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Planetary Illumination, and Its effect on Climate Models of Earth-like Exomoons
Duncan Forgan1,2 , Vergil Yotov1
1 2

SUPA, Institute for Astronomy, University of Edinburgh UK Centre for Astrobiology, School of Physics and Astronomy, University of Edinburgh

MNRAS (2014), submitted Summary
Compared to an Earth-like planet, there are several extra sources and sinks of energy available to an Earth-like exomoon, including:
Tidal Heating Planetary Illumination (thermal flux and reflected starlight) Eclipses of the star by the planet (acts as a sink)

Circumstellar HZ - Zero Moon Eccentricity
This Figure shows the result of many LEBM simulations run with moon eccentricity set to zero, and moon semi major axis set to 0.1, 0.15 and 0.2 Hill Radii (top, middle, bottom rows). In the left column, red points show moons classified too hot to be habitable; blue points show cold moons; green points show moons that are habitable over a large fraction of the surface. White points show moons that are habitable, but the fraction of habitable surface fluctuates. The right column shows the effect of adding planetary illumination. Points plotted show where the classification changes. As the moon's eccentricity is zero, tidal heating is inactive. Planetary illumination pushes the EHZ outwards by in planetary semimajor axis by 0.01 AU.

There have been many studies applying analytical calculations as to how these factors affect the potential habitability of moons, and the morphology of the exomoon habitable zone (EHZ). We present the first attempts to numerically simulate the climate of an exomoon under all of the above sources and sinks of energy. We map out the EHZ in four dimensions, and discover that the "inner circumplanetary edge" has a corresponding outer edge, due to eclipses. However, this also shows the EHZ to be of even higher dimension.

Planetary Eccentricity

Planetary Semi Major Axis

The Model
We expand on our previous 1D latitudinal energy balance models (LEBMs) which evolves the latitudinal temperature Subhead Body Text bution on an Earth-like moon orbiting a Jupiter-like distri planet, which in turn orbits a Sunlike star (Forgan and Kipping 2013). The LEBM solves a 1D diffusion equation:

Circumstellar HZ - Small Moon Eccentricity
This Figure is the same as the above, but with the moon's eccentricity now fixed at 0.05. This allows a moderate amount of tidal heating to come into play. At low moon semimajor axis, tidal heating dominates the local energy budget, pushing the inner HZ boundary outwards by 0.1 AU in planetary semimajor axis. The outer HZ boundary remains location, but the curvature of the reduced, making it closer to a ve boundary at low values of planet at a similar boundary is rtical eccentricity.

Subhead
Body Text

The heat capacity, diffusion constant, cooling and albedo are defined using functions developed for Earth-like planets (Williams and Kasting 1997, Spiegel et al 2008). To make this equation suitable for exomoons, we must: i) Add a tidal heating term (Scharf 2006)

At large moon semimajor axis, tidal heating is no longer dominant, and the EHZ looks similar to those calculated above. Planetary illumination exerts less influence on the inner HZ boundary, but it can alter the outer HZ boundary.

Planetary Eccentricity

Planetary Semi Major Axis

Circumplanetary Habitable Zones + Edges
We now fix the planet's orbit, and study the EHZ as a function of the moon's orbit. The three rows correspond to planetary semimajor axes of 0.75, 0.99 and 1 AU. Most analytical calculations report circumplanetary habitability to have only one inner edge, with the outer edge being determined by orbital stability (cf Heller 2012, Heller and Barnes 2013). We find that this is true in two out of three cases. At a planetary semimajor axis of 1 AU, the repeated eclipses produce an effective energy sink that creates an outer habitable edge. However, we are using a perfectly coplanar setup, maximising eclipse rates. This shows the exomoon habitable zone to be a manifold of even higher dimension. Further parameter studies (including moon inclination and planetary mass) are required.

ii) Add planetary insolation (Heller & Barnes 2013)

iii) Allow eclipses to reduce stellar insolation to zero We investigate the EHZ in terms of both the planet and the moon's orbital parameters.

References
Forgan D. & Kipping D. (2013), MNRAS, 432, 2994 Heller R. (2012), A&A, 545, L8 Heller R. & Barnes R. (2013), Astrobiology, 13, 18 Scharf C.A. (2006), ApJ, 648, 1196 Spiegel D.S., et al (2008), ApJ, 681, 1609 Williams and Kasting (1997), Icarus, 129, 254

Moon Eccentricity

Moon Semi Major Axis