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Article

Exoplanets around Red Giants: Distribution and Habitability

by
Ruixuan E. Chen
1,2,
Jonathan H. Jiang
2,*,
Philip E. Rosen
3,
Kristen A. Fahy
2 and
Yanbei Chen
4
1
Arcadia High School, Arcadia, CA 91006, USA
2
Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA 91099, USA
3
Independent Researcher, Vancouver, WA 98662, USA
4
Theoretical Astrophysics, California Institute of Technology, Pasadena, CA 91125, USA
*
Author to whom correspondence should be addressed.
Galaxies 2023, 11(6), 112; https://doi.org/10.3390/galaxies11060112
Submission received: 24 October 2023 / Revised: 9 November 2023 / Accepted: 13 November 2023 / Published: 16 November 2023
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Abstract

:
As the search for exoplanets continues, more are being discovered orbiting Red Giant stars. We use current data from the NASA Exoplanet Archive to investigate planet distribution around Red Giant stars and their presence in the host’s habitable zone. As well, we explore the distribution of planet mass and orbital semi major axis for evolved stars with increasing stellar radii. From the distance distribution of the planets, we found evidence of engulfment during the post-Main Sequence evolution of the star. We found 9 Red Giant-hosted exoplanets, and 21 Subgiant-hosted exoplanets to be in the optimistically calculated habitable zone, 5 and 17 of which are in a more conservatively calculated habitable zone. All the planets detected within their habitable zone orbit stars that are in early stages of evolution. We believe that with more powerful instrumentation, more habitable planets may be found around stars that are in later stages of evolution.

1. Introduction

In the distant future when our Sun becomes a Red Giant (RG), the habitable zone (HZ) in the Solar System may move towards the outer planets where the moons of Jupiter and Saturn might be candidates for our future generations to live [1]. Near-term considerations also prompt interest in exoplanet and exomoon systems of RG hosts as some of these worlds may presently be in the HZ of their parent star. In this paper, we examine data from the NASA Exoplanet Archive, focusing on exoplanets around Red Giant (or Subgiant) stars.
When a star leaves the Main Sequence (MS) and begins its evolution into the Red Giant Branch (RGB), it undergoes a series of changes. As the fusion of hydrogen progresses in the core of a Main Sequence star, its effective temperature and luminosity increase slowly over time. At the end of a star’s Main Sequence stage, its core is composed of helium while hydrogen begins to burn in the shell surrounding the core. The star then moves along the RGB of the Hertzsprung–Russell (H-R) diagram, with its temperature moderately decreasing, and its radius and luminosity significantly increasing.
As the host star evolves beyond MS, the orbits of its planets will also evolve. Due to the host’s mass loss, its surrounding planets will move outwards. On the other hand, tidal interactions tend to shrink the orbital radius of the planets [2]. In particular, Villaver et al. [3] predicted that tidal interaction would cause planets to plunge into the star, and get engulfed, before a/Rs < 3, where a is the orbital semi-major axis of the planet and Rs is the stellar radius.
The first aim of our paper is to study the distribution of planets around RGs. Previous research [4] found a power law relation between planet mass and stellar radius. The associated distribution of three variables is focused upon: the mass of the planet (Mp), the radius of the star (Rs), and the orbital semi-major axis (a). We aim to gain additional insight into the evolution of planets as the host star evolves post-Main Sequence.
To scientists and the general public alike, habitability and the existence of extraterrestrial life is a topic of high interest [5]. A habitable zone is an annular region around a given star where any hosted planets have a relatively high likelihood of moderate average surface temperature, allowing for biological life (as we know it) to possibly exist. The HZ is usually determined primarily as a function of the stellar energy flux from the host. However, a planet must not only be in the host’s HZ, but also possess the appropriate atmospheric and geological conditions that accommodate surface liquid water. A magnetic field may also be required to protect the delicate molecules which comprise life from energetic particles of stellar wind.
It has been predicted by many authors that as the Sun enters the RGB, Earth will no longer be in the Solar System’s HZ. As investigated in many studies [1,6,7,8,9,10], post-MS evolution of the Sun will alter its HZ, possibly rendering some of the outer planets’ moons habitable to life such as found on Earth.
For a grid of stars with varying mass and metallicity, Ramirez and Kaltenegger [9] explored the evolution models of planets with their stars, and subsequent durations of planets in the HZ in detail. Their findings suggest three candidate systems that will become habitable once the host star becomes an RG. In this paper, we apply the criterion used in two previous studies [1,9], initially proposed by Kopparapu and colleagues [11], to current data in the NASA Exoplanet Archive, identifying those exoplanets in the HZ and discussing further parameterized regions not yet observed which may also contain habitable planets.

2. Data Collection and Distribution of Planets around Red Giants

In this section, we briefly introduce our data collection and then discuss the distribution of Subgiant (SG) and RG planets in the (Mp, a, Rs) parameter space. In Figure 1, we plot an H-R diagram of host stars using luminosity relative to the Sun ( L / L ⊙ ) and stellar surface effective temperature (Teff) values from the NEA, identifying 210 RG planets and 229 SG planets, as indicated by red × and blue +, respectively. Parameters of each planet and their host, namely (Ms, Rs, a, Mp), are listed in Table A1 and Table A2 in Appendix A. To estimate the evolutionary stages of each star, we use MIST v1.2 stellar evolution tracks for solar metallicity stars with v/vcrit = 0.4 [12]. In the figure, the purple curve indicates the end of the main sequence, while the separation between SG and RG can be seen from the shapes of the tracks. More specifically, along each track (which moves from left to right), there is a point where the host’s luminosity begins rapidly increasing, marking the transition from SG to RG. We approximately separated SG and RG using black dashed lines. In comparison with Ref. [13], who used a color-independent Mbol = 2.82 as the boundary between SG and RGs, our criterion further includes a few more stars which, according to the evolutionary tracks, are in the RGB despite their relatively low luminosities. We caution that our identification of SG from MS stars can be inaccurate since we have not individually accounted for the metallicity of each host star.
We note that some of these planets, including 42 Dra, γ Dra (see Ref. [14] by Döllinger and Hartmann, henceforth referred to as D&H), and α Tau [15], have been questioned as false positives. D&H further speculated that a substantial fraction of planets around K-giants with radii greater than 21R⊙ can be false positives, based on the congregation of their orbital periods, lack of planet-metallicity correlation, as well as the excess number of planets around K-giants compared with MS stars. We shall make comparisons with D&H in Section 2.2 below.

2.1. Observed Evolution of Exoplanet Population as the Host Star Evolves

A previous study by Jiang and Zhu derived a planet mass-stellar radius relation for 150 exoplanets orbiting Red Giants [4]:
M p / M ⊕ = a R / R ⊙ b
with best-fit parameters a = 150 and b = 0.88. With the new data points, we still see that there is a trend between Mp and Rs, yet their distribution appears to more be in a triangular distribution rather than a linear dependence (see Figure 2). Further investigation of the origin of the Mp vs. Rs relation notes that the stellar radius tracks with the post-MS evolution stage of the host star. The fact that Mp increases with Rs corresponds to a relative lack of less massive planets around more evolved stars. In this paper, we shall use Figure 3 and Figure 4, in addition to Figure 2, to further investigate the evolution of the population of exoplanets around stars as they evolve. We will also discuss the possible observational selection bias of this distribution.
In Figure 3, we split Rs into three different intervals and plot MS/SG (silver dots) and RG planets in each interval separately as planet mass Mp (in Earth masses) vs. orbital semi-major axis a (in astronomical units). In particular, we separate RG planets into three categories according to Rs: Rs/R⊙ < 5 (blue +), 5 < Rs/R⊙ < 25 (green +), and Rs/R⊙ > 25 (red +). The (a, Mp) region occupied by RG planets shrinks as Rs increases—from its left side, with small a; from the bottom side, with low Mp; and from the right side, with large a. This shrinkage is best viewed from the right panel of Figure 3, which focuses on the specific region of RG planets and adds contours generated via Kernel Density Estimate (KDE) for clarity. In Figure 4, we plot the orbital semi-major axis vs. stellar radius ratioed to solar radii.
At this stage, it is useful to point out the relation among Figure 2, Figure 3 and Figure 4. In the right panel of Figure 3, we separate the evolution of Rs into three bins (stages) and illustrate the lumped joint (a, Mp) distribution in each bin (stage). Figure 2 and Figure 4 each separately illustrates the continuous evolutions of the marginal distributions of Mp and a, respectively, as Rs increases. The step-wise shrinkage of (a, Mp) distribution as we progress from blue to green and to red in the right panel of Figure 3 is continuously represented in Figure 4 for a and in Figure 2 for Mp. Note that these three groups are not colored accordingly in Figure 2 and Figure 4.

2.2. Interpretations of the Evolutions in Population

In the following, we shall address the disappearance of planets with low semi-major axis (left side in Figure 3), low mass (bottom side in Figure 3), and high semi-major axis (right side in Figure 3) separately.
For disappearance of planets with low semi-major axis, it is straightforward to anticipate planets with small orbital distance values to be engulfed and consumed as their host evolves and expands. According to Villaver et al. [3], tidal interactions tend to speed up the engulfment of planets, and no planets should survive once a/Rs < 3. In Figure 4, we plot the orbital semi-major axis vs. stellar radius ratioed to solar radii, clearly illustrating that a/Rs = 3 is a cutoff and providing empirical evidence for tidally accelerated engulfment. Correspondingly, in the right panel of Figure 3, we plot pink dashed lines to represent a = 15 R ⊙ and a = 75 R ⊙ . These two lines indeed bound the green (5R⊙ < Rs < 25R⊙) and red (Rs > 25R⊙) populations from the left, respectively. As the stars evolve, this engulfment cutoff moves continuously along a.
Regarding the disappearance of low-mass planets with increasing Rs, we can see from Figure 3 that for stars with a radius less than 25R⊙, many planets with masses of 200 to 1000M⊕ exist at distances of 2 to 3 AU. Yet, such planets are not seen orbiting stars with Rs > 25R⊙—even though much more massive planets are seen at the same distance. This disappearance of low-mass planets with increasing Rs corresponds directly from the Mp vs. Rs power-law fit obtained by Jiang and Zhu [4]. Note that Solar System planets lie on the lower part of the plot; only Jupiter is near the reach of current detection methods. However, Jovian mass exoplanets and comparable orbital distance (~5 AU) are not seen around Red Giants with Rs /R⊙ > 25.
This disappearance can be explained using the limitations to the radial velocity (RV) method arising from the intrinsic oscillations of evolved stars [16]. Such oscillations have also been claimed to have led to false positives for exoplanets around RGs [15]. Hekker et al. [16] noticed that for stars with lower surface gravity g (i.e., larger radii), their measured minimum amplitudes of RV variations tend to increase, given approximately with:
K 1 int = 2 × 10 3 g / ( c m / s 2 ) − 0.6 m / s ,
which they interpret as arising from intrinsic fluctuations of the star. See Figure 3 and Figure 4 of Ref. [16]. Here, g is the surface gravitational acceleration of the star. For each RG, assuming e = 0, we obtain the minimum planet mass M p min the star can host; this is in order for the K1 due to the planet to be greater than the intrinsic K 1 int :
M p min = a M s   G K 1 int
In the right panel of Figure 3, we plot this minimum planet mass as a function of a, assuming M s = 1 M ⊙ for R = 5 R ⊙ and R = 25 ⊙ in purple dashed lines. These RV cutoffs approximately indicate the trend in which planets are cut off from the bottom, and to a lesser extent, the right. Note that some planets are below the cutoff because the cutoff is an approximate one, presumably because the intrinsic RV variations of giant stars also depend on factors beyond surface gravity; some RV variations in Figure 3 and Figure 4 of Hekker et al. also extend below the line given with Equation (2).
We may further replace a in Equation (3) with its minimum value of 3 R s before engulfment, obtaining M p min for each R s , which is plotted as orange dots in Figure 2. In this plot, the RV cutoff indeed provides an excellent lower bound for the masses of planets detected using the RV method (red and blue dots) around substantially evolved stars.
Although the two cutoffs arise from a different physical mechanism, given a particular population of planets, they do not act independently from each other; they have different efficiencies in cutting off populations depending on the distribution of planets in the a, Mp space. For example, since planets with smaller a tend to be low in Mp, they are less detectable with the RV method. Furthermore, for planets subject to the engulfment and RV cutoffs simultaneously, it is unclear whether they are actually engulfed or just unseen. Nevertheless, we would like to point out the region in the right panel of Figure 3 bounded by the two pink lines and the upper purple line. The planets in this region represent a population that should be visible with the RV method, yet they are predicted to be engulfed by the a = 3 R ⊙ criterion. More specifically, we do see two planets with R s < 25 R ⊙ host stars, yet the R s > 25 R ⊙ population does not extend here. This provides some evidence that engulfment can indeed be taking place, and does contribute nontrivially to the shrinkage of the (a, Mp) distribution from the left. However, better detection methods not subject to the RV cutoff will be needed to more accurately study the engulfment phenomenon.
The disappearance of high-semi-major-axis planets as the star evolves cannot be fully explained with only the discussions above. As seen in the right panel of Figure 3, the red population has more concentrated values of a than simply applying the engulfment cutoff (the right pink line) and RV cutoff (the upper purple line) to the green and blue populations. More specifically, the log of the orbital semi-major axis of planets in the red population has a standard deviation of Δ log 10 a = 0.14 (corresponding to Δ a / a = 1.38 ); the same quantity for the green population has a value of Δ log 10 a = 0.31 (corresponding to Δ a / a = 2.04 ), while the quantity for the green population after applying the engulfment and the RV cutoffs is Δ log 10 a = 0.28 (corresponding to Δ a / a = 1.91 ). Since the three populations consist of 25, 123, and 24 samples, respectively, the small shrinkage in the overall spread of a is not statistically significant as we apply the cutoffs to the green population, while the large gap between the cutoff green population and the red population is statistically significant. In this way, the cutoffs are unfortunately not enough to explain the narrow distribution a in the red population. Since orbital semi-major axis is highly correlated with orbital period due to the similarity in masses, our concentration in a is directly related to the concentration of orbital periods (between 300 days and 800 days) for exoplanets around Red Giants with Rs > 21R⊙, pointed out by D&H.
D&H argued that since the range of period falls within the period of intrinsic variations of stars (as modeled by Saio et al. [17]), hence, a fraction of these may not be actual planets. On the other hand, they provided plausible reasons for planets outside of this period range not to be discovered. For longer periods (corresponding to larger a), this could be due to the smaller RV variation being hidden under intrinsic fluctuations of the surface of the host star. For shorter periods (corresponding to smaller a), this could be due to the engulfment of planets by their host stars. Our discussions above quantitively explored these possibilities proposed by D&H. As we have seen, the engulfment and RV limitations do explain to some extent, but not completely, the concentration of periods described by D&H.
Disappearance of large-a planets can also be explained from the inward migration of hosted planets, especially because large R s systems tend to be older; therefore, the planets had more time to migrate. Finally, regarding the fact that the more evolved host stars in our data tend to have lower metallicity and are older-aged, they were therefore apt to have differently characterized populations of planets formed around them. However, such differences will likely have to be very substantial to be influential in this respect.

3. Habitable Planets around Red Giants

In this section, we discuss the habitability of planets around RG and SG stars, briefly reviewing habitability criteria in Section 3.1, and presenting our findings in Section 3.2.

3.1. Criteria for Habitability

There exist multiple habitability conditions for a given exoplanet (or exomoon); most of which rely on the existence of water in liquid form to be present on at least a portion of that world’s surface. The simplest criterion uses equilibrium temperature, namely the black-body radiation from the planet has to balance the radiation it absorbs from the star. If we define S as the flux of radiation from the host, this is given with:
S = L s 4 π a 2
where L s is the star’s luminosity and a is the orbital semi-major axis of the star’s exoplanet; the equilibrium temperature of the exoplanet is then given with:
T eq = k S 1 − A 4 σ 1 / 4
where A is the planetary albedo and σ is the Stefan–Boltzmann constant. The simplest habitability condition is 273   K < T eq < 373   K , with the low T eq defining the outer boundary of the habitable zone (OHZ) and the high Teq defining the inner boundary of the habitable zone (IHZ). The scalar quantity k is a correction factor that can be used to approximately incorporate the greenhouse effect of an assumed planetary atmosphere; see Ref. [18]. We adopt the Earth albedo of A = 0.3 and use k = 1.13, which reproduces the Earth surface temperature.
More realistic criteria exist in the literature. In this paper, we shall adopt two criteria obtained in a previous study [11] in which an effective solar flux is expressed in terms of
S eff ≡ S / S ⊕
where S ⊕ is the current solar energy flux at the location of the Earth, as well as the temperature T of the host star. Note that Seff is dimensionless. Following Ref. [11], we use two different ways to define HZ boundaries, one conservative, the other optimistic. The conservative HZ accounts for greenhouse effects in the atmosphere of the planet, taking the inner boundary to be defined by the moist greenhouse effect where S eff allows sufficient water vapor to exist in the stratosphere. The outer boundary is defined by the maximum heat retained by the planet while still providing habitable conditions. This is also known as the maximum greenhouse effect. The optimistic approach uses the (theorized) history of Solar System planets Venus and Mars to determine the inner and outer bounds of the HZ. Here, the inner boundary of the HZ is based on the assertion that Venus has not had liquid water on its surface for only the past billion years—i.e., a billion years ago (recent) Venus might have had surface conditions suitable for water to exist. On the other hand, there is mounting evidence that (early) Mars had liquid water flowing on its surface 3.8 billion years ago. For these reasons, they define the inner boundary using the Seff of recent Venus and the outer boundary using the Seff of early Mars.
Kopperapu et al. summarized the boundaries using the following fitting formula for the host star temperature range of 2600 K < T < 7200 K [11]:
S limit T = S 0 + a T * + b T * 2 + c T * 3 + d T * 4 ,   T * = T / K − 5780   ,
where values of a, b, c, and d for conservative/optimistic, inner/outer boundaries are reproduced in Table 1. Parameters in Equation (7) are all dimensionless.
In Table 2, we list conservative and optimistic habitable zone RG-hosted planets. All planets are gas giants with masses ranging from 1 to 22 Jupiter masses (MJ). In the third and fourth columns, we list the spectral type and absolute V magnitude (obtained from apparent V-magnitude and distance data from NEA) of the host stars obtained from the NEA. Note that spectral types quoted here are not always consistent with other sources, and that classifications of stars using these values here may not be always consistent with our classification from the positions of the stars in the HR diagram (Figure 1). The hosts of planets in Table 2 are also shown as green circles in the H-R diagram of Figure 1. As can be readily perceived from Table 2 and Figure 1, these host stars are all in their early stages of evolution.

3.2. Red Giant Planets in the Habitable Zones

From the NASA Exoplanet Archive, we collected values for stellar luminosity and orbital semi-major axis to calculate Seff. In Figure 5, we show the Red Giant planets on the Teff vs. Seff plot with lines indicating HZ boundaries. From the plot, it can be seen that there is a substantial difference between boundaries for the Teq HZ and Kopparapu HZ.
Figure 6 shows Red Giant and Main Sequence planets on a semi-major axis vs. stellar radius plot with habitable planets indicated (light green dots for habitable planets around MS stars, cyan dots for those around SGs, and dark green for those around RGs). We also indicate, with purple line segments, the optimistic HZ of the host stars of all planets around RGs. As illustrated, habitable planets—and indeed habitable zones—tend to have increasing a as Rs increases, and this is attributable to stars with larger radii—and thus greater luminosity—having HZs farther out. For detected HZ planets, they have a maximum Rs of ~8R⊙, far below the maximum Rs of Red Giants; in this way, habitable planets so far discovered are either orbiting SG or RG at their early stages of evolution.
As stars evolve beyond 8R⊙, the HZ extends to larger a, beyond the region in which planets have been detected orbiting RGs. Around MS stars, planets do exist in this region, as is the case for the outer planets of the Solar System (see Figure 3). Therefore, such planets might exist around RGs, even though they are not yet detectable.
For Main Sequence hosts, planets with the longest semi-major axes were all discovered with direct imaging (yellow dots in Figure 6). However, using the same detection method to find similar planets around RGs may be difficult due to the direct imaging method disfavoring systems with large contrast. More specifically, the contrast between a one-solar-mass giant star and a potential planet is about 5 magnitudes larger than that between a one-solar-mass Main Sequence star and a potential planet. In this way, the direct imaging method is not (yet) sufficient to detect planets around giant stars.

4. Conclusions and Discussions

In this paper, we take new data from NASA’s Exoplanet Archive to update and further investigate trends regarding Red Giant systems. First, we revisit the planet mass-stellar radius relation previously found by Jiang and Zhu [4]. To further explore this trend, we separate Red Giant-hosted exoplanets according to the radii of their hosts and plot planet mass against semi-major axis (Figure 3).
Motivated by a planet mass-stellar radius relation previously found for exoplanets around Red Giant stars [4], this paper takes new data from NASA’s Exoplanet Archive to update and further investigate distributions of exoplanets around Red Giants, and searched for planets in HZs.
Figure 2, Figure 3 and Figure 4 are two-dimensional slices of the entire (Mp, a, Rs) distribution, while we take the increase in the host’s stellar radius Rs to mainly indicate its evolution stage. In Figure 3, we highlighted three groups of Red Giants at early (blue, Rs < 5R⊙), middle (green, 5R⊙ < Rs < 25R⊙), and late (red Rs > 25R⊙) stages of evolution. As Rs increases, the (Mp, a) region occupied by the planets shrinks, for which we found astrophysical and observational reasons.
For planets with smaller orbital semi-major axes, we found their disappearance to be consistent with tidal engulfment of planets when a / R s < 3 (Figure 4). For the disappearance of planets with lower masses and those with larger orbital semi-major axes, their disappearance could be due to observational selection effects of the radial velocity method used to discover the vast majority of planets in these regions. Since lower mass and larger orbital semi-major axis correspond to lower amplitudes of radial velocity, the disappearance can be attributed to a higher detection threshold for the amplitude of radial velocity oscillations among more evolved Red Giants. We showed that in order for this selection effect to be the origin of such disappearance, the level of intrinsic RV fluctuation of Red Giants should depend on surface gravity following Equation (2), which was proposed by Hekker et al. [16]. Jointly imposing a minimum RV of Equation (3) and a / R s > 3 leads to the orange dots in Figure 2 (labeled as RV bound) that provide minimum bounds for Mp that increase with Rs, thereby explaining the trend found by Jiang and Zhu [4].
The engulfment and RV limitations do not yet fully explain all features of the population, e.g., the concentration of orbital period (hence semi-major axis) for giants with large radii found by D&H [14]. Further astrophysical mechanisms and observational selection effects, e.g., due to orbital eccentricity, stellar mass, and metallicity, can still contribute. We leave such further investigations to future studies.
Next, we examine the habitability of Red Giant exoplanets. To determine the habitable zone, we adopt criteria proposed by Kopparapu et al. [11] and with this method found ten planets in the optimistic HZ, five of which are in the conservatively calculated HZ. Here, we did not consider the atmospheric, geological, and magnetic features of the planets. We caution that all of these HZ planets are gas giants and, therefore, very likely uninhabitable by life as we presently know it. Nevertheless, these planets may themselves host habitable exomoons. Even though a planet might be within the HZ at the moment, its total lifetime within the HZ may or may not be long enough for life to develop. As Ramirez and Kaltenegger [9] have shown, depending on the planet–star configuration, a planet can stay for 0.2–9 Gyr in the post-MS HZ of a star, which does provide hope for life to develop on its moon(s). An obvious next step of research is to find out how long each of the planets in Table 2 had been in the HZ. For the Solar System, on the other hand, Sparrman had shown that none of the outer planets will stay long enough in the post-MS HZ of the Sun for life to independently develop. In light of the host star’s evolution, it is conceivable that as the habitable zone shifts outward, organisms or even technologically advanced civilizations might seek refuge or inadvertently find themselves transplanted to the moons of outer planets (such as Jupiter or Saturn in our Solar System). These scenarios assume that sub-surface oceans on moons like Europa or Enceladus could offer new refuges for life as the inner Solar System becomes less hospitable due to the intense heat and radiation from the expanding Red Giant.
Finally, with habitable zone exoplanets identified, we revisited the issue of detection bias. We see that their orbital semi-major axis increases with stellar radii until R s / R ⊙ ~8. However, this does not necessarily rule out further habitable zone exoplanets and it is very likely there are more HZ Red Giant exoplanets with a semi-major axis greater than ~ 4 AU. Even though some such planets can be seen around Main Sequence stars via direct imaging, similar planets around Red Giant stars have not yet been found (see Figure 6). While the limitations of current imaging methods may preclude detecting planets around Red Giant stars, more advanced instrumentation coming online in the near term may enable this technique to be used for at least some Red Giant-hosted exoplanetary systems. The next generation of space telescopes, such as the Habitable World Observatory [44], will have enhanced capabilities and will be able to observe smaller planets including those planets around Red Giant stars. In addition to static spectroscopy, it will be possible to observe variation in the reflected starlight spectra while the planet rotates around its axis. As in the case of the Earth, the surface of a rocky exoplanet is not expected to be homogeneous (if it has oceans, lands, forests, and deserts), nor is the cloud distribution [45,46]. These factors will have an impact on the time series of the exoplanetary spectrum.

Author Contributions

Conceptualization, J.H.J.; methodology, J.H.J. and R.E.C.; software, R.E.C. and J.H.J.; validation, J.H.J. and Y.C.; formal analysis, R.E.C., J.H.J., P.E.R. and Y.C.; investigation, R.E.C., J.H.J., P.E.R., Y.C. and K.A.F.; resources, J.H.J.; data curation, R.E.C. and J.H.J.; writing—original draft preparation, R.E.C.; writing—review and editing, J.H.J., Y.C., P.E.R. and K.A.F.; visualization, R.E.C. and J.H.J.; supervision, J.H.J. and Y.C.; project administration, J.H.J.; funding acquisition, J.H.J. All authors have read and agreed to the published version of the manuscript.

Funding

This research was funded by the NASA Exoplanet Research Program NNH22ZDA001N-XRP.

Data Availability Statement

The data underlying this article can be downloaded from the NASA Exoplanet Archive at https://exoplanetarchive.ipac.caltech.edu. The method of data calculation and analysis is fully described in the article.

Acknowledgments

This research was conducted at the NASA-sponsored Jet Propulsion Laboratory, California Institute of Technology (Caltech). It has made use of 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.

Conflicts of Interest

The authors declare no conflict of interest.

Appendix A. Exoplanets around Red Giants and Subgiants from the NASA Exoplanet Archive

Table A1. Exoplanets hosted by Red Giants from the NASA Exoplanet Archive (a total of 210 planets).
Table A1. Exoplanets hosted by Red Giants from the NASA Exoplanet Archive (a total of 210 planets).
Planet NameMs
(M⊙)		Rs
(R⊙)		a
(AU)		Mp
(MJ)		Planet NameMs
(M⊙)		Rs
(R⊙)		a
(AU)		Mp
(MJ)		Planet NameMs
(M⊙)		Rs
(R⊙)		a
(AU)		Mp
(MJ)
11 Com b2.7191.2919.4HD 177830 c1.472.620.51370.15HD 95127 b3.741.011.2810.63
11 UMi b2.7829.791.5314.74HD 180053 b1.754.060.8432.194HD 96063 b1.374.751.111.27
14 And b2.2110.834.8HD 180314 b2.28.131.4620.13HD 96127 b10.9451.11.4220.96
17 Sco b1.2225.921.454.32HD 180902 b1.414.161.41.685HD 96992 b0.967.431.241.14
18 Del b2.38.52.610.3HD 181342 b1.694.711.5922.54HD 98219 b1.414.61.261.964
24 Boo b0.9910.640.190.91HD 18742 b1.365.131.823.4HD 99283 b1.7611.211.080.97
24 Sex b1.544.91.3331.99HD 192699 b1.384.411.0632.096HD 99706 b1.465.521.981.23
24 Sex c1.544.92.080.86HD 200964 b1.394.921.5651.599HD 99706 c1.725.4 5.69
4 UMa b1.2318.110.877.1HD 200964 c1.394.921.961.214HIP 105854 b2.110.310.818.2
42 Dra b0.9822.031.193.88HD 202696 b1.916.431.5661.996HIP 107773 b2.4211.60.721.98
6 Lyn b1.445.22.112.01HD 202696 c1.916.432.3421.864HIP 114933 b1.395.272.841.94
7 CMa b1.344.871.7581.85HD 206610 b1.556.121.742.036HIP 56640 b1.044.933.733.67
7 CMa c1.344.872.1530.87HD 208527 b1.651.12.19.9HIP 63242 b1.5410.280.5659.18
75 Cet b2.4910.52.13HD 208897 b1.254.981.051.4HIP 65891 b2.58.932.816
8 UMi b1.4410.30.491.31HD 210702 b1.614.921.1481.808HIP 67537 b2.418.694.9111.1
81 Cet b2.4112.55.3HD 212771 b1.565.271.192.39HIP 67851 b1.635.920.461.38
91 Aqr b1.4110.73.2HD 216536 b0.819.830.611.05HIP 67851 c1.635.923.826.3
BD+03 2562 b1.1432.351.36.4HD 219139 b1.4611.220.940.78HIP 74890 b1.745.772.12.4
BD+15 2375 b1.088.950.5761.061HD 219415 b12.93.21HIP 75092 b1.284.532.021.79
BD+15 2940 b1.114.70.5391.11HD 220074 b2.254.921.616.64HIP 8541 b1.177.832.85.5
BD+20 2457 b10.8371.021.0555.59HD 221416 b1.212.940.12280.19HIP 90988 b1.33.941.261.96
BD+20 2457 c2.8492.0112.47HD 222076 b1.074.11.831.56HIP 97233 b1.935.342.5520
BD+20 274 b0.817.31.34.2HD 22532 b1.575.691.92.12IC 4651 9122 b2.110.272.0386.3
BD+48 738 b0.741110.91HD 233604 b1.510.90.7476.575K2-132 b1.083.850.09160.49
BD+48 740 b1.0910.331.71.7HD 238914 b1.4712.735.76K2-161 b0.992.57 0.0978
BD+49 828 b1.527.64.21.6HD 240210 b0.8225.461.165.21K2-39 b0.662.970.057080.09
BD-13 2130 b2.1219.171.669.78HD 240237 b8.7671.231.9215.89K2-97 b1.24.470.0860.48
HD 100655 b2.2810.060.681.61HD 24064 b1.61401.2912.89Kepler-1004 b1.113.390.06710.102
HD 102272 b1.4510.30.514.94HD 25723 b2.1213.761.492.5Kepler-1270 b1.283.380.06630.0346
HD 102329 b3.219.821.818.16HD 27442 b1.233.181.2711.56Kepler-391 b1.033.570.0820.0325
HD 102329 c1.36.3 1.52HD 28678 b1.536.481.181.542Kepler-391 c1.033.570.1610.0386
HD 102956 b1.664.550.08070.96HD 29399 b1.174.51.9131.57Kepler-432 b1.324.060.3015.41
HD 104985 b2.3110.958.3HD 2952 b1.9710.761.231.37Kepler-432 c1.324.06 2.43
HD 108863 b1.595.741.322.414HD 30856 b1.174.41.851.547Kepler-56 b1.324.230.10280.07
HD 10975 b1.4111.160.950.45HD 32518 b1.1310.220.593.04Kepler-56 c1.324.230.16520.57
HD 110014 b2.1720.92.1411.09HD 33142 b1.414.451.071.385Kepler-56 d1.294.222.165.61
HD 111591 b1.948.032.54.4HD 33142 c1.624.14 5.97Kepler-815 b1.253.420.08880.0498
HD 112640 b1.8391.75HD 33844 b1.845.391.62.01Kepler-91 b1.316.30.07310.81
HD 113996 b1.4925.111.66.3HD 33844 c1.785.292.241.75NGC 2682 Sand 364 b9.0639.590.536.69
HD 116029 b0.834.891.651.4HD 360 b1.6910.860.980.75NGC 2682 Sand 978 b1.3721.02 2.18
HD 116029 c1.334.6 1.27HD 40956 b28.561.42.7TOI-2337 b1.323.22 1.6
HD 11755 b0.7220.581.095.63HD 4313 b1.635.141.1571.927TOI-2669 b1.194.1 0.61
HD 11977 b1.9110.091.936.54HD 4732 b1.745.41.192.37TYC 0434-04538-1 b1.049.990.666.1
HD 120084 b2.399.124.34.5HD 4732 c1.745.44.62.37TYC 1422-614-1 b1.156.850.692.5
HD 125390 b1.366.473.1622.16HD 47366 b2.196.21.282.3TYC 1422-614-1 c1.156.851.3710
HD 12648 b0.6711.020.541.96HD 47366 c2.196.21.971.88TYC 3318-01333-1 b1.195.91.4143.42
HD 131496 b1.344.442.011.8HD 47536 b2.123.471.937.32TYC 3667-1280-1 b1.876.260.215.4
HD 13189 b2.2438.411.2510.95HD 4760 b1.0542.41.1413.9TYC 4282-00605-1 b0.9716.210.42210.78
HD 136418 b1.483.781.292.14HD 4917 b1.325.011.1671.615alf Ari b1.513.91.21.8
HD 139357 b1.3511.472.369.76HD 5583 b1.019.090.535.78alf Tau b1.1345.11.466.47
HD 14067 b2.412.43.47.8HD 5608 b1.535.141.9111.681bet Cnc b1.747.21.77.8
HD 142245 b3.54.632.783.07HD 5891 b1.9310.640.647.63bet UMi b1.438.31.46.1
HD 145457 b1.2310.520.762.23HD 59686 A b1.913.21.0866.92eps CrB b1.7211.36.7
HD 145934 b1.755.384.62.28HD 60292 b1.7271.56.5eps Tau b2.713.71.937.6
HD 14787 b1.435.011.71.121HD 62509 b28.91.642.3gam 1 Leo b1.2331.881.198.78
HD 148427 b1.643.861.041.3HD 64121 b1.645.441.512.56gam Cep b1.44.92.059.4
HD 1502 b1.464.671.2622.75HD 66141 b1.121.41.26gam Lib b1.4711.11.241.02
HD 152581 b1.35.141.661.869HD 69123 b1.687.722.4823.04gam Lib c1.4711.12.174.58
HD 155233 b1.695.0322.6HD 72490 b1.214.961.881.768gam Psc b0.9911.21.321.34
HD 158038 b1.34.51.51.53HD 75784 b1.263.41.0321iot Dra b1.5411.791.45311.82
HD 158996 b1.850.32.114HD 75784 c1.263.48.45.64iot Dra c1.5411.7919.415.6
HD 1605 b1.333.491.4920.934HD 76920 b1.177.471.1493.93kap CrB b1.54.852.652
HD 1605 c1.333.493.5843.62HD 79181 b1.2811.060.90.64mu Leo b1.511.41.12.4
HD 161178 b1.0610.950.850.57HD 81688 b2.1130.812.7nu Oph b2.714.61.7922.206
HD 167042 b1.724.31.321.7HD 81817 b4.383.83.327.1nu Oph c2.714.65.93124.662
HD 1690 b1.8621.661.368.79HD 82886 b2.535.261.582.33ome Ser b2.1712.31.11.7
HD 17092 b6.7313.581.3110.13HD 86950 b1.668.82.723.6omi CrB b2.1310.50.831.5
HD 173416 b213.51.162.7HD 94834 b1.114.22.741.26tau Gem b2.326.81.1720.6
HD 175541 b1.394.190.9750.598HD 95089 b1.545.081.361.26ups Leo b1.4811.221.180.51
Table A2. Exoplanets hosted by Red Giants from the NASA Exoplanet Archive (a total of 229 planets).
Table A2. Exoplanets hosted by Red Giants from the NASA Exoplanet Archive (a total of 229 planets).
Planet NameMs
(M⊙)		Rs
(R⊙)		a
(AU)		Mp
(MJ)		Planet NameMs
(M⊙)		Rs
(R⊙)		a
(AU)		Mp
(MJ)		Planet NameMs
(M⊙)		Rs
(R⊙)		a
(AU)		Mp
(MJ)
70 Vir b1.091.890.4817.49K2-391 b0.760.57 0.00772Kepler-335 b1.031.850.0750.0359
BD+60 1417 b10.8166215K2-399 b0.781.54 0.0959Kepler-335 c1.021.850.3560.0303
CoRoT-20 c1.141.372.917K2-60 b0.971.120.0450.426Kepler-337 b1.051.760.0450.0094
CoRoT-26 b1.091.790.05260.52K2-99 b1.632.630.15970.97Kepler-337 c1.051.760.0930.0153
CoRoT-28 b1.011.780.06030.484KELT-11 b1.442.690.062290.171Kepler-363 b1.11.490.0480.00521
CoRoT-31 b1.252.150.05860.84KIC 8121913 b1.462.23 2.1Kepler-363 c1.11.490.0790.209
EPIC 248847494 b0.92.74.513KIC 9663113 b0.981.031.40620.0603Kepler-363 d1.11.490.1070.0153
EPIC 249893012 b1.051.710.0470.02753Kepler-101 b1.171.560.04740.16Kepler-368 b0.972.020.1860.0336
EPIC 249893012 c1.051.710.130.04616Kepler-101 c1.171.560.06840.01Kepler-368 c0.972.020.360.0451
EPIC 249893012 d1.051.710.220.03203Kepler-1078 b0.940.920.03880.0134Kepler-38 b0.941.750.46320.384
HAT-P-13 b1.321.760.043830.851Kepler-108 b1.252.190.2920.176Kepler-384 b0.970.880.1480.00459
HAT-P-13 c1.321.761.25814.28Kepler-108 c1.252.190.7210.16Kepler-384 c0.970.880.2360.00474
HAT-P-40 b1.031.940.06080.48Kepler-1080 b1.11.160.37810.0339Kepler-435 b1.543.210.09480.84
HAT-P-65 b1.211.860.039510.527Kepler-1125 b0.950.940.13480.0127Kepler-458 c1.152.220.1540.0516
HATS-61 b1.081.660.079083.4Kepler-1135 b0.960.940.34360.0128Kepler-473 b1.061.340.11860.0492
HATS-9 b1.11.560.03120.837Kepler-1142 b0.970.960.13430.00869Kepler-511 b11.20.85890.104
HD 103891 b1.282.223.271.44Kepler-1207 b1.061.060.11560.0102Kepler-525 b0.951.150.13960.0233
HD 10442 b1.011.972.011.487Kepler-1219 b1.251.940.14180.0162Kepler-628 b11.280.12410.168
HD 106270 b1.392.663.3410.13Kepler-1283 b1.161.250.10620.0136Kepler-638 b0.880.930.06320.0126
HD 10697 b1.131.792.146.383Kepler-129 b1.181.650.130.06293Kepler-641 b1.021.130.08790.0128
HD 114613 b1.272.145.340.357Kepler-129 c1.181.650.390.13529Kepler-643 b12.520.1261.01
HD 118203 b1.842.060.072.79Kepler-129 d1.181.6548.3Kepler-667 b0.910.870.22880.0632
HD 11964 b0.912.013.160.622Kepler-1296 b0.870.830.08960.00218Kepler-678 b0.940.910.07320.0728
HD 11964 c0.912.010.2290.0788Kepler-1304 b0.850.810.12020.0184Kepler-682 b0.920.890.10580.134
HD 13167 b1.352.394.13.31Kepler-1311 b1.051.40.09890.00651Kepler-684 b0.890.860.0640.0354
HD 1397 b1.322.340.10970.415Kepler-1311 c1.051.40.03680.00624Kepler-698 b0.940.910.12550.0413
HD 147873 b1.382.290.5225.14Kepler-1311 d1.031.670.67110.212Kepler-699 b0.810.780.1711
HD 147873 c1.382.291.362.3Kepler-1330 b0.970.940.08890.0106Kepler-7 b1.361.970.060670.441
HD 154857 b1.962.31.292.45Kepler-1336 b0.941.30.15950.0144Kepler-717 b0.880.850.0520.0203
HD 154857 c1.721.765.362.58Kepler-1336 c0.941.30.06310.0112Kepler-734 b0.850.780.05830.039
HD 156411 b1.252.161.880.74Kepler-1380 b0.960.940.09170.00829Kepler-767 b0.960.940.58740.112
HD 156668 b0.770.720.050.013Kepler-1385 b1.151.290.04150.00171Kepler-772 b0.981.110.10710.0125
HD 159868 b1.192.132.322.218Kepler-1402 b0.90.870.03220.00114Kepler-784 b11.320.19670.00982
HD 159868 c1.192.131.0320.768Kepler-1425 b0.970.950.10380.00245Kepler-796 b0.931.090.06620.00705
HD 163607 b1.121.760.3620.7836Kepler-1428 b1.281.360.10590.0105Kepler-797 b0.960.950.1810.0168
HD 163607 c1.121.762.392.201Kepler-1436 b1.061.090.09070.00714Kepler-799 c1.031.590.12140.0256
HD 168443 b0.991.510.29317.659Kepler-1437 b0.930.90.09510.00771Kepler-823 b0.980.960.05070.00972
HD 168443 c0.991.512.837317.193Kepler-1440 b0.980.960.22740.00669Kepler-848 b1.011.20.0720.0111
HD 171028 b1.532.471.322.62Kepler-1468 d1.071.50.14560.0349Kepler-852 b1.191.160.26540.022
HD 175167 b1.371.752.48.97Kepler-1484 b0.940.920.19390.016Kepler-87 b1.11.820.4811.02
HD 179079 b1.141.630.12140.081Kepler-1488 b1.051.310.22850.013Kepler-87 c1.11.820.6760.02
HD 18015 b1.493.133.873.18Kepler-1488 c11.520.06580.0106Kepler-891 b1.061.070.28810.106
HD 185269 b1.320.0771.01Kepler-1504 b0.850.810.37040.0163Kepler-896 b0.840.810.51640.0218
HD 187085 b1.191.272.10.836Kepler-1506 b0.950.930.11680.00724Kepler-903 b0.980.970.09070.0148
HD 202772 A b1.722.590.052081.017Kepler-1511 b1.171.290.17530.0109Kepler-903 c0.980.970.3020.0218
HD 206255 b1.422.220.4610.1076Kepler-1562 b1.021.050.33080.0388Kepler-913 b0.630.610.10090.0154
HD 214823 b1.312.043.2320.3Kepler-1570 b0.920.890.17840.0039Kepler-917 b0.80.760.03780.0136
HD 219077 b1.051.916.2210.39Kepler-1572 b0.970.950.06140.00245Kepler-939 b0.880.850.11530.0117
HD 221420 b1.351.9510.1522.9Kepler-1580 b1.472.150.3230.016Kepler-943 b0.930.910.25590.0928
HD 221585 b1.191.852.3061.61Kepler-1596 b0.950.920.32370.0134NGTS-13 b1.31.790.05494.84
HD 222155 b1.211.855.142.12Kepler-1605 b0.860.820.39120.00403TOI-1296 b1.171.660.04970.298
HD 224693 b1.311.930.1910.7Kepler-1625 b0.960.940.87480.0962TOI-1601 b1.522.190.068640.99
HD 33283 b1.381.970.15080.329Kepler-1658 b1.452.890.05445.88TOI-172 b1.131.780.09145.42
HD 38529 b1.412.560.12940.797Kepler-1704 b1.131.72.0264.15TOI-1789 b1.512.170.048820.7
HD 38529 c1.412.563.6412.99Kepler-1719 b1.081.770.06740.0465TOI-2180 b1.111.640.8282.755
HD 38801 b1.212.031.6239.698Kepler-1743 b1.271.610.08220.01TOI-2184 b1.532.9 0.65
HD 4203 b1.251.421.172.23Kepler-1758 b1.031.620.09190.0224TOI-4329 b1.542.31 0.45
HD 4203 c0.991.56.952.17Kepler-1772 b0.940.930.04180.0242TOI-481 b1.141.660.0971.53
HD 48265 b1.311.91.8141.525Kepler-1827 b0.921.40.04550.0129TOI-813 b1.321.940.4230.114
HD 5319 b1.274.061.571.556Kepler-1843 b1.021.780.1710.0245TOI-954 b1.21.890.049630.174
HD 5319 c1.274.061.931.053Kepler-1888 b0.91.250.09560.00729V1298 Tau b1.11.340.16880.236
HD 60532 b1.52.570.771.06Kepler-1921 b1.2520.15570.0274V1298 Tau c1.11.340.08250.0839
HD 60532 c1.52.571.62.51Kepler-1924 b1.021.280.12160.0237V1298 Tau d1.11.340.10830.106
HD 73526 b1.141.530.653.08Kepler-1927 b1.412.480.38590.0362V1298 Tau e1.11.340.3080.179
HD 73526 c1.011.531.032.25Kepler-1929 b1.011.470.29870.0304WASP-105 b0.890.90.0751.8
HD 73534 b1.162.582.991.112Kepler-1949 b1.191.450.03520.0175WASP-11 b1.420.890.04350.79
HD 87646 b1.121.550.11712.4Kepler-1951 b0.921.310.14350.0189WASP-165 b1.251.750.048230.658
HD 88133 b1.262.20.04791.02Kepler-238 e1.060.960.16580.534WASP-169 b1.342.010.06810.561
HD 89345 b1.161.750.10660.11Kepler-238 f1.060.960.27470.042WASP-171 b1.171.640.05041.084
HD 9174 b1.031.672.21.11Kepler-272 b0.860.930.0380.245WASP-187 b1.542.830.06530.8
HD 95544 b1.091.093.3866.84Kepler-272 c0.860.930.0610.308WASP-63 b1.281.860.05740.37
HD 96167 b1.271.941.3320.717Kepler-272 d0.860.930.0910.0179WASP-71 b0.761.820.046221.39
K2-108 b1.171.760.05810.18689Kepler-278 b1.082.940.2070.049WASP-73 b2.522.550.055122.86
K2-164 b1.182.2 0.0334Kepler-278 c1.082.940.2940.0396YSES 2 b1.11.191156.3
K2-171 b0.891.72 0.0242Kepler-295 b0.890.90.0990.00624
K2-238 b1.191.590.0460.86Kepler-295 c0.890.90.1420.00537

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Galaxies 11 00112 g001
Figure 1. H-R diagram of host stars from the 5063 confirmed planets in the NASA Exoplanet Archive. Separated out are the 210 RG planets and 229 SG planets via the host star’s location on the H-R diagram. The purple curve represents the end of the MS, separating SG (blue +) from the MS stars (blue dots). The black dashed line further separates the RGs (red ×) from the SGs (blue +). The pink curves are post-MS evolutionary tracks (EEP tracks) from MIST v1.2 for solar metallicity stars, with 1 M ⊙ (lower) and 2 M ⊙ (upper) tracks in solid. Green circles indicate hosts of planets in optimistic HZs; see Section 3 for definitions of HZ and parameters of HZ planets.
Figure 1. H-R diagram of host stars from the 5063 confirmed planets in the NASA Exoplanet Archive. Separated out are the 210 RG planets and 229 SG planets via the host star’s location on the H-R diagram. The purple curve represents the end of the MS, separating SG (blue +) from the MS stars (blue dots). The black dashed line further separates the RGs (red ×) from the SGs (blue +). The pink curves are post-MS evolutionary tracks (EEP tracks) from MIST v1.2 for solar metallicity stars, with 1 M ⊙ (lower) and 2 M ⊙ (upper) tracks in solid. Green circles indicate hosts of planets in optimistic HZs; see Section 3 for definitions of HZ and parameters of HZ planets.
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Figure 2. Mp vs. Rs plot for MS (light blue dots)-, SG-, and RG-hosted planets discovered with RV (blue, red) and transit (brown +, purple +) methods. Orange dots represent minimum Mp for each Red Giant that can lead to RV amplitude greater than the stellar intrinsic level obtained by Hekker et al. [16] (cf. Equation (3)).
Figure 2. Mp vs. Rs plot for MS (light blue dots)-, SG-, and RG-hosted planets discovered with RV (blue, red) and transit (brown +, purple +) methods. Orange dots represent minimum Mp for each Red Giant that can lead to RV amplitude greater than the stellar intrinsic level obtained by Hekker et al. [16] (cf. Equation (3)).
Galaxies 11 00112 g002
Galaxies 11 00112 g003
Figure 3. Left panel: Mp vs. a plot for Main Sequence (silver), Red Giant planets (blue for Rs/R⊙ < 5, green for 5 < Rs/R⊙ < 25, and red for Rs/R⊙ > 25), as well as Solar System planets (black). Right panel: zoomed-in version for Red Giant planets, with Kernel Density Estimate contours also shown. Pink dashed lines show a = 15 R ⊙ (left vertical line) and a = 75 R ⊙ (right vertical line), and purple dashed lines are obtained from Equation (3), for Ms = M⊙ and R s = 3 R ⊙ (lower line) and R s = 25 R ⊙ (upper line).
Figure 3. Left panel: Mp vs. a plot for Main Sequence (silver), Red Giant planets (blue for Rs/R⊙ < 5, green for 5 < Rs/R⊙ < 25, and red for Rs/R⊙ > 25), as well as Solar System planets (black). Right panel: zoomed-in version for Red Giant planets, with Kernel Density Estimate contours also shown. Pink dashed lines show a = 15 R ⊙ (left vertical line) and a = 75 R ⊙ (right vertical line), and purple dashed lines are obtained from Equation (3), for Ms = M⊙ and R s = 3 R ⊙ (lower line) and R s = 25 R ⊙ (upper line).
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Figure 4. a vs. Rs plot for exoplanets around Red Giants (red dots), exoplanets around SG (blue dots), and exoplanets around MS Hosts (silver dots). Solid line indicates a = 3Rs, while dashed line indicates a = Rs.
Figure 4. a vs. Rs plot for exoplanets around Red Giants (red dots), exoplanets around SG (blue dots), and exoplanets around MS Hosts (silver dots). Solid line indicates a = 3Rs, while dashed line indicates a = Rs.
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Figure 5. Teff vs. Seff plot for exoplanets around RG (red dots) and exoplanets around SG (blue dots). Boundaries for Teq, conservative HZ, and optimistic HZ are shown in solid, dotted, and dashed lines, respectively.
Figure 5. Teff vs. Seff plot for exoplanets around RG (red dots) and exoplanets around SG (blue dots). Boundaries for Teq, conservative HZ, and optimistic HZ are shown in solid, dotted, and dashed lines, respectively.
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Figure 6. Semi-major axis a vs. stellar radius Rs plot of Red Giant (red) and Main Sequence planets (blue) with optimistically habitable planets in green (light green for Main Sequence and darker green for Red Giant planets). Planets discovered with direct imaging (DI) are shown in orange. With purple vertical line segments, we indicate the optimistic HZ of each giant.
Figure 6. Semi-major axis a vs. stellar radius Rs plot of Red Giant (red) and Main Sequence planets (blue) with optimistically habitable planets in green (light green for Main Sequence and darker green for Red Giant planets). Planets discovered with direct imaging (DI) are shown in orange. With purple vertical line segments, we indicate the optimistic HZ of each giant.
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Table 1. Fitting parameters S0, a, b, c, and d adapted from Ref. [11].
Table 1. Fitting parameters S0, a, b, c, and d adapted from Ref. [11].
S 0 a b c d
Recent Venus
(optimistic inner boundary)		1.77531.4316 × 10−42.9875 × 10−9−7.5702 × 10−12−1.1635 × 10−15
Moist Greenhouse
(conservative inner boundary)		1.01408.1774 × 10−51.7063 × 10−9−4.3241 × 10−12−6.6462 × 10−16
Maximum Greenhouse
(conservative outer boundary)		0.3438 5.8942 × 10−5 1.6558 × 10−9−3.0045 × 10−12 −5.2983 × 10−16
Early Mars
(optimistic outer boundary)		0.3179 5.4513 × 10−51.5313 × 10−9 −2.7786 × 10−12 −4.8997 × 10−16
Table 2. Conservatively (shaded, 4) and optimistically (unshaded, 5) habitable planets around Red Giants using the Kopparapu et al. criterion [11] Conservatively (shaded, 17) and optimistically (unshaded, 4) habitable planets around Subgiants using the same criterion.
Table 2. Conservatively (shaded, 4) and optimistically (unshaded, 5) habitable planets around Red Giants using the Kopparapu et al. criterion [11] Conservatively (shaded, 17) and optimistically (unshaded, 4) habitable planets around Subgiants using the same criterion.
Planet NameDiscovery
Paper		Spectral Type (NEA)Abs
Mag (V)		Host Mass
(M/M⊙)		Host
Radius
(R/R⊙)		Orbital Period
(days)		SeffPlanet
Mass
(MJ)
Red Giant PlanetsHD 1605 c[19]K1 IV2.781.333.4921490.503.62
HD 219415 b[20]K0 III2.8212.92093.30.411
HD 4732 c[21]K0 IV2.211.745.427320.732.37
HIP 56640 b[22]K1 III2.501.044.932574.90.813.67
HD 125390 b[23]G7 V2.281.366.471756.21.3322.16
HD 145934 b[24]K01.711.755.3827301.072.28
HD 94834 b[23]K02.641.114.215761.311.26
HD 95089 c[25]G8/K0 IV2.241.545.0817851.203.45
HIP 67851 c[26]K0 III2.141.635.922131.81.206.3
Sub Giant PlanetsHD 103891 b[27]F92.871.282.2219190.571.44
HD 10442 b[28]K0 IV2.171.011.9710320.511.487
HD 106270 b[29]G5 IV2.721.392.6618880.5110.13
HD 10697 b[30]G5 IV3.681.131.7910760.656.383
HD 13167 b[23]G3 V2.481.352.3926130.543.31
HD 159868 b[31]G5 V3.501.192.1311840.672.218
HD 163607 c[32]G53.841.121.7612720.462.201
HD 175167 b[33]G5 IV/V3.751.371.7512900.508.97
HD 18015 b[23]G6 IV2.431.493.1322780.633.18
HD 214823 b[34]G03.031.312.0418540.4520.3
HD 221585 b[34]G8 IV3.721.191.8511730.501.61
HD 38529 c[35]G4 IV2.791.412.5621360.5112.99
HD 5319 b[36]G52.631.274.066370.571.556
HD 5319 c[28]G52.631.274.068720.381.053
HD 73534 b[37]G53.631.162.5817500.371.112
HD 9174 b[38]G8 IV3.841.031.6711790.501.11
Kepler-1704 b[39] 3.781.131.79890.694.15
HAT-P-13 c[40]G43.461.321.764461.4014.28
HD 156411 b[41]F8 IV/V2.901.252.168421.520.74
HD 4203 b[42]G54.151.251.424321.432.23
HD 48265 b[43]G5 IV/V3.271.311.97791.171.525
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Chen, R.E.; Jiang, J.H.; Rosen, P.E.; Fahy, K.A.; Chen, Y. Exoplanets around Red Giants: Distribution and Habitability. Galaxies 2023, 11, 112. https://doi.org/10.3390/galaxies11060112

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Chen RE, Jiang JH, Rosen PE, Fahy KA, Chen Y. Exoplanets around Red Giants: Distribution and Habitability. Galaxies. 2023; 11(6):112. https://doi.org/10.3390/galaxies11060112

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Chen, Ruixuan E., Jonathan H. Jiang, Philip E. Rosen, Kristen A. Fahy, and Yanbei Chen. 2023. "Exoplanets around Red Giants: Distribution and Habitability" Galaxies 11, no. 6: 112. https://doi.org/10.3390/galaxies11060112

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