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. 2013 Jan;13(1):18-46.
doi: 10.1089/ast.2012.0859. Epub 2013 Jan 10.

Exomoon habitability constrained by illumination and tidal heating

René Heller  1 , Rory Barnes
Affiliations

Exomoon habitability constrained by illumination and tidal heating

René Heller et al. Astrobiology. 2013 Jan.

Abstract

The detection of moons orbiting extrasolar planets ("exomoons") has now become feasible. Once they are discovered in the circumstellar habitable zone, questions about their habitability will emerge. Exomoons are likely to be tidally locked to their planet and hence experience days much shorter than their orbital period around the star and have seasons, all of which works in favor of habitability. These satellites can receive more illumination per area than their host planets, as the planet reflects stellar light and emits thermal photons. On the contrary, eclipses can significantly alter local climates on exomoons by reducing stellar illumination. In addition to radiative heating, tidal heating can be very large on exomoons, possibly even large enough for sterilization. We identify combinations of physical and orbital parameters for which radiative and tidal heating are strong enough to trigger a runaway greenhouse. By analogy with the circumstellar habitable zone, these constraints define a circumplanetary "habitable edge." We apply our model to hypothetical moons around the recently discovered exoplanet Kepler-22b and the giant planet candidate KOI211.01 and describe, for the first time, the orbits of habitable exomoons. If either planet hosted a satellite at a distance greater than 10 planetary radii, then this could indicate the presence of a habitable moon.

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Figures

FIG. 1.
FIG. 1.
Geometry of the triple system of a star, a planet, and a moon with illuminations indicated by different shadings (pole view). For ease of visualization, the moon's orbit is coplanar with the planet's orbit about the star, and the planet's orbital position with respect to the star is fixed. Combined stellar and planetary irradiation on the moon is shown for four orbital phases. Projection effects as a function of longitude φ and latitude θ are ignored, and we neglect effects of a penumbra. Radii and distances are not to scale, and starlight is assumed to be plane-parallel. In the right panel, the surface normal on the subplanetary point is indicated by an arrow. For a tidally locked moon this spot is a fixed point on the moon's surface. For ϕps=0 four longitudes are indicated.
FIG. 2.
FIG. 2.
Contours of constant planetary flux on an exomoon as a function of the planet-satellite semimajor axis aps and the planet's bond albedo αp. The planet-moon binary orbits at 1 AU from a Sun-like host star. Values depict the maximum possible irradiation in terms of orbital alignment, i.e., on the subplanetary point on the moon, and when the moon is over the substellar point of the planet. For αp≈0.1 contours of equal fr and ft intersect; i.e., both contributions are equal. An additional contour is added at 295 W/m2, where the sum of fr and ft induces a runaway greenhouse on an Earth-sized moon. Some examples from the Solar System are given: Miranda (Mi), Io, Rhea (Rh), Europa (Eu), Triton (Tr), Ganymede (Ga), Titan (Ti), Callisto (Ca), and Earth's moon (Moon). Color images available online at www.liebertonline.com/ast
FIG. 3.
FIG. 3.
Contours of the correction factor for the limits of the IHZ for exomoons, induced by the star's reflected light from the planet. Since we neglect the thermal component, values are lower limits. The left-most contour signifies 1.01. The dotted vertical line denotes the Roche lobe.
FIG. 4.
FIG. 4.
Stellar and planetary contributions to the illumination of our prototype moon as a function of orbital phase φps. Tiny dots label the thermal flux from the planet (ft), normal dots the reflected stellar light from the planet (fr), dashes the stellar light ([Formula: see text]), and the solid line is their sum. The panels depict different longitudes and latitudes on the moon's surface. The upper left panel is for the subplanetary point, the upper right 45° counterclockwise along the equator, the lower left panel shows a position 90° counterclockwise from the subplanetary point, and the lower right is the antiplanetary point.
FIG. 5.
FIG. 5.
Stellar and planetary contributions to the illumination of our prototype moon as in Fig. 4 but at a stellar orbital phase [Formula: see text] =0.5 in an eccentric orbit ([Formula: see text] =0.3) and with an inclination [Formula: see text] of the moon's orbit against the circumstellar orbit.
FIG. 6.
FIG. 6.
Illustration of the antiplanetary winter on the moon with the same orbital elements as in Fig. 5. The arrow in the edge view panel indicates the surface normal at φ=180°, θ=80°, i.e., close to pole and on the antiplanetary side of the moon. For all orbital constellations of the moon around the planet (φps going from 0 to 1), this location on the moon receives neither irradiation from the star nor from the planet (see lower right panel in Fig. 5). Shadings correspond to the same irradiation patterns as in Fig. 1.
FIG. 7.
FIG. 7.
Illumination of our prototype exomoon (in W/m2) averaged over the orbit of the planet-moon duet around their host star. Major panels present four different orbital inclinations: i=0° (upper left), i=22.5° (upper right), i=45° (lower left), and i=90° (lower right). The two bars beside each major panel indicate averaged flux for the northern summer (ns) and southern summer (ss) on the moon. Contours of constant irradiation are symmetric about the equator; some values are given. Color images available online at www.liebertonline.com/ast
FIG. 8.
FIG. 8.
Contours of summed absorbed stellar irradiation and tidal heating (in logarithmic units of W/m2) as a function of semimajor axis aps and eccentricity eps on an Earth-like (upper row) and a Super-Ganymede (lower row) exomoon. In the left panels, the satellite orbits a Jupiter-like planet, in the right panels a Neptune-mass planet, in both cases at 1 AU from a Sun-like host star. In the white area at the right, tidal heating is negligible and absorbed stellar flux is 239 W/m2. The right-most contours in each panel indicate Io's tidal heat flux of 2 W/m2, a tidal heating of 10 W/m2, and the critical flux for the runaway greenhouse (295 W/m2 for the Earth-like moon and 243 W/m2 for the Super-Ganymede). Positions of some massive satellites in the Solar System are shown for comparison. Color images available online at www.liebertonline.com/ast
FIG. 9.
FIG. 9.
Evolution of the orbital eccentricity (upper row) and the moon's tidal heating (lower row) following the two-body tidal models of Leconte et al. (2010) (a “constant-time-lag” model, solid line) and Ferraz-Mello et al. (2008) (a “constant-phase-lag” model, dashed line). Initially, an Earth-sized moon is set in an eccentric orbit (eps=0.1) around a Jupiter-mass planet at the distance in which Europa orbits Jupiter. In the left panels evolution is backward, in the right panel into the future. Both tidal models predict that free eccentricities are eroded and tidal heating ceases after <10 Myr.
FIG. 10.
FIG. 10.
Innermost orbits to prevent a runaway greenhouse, i.e., the “habitable edges” of an Earth-like (gray lines) and a Super-Ganymede (black lines) exomoon. Their host planet is at 1 AU from a Sun-like star. Flux contours for four eccentricities of the moons' orbits from eps=10−4 to eps=10−1 are indicated. The larger eps, the stronger tidal heating and the more distant from the planet will the critical flux be reached.
FIG. 11.
FIG. 11.
Orbit-averaged flux (in units of W/m2) at the top of an Earth-sized exomoon's atmosphere around Kepler-22b for eight different orbital configurations. Computations include irradiation from the star and the planet as well as tidal heating. The color bar refers only to the lower two rows with moderate flux. Color images available online at www.liebertonline.com/ast
FIG. 12.
FIG. 12.
Orbit-averaged flux (in units of W/m2) at the top of an Earth-sized exomoon's atmosphere around KOI211.01 for eight different orbital configurations. Computations include irradiation from the star and the planet as well as tidal heating. The color bar refers only to the first and the lower two rows with moderate flux. Color images available online at www.liebertonline.com/ast
FIG. 13.
FIG. 13.
Habitable edges for an Earth-like (upper row) and a Super-Ganymede (lower row) exomoon in orbit around Kepler-22b (left column) and KOI211.01 (right column). Masses of both host planets are not well constrained; thus abscissae run over several decades (in units of M⊕ for Kepler-22b and MJ for KOI211.01). We consider two albedos αs=0.3 (gray solid lines) and αs=0.4 (black solid lines) and three eccentricities (eps=0.001, 0.01, 0.1) for both moons. No gray solid lines are in the right column because both prototype moons would not be habitable with αs=0.3 around KOI211.01. TTVs (in units of seconds) for coplanar orbits are plotted with dashed lines.
FIG. A1.
FIG. A1.
Geometry of the triple system of a star, a planet, and a moon. In the left panel the planet-moon duet has advanced by an angle ν [Formula: see text] around the star, and the moon has progressed by an angle 2πϕps. The right panel shows a zoom-in to the planet-moon binary. As in the left panel, time has proceeded, and a projection of [Formula: see text] at time t=0 has been included to explain the orientation of the moon's orbit, which is inclined by an angle i and rotated against the star-moon periapses by an angle η.
FIG. B1.
FIG. B1.
Geometry of the planetary illumination. The subsatellite point on the planetary surface is at (φ,ϑ). The angular distance l of the moon from the substellar point (ν [Formula: see text] , 0) determines the amount of light received by the moon from the two different hemispheres.
FIG. C1.
FIG. C1.
Orbits of an exomoon and an exoplanet around their common host star as computed with our exomoon.py software. Color images available online at www.liebertonline.com/ast
See this image and copyright information in PMC

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