Edited by: Francesco Marzari, University of Padua, Italy
Reviewed by: Silvano Desidera, Osservatorio Astronomico di Padova (INAF), Italy; Diego Turrini, National Institute of Astrophysics (INAF), Italy
This article was submitted to Exoplanets, a section of the journal Frontiers in Astronomy and Space Sciences
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Determining habitable zones in binary star systems can be a challenging task due to the combination of perturbed planetary orbits and varying stellar irradiation conditions. The concept of “dynamically informed habitable zones” allows us, nevertheless, to make predictions on where to look for habitable worlds in such complex environments. Dynamically informed habitable zones have been used in the past to investigate the habitability of circumstellar planets in binary systems and Earth-like analogs in systems with giant planets. Here, we extend the concept to potentially habitable worlds on circumbinary orbits. We show that habitable zone borders can be found analytically even when another giant planet is present in the system. By applying this methodology to Kepler-16, Kepler-34, Kepler-35, Kepler-38, Kepler-64, Kepler-413, Kepler-453, Kepler-1647, and Kepler-1661 we demonstrate that the presence of the known giant planets in the majority of those systems does not preclude the existence of potentially habitable worlds. Among the investigated systems Kepler-35, Kepler-38, and Kepler-64 currently seem to offer the most benign environment. In contrast, Kepler-16 and Kepler-1647 are unlikely to host habitable worlds.
Over the past three decades exoplanet researchers have discovered more than four thousands planets outside our Solar System
The introduction of “dynamically informed habitable zones" allowed Eggl et al. (
The structure of this paper is as follows: in the next section we explain the general principles behind dynamically informed habitable zones and construct the required tools to extend the concept to include a giant planet in the system. In section 3 we investigate the potential of binary star systems with known circumbinary planets observed during the Kepler mission (e.g., Doyle et al.,
The nearly circular orbit of the Earth around the Sun ensures that the planet receives an almost constant amount of radiation on a permanent basis. That assumption falters for a circumbinary planet, however. The second star provides an additional source of radiation, and more importantly, it is also a source of gravitational perturbations for the planetary orbit. Even if a planet is on an initially circular orbit around the binary, the orbit will become elliptic over time (see e.g., Georgakarakos,
In order to account for the effect of climate inertia, we follow the general methodology as outlined in (Eggl et al.,
The extended habitable zone lies between the above extremes by assuming that the planetary climate has limited buffering capabilities. The EHZ is defined as the region where the planet stays on average plus minus one standard deviation within habitable insolation limits. In order to calculate DIHZ borders for circumbinary systems, we need to understand (a) whether or not a configuration is dynamical stable, (b) how the orbital evolution of the system affects the amount of radiation the planet receives, and (c) how the combined quantity and spectral distribution of the star light influences the climate of a potentially habitable world.
Dynamical stability is a necessary condition for habitability of a circumbinary planet. If a planet is ejected from a system, water that may be present on its surface will ultimately freeze. There are a number of ways to predict whether or not a potentially habitable world is on a stable orbit (e.g., see Georgakarakos,
where
Once we confirm that a potentially habitable planet is on a stable orbit, we can proceed to investigate how much radiation it receives from the two stars. The latter depends on the orbit of the planet which evolves over time. By modeling the evolution of the stellar and planetary orbits we can estimate the actual amount and spectral composition of the radiation the planet receives. To this end we make use of an analytic orbit propagation technique for circumbinary planets developed in Georgakarakos and Eggl (
For systems consisting of a star and a terrestrial planet on a fixed circular orbit, the limits of the classical habitable zone (CHZ) read
where
where
We will now use the above concepts to determine the permanently habitable zone. In order to find the borders of the region wherein the planet stays always within habitable insolation limits, i.e., the PHZ, we need to find the effective insolation extrema a circumbinary planet is likely to encounter. In hierarchical systems of two stars and a circumbinary planet, the planetary semi-major axis remains practically constant over time. In addition, if a system is coplanar, the time evolution of the eccentricity vectors determines the geometric configuration at any given moment. Assuming furthermore that the gravitational effect of the planet on the stellar binary is negligible, maximum and minimum insolation configurations are determined through the maximum planetary eccentricity
where
If we have two stars of equal mass, then the minimum radiation configuration is reached when ϕ = 90°. Hence, the minimum insolation condition in this case is
When the mass ratio of the binary is close to–but not exactly–equal to one (with
One can find the numeric values for the borders of the PHZ by solving Equations (5) through (8) for
A schematic representation of possible binary star - planet geometries representing irradiation minima:
Angle ϕ_{min} for the minimum planetary insolation configuration against the mass of the secondary star
We would like to point out here that for all the above insolation extrema configurations we have assumed that the stars are point masses. In reality, however, the stars have finite sizes. Depending on the distance between the two stars and on the distance between the planet and the binary, it is possible that when the three bodies are aligned the planet may receive reduced insolation due to the eclipsed star. In such a scenario, the minimum insolation configuration (
The averaged habitable zone is the region around a binary star where a planet remains habitable inspite of variations in irradiation. That is, as long as the insolation average is compatible with habitable limits a planet with a high climate inertia can remain potentially habitable. The averaged over time radiation that a planet receives when orbiting a single star is
where
where
and
Note that
The definition of the extended habitable zone in section 2 translates into the following equations:
The standard deviation σ can be found via the insolation variance
We already have an expression for 〈
Using the same approach that lead to Equation (10), namely combining the stellar binary into a “hybrid star” we can construct a closed analytic expression for 〈
Combining Equations (10) and (16) and normalizing the individual stellar contributions with the respective spectral weights
The inner border of the EHZ is then defined through
while the outer border is defined via
Numerical values for the inner and outer EHZ borders can be found via solving the above equations for
In order to demonstrate the merit of dynamically informed habitable zones, we apply our method to the Kepler circumbinary planets. For that purpose we select Kepler-16 (Doyle et al.,
Mean physical parameters and orbital elements for the Kepler-16(AB), Kepler-34(AB), Kepler-35(AB), Kepler-38(AB), Kepler-64(AB), Kepler-413(AB), Kepler-453(AB), Kepler-1647(AB), and Kepler-1661(AB) stellar binaries.
Kepler-16 | 0.6897 | 0.20255 | 0.6489 | 0.22623 | 4450.0 | 3311.0 | 0.22431 | 0.15944 |
Kepler-34 | 1.0479 | 1.0208 | 1.1618 | 1.0927 | 5913.0 | 5867.0 | 0.22882 | 0.52087 |
Kepler-35 | 0.8876 | 0.8094 | 1.0284 | 0.7861 | 5606.0 | 5202.0 | 0.17617 | 0.1421 |
Kepler-38 | 0.949 | 0.249 | 1.757 | 0.2724 | 5640.0 | 3325.0 | 0.1469 | 0.1032 |
Kepler-64 | 1.528 | 0.378 | 1.734 | 0.408 | 6407.0 | 3561.0 | 0.1744 | 0.2117 |
Kepler-413 | 0.820 | 0.5423 | 0.7761 | 0.484 | 4700.0 | 3463.0 | 0.10148 | 0.0365 |
Kepler-453 | 0.944 | 0.1951 | 0.833 | 0.2150 | 5527.0 | 3226.0 | 0.18539 | 0.0524 |
Kepler-1647 | 1.210 | 0.975 | 1.7903 | 0.9663 | 6210.0 | 5770.0 | 0.1276 | 0.1593 |
Kepler-1661 | 0.841 | 0.262 | 0.762 | 0.276 | 5100.0 | 3585.0 | 0.187 | 0.112 |
Mean mass, semi-major axis, and eccentricity for Kepler-16b, Kepler-34b, Kepler-35b, Kepler-38b, Kepler-64b, Kepler-413b, Kepler-453b, Kepler-1647b, and Kepler-1661b. The uncertainties can be found in the corresponding references in section 3.
Kepler-16 | 0.333 | 0.7048 | 0.00685 |
Kepler-34 | 0.22 | 1.0896 | 0.182 |
Kepler-35 | 0.127 | 0.60345 | 0.042 |
Kepler-38 | <0.384(95% conf.) | 0.4644 | <0.032(95% conf.) |
Kepler-64 | <0.531(99.7% conf.) | 0.634 | 0.0539 |
Kepler-413 | 0.21 | 0.3553 | 0.1181 |
Kepler-453 | <0.050 | 0.7903 | 0.0359 |
Kepler-1647 | 1.52 | 2.7205 | 0.0581 |
Kepler-1661 | 0.053 | 0.633 | 0.057 |
First, we calculate all dynamically informed habitable zones assuming no giant planets are present in the systems. That provides us with a first idea of the location of the habitable zones and how the presence of the second star affects the location and extent of the various habitable zones. Then we include the existing giant planet in our model and examine its effect on the habitability of an additional hypothetical terrestrial planet. In both stages, we allowed the eccentricities of the binary and the existing planet to vary. That way we get a better picture of the effect of orbital eccentricity, an important quantity that regulates distances between bodies, on the extent of habitable zones in the system. In order to simplify the complex dynamics in the presence of the giant planet, we acknowledge the double hierarchical structure of the problem that allows us to consider the binary as one massive body located at the barycenter. The two stars at their barycenter are considered as one body of mass
A terrestrial planet on an initially circular orbit in a star-planet-planet system is stable against either ejections or collisions with the central object when
Here,
Strictly speaking, the planetary systems investigated here do not fall in the planet-star mass ratios investigated in Petrovich (
We now proceed to calculating habitable zones for the aforementioned Kepler systems. In a first step, we ignore the presence of residing giant planets in the respective systems. Considering a potential terrestrial planet orbiting the stellar binary, we can determine the borders of the classical and dynamically informed habitable zones for all the Kepler systems under investigation. As we can see from the left column plots of
Dynamically informed habitable zones for the Kepler-16, Kepler-34, and Kepler-35 systems. Plots in the left column show the different types of habitable zones without the presence of the known giant planets. The right column includes the influence of the known giant planets. Red colored regions correspond to uninhabitable areas, blue, green, yellow, and purple colors denote the PHZ, the EHZ, the AHZ, and unstable areas according to Holman and Wiegert (
Same as
Same as
When we add the giant planet in our model (right column plots of
Regarding the remaining systems, the entire classical habitable zone is essentially dynamically stable. The difference between dynamically informed habitable zones with and without the giant planet perturbers shows, however, that the influence of giant planets goes beyond dynamical instability. In Kepler-34, potentially habitable worlds with low climate inertia could only remain habitable in a tiny region centered around 2.17 au. This can be seen from a comparison between the extent of the PHZ and the black vertical lines in the middle row right panel of
For comparison, some results from Haghighipour and Kaltenegger (
Habitable zone limits for Kepler-16, Kepler-34, Kepler-35, Kepler-38, Kepler-64, Kepler-413, Kepler-453, Kepler-1647, and Kepler-1661.
Kepler-16 | 0.40–0.74 | – | – | – | 0.46–0.70 | 0.40–0.76 | 0.41-0.74 |
Kepler-34 | 1.56–2.75 | 2.10–2.25 | 1.79–2.47 | 1.60–2.76 | 1.60–2.74 | 1.51–2.85 | 1.62–2.77 |
Kepler-35 | 1.12–1.99 | 1.23–1.90 | 1.15–1.96 | 1.12–1.99 | 1.16–1.97 | 1.09–2.10 | 1.16–2.01 |
Kepler-38 | 1.61–2.84 | 1.68–2.77 | 1.62–2.82 | 1.61–2.84 | 1.64–2.81 | 1.63–2.82 | 1.66–2.86 |
Kepler-64 | 1.96–3.41 | 2.08–3.28 | 2.00–3.36 | 1.96–3.41 | 2.00–3.37 | 2.00–3.40 | 2.02–3.44 |
Kepler-413 | 0.55–1.01 | 0.69–0.87 | 0.60–0.95 | 0.55–1.01 | 0.58–0.98 | - | - |
Kepler-453 | 0.74–1.31 | 1.00–1.20 | 1.21–1.27 | 1.27–1.31 | 0.77 -1.28 | - | - |
Kepler-1647 | 2.12–3.71 | - | - | - | 2.16– 3.67 | - | - |
Kepler-1661 | 0.60–1.08 | 0.82–0.64 | 0.94–1.03 | 1.03–1.08 | 0.64–1.04 | - | - |
We present an analytical approach to determine dynamically informed habitable zones in binary star systems with a circumbinary giant planet. The method takes into consideration the orbital evolution of the giant and terrestrial planet as well as different responses of planetary climates to variations in the quantity and spectral energy distribution of incoming radiation. It does not apply, however, during the planet formation stage, when we can have planets migrating due to interactions with the protoplanetary disk or planet-planet scattering events during late stage formation. In addition, we do not consider systems where there is significant tidal interaction between the two stars which may lead to changes in the orbit and rotation rates of the stars, as well as to changes in the emission of XUV radiation that can affect the atmosphere of a planet within the habitable zone (e.g., Sanz-Forcada et al.,
As the method mainly relies on analytical equations, it can provide a quick assessment of the capability of terrestrial circumbinary planets in complex dynamical environments to retain liquid water on their surface. The construction and comparison of dynamically informed habitable zones, i.e., the PHZ, the EHZ and the AHZ allows us to better understand where potentially habitable worlds with different climate characteristics can exist in binary star systems. The method presented here is very versatile as it has been constructed in such a way that it does not depend on the dynamical model and the insolation limits.
In this work, we investigated the effects of stellar binarity and circumbinary giant planets on the habitable zones of nine systems observed by the Kepler mission. We confirm earlier studies that suggest Kepler-16 is not suitable for hosting a terrestrial planet within its classical habitable zone. The situation is similar for Kepler-1647. In contrast, Kepler-34, Kepler-35, Kepler-38, Kepler-64, and Kepler-413 seemed more promising with Kepler-38 being the best candidate in this respect. Kepler-453 and Kepler-1661 stand between the previous two categories of systems. We find that nearly equal binary mass ratios and small eccentricities of the perturbing bodies provide favorable, from the orbital evolution point of view, conditions for an Earth-like planet to exist in the habitable zone. We show, furthermore, that the presence of a giant planet can have a significant effect on the potential habitability of terrestrial worlds in the same system. We, thus, recommend gravitational perturbations of known giant planets to be taken into account in future studies regarding habitability in binary star systems.
The original contributions presented in the study are included in the article/supplementary material, further inquiries can be directed to the corresponding author/s.
NG and SE: conceptualization, methodology, investigation, resources, and writing–original draft preparation-revised version. NG: software and data curation. NG, SE, and ID-D: validation. All authors have read and agreed to the published version of the manuscript.
The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.
SE acknowledges support from the DIRAC Institute in the Department of Astronomy at the University of Washington. The DIRAC Institute is supported through generous gifts from the Charles and Lisa Simonyi Fund for Arts and Sciences, and the Washington Research Foundation. The results reported herein benefited from collaborations and/or information exchange within NASA's Nexus for Exoplanet System Science (NExSS) research coordination network sponsored by NASA's Science Mission Directorate. This research 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.
We follow Georgakarakos and Eggl (
and
where
and
Equations (22) and (23) were also used when we added the giant planet to our model and the orbit of the giant planet was interior to that of the terrestrial planet. In order to use the above equations in that respect, we replace
When the orbit of the giant planet was exterior to that of the terrestrial planet, we used the below equations from Eggl et al. (
and
where
The above equations can be used for nearly coplanar systems and systems that are not close to mean motion resonances. Also, the equations become less reliable as the maximum planetary eccentricity gets larger than 0.2–0.25.
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