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MNRAS 000,1–14 (2018) Preprint 19 June 2018 Compiled using MNRAS L
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Exploring exomoon atmospheres with an idealized general
circulation model
Jacob Haqq-Misra1?and Ren´e Heller2
1Blue Marble Space Institute of Science, 1001 4th Ave Suite 3201, Seattle, WA 98154, USA
2Max Planck Institute for Solar System Research, Justus-von-Liebig-Weg 3, 37077 G¨
ottingen, Germany
Accepted for publication by MNRAS on 18 June 2018
ABSTRACT
Recent studies have shown that large exomoons can form in the accretion disks around
super-Jovian extrasolar planets. These planets are abundant at about 1 AU from Sun-
like stars, which makes their putative moons interesting for studies of habitability.
Technological advances could soon make an exomoon discovery with Kepler or the
upcoming CHEOPS and PLATO space missions possible. Exomoon climates might
be substantially different from exoplanet climates because the day-night cycles on
moons are determined by the moon’s synchronous rotation with its host planet. More-
over, planetary illumination at the top of the moon’s atmosphere and tidal heating at
the moon’s surface can be substantial, which can affect the redistribution of energy
on exomoons. Using an idealized general circulation model with simplified hydrologic,
radiative, and convective processes, we calculate surface temperature, wind speed,
mean meridional circulation, and energy transport on a 2.5 Mars-mass moon orbit-
ing a 10-Jupiter-mass at 1 AU from a Sun-like star. The strong thermal irradiation
from a young giant planet causes the satellite’s polar regions to warm, which remains
consistent with the dynamically-driven polar amplification seen in Earth models that
lack ice-albedo feedback. Thermal irradiation from young, luminous giant planets onto
water-rich exomoons can be strong enough to induce water loss on a planet, which
could lead to a runaway greenhouse. Moons that are in synchronous rotation with
their host planet and do not experience a runaway greenhouse could experience sub-
stantial polar melting induced by the polar amplification of planetary illumination and
geothermal heating from tidal effects.
Key words: planets and satellites: terrestrial planets – planets and satellites: atmo-
spheres – hydrodynamics – astrobiology
1 INTRODUCTION
Low-mass stars are conventionally thought to exhibit the
most promising odds for the detection of terrestrial plan-
ets, at least from an observational point of view. Their
low masses enable detections of low-mass companions like
Earth-mass planets using radial velocity measurements, and
their small radii allow findings of small transiting objects
in photometric time series. The recent detections of sub-
Earth-sized planets around the M dwarf stars TRAPPIST-1
(Gillon et al. 2016;Gillon et al. 2017), Proxima Centauri
(Anglada-Escud´e et al. 2016), and LHS 1140 (Dittmann
et al. 2017) serve as impressive benchmark discoveries.
Even cooler dwarfs exist. Brown dwarfs (BDs), with
masses between about 13 and 75 Jupiter masses (MJ) cannot
fuse hydrogen, but their eternal shrinking nevertheless con-
?E-mail: jacob@bmsis.org
verts significant amounts of gravitational energy into heat
for billions of years. From the perspective of BD formation,
one can expect that satellites of BDs should commonly form
in the dusty, gaseous disks around accreting BDs (Payne
& Lodato 2007). At the transitional mass regime to giant
planets, models of moon formation have shown that Mars-
sized moons should commonly form around the most massive
super-Jovian gas giant planets (Heller & Pudritz 2015b,a).
Photometric accuracies of 10−2have now been achieved on
BDs using the Hubble Space Telescope (Zhou et al. 2016),
and an improvement of about one order of magnitude should
allow the detection of moons transiting luminous giant plan-
ets that can be directly imaged around their host star (Cabr-
era & Schneider 2007;Heller & Albrecht 2014;Heller 2016).
The search for exomoons has recently become an active
area of research that several groups are now competing in,
mostly using space-based stellar photometry of exoplanet-
exomoons transits (Kipping et al. 2012;Szab´o et al. 2013;
©2018 The Authors
arXiv:1806.06822v1 [astro-ph.EP] 18 Jun 2018
2Haqq-Misra and Heller
Simon et al. 2015;Hippke 2015) but also using alterna-
tives such as radio emission from giant planets with mag-
netic fields that are perturbed by moons (Luki´c 2017) or
space-based coronographic methods such as spectroastrom-
etry (Agol et al. 2015). With the first tentative detection
of exomoons or exorings recently claimed in the literature
(Mamajek et al. 2012;Bennett et al. 2014;Udalski et al.
2015;Aizawa et al. 2017;Hill et al. 2017;Teachey et al.
2018;Rodenbeck et al. 2018), a first unambiguous discovery
could thus be imminent. Observational biases as well as dy-
namical constraints will preferentially reveal large, massive
moons beyond 0.1 AU around their star (Szab´o et al. 2006;
Heller 2014), similar to the moon system that we investigate
in this study.
The first step in estimating the climate conditions on a
moon is in the identification of the relevant energy sources.
Different from planets, moons receive stellar reflected light
from their planetary host (Heller & Barnes 2013) as well as
the planet’s own thermal emission (Heller & Barnes 2015).
In particular, a super-Jovian planet’s own luminosity can
desiccate its initially water-rich moons over several 100 Myr
and make it ultimately uninhabitable. But exomoons around
giant planets can also be subject to significant tidal heating
(Reynolds et al. 1987;Scharf 2006;Cassidy et al. 2009;Heller
& Barnes 2013); see Io around Jupiter for a prominent ex-
ample in the solar system (Peale et al. 1979).
For moons around giant planets in the stellar habit-
able zone (HZ), the reflected plus thermal planetary light
onto the moon is a significant source of energy (&10 W m−2)
if the moon is closer than about 10 Jupiter radii (Rjup ) to
its host planet. Global top-of-atmosphere flux maps showed
that eclipses1can decrease the average energy flux on the
moon’s subplanetary point by tens of W m−2relative to the
moon’s antiplanetary hemisphere (Heller & Barnes 2013).
Eclipses can cause a maximum decrease of the globally av-
eraged stellar flux of ≈6.4 % at most (Heller 2012).
In analogy to the stellar HZ, Heller & Barnes (2013)
defined a circumplanetary “habitable edge” (HE) that is a
critical distance to the planet interior to which a moon with
an Earth-like atmosphere (mostly N2, small amounts CO2,
see Kasting et al. 1993) and a substantial water reservoir
experiences a runaway greenhouse effect and is therefore at
least temporarily uninhabitable. In top-of-atmosphere en-
ergy flux calculations, moons orbiting planets in the stel-
lar HZ encounter an inner HE but no outer HE. Only be-
yond the stellar HZ does an outer HE appear around the
planet (Reynolds et al. 1987;Heller & Armstrong 2014).
One-dimensional latitudinal energy balance models suggest
that moons near the outer edge of the stellar HZ can face an
outer HE owing to eclipses and an ice-albedo effect if they
orbit their star near the outer edge of the HZ (Forgan &
Yotov 2014;Forgan & Dobos 2016).
Hinkel & Kane (2013) used the Heller & Barnes (2013)
model to study the effect of global energy flux variations
for hypothetical exomoons orbiting four confirmed giant ex-
oplanets in or near the stellar HZ (µAra b, HD 28185 b,
BD+14 4559 b, and HD 73534). Their focus was on the or-
bital eccentricity of the planet-moon barycenter around the
1With an eclipse we here refer to a moon moving through the
stellar shadow cast by the planet.
star with the result that fluctuations of tens of W m−2can
occur on moons orbiting on highly eccentric stellar orbits.
Significant improvements in exomoon climate simula-
tions were presented by Forgan & Kipping (2013), who
used a 1D latitudinal energy balance model to assess exo-
moon surface temperatures under the effect of tidal heat-
ing and eclipses. Forgan & Yotov (2014) advanced this
model by also including planetary illumination, and For-
gan & Dobos (2016) showed yet another update including a
global carbonate-silicate cycle and a viscoelastic tidal heat-
ing model. In any of the previous studies that estimated
surface temperatures on exomoons (Hinkel & Kane 2013;
Forgan & Kipping 2013;Forgan & Yotov 2014;Forgan & Do-
bos 2016), maximum and minimum surface temperatures on
exomoons varied by several degrees Kelvin (K) over the cir-
cumplanetary orbit at most, while variations due to a moon’s
changing stellar distance on its circumplanetary orbit or due
to eclipses were a mere ≈0.1K.
General circulation models (GCMs) have been ap-
plied to model the effects of eclipses on the atmosphere
and surface conditions on Titan, which shows up to 6hr
long eclipses during ≈20 consecutive orbits around Saturn
around equinox. Tokano (2016) showed that eclipse-induced
cooling of Titan’s surface, averaged over one orbit around
Saturn, is usually <1K on the pro-Saturnian hemisphere.
Here we present the first simulations of exomoon cli-
mates using an idealized GCM (Haqq-Misra & Kopparapu
2015). This GCM improves upon previous 1D studies by
allowing us to calculate the energy transfer not only as a
function of latitude but also of longitude and height in the
exomoon atmosphere. Our main objective is to determine
whether exomoon climates are principally different from ex-
oplanet climates, that is: how do planetary illumination and
tidal heating contribute to surface habitability in an exo-
moon atmosphere? And ultimately, could these climatic ef-
fects of the different heat sources possibly be observed with
near-future technology?
2 METHODS
2.1 Choice of the simulated systems
Most of the major moons in the solar system are in syn-
chronous rotation with their host planet; that is, one and
the same hemisphere faces the planet permanently (except
maybe for libration effects). The star, however, does not a
have fixed position in the reference frame of such a moon, as
the satellite rotates with its circumplanetary orbital period
(Pps). Hence, while stellar illumination can be averaged over
the day and night side of the moon (longitudinally but not
latitudinally), the planet will always shine on the moon’s
subplanetary point. This is a principal difference between
the illumination effects experienced by a planet and a moon.
Furthermore, there will be planet-moon eclipses. But
they will only be relevant to the global climate if the moon
is in a very close orbit that is nearly coplanar with the cir-
cumstellar orbit. Beyond Io’s orbit around Jupiter, the orbit-
averaged flux decrease will be a few percent at most, and be-
yond ten planetary radii around a Jovian planet eclipses will
be completely negligible (Heller 2012). We therefore neglect
planet-moon eclipses in our simulations.
MNRAS 000,1–14 (2018)
Exploring exomoon atmospheres with a GCM 3
As an additional heat source, we consider geothermal
energy, which can be produced via tidal heating, radiogenic
decays in the rocky part of the moon, or through release of
primordial heat from the moon’s accretion. We do not sim-
ulate the production of these heat sources in our model, but
use interesting and reasonable fiducial values in our GCM
simulations.
The moon’s mass is chosen as 0.25 Earth masses (M⊕),
which we consider as an optimal value in terms of exomoon
formation around accreting giant planets (Canup & Ward
2006;Heller et al. 2014;Heller & Pudritz 2015b), exomoon
detectability (Kipping et al. 2009;Lewis 2011;Heller 2014;
Heller & Albrecht 2014;Kipping et al. 2015), and exomoon
habitability (Lammer et al. 2014).2As these moons should
be water-rich, their radii should be about 0.7 Earth radii
(R⊕).
We consider two moon orbits, one as wide as Europa’s
orbit around Jupiter (10 RJup) and one twice that value. The
former choice is supported by simulations of moon formation
around Jupiter-mass planets, which suggest that icy moons
can migrate to ∼10 RJup within the circumplanetary disks
(Sasaki et al. 2010;Ogihara & Ida 2012). The latter choice
is motivated by the recent prediction that the most massive,
water-rich moons around super-Jovian planets beyond 1AU
should form near the circumplanetary ice line at about 20
to 30 RJup (Heller & Pudritz 2015b,a). The orbital periods
related to these two semi-major axes of the satellite orbit
(aps) are 1.175 and 3.324 d. We refer to these orbits as our
“short-period” and “long-period” cases, respectively. In all
cases, the moon’s spin-orbit misalignment with respect to its
circumplanetary orbit is assumed to be zero and variations of
planetary illumination due to the moon being on an eccentric
orbit are neglected.
As for the geothermal heat budget of the satellite (Fg),
we consider three cases of 0,10, and 100 W m−2. In those
cases where tidal heating is a major contribution, the high-
est values will only be reached in very close-in orbits within
.10 RJup around our test planet. If the moon under con-
sideration is the only major satellite, tidal processes will
usually act to circularize its orbit (Goldreich 1963), to erode
its obliquity (Heller et al. 2011), and to lock its rotation
rate with the orbital mean motion (Makarov et al. 2016).
These processes generate tidal heating in the moon, which
will gradually decay over time. Tidal surface heating rates
on moons could be >100 W m−2for about 106yr for a single
moon on an initially eccentric orbit Heller & Barnes (2013).
In this sense, the physical conditions that we model could
preferably correspond to young systems rather than evolved
systems. The system age, however, is not an input parame-
ter in our models and our results are not restricted to young
systems to begin with. In fact, large extrasolar moons have
not been detected unambiguously so far, and so it remains
unclear whether they are only subject to significant tidal
heating when they are young. If the moon is member of a
multi-satellite system, for example, then mutual interaction
and resonances could maintain significant orbital eccentrici-
2However, Awiphan & Kerins (2013) showed that photometric
red noise from stellar variability might make it difficult to detect
even Earth-mass moons in the HZ around low-mass stars with
Kepler.
ties and extend this timescale by orders of magnitude (Heller
et al. 2014;Zollinger et al. 2017).
As for the planetary illumination absorbed by the moon,
planet evolution tracks show that the luminosities of young
super-Jovian planets 10 times the mass of Jupiter can be
as high as 10−5to 10−3solar luminosities (L), depending
on the planet’s core mass, amongst others (Mordasini 2013).
Even at the lower end of this range, a moon in a Europa-
wide orbit at about 10 RJup would absorb about 500 W m−2
(maybe for some ten Myr), thereby easily triggering a run-
away greenhouse effect on the moon.3Hence, we consider
four cases of planetary illumination onto the satellite’s sub-
planetary point, namely, 0,10,100, and 500 W m−2(the lat-
ter one only in the short-period moon orbit). All these cases
are summarized in Table 1.
2.2 Climate model
We use an atmospheric GCM to simulate the climate of an
Earth-like moon in orbit around a super-Jovian planet. This
GCM was developed by the Geophysical Fluid Dynamics
Laboratory (GFDL), based upon their ‘Flexible Modeling
System’ (FMS), with idealized physical components (Frier-
son et al. 2006,2007a;Haqq-Misra et al. 2011;Haqq-Misra
& Kopparapu 2015). The dynamical core uses a spectral de-
composition method with T42 resolution to solve the Navier-
Stokes (or ‘primitive’) equations of motion. We use a shal-
low penetrative adjustment scheme to perform convective
adjustment in the model (Frierson et al. 2007a), which pro-
vides a computationally efficient method for restoring verti-
cal balance in lieu of a more explicit representation of con-
vective processes. The GCM surface is bounded with a diffu-
sive boundary layer scheme and a 50 m thick thermodynamic
ocean layer with a fixed heat capacity. This is analogous to
assuming that the moons are fully covered with a static, uni-
form ocean4; hence, topography is neglected. Our assump-
tion of aquamoon conditions with no topography or ice also
means that we neglect ice-albedo feedback. These simplifi-
cations allow for computational efficiency, and they allow us
to examine fundamental changes in climate structure with-
out any positive feedback processes causing the model to
become numerically unstable.
The GCM includes two-stream gray radiative transfer,
which uses a gray-gas radiative absorber with a specified
vertical profile to mimic a greenhouse effect (Frierson et al.
2006). The model atmosphere is transparent to incoming
stellar (i.e., shortwave) radiation, so that incoming starlight
penetrates the atmosphere and warms the surface (with a
fixed surface albedo of 0.31 for shortwave radiation). Stellar
radiation is averaged across the surface (so there is no diur-
nal cycle). Infrared (i.e., longwave) radiation is absorbed by
3This case is particularly interesting in view of the possible detec-
tion of moons around young, self-luminous giant planets via direct
imaging with the European Extremely Large Telescope (Heller &
Albrecht 2014).
4This is motivated by our assumption that our test moons
formed in the icy parts of the accretion disks around their giant
host planets at several AU from their Sun-like star. The initial
H2O ice content of the moons would then have liquefied as the
planets and moons migrated to about 1 AU, where ∼100 super-
Jovian exoplanets are known today.
MNRAS 000,1–14 (2018)
4Haqq-Misra and Heller
Table 1. Simulated exomoon systems: initialization parameters and global average quantities
Initialization parameters Average quantities
Case aps Pps FgFtTsurf ∆Tpole FOLR qstrat
1a20 RJup 3.324 d0 W m−20 W m−2289.5 K 0.0 K 236.4 W m−27.6×10−6
220 RJup 3.324 d0 W m−210 W m−2290.0 K 0.7 K 239.4 W m−27.6×10−6
320 RJup 3.324 d10 W m−20 W m−2291.7 K 4.0 K 246.0 W m−28.3×10−6
420 RJup 3.324 d10 W m−210 W m−2292.2 K 5.0 K 249.0 W m−28.1×10−6
520 RJup 3.324 d10 W m−2100 W m−2295.9 K 11.9 K 276.3 W m−23.9×10−5
6b10 RJup 1.175 d0 W m−20 W m−2287.9 K 0.0 K 234.9 W m−21.4×10−5
710 RJup 1.175 d0 W m−210 W m−2288.4 K 0.6 K 237.9 W m−21.7×10−5
810 RJup 1.175 d10 W m−20 W m−2290.0 K 3.8 K 244.4 W m−22.0×10−5
910 RJup 1.175 d10 W m−210 W m−2290.5 K 4.5 K 247.5 W m−22.3×10−5
10 10 RJup 1.175 d10 W m−2100 W m−2294.9 K 13.8 K 275.5 W m−26.8×10−5
11 10 RJup 1.175 d10 W m−2500 W m−2310.0 K 45.5 K 398.3 W m−23.3×10−3
12 10 RJup 1.175 d100 W m−2500 W m−2321.9 K 60.8 K 482.2 W m−21.4×10−2
Notes. In all cases the planet-moon binary orbits at 1 AU from a Sun-like star, Mp=10 MJup,Ms=0.25 M⊕, and Rs=0.7M⊕. The
parameter Fgis uniform geothermal heating at all latitudes. The parameter Ftis absorbed planetary illumination, with a latitudinal
distribution of Ft|cos λ|when 90◦< λ < 270◦and zero otherwise. Mean values from the set of simulations are shown for global surface
temperature Tsurf, change in polar surface temperature ∆Tpole, global outgoing longwave radiative flux at the top of the atmosphere FOLR,
and global specific humidity at the 50 hPa level qstrat.
(a,b)We also refer to 1 and 4 as our “slow rotator control” and “rapid rotator control” cases, respectively.
the gray-gas atmosphere in proportion to the optical depth
at each model layer, with the surface values of optical depth
tuned to reproduce an Earth-like value when the GCM is
configured with Earth-like parameters. Furthermore, water
vapor is decoupled from the gray radiative transfer scheme,
so that water vapor feedback is neglected. The GCM is also
cloud-free, although we remove excess moisture and energy
from the atmosphere through large-scale condensation to the
surface.
Even with these idealized assumptions, this GCM re-
mains capable of representing surface and tropospheric tem-
perature profiles, as well as the large-scale circulation fea-
tures, of Earth today (Frierson et al. 2006,2007a;Haqq-
Misra et al. 2011). The model maintains symmetry about
the equator due to the lack of a seasonal cycle, which can be
interpreted as a mean annual climate state. The model was
originally developed to explore the role of moisture on tropo-
spheric static stability (Frierson et al. 2006) and the trans-
port of static energy in moist climates (Frierson et al. 2007a).
We also note that this model has been used to demonstrate
that a realistic tropospheric profile can be maintained by
eddy fluxes alone, even in the absence of stratospheric ozone
warming (Haqq-Misra et al. 2011). Even so, our application
of this model to exomoons implies that our results should
be interpreted qualitatively, as a conservative estimate with
regard to surface temperature values, runaway greenhouse
thresholds, and large-scale dynamics.
The use of a gray-gas absorber allows us to avoid the
problem of choosing a specific atmospheric composition, as
any particular choice of greenhouse gases (such as carbon
dioxide or methane) will yield a unique GCM solution. Al-
though many GCM studies of exoplanet atmospheres use
band-dependent (e.g., non-gray) radiation with cloud pa-
rameterizations (Yang et al. 2014;Kopparapu et al. 2016;
Wolf et al. 2017;Leconte et al. 2013b;Popp et al. 2016;
Godolt et al. 2015;Haqq-Misra et al. 2018), such an ap-
proach introduces a new set of free parameters for deter-
mining the appropriate mix of greenhouse and inert gases.
We instead choose to use an idealized gray-gas GCM for
our study of exomoon habitability, as others have done for
qualitatively exploring the runaway greenhouse threshold
(Ishiwatari et al. 2002). Likewise, the assumption that wa-
ter vapor is radiatively neutral allows our model to remain
stable at high stellar flux levels without initiating a run-
away greenhouse state; thus, our assumption of a cloud-free
atmosphere and a simplified convection scheme limits the
use of our GCM for quantitatively determining the runaway
greenhouse threshold. For example, clouds beneath the sub-
planetary point could help to delay the onset of a runway
greenhouse (Yang et al. 2014), although rapid rotation may
weaken this effect (Kopparapu et al. 2016). We emphasize
that our radiation limits, particular for identifying a run-
away greenhouse, should be interpreted in a qualitative sense
in order to guide more sophisticated investigations with less-
idealized GCMs.
We fix the moon into synchronous rotation with its
planet so that the subplanetary point is centered at the
moon’s equator, and we set the moon to have a circular orbit
and an obliquity of zero. We include an additional source of
infrared heating at the top of the atmosphere, centered on
the subplanetary point, which we use to represent heating
by the super-Jovian planet in our simulations. Specifically,
we set the downward infrared flux at the top of the atmo-
sphere equal to Ft|cos λ|when 90◦< λ < 270◦, and zero
otherwise (where λis longitude). Because the atmosphere is
absorbing to infared radiation (both in upward and down-
ward directions), this planetary infrared flux is absorbed by
the uppermost atmospheric layers, with none of this infrared
radiation penetrating through to the surface in any of our
simulations. This upper atmosphere absorption of infrared
radiation from the host planet is the primary feature that
distinguishes an exomoon climate from an Earth-like exo-
planet climate.
We also add geothermal heating uniformly at the bot-
MNRAS 000,1–14 (2018)
Exploring exomoon atmospheres with a GCM 5
tom of the atmosphere, as a representation of tidal heat-
ing. The infrared flux from the surface follows the Stefan-
Boltzman law, with the geothermal heating term, Fg, added
as a secondary source of surface warming. Geothermal heat-
ing due to tidal heating may also appear on synchronously
rotating exoplanets (Haqq-Misra & Kopparapu 2015), par-
ticularly those with highly eccentric orbits. Geothermal
heating can contribute to habitability by increasing surface
temperature, while it can also alter atmospheric circulation
patterns by driving stronger poleward transport. Geother-
mal heating provides a secondary mechanisms that may con-
tribut to climatic features on exomoons.
Each case in Table 1was initialized from a state of rest
and run for a period of 3,000 d in total. The first 1,000 d
were discarded, and the average of the subsequent 2,000 d of
runtime were used to analyze our cases. The model reaches a
statistically steady state within about 500 d of initialization,
which takes approximately 4 h to complete using a Linux
workstation (6 cores at 2.0 GHz). In our presentation of re-
sults, we refer to our cases with a 1.175 d rotation rate as
‘short-peroid’ and our cases with a 3.324 d rotation rate as
‘long-period.’ We also refer to our two cases with geother-
mal heating and absorbed planetary illumination set to zero
as our ‘control’ cases. Our set of twelve cases provide an
overview of the dependence of an exomoon’s climate on the
properties of its host planet.
3 RESULTS
For all of our control and experimental cases, we calculate
global average values of surface temperature, outgoing long-
wave flux at the top of the atmosphere, and stratospheric
specific humidity (Table 1). Our control cases (1 and 6) both
show global average surface temperatures similar to that of
Earth today. Our experimental cases (2-5 and 7-12) show an
increase in temperature as geothermal and planetary fluxes
increase, with a corresponding increase in stratospheric wa-
ter vapor and outgoing infrared radiation.
3.1 Surface habitability
Surface temperature and winds are shown for the two con-
trol cases in Figure 1, with the slow rotator on the top
row, the rapid rotator on the middle row, and the differ-
ence between the two on the bottom row. The change in
rotation rate from the slow to rapid rotator results in an
increase in the strength of the easterly equatorial jet, which
also corresponds to an increase in the equator-to-pole tem-
perature contrast. This expected behavior corroborates the
classic results of Williams & Halloway (1982), who find that
even slower rotation rates will result in a global meridional
circulation cell that spans the entire hemisphere. Lacking
geothermal or planetary heating, these control cases repre-
sent Earth-like climate states for a smaller planet at different
rotation rates.
The addition of infrared planetary illumination to the
top of the atmosphere and geothermal heating to the sur-
face can lead to departures from an Earth-like climate state.
Figure 2shows surface temperature and winds for the rapid
rotator experiments with increasing contributions of infrared
heating. The top row shows cases with modest geothermal
Figure 1. Time average of surface temperature deviation from
the freezing point of water (shading) and horizontal wind (vec-
tors) for the P=3.324 d (top panel) and P=1.175 d (middle
panel) control cases. The bottom row shows the difference of the
first row minus the second. The subplanetary point falls on the
center of each panel. The lengths of the vectors are proportional
to the local wind speeds, and a reference vector with a length of
5 m s−1is shown on the last panel. (The color scale is chosen to
match the maximum temperature range shown in Figures 2and
3to ease comparison.)
and planetary heating, which leads to both warming of the
poles and destabilization of the easterly equatorial jet. As
additional heating is applied, shown in the bottom rows of
Figure 2, the predominantly zonal flow of winds becomes
disturbed in favor of a pattern dominated by large-scale vor-
tices. Figure 2also includes dark contours showing the ‘ani-
mal habitable zone’ limits of 0 and 50 degrees Celsius, which
represents the temperature range where complex animal life
could survive (Ward & Brownlee 2000;Edson et al. 2012).
The two cases in the top row of Figure 2both show that
the freezing line of 0 degrees Celsius sits near the boundary
between midlatitude and polar regions, around 60 degrees
latitude, so that the planet’s habitable real estate is con-
fined to the midlatitude and equatorial regions. The bottom
left panel of Figure 2shows a case where the entire sur-
face is within the animal habitability limits, as a result from
strong thermal heating from the host planet. The most ex-
treme case, shown in the bottom right panel of Figure 2, has
the 50 degree Celsius contour at about 30 degrees latitude,
MNRAS 000,1–14 (2018)
6Haqq-Misra and Heller
Figure 2. Time average of surface temperature deviation from the freezing point of water (shading) and horizontal surface wind (vectors)
for the P=1.175 d experiments. The geothermal (Fg) and top-of-the atmosphere heat flux from the planet (Ft) are shown on top of each
panel. Dark coutours indicate the ‘animal habitability’ temperature bounds of 0 and 50 degrees Celsius where complex life could survive.
The lengths of the vectors are proportional to the local wind speeds, and a reference vector with a length of 5 m s−1is shown on the last
panel.
with regions closer to the equator being too warm to support
complex life.
Our set of GCM cases also illustrate the propensity for
an exomoon atmosphere to enter a runaway greenhouse as
a result of strong thermal heating aloft. As we discussed
above, our idealized GCM neglects water vapor feedback and
relies upon gray-gas radiative transfer, so our consideration
of greenhouse states should be interpreted as a qualitative
and conservative estimate. Further GCM development with
band-dependent radiative transfer, cloud paramterization,
and more realistic convective processes will be required to
identify quantitative thresholds for when we should expect
to observe a runaway greenhouse state on an exomoon. Ad-
ditionally, a dry moon with a desert surface and little stand-
ing water will remain stable past these radiation limits (Abe
et al. 2011;Leconte et al. 2013b), so our moist GCM calcu-
lations also serve as a conservative estimate of the runaway
greenhouse threshold. Given these caveats, it still remains in-
structive to consider how our exomoon simulations compare
with theoretical limits for expecting a runaway greenhouse.
The long-period cases (1-5) show a maximum outgo-
ing infrared flux of 276.3 W m−2, which falls within the sta-
ble radiation limits calculated from one-dimensional (Kast-
ing 1988;Goldblatt & Watson 2012;Ramirez et al. 2014)
and three-dimensional (Leconte et al. 2013a;Wolf & Toon
2014) climate models. By contrast, the short-period cases
(6-12) include experiments with an outgoing infrared flux of
400 W m2or larger (cases 11 and 12), which exceeds stable
radiation limits and indicates the climate should be in a run-
away greenhouse state (Kasting 1988;Goldblatt & Watson
2012;Ramirez et al. 2014;Leconte et al. 2013a). The two
cases (11 and 12) with Ft=500 W m−2are also both within
the runaway greenhouse regime, which suggests that their
surface temperatures, as shown in the bottom row of Fig-
ure 2, would continue to increase in a GCM with raditively-
coupled water vapor.
Water loss can also occur prior to the runaway green-
house, due to the photodissociation of water vapor as the
stratosphere becomes wet, in a process sometimes known as
a ‘moist greenhouse’ (Kasting 1988;Kopparapu et al. 2017).
The moist greenhouse state can be inferred by amount of
water vapor that crosses the tropopause and reaches the
stratosphere, which we indicate using specific humidity (the
ratio of moist to total air), qstrat, near the model top (see
Table 1). Calculations with other models indicate that at-
mospheres enter a moist greenhouse and begin to rapidly lose
water to space when stratospheric specific humidity exceeds
a threshold of qstrat ≈10−3(Kasting 1988;Kopparapu et al.
2013;Wolf & Toon 2014;Kopparapu et al. 2016). As a qual-
itative approach to this problem, our results illustrate that
thermal heating from the host planet, as well as geothermal
heating from tides, are both plausible mechanisms for heat-
ing an exomoon atmosphere to the point of initiating water
loss.
3.2 Polar amplification of warming
We compare our potentially habitable long-peroid and short-
peroid cases with Fg=10 W m−2and Ft=100 W m−2with
the corresponding control cases in Figure 3. These cases are
MNRAS 000,1–14 (2018)
Exploring exomoon atmospheres with a GCM 7
within stable radiation limits and are not at risk of enter-
ing a runaway greenhouse or otherwise losing water to space
due to a wet stratosphere. Both panels in Figure 3show that
warming is concentrated toward the poles, with a more mod-
est degree of warming at the tropics and midlatitudes. This
‘polar amplification’ is a well-known process that occurs in
climate models, particularly in simulations of global warm-
ing, and is an expected consequence of imposing additional
heating on an atmosphere.
Polar amplification is commonly attributed to the
warming that results from ice-albedo feedback in polar re-
gions, which accelerates the loss of ice, thereby reducing
albedo and continuing to accelerate the rate of warming
(Polyakov et al. 2002;Holland & Bitz 2003). However, po-
lar amplification is also present in idealized models that
lack sea ice feedback entirely (Alexeev et al. 2005;Langen
& Alexeev 2007;Alexeev & Jackson 2013), which suggests
that atmospheric heat transport alone can provide an ex-
planatory mechanism. Alexeev et al. (2005) demonstrated
that polar amplification should occur when a GCM is forced
with an additional source of uniform surface warming, which
in principle could be casued by both infrared and visible
sources. Alexeev & Jackson (2013) argued that both ice-
albedo feedback and meridional energy transport contribute
to polar amplification, with the effects of energy transport
being masked when ice-albedo feedback is present.
Our exomoon simulations further illustrate the capabil-
ity of GCMs to show polar amplification in the absence of
ice-albedo feedback. Previous idealized GCMs have shown
polar amplification from uniform thermal heating sources,
and our results demonstrate that similar polar amplifica-
tion can be obtained from the non-uniform thermal heat-
ing of planetary illumination. Polar amplification on ice-free
planets occurs as a response to enhancement of the merid-
ional circulation on a warmer planet (Lu et al. 2007), which
leads to increased poleward transport of energy and mois-
ture (Alexeev et al. 2005).
We calculate the polar amplification, ∆Tpole as the dif-
ference in the mean temperature at the north pole between
each experiment and the corresponding control case. The
values of ∆Tpole are shown in Table 1. A constant uniform
geothermal heating of Fg=10 W m−2with no planetary il-
lumination (cases 3 and 8) yields a polar amplification of
about 4K, with the outgoing longwave radiation also about
10 W m−2greater than the control case. This indicates that
geothermal heating is entirely absorbed and re-radiated by
the lower, thicker layers of the atmosphere. Conversely, a
non-uniform planetary illumination of Ft=10 W m−2with
no geothermal heating (cases 2 and 7) shows a smaller
polar amplification of about 0.6K. Cases 2 and 7 show
an increase in outgoing longwave radiation of only about
3W m−2compared to the control; however, this is expected
because the non-uniform distribution of planetary heating
(Ft|cos λ|when 90◦< λ < 270◦) results in a net warming of
Ft/π≈3.2W m−2.Even so, the total polar amplification of
0.6Kin cases 2 and 7 is nearly seven times less than the po-
lar amplification of 4Kin cases 3 and 8. This indicates that
some planetary illumination is absorbed by the uppermost
layers of the atmosphere, with the remainder of this energy
contributing to surface warming. However, these cases (2
and 7) still demonstrate that polar amplification can occur
from a non-uniform upper-atmospheric heating source. The
experiments with equal geothermal and planetary heating of
Fg=10 W m−2and Ft=10 W m−2(cases 4 and 9) show that
the value of ∆Tpole is equal to the sum of the polar amplifi-
cation when each heating source is considered in isolation.
Likewise, the value of FOLR for case 4 (and 9) equals the
sum of the outgoing longwave radiation terms from cases 2
and 3 (7 and 8). Polar amplification continues to increase
when Ft=100 W m−2and greater (cases 5, 10-12), with cor-
responding increases in FOLR that indicate a further pen-
etration depth for incoming planetary illumination. These
results emphasize that polar amplification in GCMs that
lack ice albedo feedback can still occur with both uniform
surface warming and non-uniform stratospheric warming.
The expansion of the meridional overturining (i.e.,
Hadley) circulation is shown in Fig. 4for the P=3.324 d
experiments. The top row of Fig. 4shows the control case,
while the bottom row shows the experiment with Fg=
10 W m−2and Ft=100 W m−2. The left column of Fig. 4
shows the global average, while the middle and right columns
separate the atmosphere into the hemispheres east and west,
respectively, of the subplanetary point. The purpose of this
decomposition is to show that the atmosphere responds to
a fixed heating source by altering both the direction and
width of the Hadley circulation in each hemisphere rela-
tive. This prediction originates from the shallow water model
of Geisler (1981), which demonstrated that the Hadley cir-
culation should change directions on either side of a fixed
heating source. Although the Hadley circulation appears to
weaken and maintain its width when planetary and geother-
mal heating is applied (left column), the hemispheric decom-
position shows that the Hadley circulation in eastern hemi-
sphere reaches fully to the poles while the western hemi-
sphere shows a Hadley circulation with the opposite direc-
tion. The zonal wind pattern in these atmospheres remains
relatively consistent between the two cases, with prominent
upper-level jets associated with the descending branch of the
global Hadley cell that appear identical in the hemispheric
decomposition.
We also demonstrate this Hadley cell expansion or the
P=1.175 d experiments in Fig. 5, which shows the con-
trol experiment along with three other cases of increas-
ing planetary illumination and geothermal heating. Fig. 5
shows that the global average Hadley circulation tends to
diminish as planetary illumination increases, but the hemi-
spheric decomposition shows that the Hadley circulation is
actually expanding poleward. The two hemispheres show
circulations with opposite direction and approximately the
same strength. Geothermal heating does not significantly
alter the circulation strength, although it does change the
morphology of the ascending branch of the Hadley circula-
tion. Two upper-level midlatitude jets are present when Ft≤
100 W m−2, while a third equatorial jet emerges when Ft=
500 W m−2. Strong geothermal heating of Fg=100 W m−2
tends to sharpen the equatorial jet and raise the altitude of
the midlatitude jets.
We further demonstrate this behavior in our results
by examining the vertically integrated flux of moist static
energy as a function of latitude, following Frierson et al.
(2007b) and Kaspi & Showman (2015). Moist static energy,
m, represents the combination of dry static energy and latent
MNRAS 000,1–14 (2018)
8Haqq-Misra and Heller
Figure 3. Difference from control cases of the time average of surface temperature (shading) and horizontal wind (vectors) for the
P=3.324 d (left panel) and P=1.175 d (right panel) experiments with Fg=10 W m−2and Ft=100 W m−2. The lengths of the vectors are
proportional to the local wind speeds, and a reference vector with a length of 5 m s−1is shown on the last panel.
Figure 4. The mean meridional circulation (line contours) and zonal mean zonal wind (shading) are averaged across the entire planet (first
column), eastern hemisphere (second column), and western hemisphere (third column) from the subplanetary point for the P=3.324 d
experiments with Fg=Ft=0W m−2(top row) and Fg=10 W m−2and Ft=100 W m−2(bottom row). Contours are drawn at an interval of
±{20,100,300} × 109kg s−1. Solid contours indicate positive (northward) circulation, and dashed contours indicate negative (southward)
circulation.
energy as
m=cpT+Φ+Lvq,(1)
where cpis the specific heat capacity of air, Φis geopotential
height, Lvis the enthalpy of vaporization, and qis specific
humidity. We decompose moist static energy minto a sum
of time mean mand eddy m0contributions as m=m+m0.
This allows us to write the meridional moist static energy
flux as
vm=¯v¯m+v0m0,(2)
where vmrepresents meridional mean energy transport and
v0m0represents meridional eddy energy transport. The ver-
tically integrated flux of mis defined as
M=2πacos φ∫ps
0
vm
g
dp,(3)
where ais planetary radius, φis latitude, and the overbar
denotes a zonal and time mean. Equation (3) gives the total
value of Mfrom all dynamical contributions. We can likewise
separate the mean and eddy contributions to Mby replacing
MNRAS 000,1–14 (2018)
Exploring exomoon atmospheres with a GCM 9
Figure 5. The mean meridional circulation (line contours) and zonal mean zonal wind (shading) are averaged across the entire planet (first
column), eastern hemisphere (second column), and western hemisphere (third column) from the subplanetary point for the P=1.175 d
experiments with Fg=Ft=0W m−2(first row), Fg=10 W m−2and Ft=100 W m−2(second row), Fg=10 W m−2and Ft=500 W m−2
(third row), and Fg=100 W m−2and Ft=500 W m−2(last row). Contours are drawn at an interval of ±{20,100,3000} × 109kg s−1. Solid
contours indicate positive (northward) circulation, and dashed contours indicate negative (southward) circulation.
the meridional static energy flux vmin Eq. (3) with ¯v¯mor
v0m0, respectively.
We present the total, mean, and eddy fluxes of Min Fig-
ure 6to show the difference between our control cases and
our experiments with Fg=10 W m−2and Ft=100 W m−2.
Both panels show a poleward increase in Mwhen geother-
mal and planetary heating are added, with all of this con-
tribution due to increases in the mean component of Mat
latitudes φ > 50◦. By contrast, the eddy component of Mde-
creases in the range 30◦< φ < 50◦when heating is induced.
Polar amplification, and an associated increase in moisture,
occurs as a result of intensification of the mean poleward
transport of static and latent energy fluxes from both sur-
face geothermal and top-of-atmosphere planetary heating.
The moist static energy flux also provides an explana-
tion for the equatorial band of warming in our difference
plots shown in Figure 3, particularly in the rapid rotating
MNRAS 000,1–14 (2018)
10 Haqq-Misra and Heller
Figure 6. Vertically integrated moist static energy flux (M) for the P=3.324 d (left panel) and P=1.175d (right panel) experiments.
The total M(black curves), mean contribution to M(green curves), and eddy contribution to M(blue curves) are shown for control
cases with Fg=Ft=0(solid) and experiments with Fg=10 W m−2and Ft=100W m−2(dashed).
case. Figure 6also shows a decrease in Mat tropical latitudes
in the range 0◦< φ < 15◦, which leads to warming and an
accumulation of moisture beneath the subplanetary point.
This point corresponds to a maximum in the rising motion
of the mean meridional circulation (not shown), as a result
of planetary illumination. Although our GCM does not in-
clude cloud processes, convective processes at the subplane-
tary point should lead to cloud formation, which could con-
tribute to an expansion of the inner habitable region around
the host planet (Yang et al. 2014). In general, the circulation
patterns of climates with a fixed source of heating are not
easily characterized by longitudinally-averaged mean merid-
ional circulation functions, due to hemispheric reversals in
the direction of these circulation patterns (Haqq-Misra &
Kopparapu 2015). Nevertheless, we can still expect strong
rising motion beneath the subplanetary point, with both
zonal and meridional transport toward the opposing hemi-
sphere.
3.3 Vertical structure of the atmosphere
The redistribution of energy from planetary illumination
causes warming of both the surface as well as the po-
lar stratosphere. Figure 7shows the vertical structure of
mean zonal temperature for the short-peroid cases with
Fg=Ft=0W m−2(left panel) and Fg=10 W m−2and
Ft=100 W m−2(right panel). The height of the tropopause
is also shown as a dark curve in both panels of Figure 7,
which follows the World Meteorological Organization defini-
tion of the tropopause as the altitude at which the lapse rate
equals −2K km−1. For the control case (left panel), the trop-
ical tropopause extends up to about 100 hPa due to convec-
tive heating by both moist and dry processes (Haqq-Misra
et al. 2011). The height of the extratropical tropopause is
determined by the balance between warming from latent and
sensible heating in the troposphere below with warming in
the stratosphere from the poleward transport of the Brewer-
Dobson circulation (Haqq-Misra et al. 2011).
When planetary and geothermal heating are included
(Figure 7, right panel), the boundaries of the tropical
tropopause sharpen and act to widen the extratropical zone
while narrowing the tropics. Increased warming beneath
the subplanetary point drives stronger convection, which
causes the tropopause to extend higher. This increase in
convective heating also increases the poleward flux of moist
static energy, which causes the extratropical tropopause to
steepen. Warming in the stratosphere occurs primarily in
the polar regions, which is driven by poleward energy trans-
port processes such as the Brewer-Dobson circulation (not
shown). This stratospheric warming competes with tropo-
spheric warming in the tropics, which results in the polar
height of the tropopause remaining relatively constant be-
tween the two cases shown. One interpretation of this be-
havior is that the expanded extratropics are analogous to
an increase in efficiency of the moon’s ‘radiator fins,’ which
provide a means of transporting and dissipating energy from
the warming tropics (Pierrehumbert 1995). Planetary illumi-
nation thus serves to sharpen the distinction between tropi-
cal and extratropical climate zones by redistributing energy
poleward both along the surface and aloft in the strato-
sphere.
The effect of planetary illumination on the atmospheric
structure is also evident from examining vertical tempera-
ture profiles along the equator (Fig. 8, left panel). For all
profiles, the long-period cases show a colder stratosphere
but a warmer troposphere than the short-period cases with
the same planetary and geothermal heating. These differ-
ences correspond to the enhanced meridional transport of
energy and moisture in the long-period cases, which also
drives stronger and narrower jets in the short-period cases
(Williams & Halloway 1982). The effect of planetary illumi-
nation causes a stratospheric temperature inversion, anal-
ogous to the ozone-driven stratospheric inversion on Earth
MNRAS 000,1–14 (2018)
Exploring exomoon atmospheres with a GCM 11
Figure 7. Time average of mean zonal temperature (shading and contours) for the P=1.175 d experiments with Fg=Ft=0W m−2
(left panel) and Fg=10 W m−2and Ft=100 W m−2(right panel). The dark curve shows the height of the tropopause. (The color scale is
chosen to match previous figures, and contours are drawn every 10 ◦C.)
today. The warmest cases with Ft=500 W m−2show a profile
with increasing slope that begins approaching an isothermal
atmosphere from the additional planetary and geothermal
heating.
Some planetary illumination is absorbed in the upper-
most layers of the model atmosphere, while the rest con-
tributes to surface warming. Fig. 8(right panel) shows ver-
tical profiles of the temperature tendency due to radiation
(or radiative heating) along the equator. This reflects the di-
rect change in temperature due to radiation alone, neglect-
ing physical processes such as convection, boundary layer
diffusion, and dynamical heating. The green curves with
Ft=10 W m−2show modest warming in the upper atmo-
sphere of about 0.1K day−1, with strong cooling in the mid-
dle troposphere and surface heating of about 2.8K day−1.
The blue curves show increased upper atmosphere warming
to ∼0.2K day−1with stronger cooling in the middle tropo-
sphere. The blue curves also show a lower radiative heating
rate at the surface, even though these cases show a higher
surface temperature. The decrease in direct surface radiative
heating is accounted for by increased diffusion of the bound-
ary layer, which in turn leads to increased surface warming.
The structure of the boundary layer is also evident from the
left panel of Fig. 8as a change in lapse rate near ∼950 hPa.
The middle troposphere is characterized by strong convec-
tion, which acts to restore the radiative cooling.
The more extreme cases with Ft=500 W m−2also con-
tinue this trend, with radiative cooling of ∼1.2K day−1in-
dicating a transfer of energy to the vertical diffusion of the
atmosphere’s boundary layer—which thereby leads to sur-
face warming. Note also that case 12 shows reduced upper-
atmosphere absorption due to the large geothermal flux of
Fg=100 W m−2along with stronger cooling (and thus con-
vection) in the middle troposphere. The gray-gas radiative
absorber in this GCM assumes a specified vertical profile as
a function of optical depth, which represents a greenhouse
effect in the troposphere and stratosphere. The upper at-
mosphere absorption of planetary illumination on an actual
exomoon would depend upon the atmospheric composition
and pressure, among other factors, which could be explored
with other GCMs that use band-dependent radiative trans-
fer. Comparison of several different GCMs in a similar exo-
moon configuration would provide more robust constraints
on the expected heating profile from planetary illumination.
4 DISCUSSION
In general, these simulations illustrate that the potential
habitability of an exomoon depends upon the thermal en-
ergy emitted by its host planet. We find stable climate states
for both slow and rapid rotators with Fg≤10 W m−2and
Ft≤100 W m−2, which indicates that both geothermal heat-
ing and planetary illumination could provide an additional
source of warming for an exomoon. However, strong ther-
mal illumination by the host planet (Ft=500 W m−2in our
experiments) would likely lead to an onset of a runaway
greenhouse and the loss of all standing water.
On the one hand, the habitability of some exomoon sys-
tems may therefore be precluded based upon the presence
of a luminous host planet, although planetary illumination
itself does not necessarily limit an exomoon’s habitability
(Heller 2016). On the other hand, we expect polar ampli-
fication of warming in all cases, which may suggest that
exomoons in orbit around a luminous host planet may be
less likely to develop polar ice caps. This tendency for an
exomoon to have warmer poles due to planetary illumina-
tion suggests that such bodies may have a greater fractional
habitable area than Earth today (Spiegel et al. 2008), po-
tentially improving the prospects of an origin of life (Heller
& Armstrong 2014). This prediction of polar warming on
exomoons could eventually translate into observables from
the circumstellar phase curves of an exomoon, if the planet’s
contribution to the combined planet-moon phase curve can
be filtered out (Cowan et al. 2012;Forgan 2017).
To a lesser extent, the rotational period of the exomoon
also contributes to differences in surface habitability. The
short-period cases tend to show a greater amount of warm-
ing along the equator, near the subplanetary point (Figure 3,
right panel), which could serve as an additional source of en-
MNRAS 000,1–14 (2018)
12 Haqq-Misra and Heller
Figure 8. Vertical profiles of the zonal mean temperature (left) and radiative heating (right) at the equator for all simulations listed
in Table 1. Solid curves indicate short-period cases (1.175 d) and dashed curves indicate long-period cases (3.324 d). Black curves show
control experiments, while green indicates all simulations with Ft≤10 W m−2. Blue curves show simulations with Fg=10 W m−2and
Ft=100 W m−2, while red curves show cases with Ft=500 W m−2. Case numbers as per Table 1are given for some of the lines.
ergy to maintain regional habitable conditions. Dynamical
changes in atmospheric jet structure that result from differ-
ences in rotation rate also contribute to changes in surface
wind patterns, as well as the general circulation, which will
likely correspond to significant contrasts in resulting cloud
patterns. The large-scale circulation also shows an opposite
directional sense in the hemispheres east and west of the
subplanetary illumination point, which could also impact
the probable location of clouds.
The hemispheric differences in the Hadley circulation
(Figs. 4and 5) show similarities to simulations of terres-
trial planets in synchronous rotation around low mass stars,
where the host star is fixed upon a substellar point on the
planet. Haqq-Misra et al. (2011) used the idealized FMS
GCM to demonstrate that the Hadley circulation shows di-
rection in the opposite direction when comparing the hemi-
spheres east and west of the substellar point for plan-
ets with 1 d and 230 d rotation periods. Haqq-Misra et al.
(2018) also find the same hemispheric circulation patterns in
an analysis the Community Earth System Model (CESM),
which includes band-dependent radiation, cloud processes,
and other physical processes. Synchronously rotating plan-
ets drive such a circulation when their stellar energy source
is fixed to a single location; however, our exomoon calcu-
lations demonstrate that such a circulation can also be ob-
tained when planetary illumination is fixed, even if the moon
otherwise experiences variations in incoming starlight.
These idealized calculations provide a qualitative de-
scription of surface temperature and winds on an exomoon,
but the application of more sophisticated GCMs will help to
identify particular threshold where a runaway greenhouse
and other water loss processes occur. Non-gray radiative
transfer will allow for particular atmospheric compositions
to be examined, such as a mixture of nitrogen, carbon diox-
ide, and water vapor that is characteristic of Earth-like
atmospheres. Implementation of a cloud scheme into the
GCM will also provide important insights into habitabil-
ity, as clouds could help to delay the onset of a runaway
greenhouse state (Yang et al. 2014).
In terms of the odds of an actual detection of the cli-
matic effects described in this paper, this could in principle
be possible if the moon’s electromagnetic spectrum (either
reflection or emission) could be separated from that of the
planet. This might be possible in very fortunate cases where
a large moon is transiting its luminous giant planet (Heller &
Albrecht 2014;Heller 2016) or where both the planet and its
moon transit their common low-mass host star (Kalteneg-
ger 2010). Alternatively, if the moon is subject to extreme
tidal heating, it could even outshine its host planet in the
infrared and therefore directly present its emission spectrum
(Peters & Turner 2013) while the planet would still domi-
nate the visible part of the spectrum, where it reflects much
more light than the moon. The technological requirements,
however, will go beyond the ones offered by the James Webb
Space Telescope (Kaltenegger 2010) and might not be acces-
sible within the next decade.
5 CONCLUSIONS
We present the first GCM simulations of the atmospheres
of moons with potentially Earth-like surface conditions. Our
simulations illustrate the effects of tidal heating and of plan-
etary illumination on the atmospheres of large exomoons
that could be abundant around super-Jovian planets in the
stellar habitable zones.
Most of the energy from planetary thermal heating and
geothermal heating is transported toward the poles as a re-
sult of enhanced meridional transport of moisture and en-
ergy. This suggests that polar ice melt may be less prevalent
on exomoons that are in synchronous rotation with their
host planet. In general, these calculations further illustrate
that the poleward expansion of the Hadley circulation en-
hances meridional energy transport and can lead to polar
MNRAS 000,1–14 (2018)
Exploring exomoon atmospheres with a GCM 13
amplification of warming, even in the absence of ice albedo
feedback.
This polar heat transport could increase the fraction of
the surface that allows the presence of liquid surface water
by compensating for the lower stellar flux per area received
at the poles of a moon. In other words, illumination from
the planet might be beneficial for the development of life
on exomoons. Future observations that are able to distin-
guish exomoons from their host planet may be able to de-
tect the absence of polar ice caps due to polar amplification
of planetary illumination, such as analysis of photometric
phase-curves.
ACKNOWLEDGMENTS
The authors thank Ravi Kopparapu for helpful feedback
on a previous version of the manuscript. J.H. acknowl-
edges funding from the NASA Astrobiology Institute’s Vir-
tual Planetary Laboratory under awards NNX11AC95G and
NNA13AA93A, as well as the NASA Habitable Worlds
program under award NNX16AB61G. R.H. has been sup-
ported by the German space agency (Deutsches Zentrum
f¨
ur Luft- und Raumfahrt) under PLATO Data Center grant
50OO1501, by the Origins Institute at McMaster University,
and by the Canadian Astrobiology Program, a Collabora-
tive Research and Training Experience Program funded by
the Natural Sciences and Engineering Research Council of
Canada (NSERC). Any opinions, findings, and conclusions
or recommendations expressed in this material are those of
the authors and do not necessarily reflect the views of NASA
or NSERC.
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