Dynamics and habitability of the TESS circumbinary systems TOI-1338 and TIC-172900988

The number of discovered exoplanets keeps growing all the time. Many of these planets are found in stellar binaries or systems of higher stellar multiplicity. Our current understanding is that a significant number of stars are found in binary or multiple stellar systems (e.g. see Bonavita & Desidera, 2020, and references therein). There are several pending questions regarding the formation and evolution of planets in binaries (Marzari & Thebault, 2019). Increasing the number of detected planets in binaries will provide valuable information to answering many of these questions.

Set in operation a few years ago, the Transiting Exoplanet Survey Satellite (TESS) has been proven to be a valuable asset in our quest for planets outside our Solar System. So far, most of our recent year discoveries of circumbinary planets have been made by the Kepler mission (Borucki et al., 2010; Koch et al., 2010), with the latest one being Kepler-1661b in 2020 (Socia et al., 2020). Last year, we had the announcement of TOI-1338b, the first circumbinary planet detected by TESS (Kostov et al., 2020). That discovery has been followed by another one (Kostov et al., 2021), TIC-172900988, making two the circumbinary planets found by TESS.

Planets of the size of the Earth, not only have been an observational fact for a while now, but some of them are found in the so-called habitable zone of their host star (e.g. Gillon et al., 2016; Rodriguez et al., 2020; Gilbert et al., 2020). The habitable zone is the region around a star where a terrestrial planet on a circular orbit can retain liquid water on its surface (Kasting et al., 1993). In this work we explore the possibility of having an Earth-like planet in the habitable zone of the two recently discovered TESS circumbinary systems. By means of numerical simulations, we check whether an Earth mass planet in the habitable zone of the two systems can survive the gravitational perturbations of the stellar binary and the existing circumbinary planet over a sufficient amount of time. We also use the concept of Dynamically Informed Habitable Zones (DIHZs hereinafter) (e.g. Georgakarakos et al., 2021) in order to evaluate the potential of that planet to support liquid water on its surface. Finally, we attempt to place some constraints on the strength of the detection signal that such a planet would create.

The structure of the paper is as follows: in section 2 we analyse the two systems from the dynamical evolution point of view. In section 3 we investigate the habitable zone stability of the two systems, while in section 4 we make use of the DIHZs in order to extract more information regarding the habitable zone. In section 5 we discuss the detectability of Earth-like planets in the habitable zone of the systems, while in section 6 we provide a summary of our findings and some discussion.

In this section we investigate the dynamical stability of the habitable zone of the two TESS binary systems that have been found to host a circumbinary planet. The aim is to check whether an Earth mass body can survive the gravitational perturbations of the stellar binary and the existing planet inside the habitable zone of the system.

Dynamically Informed Habitable Zones (DIHZs) are a useful tool in the quest for habitable planets. DIHZs are constructed in a way that takes into consideration the fact that orbital elements of planets in binary systems vary over time due to the gravitational interactions among all bodies. This time dependent variation of the planetary orbit implies variation in the incoming radiation. Different planets may respond in a different ways to that time-dependent insolation variation, i.e. they may exhibit different ’climate inertia’. This is also handled by DIHZs.

Dynamically informed habitable zones were first introduced and used in the study of habitability of circumstellar planets in binary systems (Eggl et al., 2012; Eggl et al., 2013a; Georgakarakos & Eggl, 2019). Later on, DIHZs were used in single star systems with giant planets (Georgakarakos et al., 2018). Finally, the methodology was applied to circumbinary planetary systems (Eggl, 2018; Eggl et al., 2020; Georgakarakos et al., 2021). There are three DIHZs: the Permanently Habitable zone (PHZ), where the planet stays always within habitable insolation limits, the Averaged Habitable Zone (AHZ) where the insolation is on average within habitable values, and finally, the Extended Habitable Zone (EHZ), which is the region where the planet stays on average plus minus one standard deviation within habitable insolation limits. The PHZ is ideal for planets with low climate inertia. On the other hand, the AHZ assumes unlimited buffering capabilities of the planet’s atmosphere, while the EHZ stands in between the other two zones. More details about the three types of zones can be found elsewhere (e.g. Georgakarakos et al., 2018).

We now proceed with the calculation of the habitable zones for the two TESS circumbinary systems under investigation. In order to do that, we use the methodology described in detail in Georgakarakos et al. (2021). Using the equations derived in that work, we obtain the limits of the classical (CHZ) and dynamically informed habitable zones for the two solutions of TOI-1338 and the six solutions for TIC-172900988. For systems consisting of a star and a planet on a fixed circular orbit, the limits of the CHZ are found by

where $r$ is the distance of the planet to the host star in astronomical units and $L$ is the stellar luminosity in solar luminosities. $S_{I}$ and $S_{O}$ are the effective insolation values (Kasting et al., 1993), which correspond to the number of solar constants required to trigger a runaway greenhouse process evaporating surface oceans (subscript $I$), or a snowball state freezing oceans on a global scale (subscript $O$). They can be calculated from expressions found in (Kopparapu et al., 2014). For a binary star, we use the following modified version of equation (6) in order to calculate the borders of the CHZ (Eggl, 2018; Georgakarakos et al., 2021):

where the indices 1 and 2 refer to the two stars. The values of all zones can be found in Table 1. For calculating the borders of the DIHZs we used maximum eccentricity and averaged squared eccentricity values obtained from the stability simulations of the Earth-like planet.

As we saw in the previous section, the entire classical habitable zone is essentially dynamically stable for both TOI-1338 and TIC-172900988. Due to the characteristics of the two systems (masses and orbital parameters), the Earth-like planet does not acquire significant orbital eccentricity. This fact is reflected in the values of the DIHZs, especially in the values of the borders of the PHZ which depend on the maximum eccentricity. For any of the two TOI-1338 solutions we investigated, the length of the PHZ is around $70\%$ of the length of the classical habitable zone. This implies that a potentially habitable planet with low climate inertia could remain habitable in most of the classical habitable zone. If the planet has some limited buffering capabilities when there is change in the incoming insolation, then, that planet can retain its liquid water on its surface for an even larger chunk of the CHZ (around $88\%$ as the limits of the EHZ indicate).

TIC-172900988 also exhibits very good potential for hosting habitable worlds. Among the six orbital and parameter solutions proposed for that system that are in line with the observations, we notice a greater variety regarding the potential of having habitable planets. Solutions 1 and 4 provide the smallest PHZ: $68\%$ and $71\%$ respectively of the CHZ can be suitable for a planet to support liquid water on its surface no matter what its orbital evolution will be. At the other end, we have solutions 5 and 6 that provide the most extensive PHZs ($\sim 90\%$). This is due to the fact that these solutions provide the two smallest eccentricities $e_{p}$ for TIC-172900988b. Small eccentricities for the giant planet imply that a terrestrial planet on an initially circular orbit would not be expected to reach high values of its orbital eccentricity (e.g. see Georgakarakos et al., 2016). This is visible in the bottom plot of Fig.3. Solutions 2 and 3 yield PHZ lengths in between the other two groups of solutions. Finally, if our potential habitable world has a moderate capability of buffering changes in the incoming radiation, then the planet can reside at an even larger part of the CHZ, ranging from $86\%$ to $95\%$.

Fig. 4 is a graphical representation of the DIHZs for the two binary systems. In those plots we have allowed the eccentricity $e_{p}$ of TOI-1338b and TIC-172900988b to vary up to much higher values so that the reader can visualize better the effect of that quantity on the length of the various habitable zones.

We saw in the previous section that both habitable zones of TOI-1338 and TIC-172900988 are good enough to support a planet with liquid water on its surface. A valid question is, however, whether such a planet could be detected within the range of the habitable zone. In this section we provide some estimates in order to answer the above question.

It has been suggested that planets in binaries may be easier to detect compared to a single star system, as the gravitational interactions between the planet and the second star can boost radial velocity and astrometric signals (e.g. Eggl et al., 2013b). Following Eggl et al. (2013b) and modifying the RV semi-amplitude accordingly for a circumbinary system (Martin et al., 2019), the maximum value of the radial velocity achieved is

where $i$ is the inclination with respect to the plane of the sky. The subscript EL refers to the Earth-like planet.

We now evaluate equation (8) for the TOI-1338 system over the range of its habitable zone. For $e_{EL}^{max}$ we used the values acquired during our stability experiment. Also, we assume that $\sin{i}=0^{\circ}$. For both of the TOI-1338b solutions, $V_{r}^{max}$ does not exceed the value of $7cm/s$ at the inner edge of the habitable zone. As we move closer to the other end of the habitable zone, that value becomes even smaller. Of course, this is something to be expected. Earth at 1 au distance from the Sun has an RV semi-amplitude of $\sim 9cm/s$. On the other hand, TOI-1338 has a total stellar mass of $\sim 1.3M_{\odot}$ and the habitable zone starts around 1.3 au. As seen from equation (8), the increased stellar masses and Earth-like planet semimajor axis will result in smaller values of $V_{r}^{max}$. Moreover, as we saw in Fig. 2, the terrestrial planet’s maximum eccentricity $e_{EL}^{max}$ remains very small throughout the habitable zone, and therefore that is another reason that $V_{r}^{max}$, which is an increasing function of $e_{EL}^{max}$, has low values.

Generally, the maximum value $V_{r}$ of the radial velocity may not be the best indicator for us in order to evaluate the potential detectability of a planet at a certain range. This is because it is not certain that we will be able to observe the planet when it has reached its maximum orbital eccentricity or a value close to it. Depending on our system, the planet may exhibit a very long secular period with a significant eccentricity amplitude. Hence, it may be more appropriate to use different indicators, such as for example the root mean square (rms) of the radial velocity measurements. The expression has the following form (Eggl et al., 2013b):

For TOI-1338, $V_{r}^{rms}$ is just under $4.8cm/s$ at the inner edge of the habitable zone and it goes down as we move towards the outer border of the habitable zone. Fig. 5 (upper two panels) provide the evolution of $V_{r}^{max}$ and $V_{r}^{rms}$ within the habitable zone for TOI-1338 best fit solution.

If we now consider astrometry as our detection method, there are similar to the RV method expressions regarding the maximum astrometric amplitude and the astrometric rms. These are given by (Eggl et al., 2013b):

and

where $d$ is the distance (in au) between the observer and the observed system and $<e_{EL}^{2}>$ is the averaged over mean anomaly and argument of pericentre squared eccentricity. The reader should note here that $\rho^{max}$ is independent of the inclination $i$.

For TOI-1338, the maximum astrometric signal for an Earth mass planet in the habitable zone of the system is quite small, i.e. smaller than 0.014 $\mu as$. The average signal is an order of magnitude lower than that. The two bottom panels of Fig. 5 confirm that.

TIC-172900988 also displays small detection signals in its habitable zone. The radial velocity signal is lower than the ones of TOI-1338, while the astrometric indicators are larger. The total mass of the stellar binary is about twice as large as the one of TOI-1338. In addition, the inner edge of the habitable zone is about $50\%$ farther out than the inner border of the habitable zone of TOI-1338. Finally, as it was mentioned previously, the maximum eccentricity acquired by the fictitious terrestrial planet through the habitable zone is smaller in the TIC-172900988 system. On the other hand, the astrometric signals of TOI-1338 are smaller, mainly because of the fact that its distance $d$ from us is $399.017pc$, which is much larger than the $246.263pc$ of TIC-172900988. Fig. 6 is a graphical representation of the radial velocity and astrometric signals for TIC-172900988.

We have explored the dynamics and potential habitability of the two circumbinary systems that have been discovered with TESS so far. The binary system TOI-1338 hosts a planet that is about twice as massive as Neptune, while TIC-170900988 has a planet with a mass around three Jupiter masses. We have explored the habitable zones of both planets in terms of their dynamical stability. We placed a fictitious Earth mass planet throughout the two habitable zones in order to check whether its orbit is dynamical stable and we carried out a number of numerical simulations over a sufficient amount of time. From planetary formation theories it is possible to have such type of systems (e.g. Barbosa et al., 2020, 2021). We found that for the various orbital solutions of TOI-1338 and TIC-172900988 investigated, the Earth mass planetary orbit showed minimal variations in the semimajor axis and some small changes in the eccentricity. Hence, all configurations were found to be stable. Since the habitable zone of the system was found dynamically stable, we calculated dynamically informed habitable zones in order to get an assessment of the qualitative characteristics of the habitable zone. We found in all cases that the permanently habitable zone covered a large part of the classical habitable zone. In some cases that part was around $90\%$ of the latter, which means that the binary system is suitable of hosting low climate inertia terrestrial planets. This kind of result has been found in other circumbinary systems such as for example Kepler-38 or Kepler-64 (Georgakarakos et al., 2021).

Subsequently, we checked what would be the magnitude of the detection signal for an Earth mass planet in the habitable zone of the two binaries. Using the radial velocity and astrometry detection methods, we made some estimates covering the whole range of the habitable zone. The results showed that considering our current detection facilities such discovery is not possible, especially if we try to use astrometry for detecting the planet.

I would like to thank Siegfried Eggl who provided the code that was used for our numerical experiments. I would also like to thank the referee O.C. Winter for his comments that helped me improve the manuscript.

The data presented and discussed in this paper are available upon reasonable request to the corresponding author.