Longevity of moons around habitable planets Takashi Sasaki and Jason W. Barnes Department of Physics, University of Idaho, Moscow, ID 83844-0903, USA e-mail: tsasaki@vandals.uidaho.edu Abstract: We consider tidal decay lifetimes for moons orbiting habitable extrasolar planets using the constant Q approach for tidal evolution theory. Large moons stabilize planetary obliquity in some cases, and it has been suggested that large moons are necessary for the evolution of complex life. We find that the Moon in the Sun–Earth system must have had an initial orbital period of not slower than 20 h rev − 1 for the moon’s lifetime to exceed a 5 Gyr lifetime. We assume that 5 Gyr is long enough for life on planets to evolve complex life. We show that moons of habitable planets cannot survive for more than 5 Gyr if the stellar mass is less than 0.55 and 0.42 M ⊙ for Q p = 10 and 100, respectively, where Q p is the planetary tidal dissipation quality factor. Kepler-62e and f are of particular interest because they are two actually known rocky planets in the habitable zone. Kepler-62e would need to be made of iron and have Q p = 100 for its hypothetical moon to live for longer than 5 Gyr. A hypothetical moon of Kepler-62f, by contrast, may have a lifetime greater than 5 Gyr under several scenarios, and particularly for Q p = 100. Received 10 January 2014, accepted 16 May 2014 Key words: exomoon, exoplanet, planetary systems. Introduction Detecting terrestrial planets in habitable zones is exciting because life may exist on such planets. To support life, a planet must orbit in the habitable zone of its parent star and have a moderate climate. It may take a long time for life to reach complex, multicellular forms of life. For example, it took about 4 billion years for life on Earth to evolve from single-celled organisms to multicellular creatures such as plants, animals and fungi. A moderate long-term climate is crucial for life to reach multicellularity. In this paper, we assume that 5 billion years is long enough for life on other planets to evolve from the simple to the complex. Earth’s obliquity, or axis tilt, is stabilized by the Moon (Laskar et al. 1993). Mars, on the other hand, has relatively small satellites and its obliquity changes chaotically, fluc- tuating on a 100 000-year timescale (Laskar & Robutel 1993). Hence, even if an Earth-sized exoplanet has a moon, the planetary obliquity may fluctuate wildly if that moon is too small. As planetary climate depends heavily on obliquity (Williams & Kasting 1997; Dobrovolskis 2013), such a planet may not maintain a favourable climate for evolutionarily relevant timescales. Therefore, orbital longevity of a moon may be an important factor allowing a planet to have a moderate long-term climate. The prospects for habitable planets may hinge on moons (Ward & Brownlee 2000); but see also Lissauer et al. (2012). The tidal torque controls the long-term orbital stability of extrasolar moons. Counselman (1973) pointed out that in a planet–moon system with lunar 1 tides, there are three possible evolutionary states: 1. The semi-major axis of the moon’s orbit tidally evolves inward until the moon hits the planet. Mars’ moon Phobos is one such example. 2. The semi-major axis of the moon’s orbit tidally evolves outward until the moon escapes from the planet. While no solar system examples exist for this case, this result could be achieved for the Earth–Moon system if Earth’s present rotation rate was doubled. 3. Lunar orbital and planetary spin angular velocities enter mutual resonance and are kept commensurate by tidal forces. This is the case for Charon, the dwarf planet Pluto’s moon. Unlike the first two states, which are evolutionary, this state is static. Ward & Reid (1973) considered a star–planet–moon system with stellar tides and examined the impact of solar tides on planetary rotation in a limited star–planet–moon without considering the effects of lunar tides or maximum distance from the planet. Barnes & O’Brien (2002) considered a similar tidal evolution scenario, incorporating the maximum distance of the moon but not the lunar tides’ effect on planetary rotation. According to their work, the moon may either hit the planet or escape from it. Sasaki et al. (2012) studied the general tidal evolution of star–planet–moon systems, extending Barnes 1 In this paper, we use ‘lunar’ as the adjective of any moons, not just the Moon. International Journal of Astrobiology, Page 1 of 13 doi:10.1017/S1473550414000184 © Cambridge University Press 2014