THE ANGLO-AUSTRALIAN PLANET SEARCH. XXI. A GAS-GIANT PLANET IN A ONE YEAR ORBIT AND THE HABITABILITY OF GAS-GIANT SATELLITES^*

The top panels of Figures 2(a) and (b) show the results of a single Keplerian fit to this data at a period near one year. Table 3 shows the parameters of this fit (P = 363.2 ± 1.6 days, m sin i =0.34 ± 0.02 M_Jup, e = 0.41 ± 0.16) which has a reduced chi-squared (χ²_ν) value of 1.68 and an rms scatter of 4.3 m s⁻¹. A peak is evident at very low significance in the residual periodogram to this fit at 20 days. However, this is sufficiently close to the approximate estimate of the rotation period of HD 38283 (12 days; Noyes et al. 1984) that it is not considered likely to be the signature of an additional planetary body. Figure 3 shows this velocity data folded at a period of 363.2 days, demonstrating the almost uniform phase coverage we have been able to achieve for this circumpolar star.

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To test the probability that the noise in our data might have resulted in a false detection for this eccentric planet, we have run simulations using the "scrambled velocity" approach of Marcy et al. (2005). This technique makes the null hypothesis that no planet is present, and then uses the actual data as the best available proxy for the combined noise due to our observing system and the star. Multiple realizations are created by scrambling the observed velocities amongst the observed epochs. We created 5000 of these scrambled velocity sets, and then subjected them to the same analysis as our actual data set for the case of a single eccentric planet. No trial amongst 5000 showed a χ²_ν better than that obtained for the original data set, and the distribution of the scrambled χ²_ν values (see Figure 4) shows a clear separation from that obtained with the actual data. We conclude that there is a less than 0.02% probability of us having obtained a false detection due to a fortuitous selection from a system with no planet.

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In much the same manner that an elliptical orbit can be approximated by two circular orbits arranged in an epicyclic configuration, a set of radial velocity data which can be fit with one eccentric planet can often also be modeled as two planets in near-circular orbits (see, e.g., Anglada-Escudé et al. 2010, and references therein). Fitting a single planet in a circular (e = 0.0) orbit to our HD 38283 data gives a reduced chi-squared value of 1.99 and a residual rms of 4.8 m s⁻¹, and so is clearly not preferred over a single eccentric planet (see Table 3 and Figures 2(c) and (d)). The residuals to this fit show marginally significant peaks remaining at 60 and 121 days. However, fitting two planets (at ≈363 and 120 days) in circular orbits yields a reduced chi-squared value of 1.42 and a residual rms of 3.8 m s⁻¹, which is slightly better than that obtained for a single eccentric planet. (Allowing the eccentricities of the two planets to float, we obtain χ²_ν = 1.42 and an rms of 3.8 m s⁻¹, a solution which is indistinguishable in quality from the two-planet, forced-circular case.) Attempting to fit a second planet at 60 days (rather than at 120 days) results in solutions with extremely unlikely eccentricities (e > 0.8), and moreover leaves the 120 days peak behind in the residuals to that two-planet fit. The residuals to a two-planet fit with the second planet at 120 days removes both the 60 days and 120 days power-spectrum peak in the residuals to the one-planet fit. So if there is a second planet in this system then it is not at a period near 60 days.

However, the question that arises is, obviously, which of these two solutions is correct—an eccentric single planet, or two circular planets near 3:1 resonance? To test the dynamical stability of a two-planet HD 38283 system, we used the HNBody orbital integrator (Rauch & Hamilton 2002). HNBody is a symplectic integrator which also includes general relativity. The parameters of the HD 38283 system (allowing non-zero eccentricities) were used as the initial input conditions, and the simulation was allowed to run for 10⁷ yr. The two-planet system remained stable for the full duration of this simulation, so this does not rule out the two-planet solution on dynamical grounds.

To further examine whether HD 38283 contains a single or double planet system, we examined the data using a genetic algorithm. We restricted the allowed range in period for the ∼1 yr "b" planet to 300–400 days, while allowing a second "c" planet to take on periods between 50 and 200 days. The genetic algorithm employed was used in a similar manner to that which Cochran et al. (2007) used to distinguish among several possible orbital solutions for the outer planet in the HD 155358 system. Here, we ran 50,000 trials, in which the genetic algorithm performed two-planet fits and logged the resulting χ². Each trial is the result of hundreds of generations, in which a population of two-Keplerian orbital solutions evolves to a minimum χ² value. Figure 5 shows the χ² achieved for the allowed periods of the two planets. From these results, it is clear that the 363 days signal is the favored solution for planet "b." However, the putative "c" planet can take on a wide range of parameters, with no clearly favored χ² minimum. From Figure 5 we see that, while our least-squares fit prefers a 120 days second planet, the χ² surface is quite complex. In our previous experience with genetic algorithms, a correct solution should "evolve" rapidly toward a sharp χ² minimum when brought to bear on data containing real and coherent Keplerian signals. We therefore conclude that these genetic results cast doubt on the uniqueness and reliability of any two-planet solution.

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Combining these strands of evidence, we conclude that the data do not conclusively demonstrate the existence of a second planet in this system. What data we have are only suggestive, at best. Occam's Razor then leads us to conclude that the "simpler" model of a single planet in an eccentric orbit is to be preferred, until intensive monitoring can confirm the existence of the radial velocity features that would be expected on short timescales were the system to be one in a 3:1 resonance.

As noted above, scientists are generally (and justifiably) wary of time series data that show periodicities at integer multiples or divisors of one year. Bugs in the codes used for applying systematic corrections to the data are an obvious route for the creation of artificial signals like these (e.g., Bailes et al. 1991; Lyne & Bailes 1992). The only correction that (if it were in error) could conceivably generate a false signal in our data is the barycentric correction. We see no evidence in any of our other AAPS target stars for objects with periods of almost exactly one year. Moreover, the signal we see in HD 38283 is a relatively large 10 m s⁻¹ one—such a signal would be trivial to detect in systems like HD 102365, HD 16417, and 61 Vir (Tinney et al. 2011; O'Toole et al. 2009; Vogt et al. 2010), all of which were discovered by the AAPS and all of which were host planets with substantially smaller Doppler amplitudes than 10 m s⁻¹. For a barycentric correction bug to produce this signal, there would have to be something unusual about the relevant input parameters (i.e., position & proper motion) of this star. However, there is nothing unusual about HD 38283's position or proper motion—they have been precisely determined by Hipparcos, and in particular are as accurate as the vast majority of the other targets in the AAPS sample, which show no sign of an annual signature. An obvious check is to ask whether other objects close on the sky to HD 38283 show any similar effect. HD 39091 lies just 68 away from HD 38283 and has a similar spectral type (G1V), the same level of activity (R'_HK = −4.97) and is just 1.04 mag brighter in V. HD 39091 is known to host a very massive planetary companion (Jones et al. 2002). If we fit our data for this companion (P = 2086 days, m sin i = 10.1 M_Jup , e = 0.64), we find the residual LS periodogram shown in Figure 6. In this system we see no evidence for a peak at 364 days—the nearest peak in the residual periodogram is at 420 days and well separated from one year. We conclude that the periodicity we see in HD 38283 is indeed astrophysical, and therefore the signature of an exoplanet.

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Figure 7 plots the period histogram for Doppler exoplanets detected with periods in between 300 and 400 days (as compiled at 2010 November by the Exoplanet Explorer database⁷—the distribution derived from the similar Exoplanet Encyclopedia compilation⁸ is essentially identical). The figure does not include HD 38283 b. The distribution shows an obvious "hole" at the bin centered on 365 days, compared to the neighboring bins. The mean frequency of planets per 10 days bin for the whole period range plotted is 2.5 ± 0.5 (the uncertainty is the standard error in the mean), while that for the four bins adjoining the one year period is 4 ± 0.5. So, while the number statistics in the individual bins are admittedly small at present, the hole at one year is nonetheless significant.

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This dip is almost certainly due to the difficulty in sampling planets with periods close to one year, combined with the understandable desire of planet search teams to have overwhelming evidence in hand before they are prepared to publish planets at such periods. Indeed, given these considerations it would be suspicious if there was not a dip at this location. The histogram would suggest that HD 38283 b represents just one quarter of the exoplanets one would expect to find in the ensemble of exoplanets currently being surveyed, in the absence of observational and sampling biases.

One obvious strategy that could be employed to address the difficulty in reliably identifying planets with periods near one year is to specifically target samples of host stars that, like HD 38283, are circumpolar (or near-circumpolar). Such stars can be observed throughout the year, suppressing aliases and delivering a clean window function. Another strategy would be to tolerate observations at large hour angles (and so large air masses) near twilight in order to extend the time coverage of target stars further into the period each year when they are generally considered to be inaccessible.

The search for "habitable" exoplanets—where the definition of "habitability" can vary substantially (see, e.g., Horner & Jones 2010, and references therein), but usually centers on the presence of liquid water on the surface of a rocky planet—has to date generated substantially more heat than light; or at least substantially more publications describing theoretical predictions than actual detections. The profound difficulty in detecting these "habitable" planets in orbit around G dwarfs like the Sun (requiring as it does the measurement of either a 90 mm s⁻¹ amplitude Doppler variation, or a 10 μmag transit, and doing so repeatedly over several years) has seen the focus in "habitability" theory and observation move toward low-mass, M dwarf host stars. In low-mass stars, the habitable zone shrinks to much smaller orbital radii and periods, making both Doppler amplitudes and transit variations larger. And, perhaps even more critically, shorter periods mean that observing programs must only control their systematics over much shorter periods—i.e., several months, rather than several years. The m sin i = 3.1 M_⊕, P = 36 days planet Gl 581 g (Vogt et al. 2010) appears to be the most "habitable" planet yet detected, and was detected by exploiting exactly this approach—a focus on low-mass planets orbiting low-mass stars in short-period orbits.

Nonetheless, it remains true that the prototype for all habitability searches⁹ remains the Earth—a rocky, terrestrial planet orbiting at ≈1 AU in a near-circular orbit around a G dwarf star. One obvious potential location for such an environment became obvious soon after the first exoplanets were detected in the mid-1990s. This first handful of gas-giant planets were discovered at orbital radii of 0.01–2 AU, placing them substantially interior to where gas-giant planets were expected to form based on the understanding of planet formation then current (which was highly tuned to the only planetary system previously known—the solar system). It was suggested almost immediately (Williams et al. 1997) that if these gas-giant exoplanets hosted large, rocky moons, then those moons could potentially be habitable.

The formation of the gas-giant satellites of our solar system is the subject of a substantial literature which it is not feasible to completely summarize in this communication—the interested reader should consult the reviews of Mosqueira et al. (2010), Estrada et al. (2009), Canup & Ward (2009), and references therein. These models distinguish between the formation of the "regular" (or "Galilean") and "irregular" satellites. The regular satellites lie on inner, nearly circular, low inclination, prograde orbits indicating that they formed within a circumplanetary disk around their host planet. The fact that all the gas-giant planets of the solar system harbor regular satellites suggests that their formation may be an inevitable consequence of giant planet formation (Estrada et al. 2009). The irregular satellites—characterized by high eccentricities and inclinations, and a significant fraction of retrograde orbits—are considered to be captured bodies.

There is a general consensus that the primary epoch of the formation of the regular satellites takes place as (and after) the gas giant is finishing its formation, and in particular as (and after) the gas giant has cleared a gap in the protoplanetary nebula (Mosqueira et al. 2010; Canup & Ward 2009), with the result that the accretion of material into the circumplanetary disk may take place largely through the planet's two Lagrange points (Estrada et al. 2009). Sasaki et al. (2010) have recently produced updated models for the formation of the Jupiter and Saturn systems that are based on the Canup & Ward (2009) formulation, but which attempt to model both planet formation and satellite formation together in a manner informed by the enhanced knowledge we now have of exoplanet formation.

The relevant dynamical times in circumplanetary disks are typically orders of magnitude shorter than in circumstellar disks (Estrada et al. 2009), and estimates for the timescales of the formation of the satellites range from 10⁴ to 10⁷ yr. The formulation of Canup & Ward (2009) predicts timescales for the processing of material through the circumplanetary disk at the longer end of this range. Moreover, it proposes that orbital migration within the circumplanetary disk could see multiple generations of satellites formed and ultimately lost via collision with the host planet—the surviving satellites are simply the last surviving generation and reflect the inflow conditions in the circumplanetary disk at the time accretion stopped.

A complicating issue is how the timescale for the formation of exomoons compares with the timescales for the orbital migration believed to transfer gas-giant exoplanets from their formation locations at ≳5 AU to the locations at which they are commonly being discovered (and in particular at the ∼1 AU locations at which planets like HD38283 b orbit). Currently, the two predominant models for exoplanetary migration are via gravitational interaction of an exoplanet and the disk in which it is embedded, via spiral density waves (Type I migration—e.g., Ward 1986, 1997) and Type II migration which occurs after a gas giant has opened a gap in its protoplanetary disk and its orbital evolution becomes coupled to the viscous evolution of the disk (Lin & Papaloizou 1986). The relevant timescales for these two types of migration are ∼10⁴ and ∼10⁵ yr, respectively. This would suggest that satellite formation remains possible for gas giants undergoing both forms of migration— either at an inner disk location after the faster Type I migration has halted (if it halts at all), or while the slower Type II migration is taking place. The latter situation is perhaps the most intriguing, since it is the opening of a gap in the circumstellar disk that allows Type II migration to take place, and which is thought to be the point at which significant formation of the regular gas-giants satellites takes place.

These two processes (regular satellite formation and Type II planetary migration) are likely to be inextricably linked. The impact of simultaneous migration and regular satellite formation needs further modeling to determine the impact on both satellite mass and satellite composition—both of which are critical parameters for understanding exomoon habitability. Williams et al. (1997) have pointed out that for satellites to retain a substantial and long-lived atmosphere, they would need to be quite large (>0.12 M_⊕)—five times more massive than the largest satellites in our solar system (Ganymede and Titan) and 10 times more massive than the Moon. An alternative derivation by Kaltenegger (2000) determines an even more massive lower limit of >0.23 M_⊕. The four "Galilean" satellites of Jupiter (Ganymede, Callisto, Io, and Europa) together total a small fraction of Jupiter's mass (M_G/M_Jup =2.1 × 10⁻⁴), while the equivalent quantity for the Saturnian system is a very similar 2.5 × 10⁻⁴. This suggests that the process that forms regular satellites may only permit growth to a maximum size (Canup & Ward 2009). If the same formation mechanisms hold for exomoons, then massive gas giants (i.e., 5–10 M_Jup) will offer a better chance of hosting a habitable satellite than planets of Jovian mass.

What would we expect the composition of these exomoons to be? We know that in the solar system, the largest gas-giant satellites are composed of roughly 50% rock and 50% ice (Mosqueira et al. 2010). Of course, if Ganymede or Titan were moved from >5 AU to 1 AU, the volatiles which make up almost 50% of their mass budget would be significantly heated, resulting in either a very thick atmosphere, or thick oceans, or both. Williams et al. (1997), for example, note that if solar system satellites like Ganymede or Callisto were formed at ≳5 AU and migrated to 1 AU, they would be covered by oceans to a depth of ∼1000 km.

How the composition of an exomoon would differ from that of Ganymede or Titan if it were formed as it migrated from >5 AU to ∼1 AU is hard to predict—we are aware of no simulations carried out to date of satellite formation while the host planet undergoes migration. Given the prevalence of known Doppler and transit gas giants that clearly have undergone migration, this is clearly another area of research crying out for further study.

The solar system gas giants host significant populations of irregular satellites—bodies thought to have originated elsewhere in the solar system. The large orbital radii, wide range of orbital eccentricities and inclinations, and the significant fraction of retrograde orbits displayed by the irregular satellites indicate that they were captured by their host planets, rather than forming in situ (e.g., Jewitt & Sheppard 2005; Nicholson et al. 2008). The majority of these objects move in distinct collisional "families"—groups of satellites with similar orbital properties, suggesting that they have formed from the breakup of a smaller population of larger bodies (Nesvorný et al. 2003, 2004; Turrini et al. 2008). Indeed, taking into account detection biases, it seems likely that each of the giant planets harbors roughly the same number of irregular satellite families (and hence originally captured approximately the same number of larger bodies). This is remarkable when one considers that there is a factor of ∼20 difference in mass between Jupiter and Uranus (Jewitt & Sheppard 2005).

It is therefore possible that, just as Neptune captured the relatively massive irregular satellite Triton, an exoplanet may capture its own large, irregular exomoon as it migrates from its formation location to a potential habitable zone orbit. Unfortunately, none of the suggested capture mechanisms for the irregular satellites of the solar system is able to convincingly reproduce the characteristics observed for those satellites (Jewitt & Haghighipour 2007). The capture by a 1 M_Jup planet of an exomoon large enough to be habitable would require seizing control of a body at least twice as massive (relative to its host planet) as Triton compared to Neptune. It is problematic whether such a capture could be mediated via the dissipative mechanisms proposed to explain the capture of the solar system irregular satellites (i.e., "gas drag" and "pull down" – Jewitt & Haghighipour 2007). The capture of such large irregular exomoons would require a three-body encounter—i.e., either the large object encounters a pre-existing regular satellite during a close encounter (Goldreich et al. 1989; Woolfson 1999), or the large object itself has a satellite which is shed during their mutual encounter with the giant planet (Agnor & Hamilton 2006; Vokrouhlický et al. 2008). Such encounters are likely to be rare events (as evidenced by Triton being the only large irregular satellite in the solar system). On the other hand, they have obviously happened at least once in the solar system—albeit for an exomoon about a factor of two too small (relative to its host exoplanet) to be habitable. Encounters leading to capture could potentially happen even more frequently for a host exoplanet migrating inward through a denser protoplanetary disk rich in planetesimals and proto-terrestrial planets, than that which Neptune is thought to have passed through during its own outward migration through a more sparse disk (e.g., Malhotra 1993; Hahn & Malhotra 1999; Gomes et al. 2004). Dynamical simulations of the capture of irregular satellites by inward migrating exoplanets, therefore, should be another profitable area for further study.

An additional region in the "habitability phase space" is provided by the "exo-Trojans"—potential Trojan companions of gas-giant exoplanets in 0.5–2 AU orbits. Trojans are objects trapped within a planet's 1:1 mean-motion resonance, and typically librate around the L4 and L5 Lagrange points, 60° ahead and behind the planet in its orbit. Within our own solar system, large numbers of Trojans have been discovered—thousands sharing Jupiter's orbit, a couple moving with Mars, and seven in resonance with Neptune.¹⁰ When discovery biases are taken into account, it is hypothesized that the Jovian Trojan population numbers of order 1 million objects (greater than 1 km in diameter), with the Neptunian Trojan population housing potentially 10 times that number (Sheppard & Trujillo 2006). This is a substantially larger population (numerically) than the solar system irregular satellites, which likely number in the hundreds to thousands (Jewitt & Sheppard 2005).

The Trojans within our solar system move on orbits covering a range of eccentricities and inclinations, which suggest that they were captured (Lykawka & Horner 2010; Lykawka et al. 2009; Morbidelli et al. 2005), rather than formed in situ during the migration of the giant planets (see, e.g., Minton & Malhotra 2009; Hahn & Malhotra 2005, and references therein). Lykawka & Horner (2010) have modeled the capture of Trojans by Neptune during its outward migration, and found a Trojan capture efficiency (i.e., objects encountered, captured, and then remaining Trojans until migration ceases) of between 10⁻⁶ and 10⁻³. Though such a capture probability might appear small, the large distances over which exoplanets at 0.5–2 AU must migrate would allow ample opportunity for large embryos and protoplanets to be captured and carried along with the giant planet, resulting in a habitable exo-Trojan. Indeed, the presence of a large Trojan companion to the proto-Earth has been suggested as the source of the Mars-sized impactor thought to have been involved in the collision that led to the formation of the Moon (e.g., Belbruno & Gott 2005). Had that proposed body remained on a stable Trojan orbit to the current day, rather than being destabilized (ultimately to collide with the Earth), it would surely be a habitable planet.

Exo-Trojans have been the subject of some investigation to date. Laughlin & Chambers (2002), for example, studied the stability of systems in which two equal-mass planets were locked in mutual 1:1 mean-motion resonance, and showed that such scenarios could be stable so long as the cumulative mass of the two planets did not exceed ∼1/26th the mass of their host star. More relevant for the question of habitability in systems with a gas giant in the habitable zone is the study of Dvorak et al. (2004), who considered the specific example of putative terrestrial exo-Trojans for three known giant exoplanets in ∼1 AU orbits. They concluded that stable, terrestrial exo-Trojan configurations were indeed plausible. More recently—motivated by their potential detectability via Transit Timing Variations (see e.g., Ford & Holman 2007; Madhusudhan et al. 2009, and references therein)—there has been a focus on studies of Trojan companions to known transiting planets in very small orbits. Indeed, for the foreseeable future this is the only means available for the actual detection of exoplanetary Trojans (though to date no detections have emerged; Madhusudhan et al. 2009). Nonetheless, it seems prudent to consider suitably massive Trojans (≳0.12 M_⊕, Williams et al. 1997) of giant exoplanets in habitable orbits as a potential source of habitable worlds. These habitable exo-Trojans could easily have been transported many AU as their giant planet migrated inward, and so it is easy to see them having abundant water—neatly avoid the question of how telluric planets can be sufficiently hydrated to be habitable (see, e.g., Horner & Jones 2010). In addition, unlike an exomoon, they will not suffer from being immersed in the high-energy particle environment of, or be subject to tidal heating by, their host planet (see below).

Exomoon stability and habitability has been the subject of a rapidly expanding literature in recent years. However, this has been almost entirely prompted by the prospect of detecting exomoons orbiting transiting exoplanets, and so has focussed almost exclusively on the short-period, small-orbit systems that are likely to transit (e.g., Weidner & Horne 2010; Barnes & O'Brien 2002; Kaltenegger 2010; Kipping 2010). Barnes & O'Brien (2002), however, did examine the stability of massive exomoons on longer period orbits and found that, while stellar tides from a 1 M_☉ star are inimical to massive satellites orbiting a 1 M_Jup planet within ∼0.1 AU, they do not impact on the stability of 1 M_⊕ exomoons beyond 0.25 AU, or 0.1 M_⊕ exomoons beyond 0.2 AU.

In general, for a satellite to be stably bound in orbit around a 1 M_Jup planet in a 1 AU orbit, it will need to orbit well within the planet's Hill radius of ≈0.068(1 − e) AU. Detailed dynamical simulations suggest that the relevant radius is actually less than half (49%) of the Hill radius for prograde satellite orbits, and about 93% of the Hill radius for retrograde orbits (Domingos et al. 2006). Simulations of the orbital stability of satellites undergoing migration have been carried out for the simplifying assumption that they formed before any migration takes place (Namouni 2010). It was found that the Galilean satellites of Jupiter, and the equivalent inner satellites of Saturn, would remain stably bound as their host planet underwent inward migration to semimajor axes of at least 0.5 AU. For both prograde and retrograde orbits, satellites will become tidally locked to their planet within a few billion years. Such satellites will have diurnal periods ranging from a few days to a few months, with any one point on the surface potentially subject to large diurnal temperature variations as a result. In addition, these satellites will receive a varying total stellar flux as they move from conjunction to opposition with respect to the host star—e.g., a tidally locked satellite orbiting at half the Hill radius (for a 1 M_Jup planet orbiting at 1 AU) will see a conjunction to opposition flux ratio of [(1 + 0.068)/(1–0.068)]² ≈ 1.31. Similarly, if the gas giant has an elliptical orbit, the satellite will see an annual variation in the incident flux with the ratio between the planetary periastron and apastron fluxes of [(1 + e)/(1 − e)]². For low-eccentricity gas giants (i.e., e < 0.05), these two effects could be of similar magnitude, and would not appear to preclude a satellite's habitability.

One obvious question to ask then is: just how many exoplanets are currently known that could host habitable exomoons? There have been a variety of determinations of the "habitable zone" for terrestrial exoplanets, with a variety of assumptions about stellar luminosity and temperature, and planetary and atmospheric composition (e.g., Selsis et al. 2007; von Bloh et al. 2009, 2007; Kasting et al. 1993). Most of these have assumed a planet of 1 M_⊕ (or larger), and to date there has been little study of the impact on potential habitability for rocky bodies of smaller mass (like the exomoons being considered here), nor of the different composition an exomoon is likely to have.

Here, we adopt the conservative "continuously habitable zone" (i.e., the region that is habitable over the 4.6 Gyr lifetime of the solar system) of Kasting et al. (1993) for a G2V star, which was estimated to extend from 0.95 to 1.37 AU. We can scale habitable zone for stars of different luminosities using a_HZ = 1 AU(L_star/L_☉S_eff)^0.5 (and following Kaltenegger 2010, in adopting S_eff to take into account the wavelength dependent intensity distribution of the spectral classes, and then setting it to unity for F, G, and K stars, which have only a very weak dependence on this parameter). Scaling the observed semimajor axes using the luminosities of the known exoplanetary host stars of luminosity classes V and IV compiled by the Exoplanet Explorer database,¹¹ we derive the sample listed in Table 4 of gas-giant exoplanets that lie within the "Earth-like" planet habitable zone, and so could host habitable exomoons. We derived luminosities for the host stars from their measured parallaxes and V magnitudes, together with tabulated visual bolometric corrections for luminosity class V from Allen (1976). Although some of the stars in question are classified as luminosity class IV, these corrections are still useful and result in bolometric magnitudes to better than ±10%. We used M_Bol☉ = 4.75 (Torres et al. 2010) to place the resulting bolometric magnitudes from Allen (1976) on a consistent system.

The resulting list is surprisingly small—just nine of the more than 490 exoplanets currently known. We have divided these into three classes: those with e < 0.05 and so almost circular like the orbit of the Earth, those with e < 0.1 and so slightly elliptical, but similar to the ellipticity of the orbit of Mars (e = 0.0933), and those with e < 0.17, which we somewhat arbitrarily adopt as an upper limit for habitability on the basis of annual flux variations due to orbital eccentricity being less than a factor of two. In examining these classes, though, it is important to bear in mind the substantial (and usually under-estimated) uncertainties associated with the measurement of orbital eccentricities. For systems with orbital periods this long, uncertainties of ±0.1–0.2 in eccentricity are not uncommon; so it is possible that future updates to the orbits for the known exoplanets may move other objects into, or some of these objects out of, this list.

The list includes both planets orbiting within 1 AU around stars less luminous than the Sun (e.g., 55 Cnc f, HD 45364 c) and planets orbiting beyond 1 AU around more luminous stars (e.g., HD 216435 b, HD 10697 b). Due to HD 38283's overluminosity, HD 38283 b itself does not fall into this class of habitable exomoon hosts—with a bolometric absolute magnitude of 3.79 it is a factor of 2.42 times more luminous than the Sun and so its habitable zone lies at ∼1.5–2.1 AU. As noted earlier, there appears to be a maximum mass for the formation of solar system regular satellites. If similar formation processes hold in exoplanetary systems, this would argue that the most likely location for habitable exomoons is in orbit around the larger exoplanets listed in Table 4—HD 28185 b, HD 10697 b, and HD 221287 b.

Other physical processes in their environments will significantly impact on habitability, but are at present poorly understood and poorly constrained in the exoplanet context. Exomoons will be subject to tidal heating, the strength of which will depend substantially on their orbital radii. We know that in the Jupiter system, Io (orbiting at 5.9 R_Jup) suffers significant tidal heating with the result that its surface heat flux (∼2 W m⁻²; Lopes & Williams 2005) exceeds its radiogenic and gravitational contraction flux by factors of hundreds, resulting in such significant vulcanism that it would not appear habitable for any definition of habitability that was based on Earth-like conditions. On the other hand, just the right amount of tidal heating may serve to promote tectonic activity and vulcanism in an exomoon that might otherwise be too small to support such a geology by radiogenic heating alone.

Similarly, the radiation environment for an exomoon will impact on its habitability. Williams et al. (1997) noted that the high-energy electron flux for the satellites that orbit in Jupiter's inner magnetosphere (especially Io) is around one thousand times larger than that seen at the orbit of Mars. The presence of a strong exomoon magnetosphere that can protect the planetary surface from charged particle bombardment is probably a precondition for Earth-like habitability on exomoons.

The high-energy electron flux will also vary strongly as a function of orbital radius—fluxes of 11 MeV electrons (Jun et al. 2005) drop by a factor of ∼1000 between the orbits of Io (5.9 R_Jup) and Ganymede (15.1 R_Jup). So an exomoon analogous to Ganymede, therefore, may not see a particle flux much worse than that seen at Mars due to the solar wind, and could be habitable if it hosts its own protective magnetosphere. Exomoons in inner orbits like Io, however, may suffer an unsurvivable radiation flux regardless of their magnetospheric status.

Orbital radius will clearly play a critical role in the habitability of exomoons—a radius that is too small will lead to overly vigorous tidal heating and high levels of high-energy radiation, while a radius that is too large will lead to a very long, tidally locked diurnal period, and larger variations in incident solar flux as it orbits.