Finding the Drake Equation for Tidally Heated Exomoons

P.W. Overgaauw

Leiden Observatory, Leiden University, P.O. Box 9513, 2300 RA Leiden, The Netherlands

October 2014

ABSTRACT

In the past ten years several exoplanets have been directly imaged. However, none of these objects have rocky surfaces and the search for a rocky exoplanet that could potentially harbour life is still ongoing. Recent results indicate that it may be possible to directly image Tidally Heated Exomoons (THEMs) with existing and planned imaging facilities, potentially making THEMs the first objects with rocky surfaces outside our own Solar System to be directly imaged. We present a search for observable THEMs in the Hipparcos Main Catalogue and in orbit around known RV (radial velocity) selected exoplanets. Using an analogue to the Drake Equation we propose an equation to estimate the number +2.2 of THEMs in a population of stars and find that there may be 10.7−2.0 THEMs around the 782 closest AFGKM Hipparcos stars. Furthermore, we investigate the requirements for directly imaging possible THEMs around 354 RV selected planets. We find that GJ 832 b, Epsilon Eri b and Beta Gem b are the most likely candidates. Unfortunately they would require considerable eccentricities and a large planet-moon mass fraction. We estimate lifetimes on Myr timescales for potential THEMs, reducing chances for direct imaging.

1. Introduction

For thousands of years, since the ﬁrst time men looked up at the stars in awe, we have wondered whether or not we are alone in the universe. Many have tried to answer this question through philosophy, religion and, more recently, through science. Many even claim they have a deﬁnitive answer. However, no tangible evidence has ever come to light. This lack of evidence made Enrico Fermi pose the question ”Where is everybody?” in 1950, a question which was addressed in more detail by Hart(1975), and is now known as Fermi’s Paradox. Fermi stated that given the large amount of planetary systems in the Milky Way – 2 – galaxy, assuming that over the course of billions of years technological civilizations could have evolved and that even at a slow pace of interstellar travel the galaxy can be completely colonized in tens of millions of years, we should have encountered some form of physical contact with other civilizations. However, this is not the case. To add to the discussion, Frank Drake (Drake 2013) formulated an equation in 1961 to estimate the number of active, communicative extraterrestrial civilizations in our galaxy. This equation is given by

N = R∗ fp ne fl fi fc L, (1) · · · · · · where N is the number of civilizations in our galaxy with which radio-communication might be possible, R∗ is the average rate of star formation in our galaxy, fp the fraction of those stars that have planets, ne the average number of planets that can potentially support life per star that has planets, fl the fraction of planets that could support life that actually develop life at some point, fi the fraction of planets with life that go on to develop intelligent life (civilizations), fc the fraction of civilizations that develop a technology that releases detectable signs of their existence into space and L the length of time for which such civilizations release detectable signals into space. This equation was mainly intended to stimulate scientific dialogue at the first SETI (Search for Extraterrestrial Intelligence) meeting, in which it succeeded. In the following decades, scientists have relentlessly searched for a glimpse of extraterrestrial life (e.g. Project Ozma; Drake 1961) and tried to define the parameters needed for a world to be able to sustain it. This led to the formulation of the Habitable (or Goldilocks) Zone (e.g. Kasting et al. 1993), the zone around a star where liquid water is possible on a planet’s surface. The formulation of the HZ (Habitable Zone) led to several searches for Earth-size and larger planets in this zone (e.g. the Kepler Mission; Borucki et al. 2009), in the hope of finding a planet that may be able to sustain life. So far the Kepler Mission has confirmed close to a thousand exoplanets in more than 400 stellar systems1. The next step towards finding possible intelligent life would be to directly image a rocky planet. However, in order to directly image an exoplanet they need to be both young and at a large projected separation (at least tens of AU) from their primary. Rocky planets tend to be in close-in orbits around their parent star and so far only gaseous planet candidates have been directly imaged. Examples include the HR8799 system (Marois et al. 2008), β Pictoris b (Lagrange et al. 2010), HD 95086 b (Rameau et al. 2013) and HD 106906 b (Bailey et al. 2014). In recent years the possibility of and interest in the detection of exomoons have increased,

1http://kepler.nasa.gov/Mission/discoveries/ – 3 –

especially in Tidally Heated Exomoons (THEMs). Peters & Turner(2013) argue that it is possible to directly image THEMs and that this may be easier to do than with giant exoplanets, THEMs do not suﬀer from the above mentioned limitations. Peters & Turner showed that moons can be heated to hundreds of degrees, giving them a large enough luminosity so they might be able to be detected in infrared. In addition, since THEMs may be hot even if they receive negligible stellar irradiation, they may be luminous in mid-infrared at large separations from the system primary, this reduces or even eliminates the requirement of high contrast imaging capabilities. Furthermore, Barnes & O’Brien(2002) found that Earth-like satellites of Jovian planets are plausibly stable for 5 Gyr around most stars with masses

greater than 0.15 M and planet mass greater than 0.3 MJ . This means that THEMs may remain hot and luminous for periods of the order of a stellar main sequence lifetime and so could be visible around old stars as well as young ones. The main goal of this research is to estimate the number of THEMs around Hipparcos stars and then ﬁnd THEM-candidates for direct imaging around nearby stars. In Section 2 we will discuss the parameters needed for an equation that can estimate the number of THEMs. In Section 3 we will search for the values of these parameters. In Section 4 we will try to ﬁnd direct imaging candidates around nearby stars. We will end this report with a short discussion and conclusion.

2. Finding an equation for THEMs

We propose the following equation for the number of THEMs in a collection of stars

D = N fM ff fs fT . (2) · · · · Several parameters are important to take into account when formulating this equation. First and foremost is the number of stars, N, in the sample. The second term in our equation is the fraction of stars that have a massive planetary companion, fM . According to Peters & Turner(2013), if Io were as massive as Earth, it would be bright enough for the James Webb Space Telescope (JWST ) to detect at a distance of ﬁve parsec. This means that we need massive moons if we want to detect them at large distances. Moon systems of gaseous planets contain a similar fraction (1.1 10−4 × to 2.5 10−4) of their respective planets mass (Canup & Ward 2006). In order for a planet × to have a massive satellite, the planet itself needs to be massive. This second term also accounts for planets with stable orbits. Without the presence of a moon, a THEM is impossible. The third parameter in our equation – 4 –

is, therefore, the fraction of massive planets that form moons, ff . For an exomoon to be able to be detected and conﬁrmed, it needs to be in a stable orbit for a long time. Without this stability the moon might be removed from its orbit around its host. This removal can happen through several processes. Satellites induce a tidal bulge on their parent planet. This bulge perturbs the orbit of the satellite (e.g., Burns & Matthews 1986), causing migrations in the semi-major axis of the orbit. These migrations can lead to the loss of the satellite. For an isolated planet, the satellite’s orbital semi-major axis can increase until it escapes or it can decrease, making the satellite spiral inward until it impacts the planet’s surface (Counselman 1973). For planets that are not isolated, which are close enough to their parent star, stellar-induced tidal friction slows the planet’s rotation. The resulting planet-satellite tides cause the satellite to spiral inward toward the planet (Ward

& Reid 1973; Burns 1973). The fourth parameter in our equation, fs, is the fraction of exomoons that can remain in a stable orbit on a Gyr timescale. The ﬁnal parameter in our equation is the fraction of moons that are heated through tidal interaction, fT . This is the most uncertain quantity in our equation and we will spend most of this paper on investigating it.

3. Values

3.1. N

The stars in our sample are drawn from the Hipparcos Main Catalogue. This sample comprises 782 AFGKM stars with a distance of up to 20 parsec, giving our value for N. A distance of 20 parsec would potentially make the JWST able to detect planets with semi- major axis down to 7 AU in the M (4.7µm) band, which is close to the limit of current ∼ RV selected planets. Using their spectral types we estimate masses using Cox(2000). The stars have masses in the range 0.15 < M∗/M < 2.9. The sample is mostly comprised of main sequence stars, as can be seen in Figure1.

3.2. fM

As stated in Section 2, massive planets are able to form massive moons that could be large enough for detection. According to Johnson et al.(2010), who deﬁned giant planets as those with velocity semi-amplitudes K > 20ms−1 and semimajor axes a < 2.5 AU giving −1 roughly a 1.1MJ planet for a 1 solar mass star at 2.5 AU and K = 20ms , giant planet occurence is dependent on the stellar primary mass and metallicity: – 5 –

6 V M 8

14 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 B V − Fig. 1.—: H-R diagram showing our sample. The solid line is the polynomial relationship describing the mean Hipparcos main sequence (Wright 2004).

1.0±0.3 1.2±0.2[Fe/H] f(M∗, [Fe/H]) = 0.07 0.01 (M∗/M ) 10 . (3) ± × × Taking solar metallicity ([Fe/H] = 0) and given our mass estimates, we are able to estimate the occurence of giant planets in our sample. We have plotted histograms of the found values and ﬁtted them with a Poisson distribution in Figure2. We take the median of the means as the mean giant planet occurence and the minimum and maximum mean as our error margins, giving us a value of 8.17+1.81%, which is in agreement with the value (6.5% 3.0%) −1.48 ± Montet et al.(2014) found for massive planetary companions with 1 < m/MJ < 13 and 0 < a < 20AU around M dwarfs. Our value is slightly higher as our sample does not solely consist of M dwarfs, and also contains higher mass stars. – 6 –

0.20

0.15 a = -0.01 a = -0.01 a = -0.01 b = -0.3 b = 0 b = 0.3 0.10 Mean = 7.49 Mean = 7.0 Mean = 6.69

0.05

0.00 0.20

0.15 a = 0 a = 0 a = 0 b = -0.3 b = 0 b = 0.3 0.10 Mean = 8.73 Mean = 8.17 Mean = 7.8

0.05

0.00 0.20

0.15 a = 0.01 a = 0.01 a = 0.01 b = -0.3 b = 0 b = 0.3 0.10 Mean = 9.98 Mean = 9.34 Mean = 8.92

0.05

0.00 0 10 20 30 40 0 10 20 30 40 0 10 20 30 40 Giant planet occurence (%)

Fig. 2.—: Giant planet occurence for our estimated masses, using equation (8) from Johnson et al.(2010), 1.0±b 1.2 in the form of f(M∗, [Fe/H]) = 0.07 a (M∗/M ) 10 . ± × × – 7 –

3.3. ff

All the gaseous planets in our solar system have a system of at least one moon. Unfor- tunately, no exomoons have been found to date, despite multiple attempts by, for example, ”The Hunt for Exomoons with Kepler” (HEK) project (Kipping et al. 2013, Kipping et al. 2014). However, seeing as their sample size is small (they have now surveyed 17 planetary candidates for evidence of an exomoon), it is not yet possible to deduce any meaningful occurrence rate statistics. Furthermore, Heller(2014) states that satellites as large as Ganymede orbiting Sun-like stars could not possibly be detected in the available Kepler data. Because of this, our own solar system is thus far our only directly observed example for the occurrence

rate of satellites around planets and we set ff equal to one.

3.4. fs

Barnes & O’Brien(2002) show that Earth-like satellites of Jovian planets are plausibly stable for 5 Gyr around most stars with masses greater than 0.15M . The lowest estimated mass in our sample of stars is 0.15M , meaning that the fourth parameter, the fraction of exomoons in a stable orbit fs, is also equal to one.

3.5. fT

2 To ﬁnd fT , we search the exoplanets database and select the exoplanets on a few parameters. We are only interested in objects with a known distance to the primary star, radial-velocity mass, semi-major axis and Hipparcos number. Furthermore, we want to make sure that all the binary stars are out of the sample and we search for planets with a known orbital period that is greater than 300 days, to make sure we are looking at planets with a moon with a stable orbit. This leaves us with 354 objects. For these 354 objects we estimate the masses of possible moons using the moon-planet mass fraction Ms/Mp. Canup & Ward(2006) state that the largest satellites of gaseous planets −4 would contain on the order of 10 MP , so that a Jupiter-mass exoplanet would host only −5 Moon-to-Mars sized satellites. For our lower estimate we will use Ms/Mp = 4.7 10 , × which is the moon-planet mass fraction for the Io-Jupiter system. This mass fraction is two to three orders of magnitude lower than that of the largest satellites of the solid planets. Moons formed from captures (Triton; Agnor & Hamilton 2006) or impacts (the Moon; Taylor

2exoplanets.org – 8 –

Estimated Upper Limit Masses [M ] 0 1 2 3 4 5 6 7 8 80 L

30 Number of objects

0 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 Estimated Lower Limit Masses [M ]

L −3 Fig. 3.—: Histograms with masses calculated using an upper limit mass fraction Ms/MP = 10 (top −5 x-axis) and a lower limit mass fraction Ms/MP = 4.7 10 (bottom x-axis). The upper limit would allow × satellites to have masses of several ML.

2005) have no limit to their mass. Furthermore, it is possible that moons form via other processes not discussed in Canup & Ward(2006) and Ogihara & Ida(2012). Because of −3 this we will use a more optimistic estimate, Ms/Mp = 10 , as well. In Figure3 we have plotted the mass distribution of possible exomoon-companions for selected exoplanets. As can be seen, it could be possible to have an Earth mass moon orbit a massive planet, if we −3 use Ms/Mp = 10 . However, for the Io-Jupiter fraction it would only be possible to form a moon that is about 3 times less massive than Earth. Now that we have calculated the possible moon masses, we can estimate the radii of the moons. We will calculate the radii using the same method as Awiphan & Kerins(2013), from Fortney’s model, using a rock mass fraction equal to 0.66 (Earth-like planets)

2 Rs = 1.00 + 0.65log Ms + 0.14(log Ms) , (4)

where Ms and Rs are the satellite’s mass and radius in ML and RL, respectively (Fortney et al. 2007a; Fortney et al. 2007b). – 9 –

3.6. Temperature estimates

Now that we have estimated the masses and radii of the moons, it is possible to estimate

the eﬀective temperature of the moons, Ts, using Equation (8) from Peters & Turner(2013)

5/4 9/8 11 −2 1/4 1/2 −15/8 Rs ρ 36 10 dynes cm e β Ts 279K , (5) ≈ RL ρL × Q · µ × 0.0028 8

where Rs is the moon’s radius, ρ is the moon’s density, µ is the moon’s elastic rigidity, Q is the moon’s dissipation function, e is the eccentricity of the moon’s orbit and β is some multiple of the Roche radius, aR, such that the moon’s semi-major axis is

3M 1/3 a = βa = β p . (6) R 2πρ

For our analysis we will use Q = 36, µ = 10 1011 dynes cm−2 and β = 6.63, which are × Io values (Segatz et al.(1988); Peale et al.(1979)). Equation5 assumes there is only tidal heating with no additional energy sources, such as stellar irradiation or interior radiogenic heat, making this a conservative assumption since additional heat sources only serve to make the moon more luminous and easier to detect. In the top panel of Figure4 we have plotted an histogram of the calculated temperatures, using the eccentricities of Io. However, the temperature is highly dependent on eccentricity, as Peters & Turner(2013) show, and Io has a low eccentricity compared to other satellites in our solar system. Io only has an eccentricity of 0.0041, compared to 0.0101 for Europa, 0.029 for Titan and 0.055 for the Moon. The bottom ﬁgure of Figure4 shows the temperatures calculated using the eccentricity of the Moon, giving much higher temperatures. Using the eccentricity of the moon, the temperatures can be tremendous, rising to several hundreds and even thousands of degrees. These high temperatures lead to the dissipation of energy, causing the moons to cool or lose their stability. We can divide the orbital energy of the moon and the rotational energy of its host planet by the THEM’s luminosity to determine if such enormous amounts of tidal heating can be sustained over the lifetime of a planetary system. In Figure5 we show the estimated temperature versus the number of years a moon could be stable with a constant temperature. In reality a moon would slowly cool and reach an equilibrium temperature, which we have not accounted for, meaning that this is a low estimate for the lifetime of the system. As we can see, it is possible to heat a moon to temperatures of over 300 K, while being stable on a Gyr timescale. Adopting the moon’s eccentricity and using our lower mass estimate it – 10 –

60 50 40 e = 0.0041 30 20 10 0 0 200 400 600 800 1000 1200 1400 1600 40 35 30 e = 0.055 25 20 15 10 5 0 0 200 400 600 800 1000 1200 1400 1600 Estimated Temperatures [K]

Fig. 4.—: Histograms with temperatures calculated using Equation5. The grey histogram shows tempera- −3 tures calculated with the upper limit mass fraction Ms/MP = 10 , the blue histogram shows temperatures −5 calculated with the lower limit mass fraction Ms/MP = 4.7 10 . The figure shows that it could be possible × to heat a satellite to several hundreds and even thousands of degrees. is even possible for moons to reach 1000 K degrees and remain stable for several Gyr. ∼ We define a THEM as a moon with a temperature of over 300 K and that is stable for atleast 1 Gyr, the number of objects we find for different eccentricities and mass estimates can be found in Table1. Given the number of planets in our sample (354), we see that the fraction of THEMs, fT , can range from 0.166 to 0.168. In Table2 we show all the parameter values together. Using the likeliest values we find that N = 10.7. The minimum values give N = 8.7 and the maximum values N = 12.9. – 11 –

1600

1400

1200

1000 e = 0 .055 , M S /M P = 4 .7 10 5 800 × −

e = 0 600 .0041, M S/MP 3 = 10 −

Estimated lifetime (Gyr) 400 e = 0 .055, M S/M 3 P = 10 − 200

0 0 1 2 3 4 5 Estimated Temperature (K)

Fig. 5.—: Estimated temperature vs. the estimated lifetime of the system. Text inside the ﬁgure indicates eccentricities and mass fractions that were used to calculate the lifetimes, e = 0.0041 and e = 0.055 are the eccentricities for Io and the Moon, respectively. It can be seen that objects that are heated to several hundreds of degrees could be stable on a Gyr timescale. The reason that not more blue symbols are visible is because they have quite low temperatures and are stable for much longer than 5 Gyr. The same applies −5 for temperatures and lifetimes calculated with e = 0.0041 and Ms/MP = 4.7 10 . ×

4. Finding local THEMs

So far we have examined the masses, sizes and temperatures that THEMs could potentially reach, given the masses of confirmed exoplanets. In this section we will try to find the temperatures of THEMs that are needed to be able to directly image them with planned imaging facilities. In Figure6 we show the estimated moon mass versus the star-planet separation. Vertical lines in the image indicate the diffraction limited resolution of the JWST and the E-ELT in the M(4.7µm) band. As we can see, several objects are well within the diffraction limit of the E-ELT and the JWST and might be able to be directly imaged, if the THEMs are able to reach high enough temperatures. Using sensitivities of the Mid-infrared E-ELT Imager and Spectrograph (METIS, Brandl et al. – 12 –

Table 1:: Number of THEMs

Eccentricity Low mass Upper mass 0.0001 0 0 0.001 0 54 0.01 19 162 0.1 216 22 0.0041 0 160 0.055 174 19 0.0001-0.1 58.75 59.5

Notes. Shown numbers are the amount of THEMs with temperatures greater than 300 K and lifetimes greater than 1 Gyr. The high mass estimates are calculated using the upper limit for the planet-moon mass −3 fraction (Ms/MP = 10 ). The low mass estimates are calculated using the lower limit for the planet-moon −5 mass fraction (Ms/MP = 4.7 10 ). 0.0041 is Io’s eccentricity and 0.055 is the eccentricity for the Moon. × The bottom two values are calculated using the average between 0.0001 and 0.1 with logarithmic steps.

Table 2:: Parameter Values

Parameter Min Value Likeliest Value Max Value N 782 782 782

fM 0.067 0.082 0.098 ff 1.0 1.0 1.0 fs 1.0 1.0 1.0 fT 0.166 0.167 0.168

Notes. N is the Number of AFGKM Hipparcos stars within 20 parsec of the Sun; fM is calculated using Johnson et al.(2010); fs is explained in Section 3.3; fs is determined by Barnes & O’Brien(2002); the likeliest value for fT is determined using the average of the two average values in Table1.

2012) for a 3 hour integration and 5σ sensitivity in the M-band (2.76 µJy) and the L-band (0.27 µJy), the known distance to the objects and estimated radii, we are able to estimate the required THEM temperatures needed for a detection with

1 d 2 F 4 T = , (7) R σ " # where d is the distance to the object, R the radius, F the incoming ﬂux required for a detection and σ the Stefan-Boltzmann constant. In Figure7 the calculated temperatures – 13 –

101 ) ⊕ 0 M 10

1 10−

Estimated Moon Mass ( 2 10−

3 10− 3 2 1 0 10− 10− 10− 10 Star-Planet Separation (arcseconds)

Fig. 6.—: Star-planet separation in arcseconds plotted vs. the estimated moon mass in Earth masses. −3 −5 Grey symbols are calculated using Ms/MP = 10 , blue symbols are calculated with Ms/MP = 4.7 10 . × Symbol sizes indicate the distance to the primary star, larger symbols mean shorter distances. Vertical λ lines indicate the diﬀraction limited resolution (θ = 2.44 D ) of the JWST (cyan) and E-ELT (red) for the M(4.7µm) band. We see that serveral objects are within the diﬀraction limits of the two telescopes, which means that objects that are hot enough might be able to be resolved.

are shown. The temperatures we ﬁnd are all well above 1000K. Peters & Turner(2013) only

included THEMs with temperatures of up to Ts = 1000 K in their detectability calculations. Unfortunately, we have not found objects of such ’low’ temperatures in our analysis. We will investigate the objects with temperatures below 2000 K and within the diffraction limit in the L-band, as the L-band requires lower temperatures than the M-band. We find three such objects, listed in Table3. The possible temperatures we calculated in Section 3.7 are shown in Table4. The required, high temperatures could be possible with an highly eccentric orbit −3 and using Ms/MP = 10 . However, these extremely high temperatures are hard to sustain for a long period of time, as can be seen in Figure5. If we assume an eccentricity of 0.1 and −3 the upper mass fraction (Ms/MP = 10 ), which could provide high enough temperatures, the resulting THEMs would be stable for 70 Myr, 40 Myr and 8 Myr for GJ 832 b, Epsilon Eri B and Beta Gem B respectively, neglecting cooling effects. These lifetimes are quite low and far from Gyr timescales. – 14 –

1.0

0.8

104 104 0.6

0.4

Estimated Temperature (K) 0.2

100.03 103 3 2 1 0 3 2 1 0 100.−0 10− 0.2 10− 010.4 10− 0.6 10− 010.8 − 10 1.0 Star-Planet Separation (arcseconds)

Fig. 7.—: Star-planet separation in arcseconds vs. the moon temperature needed to be able to be detected with the Mid-infrared E-ELT Imager and Spectrograph (METIS) in the M-band (left) and in the L-band −3 (right), with a 3 hour integration and a 5σ sensitivity. Grey symbols are calculated using Ms/MP = 10 , −5 blue symbols are calculated with Ms/MP = 4.7 10 . Vertical lines indicate the diﬀraction limited × resolution of the E-ELT (red) for the M-band (left) and the L-band (right).

5. Conclusion & Discussion

In this paper we present an analogue to the Drake equation to estimate the number of THEMs in a population of stars. Using the numbers of stars N, the fraction of stars that

have a massive planetary companion fM , the fraction of massive planets that form moon ff , the fraction of moons that can remain in a stable orbit on Gyr timescales fs and the fraction of moons that are heated through tidal interaction fT , we were able to estimate the number of THEMs around the 782 closest AFGKM Hipparcos stars. We ﬁnd that there could be +2.2 10.7−2.0 THEMs within 20 parsec. Some of these potential THEMs could reach temperatures of 1000K and remain stable on Gyr timescales. ∼ Examining RV conﬁrmed exoplanets we determined the eccentricities and mass fractions potential THEMs would need in order to be able to be directly imaged and found the three – 15 –

Table 3:: Required temperatures for detection

Low mass High mass Distance Separation Name Mass (M ) Tempera- Tempera- J (pc) (AU) ture (K) ture (K) GJ 832 b 0.64 4.95 3.40 2416 1562 Epsilon Eri b 1.05 3.22 3.38 1860 1164 Beta Gem b 2.76 10.36 1.78 2927 1810

Notes. The high mass temperature limits are calculated using the upper limit for the planet-moon mass −3 fraction (Ms/MP = 10 ). These objects are heavier, larger and, therefore, easier to image. The low mass temperature limit are calculated using the lower limit for the planet-moon mass fraction (Ms/MP = 4.7 10−5). The Mass column indicates the planet RV masses. × most likely candidates. Due to the high eccentricity and mass fraction needed for the three exomoon-candidates and the resulting low lifetimes, we conclude that there are currently no feasible THEM candidates for direct imaging in the observed population. However, the population of planets used for this research consists solely of objects with conﬁrmed RV masses, leaving out planets in extremely wide orbits. A survey of 91 stars in the Upper Scorpius (USco) region done by Lafreni`ereet al.(2014) calculated a frequency of wide (250-

1000 AU), massive (5-40 MJ ) companions for such regions of 4%. This would yield ∼ 31 planets for the population of 782 Hipparcos stars. Several of these kinds of extremely ∼ wide orbit objects have been discovered in recent years (e.g. Chauvin et al. 2005; Luhman et al. 2006; Marois et al. 2008, Marois et al. 2010; Lagrange et al. 2009; Currie et al. 2014; Bonavita et al. 2014). This is a large fraction of planets that we did not include in our analysis. Several of these discoveries have masses of 10 20MJ . Planets of these sizes could − potentially have enormous moons as companions at extremely large separations from their parent star, making them prime candidates for THEM imaging in future with JWST and the E-ELT.

6. Acknowledgements

This research has made use of the Exoplanet Orbit Database and the Exoplanet Data Explorer at exoplanets.org. – 16 –

Table 4:: Calculated possible temperatures

Name Eccentricity Low mass Temperature (K) High Mass Temperature (K) GJ 832 b 0.0041 46 224 0.055 168 819 0.1 226 1104 Epsilon Eri b 0.0041 66 280 0.055 241 1024 0.1 324 1380 Beta Gem b 0.0041 111 448 0.055 406 1641 0.1 548 2213

Notes. The high mass temperature limits are calculated using the upper limit for the planet-moon mass −3 fraction (Ms/MP = 10 ). The objects are heavier, larger and therefore easier to image. The low mass temperature limit are calculated using the lower limit for the planet-moon mass fraction (Ms/MP = 4.7 × 10−5). Because the eccentricity of the Moon is not large enough to obtain the high mass temperatures, we include an higher eccentricity of 0.1 as well.

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