Exoplanets Around Red Giants: Distribution and Habitability

doi:10.21203/rs.3.rs-2231648/v1

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Exoplanets Around Red Giants: Distribution and Habitability

https://doi.org/10.21203/rs.3.rs-2231648/v1

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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 update the power law relation between planet mass and stellar radius found in previous studies and provide more detailed investigations on this topic. Ten Red Giant-hosted exoplanets are found to be in the optimistically calculated habitable zone, while five of which are in the conservative habitable zone. We believe additional exoplanets can be found in habitable zones around Red Giants using the direct imaging method and more powerful detection instrumentation.

Physical sciences/Astronomy and planetary science

Physical sciences/Physics

Exoplanet

Red Giant

Habitable Zone

In the distant future when our sun becomes a Red Giant, 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 live¹. Near-term considerations also prompt interest in exoplanet and exomoon systems of Red Giant hosts as some of these worlds may presently be in the HZ of their parent star. In this paper we examine the data from the NASA Exoplanet Archive, focusing on exoplanets around Red Giant (or Red Subgiant) stars.

When a star leaves the Main Sequence 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 Red-Giant Branch 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 Main Sequence, the orbits of its planets will also evolve. Due to the host’s mass loss, its surrounding planets will move outwards². On the other hand, tidal interactions tend to shrink the orbital radius of the planets³. In particular, a previous study³ predicted that tidal interaction would cause planets to plunge into the star, and get engulfed, before a/R_s<3, where a is the orbital semi-major axis of the planet and R_s is the stellar radius.

The first aim of our paper is to study the distribution of planets around Red Giants. Previous research⁴ found a power law relation between planet mass and stellar radius. Using the data of newfound exoplanets, we update their results and make further explorations. We will look at the joint distribution of three variables: the mass of the planet, the radius of the star, and the orbital semi-major axis — with the hope of shedding additional light on 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 interest⁵. 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 by the stellar energy flux from the host. More specifically, however, for a planet to be habitable it must not only be in its host’s HZ, but also possess the appropriate atmospheric and geological conditions.

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 by many studies^6,7,8,9,10,1, post-Main Sequence evolution of the Sun will alter its HZ, possibly rendering some of the outer planets’ moons habitable to life as we now know it.

For a grid of stars with various mass and metallicity, Ramirez and Kaltenegger⁹ 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 a Red Giant. In this paper we apply the criterion used by two previous studies^9,1, initially proposed by Kopparapu and colleagues¹¹, 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.

In this section, we briefly introduce our data collection and then discuss the distribution of RG planets in the (M_p, a, R_s) parameter space. In Fig. 1, below, we plot an H-R diagram of host stars using luminosity relative to the Sun ($L/{L}_{\odot }$) and stellar surface effective temperature (T_eff) values from the NASA Exoplanet Archive, identifying 214 Red Giants (and sub-Giants) - plotted in red.

Previous study⁴ derived a planet mass-stellar radius relation for 150 exoplanets orbiting Red Giants:

${M}_{p}/{M}_{\oplus }=a{\left(R/{R}_{\odot }\right)}^{b}$ (Eq. 1)

with best-fit parameters a = 150 and b = 0.88. They further argued that Eq. 1 is not due to observational bias from the radial-velocity detection method. Folding in the Archive’s new data as well, we updated the relation and found a comparably similar result: a = 89.8 and b = 1.03, as shown in Fig. 2, below. The adjustment to a lower a value and higher b value obtained here can most likely be attributed to the post-2018 data points, which have lower values for both planetary mass and stellar radius.

Let us further investigate the origin of this M_p vs. R_s relation by noting that the stellar radius indicates the post-Main-Sequence evolution stage of the host star. The fact that M_p increases with R_s corresponds to the lack of less massive planets around more evolved stars.

In Fig. 3a and 3b, below, we split R_s into three different intervals and plot Main Sequence (silver dots) and Red Giant planets in each interval separately as planet mass M_p (in Earth masses) vs. orbital semi-major axis a (in astronomical units). In particular, we separate RG planets into three categories according to R_s: R_s/R_⊙ < 5 (blue dots), 5 < R_s/R_⊙ < 25 (green dots), and R_s/R_⊙ > 25 (red dots). The (a, M_p) region occupied by RG planets shrinks as R_s increases — from its left side, with small a, from the bottom side, with low M_p, and from the right side, with large a. This shrinkage is best viewed from the right (b) panel of Fig. 3, which zooms into the specific region of RG planets and adds contours generated via Kernel Density Estimate (KDE) for clarity. If this shrinkage were due to observational selection effects, then the selection would have to be based on the radius of the host star but not on the mass of the planet or the orbital semi-major axis. Therefore, we suspect this phenomenon is unlikely to be due to observational selection. We next comment on the possible reasons for the shrinkage.

For disappearance of planets with small a, it is straightforward to anticipate planets with small orbital semi-major axis values to be engulfed and consumed as their host evolves and expands. According to Villaver et al. 2014, tidal interactions tend to speed up the engulfment of planets, and no planets should survive once a/R_s < 3. In Fig. 4, below, we plot the orbital semi-major axis vs. stellar radius ratioed to solar radii, clearly illustrating that a/R_s=3 is a cutoff and providing empirical evidence for tidally-accelerated engulfment.

Moving on to the disappearance of low-mass planets with increasing R_s, we can see from the left panel of Fig. 3a that for stars with a radius less than 25 R_⊙ many planets with masses 200 to 1000 M_⊕ exist at distances 2 to 3 AU. Yet, these planets are not seen orbiting stars with R_s > 25R_⊙ - even though much more massive planets are seen at the same distance. For example, the red points and corresponding contours lie well within the detectable region in the M_p vs. a plots. Since the disappearance of low-mass planets with increasing R_s is the direct reason for the M_p vs. R_s power-law fit in Fig. 2, we have therefore confirmed that this is likely not merely an observational effect. 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 R_s /R_⊙ > 25.

We also observe the disappearance of high semi-major axis planets as the star evolves. One apparent explanation will be the inward migration of hosted planets. In fact, if low-mass planets migrate inward more efficiently, the migration may also explain their disappearance as well. However, it remains unclear whether migration can be sufficiently substantial within the lifetimes of these stars. Another possibility may be that more evolved host stars in our data tend to have higher metallicity and are older aged, and therefore were 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.

In this section we discuss the habitability of planets around Red Giants, briefly reviewing habitability criteria in 3.1 and presenting our findings in 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 given by

$S=\frac{{L}_{s}}{4{\pi }{a}^{2}}$ (Eq. 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 by

${T}_{\text{eq}}=k{\left[\frac{S\left(1-A\right)}{4{\sigma }}\right]}^{1/4}$ (Eq. 3)

where $A$ is the planetary albedo and ${\sigma }$ is the Stefan-Boltzmann constant. The simplest habitability condition is $273\hspace{0.17em}\text{K}<{\text{T}}_{\text{eq}}<373\hspace{0.17em}\text{K}$, with the low ${T}_{\text{eq}}$ defining the Outer boundary of the Habitable Zone (OHZ) and the high T_eq defining the Inner boundary of the Habitable Zone (IHZ). The quantity $\text{k}$ is a correction factor that can be used to incorporate the greenhouse effect of an assumed planetary atmosphere.

More realistic criteria exist in the literature. In this paper, we shall adopt two criteria obtained by previous study¹¹, in which, they are expressed in terms of

$${S}_{\text{eff}}\equiv S/{S}_{\oplus }$$

where ${S}_{\oplus }$ is the current solar energy flux at the location of the Earth, as well as the temperature T of the host star. One way to define the HZ boundaries is with a conservative and optimistic treatment of the HZ calculation. 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 ${S}_{\text{eff}}$ 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.

We also summarized the boundaries using the following fitting formula¹¹ for 2600 K < T < 7200 K:

$${S}_{\text{limit}}\left(T\right)={S}_{0}+a{T}_{*}+b{T}_{*}^{2}+c{T}_{*}^{3}+d{T}_{*}^{4},{ T}_{*}=T-5780\hspace{0.17em}\text{K}$$,

where values of a, b, c, d for conservative/optimistic, inner/outer boundaries are reproduced in Table 1, below.

Table 1

Fitting parameters S₀, a, b, c and d adapted from previous study¹¹
	${{S}}_{0}$	${a}$	${b}$	${c}$	${d}$
Recent Venus (optimistic inner boundary)	1.7753	1.4316×10⁻⁴	2.9875×10⁻⁹	−7.5702×10⁻¹²	−1.1635×10⁻¹⁵
Moist Green House (conservative inner boundary)	1.0140	8.1774×10⁻⁵	1.7063×10⁻⁹	−4.3241 ×10⁻¹²	−6.6462×10⁻¹⁶
Maximum Green House (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	5.4513×10⁻⁵	1.5313×10⁻⁹	−2.7786×10⁻¹²	−4.8997×10⁻¹⁶

As noted in Table 1, a more 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 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 S_eff of recent Venus and the outer boundary using the S_eff of early Mars.

In Table 2, below, we list conservative and optimistic habitable zone RG-hosted planets. All planets are gas giants with masses ranging from 1 to 22 Jupiter masses (M_J). It should be noted for HD 73534 the luminosity class was missing from the archive and is backfilled here from other sourcing as IV (indicating subgiant). As well for HD 125390, its luminosity was mistyped as V (dwarf) but has been correctly listed in Table 2 as III (giant). The Red Giant hosts of planets in Table 2 are also shown as green dots in the H-R diagram of Fig. 1. As can be readily perceived from their positions on the H-R diagram, these host stars are in the early stages of evolution in the RGB.

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 S_eff. In Fig. 5, below, we show the Red Giant planets on the T_eff vs. S_eff plot with lines indicating HZ boundaries. From the plot, it can be seen that there is a substantial difference between boundaries for the T_eq HZ and Kopparapu HZ. We highlighted Kopparapu¹¹optimistically habitable planets in green.

Table 2. Conservative (shaded) and optimistically habitable planets using the same criterion¹¹.

Planet Name	S_eff	Spectral Type	Discovery Year	Discovery Method	Planet Mass: Jupiter Mass (M_J)
HD 1605 c	0.503	K1 IV	2015	rad v	3.62
HD 219415 b	0.41	K0 III	2012	rad v	1
HD 4732 c	0.73	K0 IV	2012	rad v	2.37
HD 73534 b	0.37	G5 IV	2008	rad v	1.112
HIP 56640 b	0.81	K1 III	2021	rad v	3.67
HD 125390 b	1.33	G7 V (III)	2019	rad v	22.16
HD 145934 b	1.07	K0	2015	rad v	2.28
HD 94834 b	1.31	K0	2018	rad v	1.26
HD 95089 c	1.20	G8/K0 IV	2018	rad v	3.45
HIP 67851 c	1.20	K0 III	2015	rad v	6.3

Figure 6, below, shows Red Giant and Main Sequence planets on a semi-major axis vs. stellar radius plot with habitable planets indicated. As shown in the plot, habitable planets follow a track with a increasing as R_s increases. This is because for stars with larger radii, the luminosity is larger, therefore making their HZ farther away. We also see that the track stops at R_s ~ 8R_⊙, far below the maximum R_s of Red Giants. From the plot, it is clear that there is a missing population of planets around Red Giants with a above 10 AU. If there are more Red Giant planets in this undetected region, it is likely there are undiscovered habitable zone planets as well. As with Main Sequence hosts, these large semi-major axis planets were all discovered by direct imaging. However, using the same detection method to find similar planets around Red Giants may be difficult due to the direct imaging method disfavoring systems with large radii hosts.

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 found⁴. It can be observed that a similar power law relationship is bolstered with the addition of more than 50 new data points. However, in our results we noted a steeper power law relation due to the additional data points with lower mass and stellar radius values. 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 (Fig. 3). We see that as stellar radius increases, the region occupied by planets in the graph shrinks. We also found (Fig. 4) no planets with $a/{R}_{s}<3$, which is consistent with tidal augmented engulfment.

Next, we examine the habitability of Red Giant exoplanets. To find the Habitable Zone, we adopt criteria proposed by previous study¹¹. With this method, we found ten planets in the optimistic HZ, five of which are in the conservative HZ. However, all of these planets are gas giants and, therefore, very likely uninhabitable by life as we presently know it. Nevertheless, these planets may have habitable exomoons.

Finally, with habitable zone exoplanets identified, we look at possible detection bias. We see that their orbital semi-major axis increases with stellar radii until ${R}_{s}/{R}_{\odot }$ ~ 7. However, this does not necessarily rule out further habitable zone exoplanets. It is very likely that there 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. 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.

Acknowledgements

This research was conducted at the NASA sponsored Jet Propulsion Laboratory, California Institute of Technology (Caltech) and has made use of the NASA Exoplanet Archive, which is operated by the Caltech, under contract with the NASA under the Exoplanet Exploration Program.

Data 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 are fully described in the article.

Author Contributions:

Conceptualization, J.H.J.; methodology, J.H.J., R.E.C; software, R.E.C and J.H.J; validation, J.H.J. and Y.C.; formal analysis, R.E.C and J.H.J.; investigation, R.E.C., J.H.J. and P.E.R.; 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., 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.

Competing Interest:

Authors declare no competing interest

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No competing interests reported.

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Exoplanets Around Red Giants: Distribution and Habitability

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Abstract

Figures

1. Introduction

2. Data Collection And Distribution Of Planets Around Red Giants

3. Habitable Planets Around Red Giants

3.1 Criteria for Habitability

3.2 Red Giant Planets in the Habitable Zones

4. Conclusions

Declarations

References

Additional Declarations

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