities, and effective temperatures are assumed constant on the timescale of the orbital evolution of the terrestrial planet. Hence, the borders of dynamically informed habitable zones are functions of constant system parameters only and independent of time. Expressions for e^max and $\langle {e}^{2}\rangle$ are given in Appendix A. The equations for PHZ, EHZ, and AHZ do not depend on any details of the underlying dynamical model. They work as long as values for e^max and $\langle {e}^{2}\rangle$ can be provided. Similarly, limits for the habitable insolation values S_I and S_O can be chosen differently from those used (Kopparapu et al. 2014) in this work, if so desired. This makes the here-presented method extremely versatile. Figure 1 contains a graphical representation of DIHZ for the HD 150706 system.

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4.3. Dynamically Informed versus Classical Habitable Zones

Do the changes in the orbit of a terrestrial planet induced by a gas giant merit the additional effort of calculating dynamically informed habitable zones? In order to answer this question, we can determine the percentage relative displacement of the PHZ borders with respect to the CHZ borders:

$$\begin{eqnarray*}&&{D}_{I,O}=100\displaystyle \frac{| {r}_{I,O}-{\mathrm{PHZ}}_{I,O}| }{{r}_{I,O}}.\end{eqnarray*}$$

Using Equations (1) and (4), we find

$$\begin{eqnarray*}&&{D}_{I}=100\displaystyle \frac{{e}^{\max }}{1-{e}^{\max }},\quad {D}_{O}=100\displaystyle \frac{{e}^{\max }}{1+{e}^{\max }}.\end{eqnarray*}$$

We choose the PHZ for the comparison as it provides the most conservative estimates of all the types of habitable zones. Planets in the PHZ are the most likely to be habitable. Figure 2 is a graphical representation of the percentage relative displacement for both inner and outer habitable zone borders assuming a giant planet at various distances in S-type (the giant planet's pericenter distance is larger than the distance of the outer border of the CHZ) and P-type configuration (the apocenter distance of the giant planet is smaller than the distance of the inner border of the CHZ). We use the lowest-order secular model, and we also assume that the stellar mass is much larger than the planetary masses; then the expression for e^max is independent of the masses of the system (see Appendix A.2). The displacement increases as ${a}_{g}/{r}_{I,O}$ gets smaller for an S-type system or as ${r}_{I,O}/{a}_{g}$ decreases when we deal with a P-type system. Higher eccentricities of the giant planet's orbit also shrink the PHZ with respect to the CHZ. In fact, even at a distance of 30 au a Jupiter-sized planet with ${e}_{g}\gt 0.8$ can displace the HZ borders around a Sun-like star by up to 50%. It is worth noting that for a given distance of the giant planet to the Earth analog, terrestrial planets close to the inner edge of the HZ are more severely affected by the gravitational influence of the giant planet than Earth-like worlds close to the outer edge of the HZ. This is due to the fact that the magnitude of the insolation gradient $| {\rm{\nabla }}S(r)| \propto {r}^{-3}$ is steeper closer to the host star, causing larger changes in insolation for the same orbital eccentricity. Figure 2 becomes less accurate for smaller semimajor axis ratios (e.g., lower than 4), as the plots were constructed using only the lowest-order secular model. For semimajor axis ratios lower than 4 the higher-order model mentioned in Appendix A.2 would be more appropriate. Similarly, resonances start to become important as well in this region, so that a more complete dynamical model should be used.

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The DIHZs are used to assess which of the currently known exoplanet systems hosting a main-sequence star and a giant planet offer the highest chances of finding additional, potentially habitable worlds. Out of the known exoplanet population, we have selected 147 systems consisting of a star on the main sequence and a single giant planet with well-determined orbital parameters. We choose giant planets with masses in the range of $0.1{M}_{J}\mbox{--}13{M}_{J}$, M_J being the mass of Jupiter, and stars with an effective temperature 2600 K ≤ T_eff ≤ 7200 K and R_* ≤ 1.3 R_⊙. Our sample does not contain systems where the giant planet crosses the borders of the CHZ, as they could harbor habitable moons or Trojan planets, both of which require special treatment. Assuming the presence of an additional, fictitious Earth-like planet, we investigate the effect of the actual giant planet on the former if it were orbiting its host star in the vicinity of the system's CHZ.

In our sample, we have 131 P-type configurations and 16 S-type systems. Classifying the systems based on the orbital period of the giant planet, we have 123 hot Jupiters (T_g < 10 days, T_g being the orbital period of the giant planet), 9 warm Jupiters (10 days < T_g < 400 days), and 16 cold Jupiters (T_g > 400 days). The selected systems, together with their key parameters and corresponding uncertainties, can be found in Appendix B. In order to assess the influence a giant planet exerts on a terrestrial planet and its habitability, we calculate the extent of the CHZ and compare it to the extent of dynamically informed habitable zones. This comparison allows us to quantify the effect of the giant planet on the habitability of additional terrestrial planets yet to be discovered in those systems. For the borders of the CHZ, we have used the runaway greenhouse and the maximum greenhouse insolation limits. The percentage shrinkage (Σ),

$$\begin{eqnarray}&&{\rm{\Sigma }}(\mathrm{DIHZ})=100\left(1-\displaystyle \frac{{\mathrm{DIHZ}}_{O}-{\mathrm{DIHZ}}_{I}}{{r}_{O}-{r}_{I}}\right),\end{eqnarray} \tag{ 9 }$$

quantifies that notion, where DIHZ stands for the respective dynamically informed habitable zone (PHZ, EHZ, or AHZ). As before, subscripts I and O denote the inner and outer borders, respectively. If atmospheric buffering plays a large role in determining whether a system is habitable or not, values for Σ(PHZ) and Σ(AHZ) will differ substantially. Negative shrinkage values mean that the respective dynamically informed habitable zone is larger than the CHZ.

Figure 3 is a graphical representation of the habitable zone shrinkage as given in Equation (9) for the systems in our sample, where we have assumed that the terrestrial planet occupies the least excited dynamical state after the formation phase, i.e., its orbit's eccentricity corresponds to the forced eccentricity. Panel (b) in Figure 3 shows that hot Jupiters orbiting close to their host star have very little influence on a system's capability to host habitable worlds. In most hot Jupiter systems Σ(DIHZ) ≪ 1%. While terrestrial worlds seem to be sensitive to atmospheric buffering capabilities in such environments—there are differences of several orders of magnitude between AHZ and PHZ shrinkage values—both PHZ shrinkage and AHZ shrinkage are insignificant in absolute terms, however. This is to be expected, as most of the giant planets have zero or nearly zero eccentricities owing to tidal interactions with the host star, resulting in very small perturbations on the orbit of the terrestrial world. Such systems, therefore, appear to be good candidates for follow-up observations attempting to find additional habitable worlds. Moreover, the CHZ is an excellent approximation to the actual habitable region around the host star in systems with one hot Jupiter on a short-period orbit (P_g < 3 days). This assumes, of course, that no other planets populate the system. In systems with hot Jupiters on orbits with periods between 3 and 5 days habitable zones are somewhat smaller with a larger scatter compared to systems where giant planets have shorter orbital periods. This is a direct consequence of the larger variety of orbital eccentricities of those giant planets. Increased orbital eccentricity in giant planets close to their host star may be attributed to an unseen companion or less efficient tidal damping due to the larger distance from the host star. Higher giant planet eccentricities result in higher maximum and averaged square eccentricity for fictitious terrestrial planets in the system, which, in turn, cause smaller DIHZs.

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Those systems in our sample that contain warm or cold Jupiters exhibit the greatest shrinkage of the actual region where an Earth-like planet can harbor liquid water near its surface. In fact, in certain cases the habitable zones are completely eliminated (shrinkage of 100%), due to either a substantial growth in the orbital eccentricity of the terrestrial planet violating insolation constraints for habitability or complete dynamical instability of the CHZ. Warm and cold Jupiter systems are also more sensitive to climate inertia as demonstrated by the greater differences between AHZ and PHZ. Although such systems do not appear to be the most attractive targets in the search for habitable worlds, further interpretation is required here. There is a clear observational bias in our sample toward giant planets with short orbital periods and high eccentricities. Cold Jupiters on circular orbits will affect habitable zones significantly less than similar planets on eccentric orbits. As the former are more difficult to discover, our sample becomes very sparse in that domain. We therefore have to resort to theory-derived arguments rather than observational data to assess the consequences for habitable zones in systems where the giant planet orbits its host star at a greater distance. As seen in Section 4.3, we find that cold Jupiters well beyond the habitable zone (e.g., a_g/HZ_I > 4) on orbits with eccentricities lower than e_g < 0.3 do not substantially influence potentially habitable planets. In our solar system, for instance, Jupiter is located at 5.2 au with an eccentricity of e_g ≈ 0.05. Assuming an initially circular orbit for Earth, this translates into a Σ (PHZ) of 12%. If Jupiter had an e_g ≈ 0.1 eccentricity instead, the border displacements would double, leading to a PHZ shrinkage of around 22.

A glance at two systems from our sample, HD 13931 and HD 150706, confirms that higher eccentricities of giant planets can cause a substantial reduction of a system's habitable zone, even if the giant planets are relatively far out. HD 13931 hosts a giant planet roughly three times as massive as Jupiter on an almost circular orbit (e_g ≈ 0.02) with a semimajor axis of 5.15 au and an orbital period of 4218 days. The fact that HD 13931b orbits a Sun-like star makes this system very similar to our solar system. Panel (d) of Figure 3 shows that, unlike most of the other cold Jupiter systems in our sample, HD 13931 suffers relatively little HZ shrinkage, at most Σ(PHZ) ≈ 23%. The discrepancy between PHZ and AHZ is low as well, indicating that atmospheric buffering capabilities of additional terrestrial worlds are not crucial in this system. Thus, HD 13931 is a good candidate for follow-up observations. HD 150706b, on the other hand, orbits its Sun-like host star at a nominal distance of 6.7 au with an orbital eccentricity of 0.38. The planet has an expected mass around 9 M_J and an orbital period of a little more than 16 yr. The nominal PHZ shrinkage Σ(PHZ) in this system lies between 37% (e₀ = e_f) and 72% (e₀ = 0) depending on the dynamical state of the terrestrial planet. However, uncertainties in the system parameters allow the PHZ to vanish completely, i.e., Σ (PHZ) = 100%. Even if the terrestrial planet's atmosphere has a limited capability to buffer changes in insolation, only roughly two-thirds of the CHZ could support a planet with liquid water on its surface, since the nominal Σ(EHZ) ≈ 28% for (e₀ = e_f) and 38% for (e₀ = 0). If the Earth-like planet has a high climate inertia instead, the HD 150706 system offers a slightly larger AHZ compared to CHZ estimates since Σ(AHZ) ≈ −0.1% for e₀ = e_f and −1.5% for e₀ = 0, albeit at a greater distance from the host star. HD 150706 is not the only system experiencing a slight enlargement of the AHZ compared to a shrinkage in the other dynamically informed habitable zones. About 6% of the systems in our sample have a larger AHZ than suggested by classical estimates under the condition that the atmosphere of an additional terrestrial world is capable of buffering variations in insolation.

All in all, from the gravitational interactions between the terrestrial planet and the giant planet point of view, systems with giant planets on almost circular orbits seem to be the best places to look for habitable worlds independent of the climate inertia of the latter. Tidal interactions between the giant planet and the host star naturally create these conditions for close-in hot Jupiters. The fact that those systems have largely unperturbed habitable zones may be counterbalanced by recent results suggesting that hot Jupiters could have fewer sub-Jovian companions compared to giant planets farther from the host star (Steffen et al. 2012; Huang et al. 2016). Table 1 contains those systems from our sample that are suitable for follow-up observations. Most of the selected systems have habitable zone shrinkages of under 1%, while few of them have a maximum shrinkage of the PHZ of the order of 10%. More observational data are needed, however, to correctly estimate occurrence rates for Earth-like companions in systems with a gas giant and assess their effect on habitability.

5.1. The Role of the Initial Orbit Eccentricity of the Terrestrial Planet

The results presented in Figure 3 were calculated assuming dynamically relaxed systems, where e₀ = e_f. However, a terrestrial planet is not guaranteed to end up in such a state after the planet formation phase is over. In fact, it will most likely experience larger orbit perturbations than those assumed when plotting Figure 3. In order to see how robust the presented results are against variation in the initial orbital eccentricity of potentially habitable planets, we have examined habitable zone shrinkages for e₀ = 0 as well. The results were qualitatively similar to the case of e₀ = e_f, although shrinkage values were higher, as was to be expected. Especially the extent of the PHZ decreases in dynamically excited systems, since e^max can increase by 50% compared to the most relaxed dynamical states (see Equations (10) and (11) in Appendix A.2). Figure 4 shows Σ(PHZ) and Σ(EHZ) for dynamically relaxed (e₀ = e_f) and excited (e₀ = 0) systems. As expected, the PHZs and EHZs are smaller in excited systems. Note that the scale of the axis indicating the shrinkage is logarithmic. One can also see that EHZ and PHZ show very similar behavior, indicating that only extremely high climate buffering capabilities (AHZ) protect a terrestrial planet against variations in insolation that are a consequence of the orbit perturbations induced by the giant planet.

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5.2. Analytical versus Numerical Habitable Zones

In order to make sure that our analytical method works well, we performed a number of numerical experiments in which we calculated insolation extrema numerically. For that purpose, we chose the six systems from Table 1 that had a maximum PHZ shrinkage of ∼10%, which makes these systems from Table 1 the most interesting candidates for that kind of numerical experiment. We also considered dynamically excited systems (i.e., e₀ = 0), as this way any problem with the theory becomes more noticeable.

For our simulations we used a symplectic integrator designed to integrate hierarchical triple systems (Mikkola 1997). The code uses standard Jacobi coordinates, i.e., it calculates the relative position and velocity vectors of the inner and outer orbit at every time step. Those were used to generate orbital elements of the two planetary orbits and determine subsequently the borders of the PHZ. For this series of simulations we only used the nominal values of the six systems.

The results of the numerical simulations and the comparison against the analytical values can be found in Table 2. As seen there, the analytical estimates are in excellent agreement with the results from the numerical simulations. We would like to point out that for the four P-type systems we only took into account Newtonian gravity between point masses. This, however, does not affect qualitatively the outcome of the comparison. As seen in Appendix A, our analytical method takes into consideration all dynamical effects that may be important for the determination of the dynamically informed habitable zones.

Table 2.  Borders of the PHZ for Six Systems Calculated by Theoretical and Numerical Means

Name	HZI (au)	HZO (au)	${\mathrm{PHZ}}_{I}^{n}(\mathrm{au})$	${\mathrm{PHZ}}_{O}^{n}(\mathrm{au})$	${\mathrm{PHZ}}_{I}(\mathrm{au})$	PHZO (au)
BD –114672	0.32	0.59	0.32	0.57	0.32	0.57
CoRoT-6	1.06	1.85	1.08	1.83	1.08	1.83
HAT-P-54	0.36	0.68	0.37	0.67	0.37	0.67
HD 13931	1.19	2.09	1.20	2.05	1.20	2.05
Kepler-63	0.81	1.43	0.89	1.35	0.89	1.35
WASP-89	0.68	1.23	0.70	1.21	0.70	1.21

Note. The first two columns are the borders of the CHZ, while the exponent "n" denotes the values obtained from numerical simulations.

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Are giant planets good neighbors for habitable worlds? In terms of supporting planetary habitability, the answer to this question mainly depends on the location of the giant planet with respect to the CHZ, the giant planet's eccentricity, and the terrestrial planet's capacity to buffer time-dependent insolation variability. If these factors are combined in an unfavorable fashion, giant planets diminish a system's chances of hosting a habitable world. This is the case for the majority of warm and cold Jupiter systems discovered so far. The presence of close-in hot Jupiters, as well as cold Jupiters farther out, can be more benign as far as their influence on the habitable zone is concerned. Some even allow for an extension of the CHZ if the terrestrial planet's climate inertia is high. Especially when potentially habitable worlds have low climate inertia, however, giant planets have to have near-circular orbits in order not to reduce the size of the habitable zone. The tidal interaction with the host star practically guarantees that hot Jupiter systems fulfill such criteria. If terrestrial planets survive the formation and migration phase, hot Jupiters make excellent neighbors for habitable worlds. This hypothesis is backed by our analysis of 147 exoplanet systems hosting a single gas giant orbiting a main-sequence star.

In this work, we have developed a general method that can assess the level at which planetary systems can sustain habitable conditions on Earth-like planets as we know them and hence provide observers with a tool to select possible targets in search for habitable worlds. The method has been constructed in such a way that can be applied to different planetary masses and is independent of the dynamical model and the insolation limits. As seen to some extent in the introduction, our assessment of habitablity is not related to the formation history of the system, as our intention is not to investigate whether a terrestrial planet can form in a specific system. The method developed here can be applied without any further assumption regarding the formation history of the system under investigation. It is currently thought that the orbital distribution of giant planets has been mainly sculpted by two processes: orbital migration and planet–planet scattering (e.g., Morbidelli 2014; Kley 2017). Each of these processes may have a strong effect on the formation and stability of rocky planets. Migration can be good or bad for terrestrial planet formation depending on the assumptions made (e.g., Fogg & Nelson 2005; Raymond et al. 2006; Mandell et al. 2007; Fogg & Nelson 2009). The large eccentricities of many gas giants are likely to be the result of planet–planet scattering events that are decisive for the formation of rocky planets and their subsequent fate (e.g., Raymond et al. 2011, 2012; Carrera et al. 2016). In addition, water delivery to rocky planets may also be related to the masses and eccentricities of the giant planets of the system (e.g., Raymond et al. 2004; Bancelin et al. 2016). Rocky planets can also be formed having a significant amount of water (e.g., Raymond 2006). To conclude, it is possible that the present architecture of a planetary system may be strongly related to its formation history and subsequent dynamical evolution. This may place additional constrains on whether a rocky planet exists in such a system. However, the outcome of terrestrial planet formation strongly depends on the initial setup and physics incorporated in the simulation, and a quantitative link between results from planet formation simulations and observed system configurations has not yet been established.

This research has received funding from the Jet Propulsion Laboratory through the California Institute of Technology postdoctoral fellowship program, under a contract with the National Aeronautics and Space Administration, USA, as well as the IMCCE Observatoire de Paris, France. The authors have used the NASA Exoplanet Archive, which is operated by the California Institute of Technology, under contract with the National Aeronautics and Space Administration under the Exoplanet Exploration Program. Furthermore, the authors would like to thank the High Performance Computing Resources team at New York University Abu Dhabi and especially Jorge Naranjo for helping us with certain aspects of the evaluation of the habitable zones.

A.1. Orbital Stability

An important aspect of trying to determine the limits of dynamically informed habitable zones is to ensure that the terrestrial planetary orbit is stable under the gravitational perturbations of the giant planet. In the context of this work, a system is classified as stable if the terrestrial planet neither collides with the star nor escapes the system. Several stability criteria have been developed in recent years (Georgakarakos 2008). Here, we make use of a criterion that applies specifically to systems with two planets (Petrovich 2015). A two-planet system is stable against either ejection or collision with the star when

$$\begin{eqnarray*}&&\displaystyle \frac{{a}_{g0}(1-{e}_{g0})}{{a}_{0}(1+{e}_{0})}\gt 2.4{\left(\displaystyle \frac{{m}_{g}}{{m}_{* }}\right)}^{\tfrac{1}{3}}{\left(\displaystyle \frac{{a}_{g0}}{{a}_{0}}\right)}^{\displaystyle \frac{1}{2}}+1.15\\ &&\quad \times \,{\rm{(the}}\,{\rm{giant}}\,{\rm{planet}}\,{\rm{is}}\,{\rm{the}}\,{\rm{outer}}\,{\rm{planet)}}\\ &&\displaystyle \frac{{a}_{0}(1-{e}_{0})}{{a}_{g0}(1+{e}_{g0})}\gt 2.4{\left(\displaystyle \frac{{m}_{g}}{{m}_{* }}\right)}^{\tfrac{1}{3}}{\left(\displaystyle \frac{{a}_{0}}{{a}_{g0}}\right)}^{\displaystyle \frac{1}{2}}+1.15\\ &&\quad \times \,{\rm{(the}}\,{\rm{giant}}\,{\rm{planet}}\,{\rm{is}}\,{\rm{the}}\,{\rm{inner}}\,{\rm{planet),}}\end{eqnarray*}$$

where the index 0 indicates that initial conditions rather than evolved sets of orbital elements are to be used in the above equations.

A.2. Orbital Evolution of the Terrestrial Planet

In order to calculate dynamically informed habitable zones, i.e., PHZ, EHZ, and AHZ, we need expressions for the maximum and the averaged square eccentricity of the terrestrial planet. For this purpose, we use a recently published work that deals with the orbital evolution of a terrestrial planet under the gravitational influence of a giant planet (Georgakarakos et al. 2016). This work deals with secular evolution only. Short-period effects on the orbital evolution of the terrestrial planet are more prominent when the giant planet is on a circular or nearly circular orbit. They have been neglected in this work, since their influence on the extent of the dynamically informed HZs is believed to be small. Further investigations in this respect are necessary to confirm this notion, however. The dynamical model describing the orbital motion of the planets is based on the assumption that all orbits are coplanar and nonresonant. Moreover, the orbit of the giant planet is assumed to be unchanged owing to the gravitational perturbations of the terrestrial planet. Finally, we would like to point out that since we deal with secular motion only, the semimajor axes of both planets are assumed to remain constant (Harrington 1968). Given those assumptions, the components of the Earth-like planet's eccentricity vector read (Georgakarakos et al. 2016)

$$\begin{eqnarray*}{e}_{x} & = & {C}_{1}\,\cos \sqrt{{B}^{2}-2{AB}}t+{C}_{2}\,\sin \sqrt{{B}^{2}-2{AB}}t-\displaystyle \frac{C}{B}\cos {\varpi }_{g}\\ {e}_{y} & = & \displaystyle \frac{1}{B-2A\,{\cos }^{2}{\varpi }_{g}}[({C}_{2}\sqrt{{B}^{2}-2{AB}}-{{AC}}_{1}\,\sin 2{\varpi }_{g})\\ & & \times \cos \sqrt{{B}^{2}-2{AB}}t-({C}_{1}\sqrt{{B}^{2}-2{AB}}\\ & & +{{AC}}_{2}\,\sin 2{\varpi }_{g})\sin \sqrt{{B}^{2}-2{AB}}t]-\displaystyle \frac{C}{B}\sin {\varpi }_{g},\end{eqnarray*}$$

where C₁ and C₂ are constants of integrations. It follows that

$$\begin{eqnarray*}&&e=\sqrt{{e}_{x}^{2}+{e}_{y}^{2}}\hspace{0.5cm}{\rm{and}}\hspace{0.5cm}\varpi =\arctan \left(\displaystyle \frac{{e}_{y}}{{e}_{x}}\right).\end{eqnarray*}$$

The quantities A, B, and C depend on the masses and orbital elements of the star and the two planets, and they are given by Equations (32)–(48) for the S-type case and Equations (69)–(85) for the P-type case in the above-mentioned paper. The required expressions for the averaged square and maximum eccentricity of the terrestrial planet are

$$\begin{eqnarray*}&&\langle {e}^{2}\rangle ={\left(\displaystyle \frac{C}{B}\right)}^{2}\displaystyle \frac{2B-3A}{B-2A}\hspace{1cm}\end{eqnarray*}$$

and

$$\begin{eqnarray}&&{e}^{\max }=-2\displaystyle \frac{C}{B}.\end{eqnarray} \tag{ 10 }$$

Also, the period of the oscillation is

$$\begin{eqnarray*}&&{P}_{s}=\displaystyle \frac{2\pi }{\nu }=\displaystyle \frac{2\pi }{\sqrt{{B}^{2}-2{AB}}}.\end{eqnarray*}$$

The above equations for the averaged square and maximum eccentricity hold for an initially circular terrestrial planetary orbit. When the initial eccentricity is equal to the forced eccentricity e_f = −C/B, then we have

$$\begin{eqnarray*}&&\langle {e}^{2}\rangle ={\left(\displaystyle \frac{C}{B}\right)}^{2}\end{eqnarray*}$$

and

$$\begin{eqnarray}&&{e}^{\max }=-\displaystyle \frac{C}{B}.\end{eqnarray} \tag{ 11 }$$

The above expressions are valid for both S-type and P-type configurations.

Assuming that a/a_g ≪ 1, for e₀ = 0, we obtain the classical result for S-type systems (Heppenheimer 1978; Georgakarakos 2003)

$$\begin{eqnarray}&&{e}^{\max }\approx \displaystyle \frac{5}{2}\displaystyle \frac{a}{{a}_{g}}\displaystyle \frac{{e}_{g}}{1-{e}_{g}^{2}}=\epsilon ,\quad \langle {e}^{2}\rangle =\displaystyle \frac{1}{2}{\epsilon }^{2}.\end{eqnarray} \tag{ 12 }$$

For S-type systems with e₀ = e_f we find

$$\begin{eqnarray}&&{e}^{\max }\approx \displaystyle \frac{1}{2}\epsilon ,\quad \langle {e}^{2}\rangle =\displaystyle \frac{1}{4}{\epsilon }^{2}.\end{eqnarray} \tag{ 13 }$$

Similarly, for P-type configurations, assuming a_g/a ≪ 1, the corresponding equations for e₀ = 0 read (Moriwaki & Nakagawa 2004; Georgakarakos & Eggl 2015)

$$\begin{eqnarray}&&{e}^{\max }\approx \displaystyle \frac{5}{4}\displaystyle \frac{{a}_{g}}{a}\displaystyle \frac{4{e}_{g}+3{e}_{g}^{3}}{2+3{e}_{g}}=\eta ,\quad \langle {e}^{2}\rangle =\displaystyle \frac{1}{2}{\eta }^{2},\end{eqnarray} \tag{ 14 }$$

while for e₀ = e_f we get

$$\begin{eqnarray}&&{e}^{\max }\approx \displaystyle \frac{1}{2}\eta ,\qquad \langle {e}^{2}\rangle =\displaystyle \frac{1}{4}{\eta }^{2}.\end{eqnarray} \tag{ 15 }$$

Note that the above equations represent but the crudest approximation to the secular behavior of the two planetary orbits. The reader is advised to follow the authors in using the full expressions (Georgakarakos et al. 2016) in order to calculate the maximum and average squared eccentricities. This avoids unnecessary inaccuracies in the dynamic model when the giant planet orbits in the vicinity of the habitable zone.

A.3. Other Dynamical Effects

When the giant planet is close to the star, other dynamical effects than Newtonian gravity between point masses become important. The main contribution of these effects, namely, general relativity, nondissipative tidal bulge deformation and deformation due to rotation, is an increase in the precession rate of the pericenter of the giant planet. The relevant precession rates, assuming alignment between the spin axis and the orbit normal, are (e.g., Fabrycky & Tremaine 2007; Fabrycky 2010)

$$\begin{eqnarray*}&&{\dot{\varpi }}_{{gr}}=\displaystyle \frac{3{G}^{\tfrac{3}{2}}{({m}_{* }+{m}_{g})}^{\tfrac{3}{2}}}{{a}_{g}^{\tfrac{5}{2}}{c}^{2}(1-{e}_{g}^{2})},\end{eqnarray*}$$

$$\begin{eqnarray*}{\dot{\varpi }}_{{tb}} & = & \displaystyle \frac{15\sqrt{G({m}_{* }+{m}_{g})}}{8{a}_{g}^{\tfrac{13}{2}}}\displaystyle \frac{8+12{e}_{g}^{2}+{e}_{g}^{4}}{{(1-{e}_{g}^{2})}^{5}}\\ & & \times \left(\displaystyle \frac{{m}_{g}}{{m}_{* }}{k}_{* }{R}_{* }^{5}+\displaystyle \frac{{m}_{* }}{{m}_{g}}{k}_{g}{R}_{g}^{5}\right)\end{eqnarray*}$$

$$\begin{eqnarray*}{\dot{\varpi }}_{{rot}} & = & \displaystyle \frac{\sqrt{{m}_{* }+{m}_{g}}}{\sqrt{G}{a}_{g}^{\tfrac{7}{2}}{(1-{e}_{g}^{2})}^{2}}\\ & & \times \left(\displaystyle \frac{{k}_{* }{R}_{* }^{5}}{{m}_{* }}{{\rm{\Omega }}}_{* }+\displaystyle \frac{{k}_{g}{R}_{g}^{5}}{{m}_{g}}{{\rm{\Omega }}}_{g}\right),\end{eqnarray*}$$

where G is the gravitational constant, c is the speed of light, R_* denotes the radius of the star, R_g is the radius of the giant planet, k_* and k_g denote the classical apsidal motion constants of the star and the giant planet, respectively (Russell 1928), Ω_* denotes the stellar spin angular velocity, and Ω_g is the giant planetary spin angular velocity. For the latter, we use the following pseudo-synchronization expression (Hut 1981):

$$\begin{eqnarray*}&&{{\rm{\Omega }}}_{g}={n}_{g}\displaystyle \frac{1+(15/2){e}_{g}^{2}+(45/8){e}_{g}^{4}+(5/16){e}_{g}^{6}}{[1+3{e}_{g}^{2}+(3/8){e}_{g}^{4}]{(1-{e}_{g}^{2})}^{\tfrac{3}{2}}},\end{eqnarray*}$$

where n_g is the mean motion of the giant planet. For the apsidal motion constants we use the values k_* = 0.014 and k_g = 0.25 (Fabrycky & Tremaine 2007).

The analytical model that describes the orbital evolution of the terrestrial planet (Georgakarakos et al. 2016) assumes that the pericenter of the giant planet remains constant. Therefore, in order to incorporate the above dynamical effects in our model, we use an orbital solution that allows the inclusion of such effects and has been developed originally to model circumbinary planetary motion (Georgakarakos & Eggl 2015). In addition, that orbital solution includes short periodic terms. When the giant planet is on a nearly circular orbit (e_g ∼ 0.001 or less), the orbit of the perturbed body shows no secular evolution, and consequently, in the absence of a mean motion resonance, the motion is dominated by short-period effects. Hence, for P-type systems that require the addition of the previously mentioned dynamical effects, the relevant eccentricity expressions are the following:

$$\begin{eqnarray}\langle {e}^{2}\rangle & = & \displaystyle \frac{{m}_{* }^{2}{m}_{g}^{2}}{{({m}_{* }+{m}_{g})}^{\tfrac{8}{3}}{M}^{\tfrac{4}{3}}}\displaystyle \frac{1}{{X}^{\tfrac{8}{3}}}\left[\displaystyle \frac{9}{8}+\displaystyle \frac{27}{8}{e}_{g}^{2}+\displaystyle \frac{887}{64}{e}_{g}^{4}\right.\\ & & -\displaystyle \frac{975}{64}\displaystyle \frac{1}{X}{e}_{g}^{4}\sqrt{1-{e}_{g}^{2}}+\displaystyle \frac{1}{{X}^{2}}\left(\displaystyle \frac{225}{64}+\displaystyle \frac{6619}{64}{e}_{g}^{2}\right.\\ & & \left.\left.-\displaystyle \frac{26309}{512}{e}_{g}^{4}-\displaystyle \frac{393}{64}{e}_{g}^{6}\right)\right]+2{\left(\displaystyle \frac{{K}_{2}}{{K}_{1}-{K}_{3}}\right)}^{2}.\end{eqnarray} \tag{ 16 }$$

$$\begin{eqnarray}{e}^{\max } & = & \displaystyle \frac{{m}_{* }{m}_{g}}{{({m}_{* }+{m}_{g})}^{\tfrac{4}{3}}{M}^{\tfrac{2}{3}}}\displaystyle \frac{1}{{X}^{\tfrac{4}{3}}}\left[\displaystyle \frac{3}{2}+\displaystyle \frac{17}{2}{e}_{g}^{2}\right.\\ & & +\left.\displaystyle \frac{1}{X}\left(3+19{e}_{g}+\displaystyle \frac{21}{8}{e}_{g}^{2}-\displaystyle \frac{3}{2}{e}_{g}^{3}\right)\right]\\ & & +2\left|\displaystyle \frac{{K}_{2}}{{K}_{1}-{K}_{3}}\right|.\end{eqnarray} \tag{ 17 }$$

where

$$\begin{eqnarray*}{K}_{1} & = & \displaystyle \frac{3}{8}\displaystyle \frac{\sqrt{{ \mathcal G }M}{m}_{* }{m}_{g}{a}_{g}^{2}}{{({m}_{* }+{m}_{g})}^{2}{a}^{\tfrac{7}{2}}}(2+3{e}_{g}^{2})\\ {K}_{2} & = & \displaystyle \frac{15}{64}\displaystyle \frac{\sqrt{{ \mathcal G }M}{m}_{* }{m}_{g}({m}_{* }-{m}_{g}){a}_{g}^{3}}{{({m}_{* }+{m}_{g})}^{3}{a}^{\tfrac{9}{2}}}{e}_{g}(4+3{e}_{g}^{2})\\ {K}_{3} & = & {\dot{\varpi }}_{{gr}}+{\dot{\varpi }}_{{hb}}+{\dot{\varpi }}_{{rot}}.\end{eqnarray*}$$

M is the total mass of the system, and X is the ratio of the the two planetary orbital periods given by

$$\begin{eqnarray*}&&X=\sqrt{\displaystyle \frac{{m}_{* }+{m}_{g}}{M}{\left(\displaystyle \frac{a}{{a}_{g}}\right)}^{3}}.\end{eqnarray*}$$

Equations (16) and (17) apply to an initially circular terrestrial planetary orbit. If the initial eccentricity is equal to the forced eccentricity, then the factor 2 in front of the K factors (which denote the secular contribution) should be dropped.

A.4. Explicit Formulae for the PHZ and AHZ

Although the formulae for the dynamically informed HZ borders have to be calculated numerically in most cases, one can acquire an explicit analytical solution for the PHZ and the AHZ borders if a simple secular orbit evolution model is implemented. If one uses a first-order secular evolution model for the planetary orbit, for instance, by combining Equations (4), (12), and (13) we find the following PHZ limits for S-type systems:

$$\begin{eqnarray}\quad {a}_{I} & = & \displaystyle \frac{p}{5\ w\ {e}_{g}}\left[1-{\left(1-\displaystyle \frac{10w{e}_{g}}{p}{r}_{I}\right)}^{1/2}\right]\hspace{0.6cm}{\rm{and}}\\ {a}_{O} & = & \displaystyle \frac{p}{5\ w\ {e}_{g}}\left[-1+{\left(1+\displaystyle \frac{10w{e}_{g}}{p}{r}_{O}\right)}^{1/2}\right],\end{eqnarray} \tag{ 18 }$$

where a_I and a_O are the inner and outer borders of the PHZ and $p={a}_{g}(1-{e}_{g}^{2})$ is the semilatus rectum of the giant planet's orbit. Furthermore, w is a weighting factor that depends on the initial eccentricity of the terrestrial planet's orbit, and w = 1 if e₀ = 0, while w = 1/2 for e₀ = e_f. It may seem that Equations (18) for the inner and outer PHZ border become singular for ${e}_{g}\to 0$. This is not the case, however, as the limit reads

$$\begin{eqnarray*}&&\mathop{\mathrm{lim}}\limits_{{e}_{g}\to 0}\ {a}_{I,O}={r}_{I,O}.\end{eqnarray*}$$

In other words, for a giant planet on a circular orbit, the PHZ becomes identical to the CHZ. Similarly, for P-type systems and using Equations (4), (14), and (15), the corresponding PHZ equations read

$$\begin{eqnarray*}\quad {a}_{I} & = & {r}_{I}+\displaystyle \frac{5}{4}\displaystyle \frac{w\ {a}_{g}\ {e}_{g}\ (4+3\ {e}_{g}^{2})}{2+3\ {e}_{g}}\qquad {\rm{and}}\\ {a}_{O} & = & {r}_{O}-\displaystyle \frac{5}{4}\displaystyle \frac{w\ {a}_{g}\ {e}_{g}\ (4+3\ {e}_{g}^{2})}{2+3\ {e}_{g}},\end{eqnarray*}$$

with w having the same values as previously.

An explicit solution for the AHZ can be obtained if one uses Equations (5) and (12)–(15). For S-type systems we get

$$\begin{eqnarray}&&\quad {a}_{I,O}={2}^{3/2}\ p\ {r}_{I,O}\ {[8{p}^{2}-25{w}^{2}{e}_{g}^{2}{({r}_{I,O})}^{2}]}^{-1/2}\end{eqnarray} \tag{ 19 }$$

with $w=1/\sqrt{2}$ for e₀ = 0 and w = 1/2 for e₀ = e_f. For a P-type configuration, we obtain

$$\begin{eqnarray}\mathrm{AHZ}:\quad {a}_{I,O} & = & \displaystyle \frac{{r}_{I,O}}{\sqrt{2}}\left\{1+\left[1+\displaystyle \frac{25}{8}\ {w}^{2}{a}_{g}^{2}{({r}_{I,O})}^{-2}\right.\right.\\ & & {\left.{\left.\times {\left(\displaystyle \frac{4{e}_{g}+3{e}_{g}^{3}}{2+3{e}_{g}}\right)}^{2}\right]}^{1/2}\right\}}^{1/2},\end{eqnarray} \tag{ 20 }$$

where w has the same value as in the S-type case. The equations governing the EHZ do not allow for trivial solutions even using simplified secular dynamics.

A.5. Mass and Rotational Velocity Calculation

For systems where we only know m_g sin i (i being the inclination of the planet's orbit to the plane perpendicular to the line of sight) and not the real mass of the giant planet, we use the expected value of the mass. The same approach is applied to stellar rotational velocities V_* sin i. We may write m_g = m_g sin i/sin i = m_sg/sin i, where i is the inclination angle between the orbital plane and the plane of the sky. Adopting the 13M_J limit as the upper bound for the giant planet's mass, this is achieved when the angle i is ${i}_{b}=\arcsin ({m}_{{sg}}/13)$. Assuming that the probability to have a specific angle i is the same for all i, we get for the expected value of m_g

$$\begin{eqnarray*}&&\langle {m}_{g}\rangle =\displaystyle \frac{1}{\pi /2-{i}_{b}}{\int }_{{i}_{b}}^{\tfrac{\pi }{2}}\displaystyle \frac{{m}_{{sg}}}{\sin \,i}{di}=\displaystyle \frac{{m}_{{sg}}}{\pi /2-{i}_{b}}| -\mathrm{ln}\left(\tan \displaystyle \frac{{i}_{b}}{2}\right)| .\end{eqnarray*}$$

Similarly, we can apply the same idea for the stellar rotational velocity. For the upper limit of the velocity we adopt the equatorial breakup velocity (Maeder & Meynet 2000) ${V}_{\mathrm{crit}}={(2{{Gm}}_{* }/3{R}_{* })}^{1/2}$. If we denote ${V}_{s* }={V}_{* }\,\sin \,i$ and ${i}_{b}=\arcsin ({V}_{s* }/{V}_{\mathrm{crit}})$, then we have

$$\begin{eqnarray*}&&\langle {V}_{* }\rangle =\displaystyle \frac{1}{\pi /2-{i}_{b}}{\int }_{{i}_{b}}^{\tfrac{\pi }{2}}\displaystyle \frac{{V}_{s* }}{\sin \,i}{di}=\displaystyle \frac{{V}_{s* }}{\pi /2-{i}_{b}}| -\mathrm{ln}\left(\tan \displaystyle \frac{{i}_{b}}{2}\right)| .\end{eqnarray*}$$

The masses used in this work, as well as the rotational velocities, can be found in Appendix B.

Table 3 provides the orbital elements and the physical parameters of our systems. The corresponding data were extracted from the NASA Exoplanet Archive (http://exoplanetarchive.ipac.caltech.edu). Table 4 gives the borders of all habitable zones for systems with the terrestrial planet having formed on an initially circular orbit e₀ = 0. Table 5 contains the habitable zone shrinkages for systems with e₀ = 0. Tables 6 and 7 are similar to Tables 4 and 5 but for systems with e₀ = e_f, i.e., where the terrestrial planet had an initially eccentric orbit. The occurrence of the "*" symbol in Tables 4 and 6 indicates that the perturbations of the giant planet are strong enough to render the respective system uninhabitable (i.e., the respective habitable zone vanishes). Tables 8 and 9 give the expected values of the giant planet masses and the stellar rotational velocities, respectively. All the values in our tables are given with their uncertainties. Finally, Table 10 contains a list of the symbols, variables, and acronyms used in this work.

Table 3.  Exoplanetary Systems with a Giant Planet

Name	Pg (d)	ag (au)	eg	mg (MJ)	Mass Type	Rg (RJ)	Teff (K)	${m}_{* }({M}_{\odot })$	${R}_{* }({R}_{\odot })$	${V}_{* }\,\sin \,i\,(\mathrm{km}\,{{\rm{s}}}^{-1})$
BD –114672	${1667.000}_{-31.000}^{+33.000}$	${2.280}_{-.070}^{+.070}$	$.{050}_{-.040}^{+.060}$	$.{530}_{-.050}^{+.050}$	Msini	...	${4475}_{-100}^{+100}$	$.{570}_{-.010}^{+.010}$	$.{520}_{-.020}^{+.020}$	$\lt {2.000}_{}^{}$
CoRoT-10	${13.241}_{.000}^{+.000}$	$.{105}_{-.002}^{+.002}$	$.{530}_{-.040}^{+.040}$	${2.750}_{-.160}^{+.160}$	Mass	$.{970}_{-.070}^{+.070}$	${5075}_{-75}^{+75}$	$.{890}_{-.050}^{+.050}$	$.{790}_{-.050}^{+.050}$	$\lt {2.000}_{-.500}^{+.500}$
CoRoT-12	${2.828}_{.000}^{+.000}$	$.{040}_{-.001}^{+.001}$	$.{070}_{-.042}^{+.063}$	$.{917}_{-.065}^{+.070}$	Mass	${1.440}_{-.130}^{+.130}$	${5675}_{-80}^{+80}$	${1.080}_{-.070}^{+.080}$	${1.120}_{-.090}^{+.100}$	${1.000}_{-1.000}^{+1.000}$
CoRoT-13	${4.035}_{.000}^{+.000}$	$.{051}_{-.003}^{+.003}$	$.{000}_{}^{}$	${1.308}_{-.066}^{+.066}$	Mass	$.{885}_{-.014}^{+.014}$	${5945}_{-90}^{+90}$	${1.090}_{-.020}^{+.020}$	${1.010}_{-.030}^{+.030}$	${4.000}_{-1.000}^{+1.000}$
CoRoT-14	${1.512}_{.000}^{+.000}$	$.{027}_{-.002}^{+.002}$	$.{000}_{}^{}$	${7.600}_{-.600}^{+.600}$	Mass	${1.090}_{-.070}^{+.070}$	${6035}_{-100}^{+100}$	${1.130}_{-.090}^{+.090}$	${1.210}_{-.080}^{+.080}$	${9.000}_{-.500}^{+.500}$
CoRoT-16	${5.352}_{.000}^{+.000}$	$.{062}_{-.002}^{+.002}$	$.{330}_{-.100}^{+.090}$	$.{535}_{-.083}^{+.085}$	Mass	${1.170}_{-.140}^{+.160}$	${5650}_{-100}^{+100}$	${1.100}_{-.080}^{+.080}$	${1.190}_{-.130}^{+.140}$	${1.000}_{}^{}$
CoRoT-18	${1.900}_{.000}^{+.000}$	$.{029}_{-.002}^{+.002}$	$\lt {0.080}_{}^{}$	${3.470}_{-.380}^{+.380}$	Mass	${1.310}_{-.180}^{+.180}$	${5440}_{-100}^{+100}$	$.{950}_{-.150}^{+.150}$	${1.000}_{-.130}^{+.130}$	${8.000}_{-1.000}^{+1.000}$
CoRoT-2	${1.743}_{.000}^{+.000}$	$.{028}_{-.001}^{+.001}$	$.{014}_{-.008}^{+.008}$	${3.470}_{-.220}^{+.220}$	Mass	${1.466}_{-.044}^{+.042}$	${5625}_{-120}^{+120}$	$.{960}_{-.080}^{+.080}$	$.{910}_{-.030}^{+.030}$	${10.870}_{-.320}^{+.320}$
CoRoT-25	${4.861}_{.000}^{+.000}$	$.{058}_{-.001}^{+.002}$	$.{000}_{}^{}$	$.{270}_{-.040}^{+.040}$	Mass	${1.080}_{-.100}^{+.300}$	${6040}_{-90}^{+90}$	${1.090}_{-.050}^{+.110}$	${1.190}_{-.030}^{+.140}$	${4.300}_{-.500}^{+.500}$
CoRoT-27	${3.575}_{.000}^{+.000}$	$.{048}_{-.007}^{+.007}$	$\lt {0.065}_{}^{}$	${10.390}_{-.550}^{+.550}$	Mass	${1.007}_{-.044}^{+.044}$	${5900}_{-120}^{+120}$	${1.050}_{-.110}^{+.110}$	${1.080}_{-.060}^{+.180}$	${4.000}_{-1.000}^{+1.000}$
CoRoT-29	${2.851}_{.000}^{+.000}$	$.{039}_{-.006}^{+.006}$	$.{082}_{-.081}^{+.081}$	$.{850}_{-.200}^{+.200}$	Mass	$.{900}_{-.160}^{+.160}$	${5260}_{-100}^{+100}$	$.{970}_{-.140}^{+.140}$	$.{900}_{-.120}^{+.120}$	${3.500}_{-.500}^{+.500}$
CoRoT- 4	${9.202}_{.000}^{+.000}$	$.{090}_{-.001}^{+.001}$	$.{000}_{-.100}^{+.100}$	$.{720}_{-.080}^{+.080}$	Mass	${1.190}_{-.050}^{+.060}$	${6190}_{-60}^{+60}$	${1.160}_{-.020}^{+.030}$	${1.170}_{-.030}^{+.010}$	${6.400}_{-1.000}^{+1.000}$
CoRoT-5	${4.038}_{.000}^{+.000}$	$.{049}_{.000}^{+.000}$	$.{090}_{-.040}^{+.090}$	$.{467}_{-.024}^{+.047}$	Mass	${1.388}_{-.047}^{+.046}$	${6100}_{-65}^{+65}$	${1.000}_{-.020}^{+.020}$	${1.190}_{-.040}^{+.040}$	${1.000}_{-1.000}^{+1.000}$
CoRoT-6	${8.887}_{.000}^{+.000}$	$.{086}_{-.002}^{+.002}$	$\lt {0.100}_{}^{}$	${2.960}_{-.340}^{+.340}$	Mass	${1.166}_{-.035}^{+.035}$	${6090}_{-70}^{+70}$	${1.050}_{-.050}^{+.050}$	${1.020}_{-.030}^{+.030}$	${7.600}_{-1.000}^{+1.000}$
CoRoT-8	${6.212}_{.000}^{+.000}$	$.{063}_{-.001}^{+.001}$	$.{000}_{}^{}$	$.{220}_{-.030}^{+.030}$	Mass	$.{570}_{-.020}^{+.020}$	${5080}_{-80}^{+80}$	$.{880}_{-.040}^{+.040}$	$.{770}_{-.020}^{+.020}$	${2.000}_{-1.000}^{+1.000}$
CoRoT-9	${95.274}_{-.001}^{+.001}$	$.{407}_{-.005}^{+.005}$	$.{110}_{-.040}^{+.040}$	$.{840}_{-.070}^{+.070}$	Mass	${1.050}_{-.040}^{+.040}$	${5625}_{-80}^{+80}$	$.{990}_{-.040}^{+.040}$	$.{940}_{-.040}^{+.040}$	${3.500}_{}^{}$
GJ 179	${2288.000}_{-59.000}^{+59.000}$	${2.410}_{-.040}^{+.040}$	$.{210}_{-.080}^{+.080}$	$.{820}_{-.070}^{+.070}$	Msini	...	${3370}_{-100}^{+100}$	$.{360}_{-.030}^{+.030}$	$.{380}_{-.020}^{+.020}$	${1.500}_{}^{}$
GJ 3021	${133.710}_{-.200}^{+.200}$	$.{490}_{}^{}$	$.{511}_{-.017}^{+.017}$	${3.370}_{-.090}^{+.090}$	Msini	...	${5540}_{-75}^{+75}$	$.{900}_{}^{}$	$.{900}_{}^{}$	${5.500}_{-1.000}^{+1.000}$
HAT-P-12	${3.213}_{.000}^{+.000}$	$.{038}_{.000}^{+.000}$	$.{000}_{}^{}$	$.{211}_{-.012}^{+.012}$	Mass	$.{959}_{-.021}^{+.029}$	${4650}_{-60}^{+60}$	$.{730}_{-.020}^{+.020}$	$.{700}_{-.010}^{+.020}$	$.{500}_{-.400}^{+.400}$
HAT-P-18	${5.508}_{.000}^{+.000}$	$.{056}_{-.001}^{+.001}$	$.{084}_{-.048}^{+.048}$	$.{197}_{-.013}^{+.013}$	Mass	$.{995}_{-.052}^{+.052}$	${4803}_{-80}^{+80}$	$.{770}_{-.030}^{+.030}$	$.{750}_{-.040}^{+.040}$	$.{500}_{-.500}^{+.500}$
HAT-P-19	${4.009}_{.000}^{+.000}$	$.{047}_{-.001}^{+.001}$	$.{067}_{-.042}^{+.042}$	$.{292}_{-.018}^{+.018}$	Mass	${1.132}_{-.072}^{+.072}$	${4990}_{-130}^{+130}$	$.{840}_{-.040}^{+.040}$	$.{820}_{-.050}^{+.050}$	$.{700}_{-.500}^{+.500}$
HAT-P-21	${4.124}_{.000}^{+.000}$	$.{049}_{-.001}^{+.001}$	$.{228}_{-.016}^{+.016}$	${4.063}_{-.161}^{+.161}$	Mass	${1.024}_{-.092}^{+.092}$	${5588}_{-80}^{+80}$	$.{950}_{-.040}^{+.040}$	${1.100}_{-.080}^{+.080}$	${3.500}_{-.500}^{+.500}$
HAT-P-22	${3.212}_{.000}^{+.000}$	$.{041}_{-.001}^{+.001}$	$.{016}_{-.009}^{+.009}$	${2.147}_{-.061}^{+.061}$	Mass	${1.080}_{-.058}^{+.058}$	${5302}_{-80}^{+80}$	$.{920}_{-.040}^{+.040}$	${1.040}_{-.040}^{+.040}$	$.{500}_{-.500}^{+.500}$
HAT-P-23	${1.213}_{.000}^{+.000}$	$.{023}_{.000}^{+.000}$	$.{000}_{}^{}$	${2.070}_{-.120}^{+.120}$	Mass	${1.224}_{-.037}^{+.037}$	${5885}_{-72}^{+72}$	${1.100}_{-.050}^{+.050}$	${1.090}_{-.030}^{+.030}$	${8.100}_{-.500}^{+.500}$
HAT-P-25	${3.653}_{.000}^{+.000}$	$.{047}_{-.001}^{+.001}$	$.{032}_{-.022}^{+.022}$	$.{567}_{-.022}^{+.022}$	Mass	${1.190}_{-.056}^{+.081}$	${5500}_{-80}^{+80}$	${1.010}_{-.030}^{+.030}$	$.{960}_{-.040}^{+.050}$	$.{500}_{-.500}^{+.500}$
HAT-P-27	${3.040}_{.000}^{+.000}$	$.{040}_{-.001}^{+.001}$	$.{000}_{}^{}$	$.{620}_{-.030}^{+.030}$	Mass	${1.020}_{-.060}^{+.070}$	${5300}_{-90}^{+90}$	$.{940}_{-.040}^{+.040}$	$.{900}_{-.040}^{+.050}$	$.{400}_{-.400}^{+.400}$
HAT-P-28	${3.257}_{.000}^{+.000}$	$.{043}_{-.001}^{+.001}$	$.{051}_{-.033}^{+.033}$	$.{626}_{-.037}^{+.037}$	Mass	${1.212}_{-.082}^{+.113}$	${5680}_{-90}^{+90}$	${1.020}_{-.050}^{+.050}$	${1.100}_{-.070}^{+.090}$	$.{200}_{-.200}^{+.500}$
HAT-P-29	${5.723}_{.000}^{+.000}$	$.{067}_{-.001}^{+.001}$	$.{095}_{-.047}^{+.047}$	$.{778}_{-.040}^{+.076}$	Mass	${1.107}_{-.082}^{+.136}$	${6087}_{-88}^{+88}$	${1.210}_{-.050}^{+.050}$	${1.220}_{-.070}^{+.130}$	${3.900}_{-.500}^{+.500}$
HAT-P-3	${2.900}_{.000}^{+.000}$	$.{039}_{.000}^{+.000}$	$.{000}_{}^{}$	$.{591}_{-.018}^{+.018}$	Mass	$.{827}_{-.055}^{+.055}$	${5185}_{-80}^{+80}$	$.{920}_{-.030}^{+.030}$	$.{800}_{-.040}^{+.040}$	$.{500}_{-.500}^{+.500}$
HAT-P-36	${1.327}_{.000}^{+.000}$	$.{024}_{.000}^{+.000}$	$.{063}_{-.032}^{+.032}$	${1.832}_{-.099}^{+.099}$	Mass	${1.264}_{-.071}^{+.071}$	${5560}_{-100}^{+100}$	${1.020}_{-.050}^{+.050}$	${1.100}_{-.060}^{+.060}$	${3.580}_{-.500}^{+.500}$
HAT-P-37	${2.797}_{.000}^{+.000}$	$.{038}_{-.001}^{+.001}$	$.{058}_{-.038}^{+.038}$	${1.169}_{-.103}^{+.103}$	Mass	${1.178}_{-.077}^{+.077}$	${5500}_{-100}^{+100}$	$.{930}_{-.040}^{+.040}$	$.{880}_{-.060}^{+.060}$	${3.070}_{-.500}^{+.500}$
HAT-P-38	${4.640}_{.000}^{+.000}$	$.{052}_{-.001}^{+.001}$	$.{067}_{-.047}^{+.047}$	$.{267}_{-.020}^{+.020}$	Mass	$.{825}_{-.063}^{+.092}$	${5330}_{-100}^{+100}$	$.{890}_{-.040}^{+.040}$	$.{920}_{-.100}^{+.100}$	$.{400}_{-.500}^{+.500}$
HAT-P-43	${3.333}_{.000}^{+.000}$	$.{044}_{-.001}^{+.000}$	$.{000}_{}^{}$	$.{662}_{-.060}^{+.060}$	Mass	${1.281}_{-.033}^{+.062}$	${5645}_{-74}^{+74}$	${1.050}_{-.040}^{+.030}$	${1.100}_{-.020}^{+.040}$	${2.400}_{-.500}^{+.500}$
HAT-P-5	${2.788}_{.000}^{+.000}$	$.{041}_{-.001}^{+.001}$	$.{000}_{}^{}$	${1.060}_{-.110}^{+.110}$	Mass	${1.260}_{-.050}^{+.050}$	${5960}_{-100}^{+100}$	${1.160}_{-.060}^{+.060}$	${1.170}_{-.050}^{+.050}$	${2.600}_{-1.500}^{+1.500}$
HAT-P-51	${4.218}_{.000}^{+.000}$	$.{051}_{.000}^{+.000}$	$\lt {0.123}_{}^{}$	$.{309}_{-.018}^{+.018}$	Mass	${1.293}_{-.054}^{+.054}$	${5449}_{-50}^{+50}$	$.{980}_{-.030}^{+.030}$	${1.040}_{-.030}^{+.040}$	${1.700}_{-.500}^{+.500}$
HAT-P-52	${2.754}_{.000}^{+.000}$	$.{037}_{.000}^{+.000}$	$\lt {0.047}_{}^{}$	$.{818}_{-.029}^{+.029}$	Mass	${1.009}_{-.072}^{+.072}$	${5131}_{-50}^{+50}$	$.{890}_{-.030}^{+.030}$	$.{890}_{-.050}^{+.050}$	$.{600}_{-.500}^{+.500}$
HAT-P-53	${1.962}_{.000}^{+.000}$	$.{032}_{.000}^{+.000}$	$\lt {0.134}_{}^{}$	${1.484}_{-.056}^{+.056}$	Mass	${1.318}_{-.091}^{+.091}$	${5956}_{-50}^{+50}$	${1.090}_{-.040}^{+.040}$	${1.210}_{-.060}^{+.080}$	${4.100}_{-.500}^{+.500}$
HAT-P-54	${3.800}_{.000}^{+.000}$	$.{041}_{.000}^{+.000}$	$\lt {0.074}_{}^{}$	$.{760}_{-.032}^{+.032}$	Mass	$.{944}_{-.028}^{+.028}$	${4390}_{-50}^{+50}$	$.{650}_{-.020}^{+.020}$	$.{620}_{-.010}^{+.010}$	${2.350}_{-.500}^{+.500}$
HAT-P-55	${3.585}_{.000}^{+.000}$	$.{046}_{-.001}^{+.001}$	$\lt {0.139}_{}^{}$	$.{582}_{-.056}^{+.056}$	Mass	${1.182}_{-.055}^{+.055}$	${5808}_{-50}^{+50}$	${1.010}_{-.040}^{+.040}$	${1.010}_{-.040}^{+.040}$	${1.800}_{-.500}^{+.500}$
HATS-1	${3.446}_{.000}^{+.000}$	$.{044}_{-.001}^{+.001}$	$.{120}_{-.092}^{+.092}$	${1.855}_{-.196}^{+.262}$	Mass	${1.302}_{-.098}^{+.162}$	${5870}_{-100}^{+100}$	$.{990}_{-.050}^{+.050}$	${1.040}_{-.130}^{+.130}$	${2.520}_{-.500}^{+.500}$
HATS-10	${3.313}_{.000}^{+.000}$	$.{045}_{-.001}^{+.001}$	$\lt {0.501}_{}^{}$	$.{526}_{-.081}^{+.081}$	Mass	$.{969}_{-.045}^{+.061}$	${5880}_{-120}^{+120}$	${1.100}_{-.050}^{+.050}$	${1.100}_{-.040}^{+.060}$	${5.680}_{-.700}^{+.700}$
HATS-13	${3.044}_{.000}^{+.000}$	$.{041}_{.000}^{+.000}$	$\lt {0.181}_{}^{}$	$.{543}_{-.072}^{+.072}$	Mass	${1.212}_{-.035}^{+.035}$	${5523}_{-69}^{+69}$	$.{960}_{-.030}^{+.030}$	$.{890}_{-.020}^{+.020}$	${2.820}_{-.300}^{+.300}$
HATS-14	${2.767}_{.000}^{+.000}$	$.{038}_{.000}^{+.000}$	$\lt {0.142}_{}^{}$	${1.071}_{-.070}^{+.070}$	Mass	${1.039}_{-.022}^{+.032}$	${5346}_{-60}^{+60}$	$.{970}_{-.020}^{+.020}$	$.{930}_{-.010}^{+.020}$	${3.800}_{-1.200}^{+1.200}$
HATS-15	${1.747}_{.000}^{+.000}$	$.{027}_{.000}^{+.000}$	$\lt {0.126}_{}^{}$	${2.170}_{-.150}^{+.150}$	Mass	${1.105}_{-.040}^{+.040}$	${5311}_{-77}^{+77}$	$.{870}_{-.020}^{+.020}$	$.{920}_{-.030}^{+.030}$	${4.180}_{-.500}^{+.500}$
HATS-16	${2.687}_{.000}^{+.000}$	$.{037}_{.000}^{+.000}$	$.{000}_{}^{}$	${3.270}_{-.190}^{+.190}$	Mass	${1.300}_{-.150}^{+.150}$	${5738}_{-79}^{+79}$	$.{970}_{-.040}^{+.040}$	${1.240}_{-.130}^{+.100}$	${6.170}_{-.220}^{+.220}$
HATS-18	$.{838}_{.000}^{+.000}$	$.{018}_{.000}^{+.000}$	$\lt {0.166}_{}^{}$	${1.980}_{-.077}^{+.077}$	Mass	${1.337}_{-.049}^{+.102}$	${5600}_{-120}^{+120}$	${1.040}_{-.050}^{+.050}$	${1.020}_{-.030}^{+.060}$	${6.230}_{-.470}^{+.470}$
HATS-2	${1.354}_{.000}^{+.000}$	$.{023}_{.000}^{+.000}$	$.{000}_{}^{}$	${1.345}_{-.150}^{+.150}$	Mass	${1.168}_{-.030}^{+.030}$	${5227}_{-95}^{+95}$	$.{880}_{-.040}^{+.040}$	$.{900}_{-.020}^{+.020}$	${1.500}_{-.500}^{+.500}$
HATS-25	${4.299}_{.000}^{+.000}$	$.{052}_{-.001}^{+.001}$	$\lt {0.176}_{}^{}$	$.{613}_{-.042}^{+.042}$	Mass	${1.260}_{-.100}^{+.100}$	${5715}_{-73}^{+73}$	$.{990}_{-.040}^{+.040}$	${1.110}_{-.070}^{+.070}$	${3.880}_{-.500}^{+.500}$
HATS-28	${3.181}_{.000}^{+.000}$	$.{041}_{-.001}^{+.001}$	$\lt {0.202}_{}^{}$	$.{672}_{-.087}^{+.087}$	Mass	${1.194}_{-.070}^{+.070}$	${5498}_{-84}^{+84}$	$.{930}_{-.040}^{+.040}$	$.{920}_{-.040}^{+.040}$	${2.600}_{-1.000}^{+1.000}$
HATS-29	${4.606}_{.000}^{+.000}$	$.{055}_{-.001}^{+.001}$	$\lt {0.158}_{}^{}$	$.{653}_{-.063}^{+.063}$	Mass	${1.251}_{-.061}^{+.061}$	${5670}_{-110}^{+110}$	${1.030}_{-.050}^{+.050}$	${1.070}_{-.040}^{+.040}$	${2.350}_{-.800}^{+.800}$
HATS-30	${3.174}_{.000}^{+.000}$	$.{044}_{.000}^{+.000}$	$\lt {0.096}_{}^{}$	$.{706}_{-.039}^{+.039}$	Mass	${1.175}_{-.052}^{+.052}$	${5943}_{-70}^{+70}$	${1.090}_{-.030}^{+.030}$	${1.060}_{-.040}^{+.040}$	${4.110}_{-.500}^{+.500}$
HATS-32	${2.813}_{.000}^{+.000}$	$.{040}_{-.001}^{+.001}$	$\lt {0.471}_{}^{}$	$.{920}_{-.100}^{+.100}$	Mass	${1.249}_{-.096}^{+.144}$	${5700}_{-110}^{+110}$	${1.100}_{-.040}^{+.040}$	${1.100}_{-.060}^{+.100}$	${3.560}_{-.690}^{+.690}$
HATS-33	${2.550}_{.000}^{+.000}$	$.{037}_{.000}^{+.000}$	$\lt {0.080}_{}^{}$	${1.192}_{-.053}^{+.053}$	Mass	${1.230}_{-.081}^{+.112}$	${5659}_{-85}^{+85}$	${1.060}_{-.030}^{+.030}$	${1.020}_{-.040}^{+.050}$	${3.870}_{-.420}^{+.420}$
HATS-34	${2.106}_{.000}^{+.000}$	$.{032}_{.000}^{+.000}$	$\lt {0.108}_{}^{}$	$.{941}_{-.072}^{+.072}$	Mass	${1.430}_{-.190}^{+.190}$	${5380}_{-73}^{+73}$	$.{950}_{-.030}^{+.030}$	$.{980}_{-.050}^{+.050}$	${4.070}_{-.580}^{+.580}$
HATS-4	${2.517}_{.000}^{+.000}$	$.{036}_{.000}^{+.000}$	$.{013}_{-.016}^{+.016}$	${1.323}_{-.028}^{+.028}$	Mass	${1.020}_{-.037}^{+.037}$	${5403}_{-50}^{+50}$	${1.000}_{-.020}^{+.020}$	$.{930}_{-.020}^{+.020}$	$.{700}_{-.500}^{+.500}$
HATS-5	${4.763}_{.000}^{+.000}$	$.{054}_{-.001}^{+.001}$	$.{019}_{-.019}^{+.019}$	$.{237}_{-.012}^{+.012}$	Mass	$.{912}_{-.025}^{+.025}$	${5304}_{-50}^{+50}$	$.{940}_{-.030}^{+.030}$	$.{870}_{-.020}^{+.020}$	$.{800}_{-.500}^{+.500}$
HATS-8	${3.584}_{.000}^{+.000}$	$.{047}_{-.001}^{+.001}$	$\lt {0.376}_{}^{}$	$.{138}_{-.019}^{+.019}$	Mass	$.{873}_{-.075}^{+.123}$	${5679}_{-50}^{+50}$	${1.060}_{-.040}^{+.040}$	${1.090}_{-.060}^{+.150}$	${2.000}_{-.500}^{+.500}$
HD 109246	${68.270}_{-.130}^{+.130}$	$.{330}_{-.080}^{+.080}$	$.{120}_{-.040}^{+.040}$	$.{770}_{-.090}^{+.090}$	Msini	...	${5844}_{-21}^{+21}$	${1.010}_{-.110}^{+.110}$	${1.020}_{-.070}^{+.070}$	${3.000}_{-1.000}^{+1.000}$
HD 13931	${4218.000}_{-388.000}^{+388.000}$	${5.150}_{-.290}^{+.290}$	$.{020}_{-.050}^{+.050}$	${1.880}_{-.150}^{+.150}$	Msini	...	${5829}_{-44}^{+44}$	${1.020}_{-.020}^{+.020}$	${1.230}_{-.060}^{+.060}$	${2.000}_{-.500}^{+.500}$
HD 143361	${1046.200}_{-3.200}^{+3.200}$	${1.980}_{-.070}^{+.070}$	$.{193}_{-.015}^{+.015}$	${3.480}_{-.240}^{+.240}$	Msini	...	${5505}_{-100}^{+100}$	$.{950}_{-.050}^{+.050}$	$.{990}_{-.080}^{+.080}$	${1.500}_{-.100}^{+.100}$
HD 145377	${103.950}_{-.130}^{+.130}$	$.{450}_{-.004}^{+.004}$	$.{307}_{-.017}^{+.017}$	${5.760}_{-.100}^{+.100}$	Msini	...	${6046}_{-15}^{+15}$	${1.120}_{-.030}^{+.030}$	${1.140}_{}^{}$	${5.000}_{}^{}$
HD 150706	${5894.000}_{-1498.000}^{+5584.000}$	${6.700}_{-1.400}^{+4.000}$	$.{380}_{-.320}^{+.280}$	${2.710}_{-.660}^{+1.140}$	Msini	...	${5961}_{-27}^{+27}$	${1.170}_{-.120}^{+.120}$	$.{960}_{-.020}^{+.020}$	${3.700}_{-1.000}^{+1.000}$
HD 152079	${2899.000}_{-52.000}^{+52.000}$	${3.980}_{-.150}^{+.150}$	$.{520}_{-.020}^{+.020}$	${2.180}_{-.170}^{+.170}$	Msini	...	${5726}_{-100}^{+100}$	${1.100}_{-.050}^{+.050}$	${1.150}_{-.130}^{+.130}$	${1.800}_{-.100}^{+.100}$
HD 204941	${1733.000}_{-74.000}^{+74.000}$	${2.560}_{-.080}^{+.080}$	$.{370}_{-.080}^{+.080}$	$.{266}_{-.032}^{+.032}$	Msini	...	${5056}_{-52}^{+52}$	$.{740}_{}^{}$	$.{720}_{}^{}$	−
HD 220689	${2209.000}_{-81.000}^{+103.000}$	${3.360}_{-.090}^{+.090}$	$.{160}_{-.070}^{+.100}$	${1.060}_{-.090}^{+.090}$	Msini	...	${5921}_{-26}^{+26}$	${1.040}_{-.030}^{+.030}$	${1.070}_{-.040}^{+.040}$	${2.300}_{}^{}$
HD 25171	${1845.000}_{-167.000}^{+167.000}$	${3.020}_{-.160}^{+.160}$	$.{080}_{-.060}^{+.060}$	$.{950}_{-.100}^{+.100}$	Msini	...	${6160}_{-65}^{+65}$	${1.090}_{-.030}^{+.030}$	${1.180}_{-.040}^{+.040}$	${1.000}_{}^{}$
HD 27631	${2208.000}_{-66.000}^{+66.000}$	${3.250}_{-.070}^{+.070}$	$.{120}_{-.060}^{+.060}$	${1.450}_{-.140}^{+.140}$	Msini	...	${5737}_{-36}^{+36}$	$.{940}_{-.040}^{+.040}$	${1.000}_{}^{}$	${1.340}_{}^{}$
HD 290327	${2443.000}_{-117.000}^{+205.000}$	${3.430}_{-.120}^{+.200}$	$.{080}_{-.030}^{+.080}$	${2.540}_{-.140}^{+.170}$	Msini	...	${5552}_{-21}^{+21}$	$.{900}_{}^{}$	${1.000}_{-.010}^{+.010}$	${1.440}_{-1.000}^{+1.000}$
HD 30669	${1684.000}_{-61.000}^{+61.000}$	${2.690}_{-.080}^{+.080}$	$.{180}_{-.150}^{+.150}$	$.{470}_{-.060}^{+.060}$	Msini	...	${5400}_{-74}^{+74}$	$.{920}_{-.030}^{+.030}$	$.{910}_{-.040}^{+.040}$	$\lt {1.700}_{}^{}$
HD 52265	${119.600}_{-.420}^{+.420}$	$.{500}_{}^{}$	$.{350}_{-.030}^{+.030}$	${1.050}_{-.030}^{+.030}$	Msini	...	${6060}_{-50}^{+50}$	${1.180}_{}^{}$	${1.100}_{}^{}$	${5.200}_{-1.000}^{+1.000}$
HD 63454	${2.818}_{.000}^{+.000}$	$.{037}_{}^{}$	$.{000}_{-.022}^{+.022}$	$.{398}_{}^{}$	Msini	${1.098}_{}^{}$	${4840}_{-66}^{+66}$	$.{840}_{}^{}$	${1.050}_{}^{}$	${1.900}_{}^{}$
HD 6718	${2496.000}_{-176.000}^{+176.000}$	${3.560}_{-.150}^{+.240}$	$.{100}_{-.040}^{+.110}$	${1.560}_{-.100}^{+.110}$	Msini	...	${5746}_{-19}^{+19}$	$.{960}_{}^{}$	${1.020}_{-.030}^{+.030}$	${1.760}_{-1.000}^{+1.000}$
HD 68402	${1103.000}_{-33.000}^{+33.000}$	${2.180}_{-.090}^{+.090}$	$.{030}_{-.060}^{+.060}$	${3.070}_{-.350}^{+.350}$	Msini	...	${5950}_{-100}^{+100}$	${1.120}_{-.050}^{+.050}$	${1.020}_{-.050}^{+.050}$	${2.900}_{-.200}^{+.200}$
HD 73267	${1260.000}_{-7.000}^{+7.000}$	${2.198}_{-.025}^{+.025}$	$.{256}_{-.009}^{+.009}$	${3.060}_{-.070}^{+.070}$	Msini	...	${5317}_{-34}^{+34}$	$.{890}_{-.030}^{+.030}$	${1.040}_{}^{}$	${1.650}_{}^{}$
HD 86226	${1695.000}_{-58.000}^{+58.000}$	${2.840}_{-.060}^{+.060}$	$.{150}_{-.090}^{+.090}$	$.{920}_{-.100}^{+.100}$	Msini	...	${5903}_{-31}^{+31}$	${1.060}_{-.030}^{+.030}$	${1.020}_{-.030}^{+.030}$	${2.400}_{}^{}$
K2-29	${3.259}_{.000}^{+.000}$	$.{042}_{.000}^{+.000}$	$.{066}_{-.022}^{+.022}$	$.{730}_{-.040}^{+.040}$	Mass	${1.190}_{-.020}^{+.020}$	${5358}_{-38}^{+38}$	$.{940}_{-.020}^{+.020}$	$.{860}_{-.010}^{+.010}$	${3.700}_{-.500}^{+.500}$
K2-30	${4.099}_{.000}^{+.000}$	$.{048}_{-.001}^{+.001}$	$.{000}_{}^{}$	$.{579}_{-.027}^{+.028}$	Mass	${1.039}_{-.051}^{+.050}$	${5425}_{-40}^{+40}$	$.{900}_{-.040}^{+.040}$	$.{840}_{-.030}^{+.030}$	${1.400}_{-.300}^{+.300}$
K2-31	${1.258}_{.000}^{+.000}$	$.{022}_{-.002}^{+.002}$	$.{000}_{}^{}$	${1.774}_{-.079}^{+.079}$	Mass	${1.060}_{-.350}^{+.350}$	${5280}_{-70}^{+70}$	$.{910}_{-.060}^{+.060}$	$.{780}_{-.070}^{+.070}$	${2.600}_{-.500}^{+.500}$
Kepler-15	${4.943}_{.000}^{+.000}$	$.{057}_{-.001}^{+.001}$	$.{060}_{}^{}$	$.{660}_{-.090}^{+.080}$	Mass	$.{960}_{-.070}^{+.060}$	${5515}_{-130}^{+122}$	${1.020}_{-.050}^{+.040}$	$.{990}_{-.070}^{+.060}$	${2.000}_{-2.000}^{+2.000}$
Kepler-17	${1.486}_{.000}^{+.000}$	$.{026}_{.000}^{+.000}$	$\lt {0.011}_{}^{}$	${2.450}_{-.110}^{+.110}$	Mass	${1.310}_{-.020}^{+.020}$	${5781}_{-85}^{+85}$	${1.160}_{-.060}^{+.060}$	${1.050}_{-.030}^{+.030}$	${6.000}_{-2.000}^{+2.000}$
Kepler-22	${289.862}_{-.002}^{+.002}$	$.{849}_{-.017}^{+.018}$	$.{000}_{}^{}$	$\lt {0.113}_{}^{}$	Mass	$.{212}_{-.012}^{+.012}$	${5518}_{-44}^{+44}$	$.{970}_{-.060}^{+.060}$	$.{980}_{-.020}^{+.020}$	$.{600}_{-1.000}^{+1.000}$
Kepler-41	${1.856}_{.000}^{+.000}$	$.{031}_{.000}^{+.000}$	$.{000}_{}^{}$	$.{560}_{-.080}^{+.080}$	Mass	${1.290}_{-.020}^{+.020}$	${5750}_{-100}^{+100}$	${1.150}_{-.040}^{+.040}$	${1.290}_{-.020}^{+.020}$	${6.000}_{-2.000}^{+2.000}$
Kepler-420	${86.648}_{.000}^{+.000}$	$.{382}_{-.006}^{+.006}$	$.{772}_{-.045}^{+.045}$	${1.450}_{-.350}^{+.350}$	Mass	$.{940}_{-.120}^{+.120}$	${5520}_{-80}^{+80}$	$.{990}_{-.050}^{+.050}$	${1.130}_{-.140}^{+.140}$	${4.600}_{-.200}^{+.200}$
Kepler-423	${2.684}_{.000}^{+.000}$	$.{036}_{-.001}^{+.001}$	$.{019}_{-.014}^{+.028}$	$.{595}_{-.081}^{+.081}$	Mass	${1.192}_{-.052}^{+.052}$	${5560}_{-80}^{+80}$	$.{850}_{-.040}^{+.040}$	$.{950}_{-.040}^{+.040}$	${2.500}_{-.500}^{+.500}$
Kepler-425	${3.797}_{.000}^{+.000}$	$.{046}_{-.001}^{+.001}$	$\lt {0.330}_{}^{}$	$.{250}_{-.080}^{+.080}$	Mass	$.{978}_{-.022}^{+.022}$	${5170}_{-70}^{+70}$	$.{930}_{-.050}^{+.050}$	$.{860}_{-.020}^{+.020}$	${3.000}_{-1.000}^{+1.000}$
Kepler-426	${3.218}_{.000}^{+.000}$	$.{041}_{-.001}^{+.001}$	$\lt {0.180}_{}^{}$	$.{340}_{-.080}^{+.080}$	Mass	${1.090}_{-.030}^{+.030}$	${5725}_{-90}^{+90}$	$.{910}_{-.060}^{+.060}$	$.{920}_{-.020}^{+.020}$	${3.000}_{-1.000}^{+1.000}$
Kepler-428	${3.526}_{.000}^{+.000}$	$.{043}_{-.001}^{+.001}$	$\lt {0.220}_{}^{}$	${1.270}_{-.190}^{+.190}$	Mass	${1.080}_{-.030}^{+.030}$	${5150}_{-100}^{+100}$	$.{870}_{-.050}^{+.050}$	$.{800}_{-.020}^{+.020}$	${2.000}_{-2.000}^{+2.000}$
Kepler-63	${9.434}_{.000}^{+.000}$	$.{080}_{-.002}^{+.002}$	$\lt {0.450}_{}^{}$	$\lt {0.378}_{}^{}$	Mass	$.{545}_{-.018}^{+.018}$	${5576}_{-50}^{+50}$	$.{980}_{-.040}^{+.040}$	$.{900}_{-.020}^{+.030}$	${5.600}_{-.800}^{+.800}$
Kepler-74	${7.341}_{.000}^{+.000}$	$.{078}_{-.001}^{+.001}$	$.{000}_{}^{}$	$.{630}_{-.120}^{+.120}$	Mass	$.{960}_{-.020}^{+.020}$	${6000}_{-100}^{+100}$	${1.180}_{-.040}^{+.040}$	${1.120}_{-.040}^{+.040}$	${5.000}_{-1.000}^{+1.000}$
Kepler-75	${8.885}_{.000}^{+.000}$	$.{082}_{-.001}^{+.001}$	$.{570}_{-.010}^{+.010}$	${10.100}_{-.400}^{+.400}$	Mass	${1.050}_{-.030}^{+.030}$	${5200}_{-100}^{+100}$	$.{910}_{-.040}^{+.040}$	$.{890}_{-.020}^{+.020}$	${3.500}_{-1.500}^{+1.500}$
Kepler-77	${3.579}_{.000}^{+.000}$	$.{045}_{-.001}^{+.001}$	$.{000}_{}^{}$	$.{430}_{-.032}^{+.032}$	Mass	$.{960}_{-.016}^{+.016}$	${5520}_{-60}^{+60}$	$.{950}_{-.040}^{+.040}$	$.{990}_{-.020}^{+.020}$	${1.800}_{-1.000}^{+1.000}$
Qatar-1	${1.420}_{.000}^{+.000}$	$.{023}_{.000}^{+.000}$	$.{000}_{}^{}$	${1.294}_{-.049}^{+.052}$	Mass	${1.143}_{-.025}^{+.026}$	${5013}_{-88}^{+93}$	$.{840}_{-.040}^{+.040}$	$.{800}_{-.020}^{+.020}$	${1.760}_{-.210}^{+.210}$
Qatar-2	${1.337}_{.000}^{+.000}$	$.{022}_{.000}^{+.000}$	$.{000}_{}^{}$	${2.494}_{-.054}^{+.054}$	Mass	${1.254}_{-.013}^{+.013}$	${4645}_{-50}^{+50}$	$.{740}_{-.020}^{+.020}$	$.{780}_{-.010}^{+.010}$	${3.280}_{-.040}^{+.040}$
TrES-3	${1.306}_{}^{}$	$.{023}_{.000}^{+.000}$	$.{000}_{}^{}$	${1.910}_{-.080}^{+.075}$	Mass	${1.336}_{-.037}^{+.031}$	${5650}_{-75}^{+75}$	$.{930}_{-.050}^{+.050}$	$.{830}_{-.020}^{+.020}$	${1.500}_{-1.000}^{+1.000}$
WASP-101	${3.586}_{.000}^{+.000}$	$.{051}_{-.001}^{+.001}$	$.{000}_{}^{}$	$.{500}_{-.040}^{+.040}$	Mass	${1.410}_{-.050}^{+.050}$	${6400}_{-110}^{+110}$	${1.340}_{-.070}^{+.070}$	${1.290}_{-.040}^{+.040}$	${12.400}_{-.500}^{+.500}$
WASP-104	${1.755}_{.000}^{+.000}$	$.{029}_{.000}^{+.000}$	$.{000}_{}^{}$	${1.272}_{-.047}^{+.047}$	Mass	${1.137}_{-.037}^{+.037}$	${5475}_{-127}^{+127}$	${1.080}_{-.050}^{+.050}$	$.{960}_{-.030}^{+.030}$	$.{400}_{-.700}^{+.700}$
WASP-117	${10.022}_{-.001}^{+.001}$	$.{095}_{-.001}^{+.001}$	$.{302}_{-.023}^{+.023}$	$.{276}_{-.009}^{+.009}$	Mass	${1.021}_{-.065}^{+.076}$	${6038}_{-88}^{+88}$	${1.130}_{-.030}^{+.030}$	${1.170}_{-.060}^{+.070}$	${1.670}_{-.240}^{+.310}$
WASP-119	${2.500}_{.000}^{+.000}$	$.{036}_{-.001}^{+.001}$	$\lt {0.058}_{}^{}$	${1.230}_{-.080}^{+.080}$	Mass	${1.400}_{-.200}^{+.200}$	${5650}_{-100}^{+100}$	${1.020}_{-.060}^{+.060}$	${1.200}_{-.100}^{+.100}$	$.{700}_{-.900}^{+.900}$
WASP-123	${2.978}_{.000}^{+.000}$	$.{043}_{-.001}^{+.001}$	$.{000}_{}^{}$	$.{899}_{-.036}^{+.036}$	Mass	${1.318}_{-.065}^{+.065}$	${5740}_{-130}^{+130}$	${1.170}_{-.060}^{+.060}$	${1.280}_{-.050}^{+.050}$	${1.000}_{-.700}^{+.700}$
WASP-124	${3.373}_{.000}^{+.000}$	$.{045}_{-.001}^{+.001}$	$\lt {0.017}_{}^{}$	$.{600}_{-.070}^{+.070}$	Mass	${1.240}_{-.030}^{+.030}$	${6050}_{-100}^{+100}$	${1.070}_{-.050}^{+.050}$	${1.020}_{-.020}^{+.020}$	${3.200}_{-.900}^{+.900}$
WASP-126	${3.289}_{.000}^{+.000}$	$.{045}_{-.001}^{+.001}$	$\lt {0.180}_{}^{}$	$.{280}_{-.040}^{+.040}$	Mass	$.{960}_{-.050}^{+.100}$	${5800}_{-100}^{+100}$	${1.120}_{-.060}^{+.060}$	${1.270}_{-.050}^{+.100}$	$.{500}_{-.500}^{+.500}$
WASP-129	${5.748}_{.000}^{+.000}$	$.{063}_{-.001}^{+.001}$	$\lt {0.096}_{}^{}$	${1.000}_{-.100}^{+.100}$	Mass	$.{930}_{-.030}^{+.030}$	${5900}_{-100}^{+100}$	${1.000}_{-.030}^{+.030}$	$.{900}_{-.020}^{+.020}$	${2.700}_{-.600}^{+.600}$
WASP-132	${7.134}_{.000}^{+.000}$	$.{067}_{-.001}^{+.001}$	$.{000}_{}^{}$	$.{410}_{-.030}^{+.030}$	Mass	$.{870}_{-.030}^{+.030}$	${4775}_{-100}^{+100}$	$.{800}_{-.040}^{+.040}$	$.{740}_{-.020}^{+.020}$	$.{900}_{-.800}^{+.800}$
WASP-135	${1.401}_{.000}^{+.000}$	$.{024}_{-.001}^{+.001}$	$.{000}_{}^{}$	${1.900}_{-.080}^{+.080}$	Mass	${1.300}_{-.090}^{+.090}$	${5675}_{-60}^{+60}$	$.{980}_{-.060}^{+.060}$	$.{960}_{-.050}^{+.050}$	${4.670}_{-.890}^{+.890}$
WASP-139	${5.924}_{.000}^{+.000}$	$.{062}_{-.002}^{+.002}$	$.{000}_{}^{}$	$.{117}_{-.017}^{+.017}$	Mass	$.{800}_{-.050}^{+.050}$	${5310}_{-90}^{+90}$	$.{920}_{-.100}^{+.100}$	$.{800}_{-.040}^{+.040}$	${4.200}_{-1.100}^{+1.100}$
WASP-140	${2.236}_{.000}^{+.000}$	$.{032}_{-.001}^{+.001}$	$.{047}_{-.004}^{+.004}$	${2.440}_{-.070}^{+.070}$	Mass	${1.440}_{-.180}^{+.420}$	${5260}_{-100}^{+100}$	$.{900}_{-.040}^{+.040}$	$.{870}_{-.040}^{+.040}$	${3.100}_{-.800}^{+.800}$
WASP-157	${3.952}_{.000}^{+.000}$	$.{053}_{-.002}^{+.002}$	$.{000}_{}^{}$	$.{574}_{-.093}^{+.093}$	Mass	${1.065}_{-.047}^{+.047}$	${5838}_{-140}^{+140}$	${1.260}_{-.120}^{+.120}$	${1.130}_{-.050}^{+.050}$	${1.000}_{-.900}^{+.900}$
WASP-16	${3.119}_{.000}^{+.000}$	$.{042}_{-.002}^{+.001}$	$.{000}_{}^{}$	$.{855}_{-.076}^{+.043}$	Mass	${1.008}_{-.060}^{+.083}$	${5700}_{-150}^{+150}$	${1.020}_{-.130}^{+.130}$	$.{950}_{-.060}^{+.060}$	${3.000}_{-1.000}^{+1.000}$
WASP-18	$.{941}_{.000}^{+.000}$	$.{020}_{-.001}^{+.001}$	$.{009}_{-.003}^{+.003}$	${10.430}_{-.380}^{+.380}$	Mass	${1.165}_{-.057}^{+.057}$	${6400}_{-100}^{+100}$	${1.280}_{-.070}^{+.070}$	${1.230}_{-.050}^{+.050}$	${11.000}_{-1.500}^{+1.500}$
WASP-19	$.{789}_{.000}^{+.000}$	$.{016}_{.000}^{+.000}$	$.{002}_{-.002}^{+.014}$	${1.069}_{-.037}^{+.038}$	Mass	${1.392}_{-.040}^{+.040}$	${5568}_{-71}^{+71}$	$.{900}_{-.040}^{+.040}$	${1.000}_{-.020}^{+.020}$	${4.630}_{-.260}^{+.260}$
WASP-21	${4.322}_{.000}^{+.000}$	$.{052}_{.000}^{+.000}$	$.{000}_{}^{}$	$.{300}_{-.011}^{+.011}$	Mass	${1.070}_{-.060}^{+.060}$	${5800}_{-100}^{+100}$	$.{890}_{-.080}^{+.080}$	${1.140}_{-.050}^{+.050}$	${1.500}_{-.600}^{+.600}$
WASP-23	${2.944}_{.000}^{+.000}$	$.{038}_{-.002}^{+.002}$	$\lt {0.062}_{}^{}$	$.{884}_{-.099}^{+.088}$	Mass	$.{962}_{-.056}^{+.047}$	${5150}_{-100}^{+100}$	$.{780}_{-.130}^{+.130}$	$.{770}_{-.050}^{+.050}$	${2.200}_{-.300}^{+.300}$
WASP-25	${3.765}_{.000}^{+.000}$	$.{047}_{.000}^{+.000}$	$.{000}_{}^{}$	$.{580}_{-.040}^{+.040}$	Mass	${1.220}_{-.050}^{+.060}$	${5703}_{-100}^{+100}$	${1.000}_{-.030}^{+.030}$	$.{920}_{-.040}^{+.040}$	${3.000}_{-1.000}^{+1.000}$
WASP-26	${2.757}_{.000}^{+.000}$	$.{040}_{.000}^{+.000}$	$.{000}_{}^{}$	${1.028}_{-.021}^{+.021}$	Mass	${1.281}_{-.075}^{+.075}$	${5939}_{-100}^{+100}$	${1.110}_{-.030}^{+.030}$	${1.300}_{-.060}^{+.060}$	${3.900}_{-.400}^{+.400}$
WASP-28	${3.409}_{.000}^{+.000}$	$.{045}_{-.001}^{+.001}$	$.{000}_{}^{}$	$.{907}_{-.043}^{+.043}$	Mass	${1.213}_{-.042}^{+.042}$	${6150}_{-140}^{+140}$	${1.020}_{-.050}^{+.050}$	${1.090}_{-.030}^{+.030}$	${3.250}_{-.340}^{+.340}$
WASP-29	${3.923}_{.000}^{+.000}$	$.{046}_{-.001}^{+.001}$	$.{030}_{-.030}^{+.050}$	$.{244}_{-.020}^{+.020}$	Mass	$.{792}_{-.035}^{+.056}$	${4800}_{-150}^{+150}$	$.{820}_{-.030}^{+.030}$	$.{810}_{-.040}^{+.040}$	${1.500}_{-.600}^{+.600}$
WASP-31	${3.406}_{.000}^{+.000}$	$.{047}_{.000}^{+.000}$	$.{000}_{}^{}$	$.{478}_{-.029}^{+.029}$	Mass	${1.549}_{-.050}^{+.050}$	${6302}_{-102}^{+102}$	${1.160}_{-.030}^{+.030}$	${1.250}_{-.030}^{+.030}$	${7.900}_{-.600}^{+.600}$
WASP-32	${2.719}_{.000}^{+.000}$	$.{039}_{.000}^{+.000}$	$.{018}_{-.006}^{+.006}$	${3.600}_{-.070}^{+.070}$	Mass	${1.180}_{-.070}^{+.070}$	${6100}_{-100}^{+100}$	${1.100}_{-.030}^{+.030}$	${1.110}_{-.050}^{+.050}$	${4.800}_{-.800}^{+.800}$
WASP-34	${4.318}_{.000}^{+.000}$	$.{052}_{.000}^{+.000}$	$.{038}_{-.012}^{+.012}$	$.{590}_{-.010}^{+.010}$	Mass	${1.220}_{-.080}^{+.110}$	${5700}_{-100}^{+100}$	${1.010}_{-.070}^{+.070}$	$.{930}_{-.120}^{+.120}$	${1.400}_{-.600}^{+.600}$
WASP-35	${3.162}_{.000}^{+.000}$	$.{043}_{.000}^{+.000}$	$.{000}_{}^{}$	$.{720}_{-.060}^{+.060}$	Mass	${1.320}_{-.050}^{+.050}$	${5990}_{-90}^{+90}$	${1.070}_{-.030}^{+.030}$	${1.090}_{-.030}^{+.030}$	${3.900}_{-.400}^{+.400}$
WASP-37	${3.577}_{.000}^{+.000}$	$.{045}_{-.002}^{+.002}$	$.{000}_{}^{}$	${1.800}_{-.170}^{+.170}$	Mass	${1.160}_{-.060}^{+.070}$	${5800}_{-150}^{+150}$	$.{930}_{-.120}^{+.120}$	${1.000}_{-.050}^{+.050}$	${2.400}_{-1.600}^{+1.600}$
WASP-39	${4.055}_{.000}^{+.000}$	$.{049}_{-.001}^{+.001}$	$.{000}_{}^{}$	$.{280}_{-.030}^{+.030}$	Mass	${1.270}_{-.040}^{+.040}$	${5400}_{-150}^{+150}$	$.{930}_{-.030}^{+.030}$	$.{900}_{-.020}^{+.020}$	${1.400}_{-.600}^{+.600}$
WASP-43	$.{813}_{.000}^{+.000}$	$.{014}_{.000}^{+.000}$	$.{000}_{}^{}$	${1.780}_{-.100}^{+.100}$	Mass	$.{930}_{-.090}^{+.070}$	${4400}_{-200}^{+200}$	$.{580}_{-.050}^{+.050}$	$.{600}_{-.040}^{+.040}$	${4.000}_{-.400}^{+.400}$
WASP-44	${2.424}_{.000}^{+.000}$	$.{035}_{.000}^{+.000}$	$.{000}_{}^{}$	$.{889}_{-.062}^{+.062}$	Mass	${1.140}_{-.110}^{+.110}$	${5410}_{-150}^{+150}$	$.{950}_{-.030}^{+.030}$	$.{930}_{-.070}^{+.070}$	${3.200}_{-.900}^{+.900}$
WASP-49	${2.782}_{.000}^{+.000}$	$.{038}_{-.001}^{+.001}$	$.{000}_{}^{}$	$.{378}_{-.027}^{+.027}$	Mass	${1.115}_{-.047}^{+.047}$	${5600}_{-150}^{+150}$	$.{940}_{-.080}^{+.080}$	$.{980}_{-.030}^{+.030}$	$.{900}_{-.300}^{+.300}$
WASP-5	${1.628}_{.000}^{+.000}$	$.{027}_{-.001}^{+.001}$	$.{038}_{-.018}^{+.026}$	${1.580}_{-.100}^{+.130}$	Mass	${1.087}_{-.071}^{+.068}$	${5700}_{-100}^{+100}$	$.{960}_{-.090}^{+.130}$	${1.030}_{-.070}^{+.060}$	${3.050}_{-.410}^{+.410}$
WASP-50	${1.955}_{.000}^{+.000}$	$.{029}_{-.001}^{+.001}$	$.{009}_{-.006}^{+.011}$	${1.468}_{-.086}^{+.091}$	Mass	${1.153}_{-.048}^{+.048}$	${5400}_{-100}^{+100}$	$.{890}_{-.080}^{+.080}$	$.{840}_{-.030}^{+.030}$	${2.600}_{-.500}^{+.500}$
WASP-52	${1.750}_{.000}^{+.000}$	$.{027}_{.000}^{+.000}$	$.{000}_{}^{}$	$.{460}_{-.020}^{+.020}$	Mass	${1.270}_{-.030}^{+.030}$	${5000}_{-100}^{+100}$	$.{870}_{-.030}^{+.030}$	$.{790}_{-.020}^{+.020}$	${3.600}_{-.900}^{+.900}$
WASP-56	${4.617}_{.000}^{+.000}$	$.{055}_{.000}^{+.000}$	$.{000}_{}^{}$	$.{571}_{-.035}^{+.034}$	Mass	${1.092}_{-.033}^{+.035}$	${5600}_{-100}^{+100}$	${1.020}_{-.020}^{+.020}$	${1.110}_{-.020}^{+.030}$	${1.500}_{-.900}^{+.900}$
WASP-58	${5.017}_{.000}^{+.000}$	$.{056}_{-.002}^{+.002}$	$.{000}_{}^{}$	$.{890}_{-.070}^{+.070}$	Mass	${1.370}_{-.200}^{+.200}$	${5800}_{-150}^{+150}$	$.{940}_{-.100}^{+.100}$	${1.170}_{-.130}^{+.130}$	${2.800}_{-.900}^{+.900}$
WASP-6	${3.361}_{.000}^{+.000}$	$.{041}_{-.001}^{+.001}$	$.{054}_{-.015}^{+.018}$	$.{485}_{-.027}^{+.027}$	Mass	${1.230}_{-.035}^{+.035}$	${5375}_{-65}^{+65}$	$.{840}_{-.060}^{+.060}$	$.{860}_{-.020}^{+.020}$	${1.600}_{-.270}^{+.270}$
WASP-60	${4.305}_{.000}^{+.000}$	$.{053}_{-.001}^{+.001}$	$.{000}_{}^{}$	$.{514}_{-.034}^{+.034}$	Mass	$.{860}_{-.120}^{+.120}$	${5900}_{-100}^{+100}$	${1.080}_{-.040}^{+.040}$	${1.140}_{-.130}^{+.130}$	${3.400}_{-.800}^{+.800}$
WASP-62	${4.412}_{.000}^{+.000}$	$.{057}_{-.001}^{+.001}$	$\lt {0.210}_{}^{}$	$.{570}_{-.040}^{+.040}$	Mass	${1.390}_{-.060}^{+.060}$	${6280}_{-80}^{+80}$	${1.250}_{-.050}^{+.050}$	${1.280}_{-.050}^{+.050}$	${8.700}_{-.400}^{+.400}$
WASP-64	${1.573}_{.000}^{+.000}$	$.{026}_{.000}^{+.000}$	$.{000}_{}^{}$	${1.271}_{-.068}^{+.068}$	Mass	${1.271}_{-.039}^{+.039}$	${5400}_{-100}^{+100}$	${1.000}_{-.030}^{+.030}$	${1.060}_{-.030}^{+.030}$	${3.400}_{-.800}^{+.800}$
WASP-65	${2.311}_{.000}^{+.000}$	$.{033}_{-.002}^{+.002}$	$.{000}_{}^{}$	${1.550}_{-.160}^{+.160}$	Mass	${1.112}_{-.059}^{+.059}$	${5600}_{-100}^{+100}$	$.{930}_{-.140}^{+.140}$	${1.010}_{-.050}^{+.050}$	${3.600}_{-.500}^{+.500}$
WASP-67	${4.614}_{.000}^{+.000}$	$.{052}_{-.001}^{+.001}$	$\lt {0.200}_{}^{}$	$.{420}_{-.040}^{+.040}$	Mass	${1.400}_{-.200}^{+.300}$	${5240}_{-10}^{+10}$	$.{870}_{-.040}^{+.040}$	$.{870}_{-.040}^{+.040}$	${2.100}_{-.400}^{+.400}$
WASP-69	${3.868}_{.000}^{+.000}$	$.{045}_{-.001}^{+.001}$	$.{000}_{}^{}$	$.{260}_{-.017}^{+.017}$	Mass	${1.057}_{-.047}^{+.047}$	${4715}_{-50}^{+50}$	$.{830}_{-.030}^{+.030}$	$.{810}_{-.030}^{+.030}$	${2.200}_{-.400}^{+.400}$
WASP-75	${2.484}_{.000}^{+.000}$	$.{037}_{-.001}^{+.001}$	$.{000}_{}^{}$	${1.070}_{-.050}^{+.050}$	Mass	${1.270}_{-.048}^{+.048}$	${6100}_{-100}^{+100}$	${1.140}_{-.070}^{+.070}$	${1.260}_{-.040}^{+.040}$	${4.300}_{-.800}^{+.800}$
WASP-80	${3.068}_{.000}^{+.000}$	$.{034}_{-.001}^{+.001}$	$.{002}_{-.002}^{+.010}$	$.{538}_{-.036}^{+.035}$	Mass	$.{999}_{-.031}^{+.030}$	${4143}_{-94}^{+92}$	$.{580}_{-.050}^{+.050}$	$.{590}_{-.020}^{+.020}$	${1.270}_{-.170}^{+.140}$
WASP-83	${4.971}_{.000}^{+.000}$	$.{059}_{-.001}^{+.001}$	$.{000}_{}^{}$	$.{300}_{-.030}^{+.030}$	Mass	${1.040}_{-.050}^{+.080}$	${5510}_{-110}^{+110}$	${1.110}_{-.090}^{+.090}$	${1.050}_{-.040}^{+.060}$	$\lt {0.500}_{}^{}$
WASP-89	${3.356}_{.000}^{+.000}$	$.{043}_{-.001}^{+.001}$	$.{193}_{-.009}^{+.009}$	${5.900}_{-.400}^{+.400}$	Mass	${1.040}_{-.040}^{+.040}$	${5130}_{-90}^{+90}$	$.{920}_{-.080}^{+.080}$	$.{880}_{-.030}^{+.030}$	${2.500}_{-.900}^{+.900}$
WASP-95	${2.185}_{.000}^{+.000}$	$.{034}_{-.001}^{+.001}$	$.{000}_{}^{}$	${1.130}_{-.040}^{+.100}$	Mass	${1.210}_{-.060}^{+.060}$	${5630}_{-130}^{+130}$	${1.110}_{-.090}^{+.090}$	${1.130}_{-.040}^{+.080}$	${3.100}_{-.600}^{+.600}$
WASP-96	${3.425}_{.000}^{+.000}$	$.{045}_{-.001}^{+.001}$	$.{000}_{}^{}$	$.{480}_{-.030}^{+.030}$	Mass	${1.200}_{-.060}^{+.060}$	${5540}_{-140}^{+140}$	${1.060}_{-.090}^{+.090}$	${1.050}_{-.050}^{+.050}$	${1.500}_{-1.300}^{+1.300}$
WASP-97	${2.073}_{.000}^{+.000}$	$.{033}_{-.001}^{+.001}$	$.{000}_{}^{}$	${1.320}_{-.050}^{+.050}$	Mass	${1.130}_{-.060}^{+.060}$	${5640}_{-100}^{+100}$	${1.120}_{-.060}^{+.060}$	${1.060}_{-.040}^{+.040}$	${1.100}_{-.500}^{+.500}$
WTS-1	${3.352}_{.000}^{+.000}$	$.{047}_{-.001}^{+.001}$	$\lt {0.100}_{}^{}$	${4.010}_{-.350}^{+.350}$	Mass	${1.490}_{-.180}^{+.160}$	${6250}_{-200}^{+200}$	${1.200}_{-.100}^{+.100}$	${1.150}_{-.120}^{+.100}$	${7.000}_{-2.000}^{+2.000}$
WTS-2	${1.019}_{.000}^{+.000}$	$.{019}_{-.001}^{+.001}$	$.{000}_{}^{}$	${1.120}_{-.160}^{+.160}$	Mass	${1.363}_{-.061}^{+.061}$	${5000}_{-250}^{+250}$	$.{820}_{-.080}^{+.080}$	$.{750}_{-.030}^{+.030}$	${2.200}_{-1.000}^{+1.000}$
XO-5	${4.188}_{.000}^{+.000}$	$.{051}_{-.001}^{+.001}$	$.{000}_{}^{}$	${1.190}_{-.030}^{+.030}$	Mass	${1.140}_{-.030}^{+.030}$	${5430}_{-70}^{+70}$	${1.040}_{-.030}^{+.030}$	${1.130}_{-.030}^{+.030}$	$.{700}_{-.500}^{+.500}$

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