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The Mass and Radius of Potential Exomoons

posted Aug 14, 2011, 9:01 AM by Abel Mendez   [ updated Sep 30, 2011, 10:35 AM ]
We barely have the capability to detect Earth-size exoplanets, less moons around them. Small exomoons will be atmosphere-less bodies, like our own Moon that shares with Earth the habitable zone (HZ). However, large exomoons are a very interesting target for astrobiology because they could be habitable if orbiting exoplanets in the HZ. They will be able to hold denser atmospheres, and liquid water, specially if farther away from the center of their HZ (Williams et al., 1997). Terrestrial-size habitable exomoons are more probable around gas giants as only larger planets can have larger moons, as the moon Pandora depicted in the movie Avatar. The good news is that we already have the capability to detect gas giants in the HZ.
    
    There are some interesting relations between moons and planets masses if we use the Solar System as an example (Figure 1). Earth and Pluto are two exceptional cases, with very large moons relative to their size. Our Moon is 1.2 % and Charon is 13% of Earth and Pluto mass, respectively. However, the four giant planets have a similar moon-planet ratio of 1-3 x 10-4 (0.01-0.03%), a much smaller fraction. This is even true for Neptune, which acquired Triton after its formation. For comparison, the combined mass of the planets and moons are 0.13% of the Sun's mass. It seems that there is some deeper relation between the mass of the moons and the giant gas planets.
Figure 1. Moon to planet mass ratio for planets of the Solar System. The mass ratio between the planets and the Sun is shown for comparison.

    Indee, Canup and Ward (2006) showed that the moon-planet mass fraction for the gas giants in our Solar System is probably the norm too for gas giant exoplanets. Although other process can bring exomoons to different sizes, they generally should be nearly 10-4 masses of their parent planet. This means that there are probably Moon to Mars size around gas giants. Ocean exomoons will generally be larger than rocky ones with the same mass. In the HZ they might be able to hold an atmosphere with liquid water surface for those with masses over 0.12 Earth masses (Williams et al., 1997). Exomoons are probably very abundant around gas giants but less likely for those orbiting very close together (Namouni, 2010).

    Candidates for habitable exomoons have already been identified (Tinney et al., 2011). With new discoveries, including Kepler, results, there will be a need to catalog potential habitable exomoons sites. We need a simple relationship between a gas giant mass and their potential moons mass and radius. These properties are related to their habitability as they constrain the ability of the moon to hold an atmosphere in the HZ. Assuming exomoons with a high water fraction, a likely event for those orbiting gas giants, a simple relation can be derived from the 10-4 ratio and a mass-radius relationship for ocean worlds (Sotin et al., 2007) as 
where mp is the mass of the gas giant exoplanet in Jupiter masses, mm and rm are the mass and radius of the exomoon in Earth's units, respectively. Figure 1 plots this relation for gas giants between 0.03 to 13 Jupiter masses. This analysis will be used as part of many other considerations that are needed to identify habitable exomoons sites for the Habitable Exoplanets Catalog.  
Figure 2. Potential mass and radius of water-rich exomoons around gas giant exoplanets. Water-rich exomoons around giants over 10 Jupiter masses could approach Earth size. Those of rocky composition will be smaller. Exomoons in gas giants of more than 4 Jupiter masses in the habitable zone probably have atmosphere with ocean or mushy surfaces, a "melted Europa." 

For more general discussions about exomoons, including direct detection methods, see:

References

  • Canup RM, Ward WR. (2006) A common mass scaling for satellite systems of gaseous planets. Nature, 441: 834-839.
  • Sotin, C., Grasset, O., and Mocquet, A. (2007). Mass-radius curve for extrasolar Earth-like planets and ocean planets. Icarus, 191, 1, 337-351.
  • Tinney CG, Wittenmyer RA, Butler RP, Jones HR, O’Toole SJ, Bailey JA, Carter BD, Horner J. (2011) The Anglo-Australian Planet Search. XXI. A gas-giant planet in a one year orbit and the habitability of gas-giant satellites. Astrophysical Journal, 732: 31.
  • Williams DM, Kasting JF, Wade RA. (1997) Habitable moons around extrasolar giant planets. Nature, 385: 234-236.
  • Namouni F. (2010) The fate of moons of close-in giant exoplanets. Astrophysical Journal Letters, 719: L145-L147.
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