Atmospheric Dynamics
of Giant Planets Insideand Outside the SolarSystem
Adam P. Showman
University of Arizona
Collaborators: Yuan Lian, Yohai Kaspi, LorenzoPolvani, Jonathan Fortney, Nikole Lewis, Daniel
Perez-Becker, Mark Marley, Heather Knutson,

Outline• Giant planets in the Solar System– Observational background– New results inferring the depth of jet streams on Uranus and Neptune– How are the jets formed?
• brief background• results of global 3D models with a hydrological cycle• Exoplanets: the hot Jupiters– Motivations and observational methods/results– Explanation for equatorial superrotation in hot Jupiter regime– Regime transitions: day-night temperature differences and wind regimes, andtests with data
– From hot to cool Jupiters and the continuum to Jupiter itself• Brown dwarfs– Observational aspects and expected dynamical regimes– Convective interior structure– Atmospheric circulation via absorption of waves propagating from below

Zonal (east-west) winds on the giant planetsTemperatures are relatively homogeneous:

Ingersoll (1990)

Rotation causes east-west (zonal) bandingin planetary atmospheres

Hayashi et al. (2000)

What controls the size and shape of flow structures?

• Rhines length, (U/β)1/2, is the scale at which planetary rotation causes east-west
elongation (jets).

• Deformation radius, c/Ω, is a natural scale of vortex formation and flow
instability

On Jupiter/Saturn and brown dwarfs,
these lengths are << planetary radius
On most hot Jupiters, they are close toplanetary radius. Jets and vortices should
therefore be global in scale.

Basic Jet Scenarios• Models for jet structure:– Shallow: Jets confined to outermost scaleheights below the clouds– Deep: Jets extend through molecularenvelope (Taylor-Proudman theorem)• Models for jet pumping:– Shallow: Turbulence at cloud level(thunderstorms or baroclinicinstabilities)– Deep: Convective plumes penetrating
the molecular envelope

These issues are among the mostimportant unsolved problems inplanetary atmospheres!

Evidence for eddy-momentum convergences at cloud level

These measurements demonstrate that the jets are being driven at cloud level.
Salyk et al. (2006); Del Genio et al. (2007, 2012)Puzzles• What causes the banded structure, with ~20 jets on Jupiter andSaturn yet only ~3 on Uranus and Neptune? What is the jetpumping mechanism?

• How deep do the jets extend?
• Why do Jupiter and Saturn have superrotating equatorial jets
whereas Uranus and Neptune do not?

• What causes the vortices? What controls their behavior? How
do they interact with the jets?

• What is the temperature structure and mean circulation of thestratosphere and upper troposphere?

Gravitational sounding of giant planet interiors: answering
the question of how deep the jets extend

Juno preparation and launch August 5, 2011

Gravitational potential represented as∞
 a nr GM V (r ) =1− ∑  J n Pn (µ)r  n= 2 r where Jn are the gravitational harmonics,defined as

1 a 2 π 1 2+n
r' Pn (µ') ρ(r', µ', φ ')dµ' dφ ' dr'
Jn = −n ∫ ∫ ∫Ma 0 0 −1
where ρ is density, Pn are Legendre
polynomials, a is planetary radius, r isradial distance, φ is longitude, and µ is
cosine of angle from rotation axis to agiven point.
(See Hubbard 1984 for a review.)

Kaspi, Hubbard, Showman, & Flierl (2010)

Gravitational signature ofinternal dynamics

Kaspi, Hubbard, Showman, & Flierl (2010)

Predicted Jupiter gravity spectrum for various
depths of zonal flow

Key point: gravitational signature of jets will be detectable by Juno if jets extend at least~500 km into the interior. Juno will measure to J12 or J14. Jets dominate over solid-bodyrotation beyond J10 if they extend deeply enough.

Deep convection models

Thick shell(Christensen 2001, 2002;
Aurnou & Olson 2001;
Kaspi et al. 2009,
Jones & Kuzanyan 2009,
Showman et al. 2011, etc)

Thin shell(Heimpel et al. 2005;
Heimpel & Aurnou 2007;
Aurnou et al. 2008)

One-layer shallow-water models

Jupiter

Uranus/Neptune

Scott & Polvani (2007); Showman (2007); Cho & Polvani (1996)
These deep and one-layer shallow models have not self-consistently predicted theequatorial jet directions

Importance of Latent Heating• Moist convection has been observed on Jupiter and Saturn: bright clouds
that exhibit lightning and expand to ~1000 km over a few days

• Water abundances are uncertain, but best guesses range from ~3 times
solar (Jupiter) to ~30-40 times solar or more (Uranus/Neptune)• Cloud-tracking observations show that eddies at cloud level pump
momentum up-gradient into the jets

Motivating questions
1. Can a model with latent heating in the cloud layer produce
multiple jet streams with the properties observed on
Jupiter, Saturn, Uranus, and Neptune?

2. Why do Jupiter and Saturn have superrotating equatorial
jets whereas Uranus and Neptune do not? Can the jet
profiles on all four planets be explained by a single
unifying mechanism?

3. Can we explain other observations, such as the small
latitudinal temperature variations, the existence of storms,etc?

The Model• We solved the full nonlinear 3D primitive equations on a sphere using theMITgcm including advection of water vapor• If water vapor is supersaturated, we relax its mixing ratio back tosaturation and apply latent heating to the energy equation.

• Radiation treated with Newtonian cooling.
• No microphysics.

 q − qsat dqδ + Qdeep= −dt τ cond dθ θ eq − θ Lθ  q − qsat δ=+dt
c pT  τ cond τ rad• Where δ=1 when q ≥ qsat and δ=0 otherwise.

Lian & Showman (2010)

Jupiter

SaturnUranus/Neptune

Eddy pumping of equatorial jet

Latitude [deg]Latitude [deg]Lian & Showman (2010)

Uranus/Neptune zonal winds

Pressure (bar)solar water

Pressure (bar)Pressure (bar)

3 x solar

30 x solar
Lian & Showman (2010)

The importance of Rossby waves: jet formationGroup
propagation

Phase
propagation

Phase
propagationGroup
propagation

Jupiter temperature structure

0.1 bar

0.2 bar

0.9 barLian & Showman (2010)

Temperature (5 bars)

Humidity (5 bars)

Vertical velocity (1 bar)Vorticity (1 bars)

Lian & Showman (2010)

Gierasch et al.
(2000)

Lian & Showman (2010)

Lian & Showman (2010)

Lian & Showman (AGU 2012)

Jupiter models including hydrological cycle and water clouds

Conclusions• Juno should be able to detect the gravitational signature of Jupiter’s jets if theyextend 500 km or deeper into the interior. The internal dynamics should
dominate over rotation in gravitational moments beyond J10.

• On Uranus and Neptune, the observed J4 implies that the fast zonal jets seen atthe cloud layer must be confined to these planets’ atmospheres. This would seemto emphasize atmospheric processes for the mechanisms maintaining the jets.

• 3D models with a hydrological cycle and latent heating show the development ofnumerous banded jet streams similar to those on the giant planets. Jupiter andSaturn-like cases naturally develop ~20-odd jets, while Uranus/Neptune-likecases develop ~3 jets.

• Consistent with observations, the Jupiter-like and Saturn-like cases
spontaneously develop equatorial superrotation while the Uranus/Neptune-likecases develop equatorial subrotation.

• These models show the spontaneous development of storm-like features,qualitatively consistent with observed storms on Jupiter and Saturn

Exoplanets: theAtmospheric Dynamics ofhot Jupiters

Exoplanets: an exploding new field•

Almost 900 known extrasolar planets, most discovered with the “Doppler” method(plus ~2300 candidates from the NASA Kepler mission).

•~300 planets detected with “transit” method (allows characterization)•Together, these data give mass, radius, mean density, and orbital properties•

Many are Jupiter-mass planets very close to their stars: the “hot Jupiters”

Spitzer light curves for HD 189733b

Knutson et al. (2007, 2009)

8 µm

24 µm

Lightcurves for hot Jupiters

HD209458b (Cowan et al. 2007)
HAT-P-7b (Knutson et al., unpublished;
Borucki et al. 2009)

CoRoT-1b (Snellen et al. 2009)

Ups And b (Crossfield et al. 2010)

Results from lightcurves: dependence of day-night flux contrast
on effective temperature

A trend seems to be emerging: more strongly irradiated planets have larger
fractional day-night temperature differences at the photosphereShowman (2008)

Exoplanet characterization: Transit spectroscopy

Sing et al. (2008, 2009), Vidal-Madjar et al. (2011), Huitson et al. (2012),Gibson et al. (2012),Barman (2007), Tinetti et al. (2007), Swain et al. (2008),…..

Doppler detection of winds on HD 209458b?
• Snellen et al. (2010, Nature) obtained high-resolution 2 µm spectra ofHD 209458b during transit with the CRIRES spectrograph on the VLT• Tentative detection of ~2 km/sec blueshift in CO lines during transit of HD 209458b• Interpreted as winds flowing from day to night at high altitude (~0.01-0.1 mbar)

Motivating questions•What are the fundamental dynamics of this novel, highly irradiated circulation regime?

•What is the temperature distribution of exoplanets? What are mechanisms forcontrolling the day-night temperature contrast on hot Jupiters? What is themechanism for displacing the hottest regions on HD 189733b?

•

What are the fundamental wind regimes? Are there regime transitions, and if so, whatcauses them? What is the connection to dynamical regimes of solar-system planets?

•How does the circulation interact with the interior? Does it affect the evolution andradius?

•What processes control mixing in hot-Jupiter atmospheres? To what extent canchemistry affect and/or probe the dynamics?

•What is the atmospheric state and climate of terrestrial exoplanets? How does
circulation help control habitability on these worlds?

Spectroscopy, lightcurves, eclipse mapping, Doppler measurements, etc--both from the groundand space—can address these questions

Dynamical regime of hot Jupiters•

Circulation driven by global-scale heating contrast: ~105 W/m2 of stellar heating on
dayside and IR cooling on nightside•

Rotation expected to be synchronous with the 1-10 day orbital periods; Coriolis
forces important but not dominant•

Weather occurs in a statically stableradiative zone extending to ~100-1000 bar• Rossby deformation radius typicallycomparable to a planetary radius• Simple scaling suggests fast wind speeds, e.g.,
u~2 km/sec, implying Rossby numbers Ro ~ 1.

Fortney et al. (2007)

Showman &Guillot (2002)

Knutson et al.
(2007)

Hot Jupiter circulation models typically predict several
broad, fast jets, often including equatorial superrotation

Showman et al. (2009)

Heng et al. (2010)

Rauscher & Menou (2010)

Dobbs-Dixon & Lin (2008)

Data-model comparisons

Knutson et al. (2012), Showman et al. (2009)

Let’s focus on three topics for hot Jupiters• What is the mechanism for the equatorial superrotation?

• How should the day-night temperature difference and wind regime varyfrom hot to very hot Jupiters? Can we explain the emerging observational
trend from lightcurves? What are implications for Doppler detections ofatmospheric winds?

• How should dynamics vary for exoplanets more distant from their stars?
What is the continuum between hot Jupiters and Jupiter itself?

Simple models to isolate superrotation mechanism• To capture the mechanism in the simplest possible context, adopt theshallow-water equations for a single fluid layer:

rrr Qhrv
dv−v δ+ g∇h + fk × v = −hτ dragdt∂hr [heq (x, y) − h]+ ∇ ⋅ (hv ) =≡ Qh∂tτ rad

where [heq-h]/τrad represents thermal forcing/damping, −v/τdrag represents
drag, and where δ=1 when Qh>0 and δ=0 otherwise• First consider linear, steady analytic solutions and then consider full
nonlinear solutions on a sphere.

Forcing

Showman & Polvani (2011), ApJ 738, 71

Analytical solution ofstanding, steady wave
response to day-night
thermal forcing•The response corresponds to standing, equatorially trapped Kelvin and Rossby waves•The Kelvin waves propagate to east, Rossby waves to west, leading to a chevron patternwith velocities tilted NW-SE (SW-NE) in northern (southern) hemisphere•This causes an equatorward flux of eddy momentum and drives superrotation

Linear response of shallow-water model to steady daynight forcing in full spherical geometry: the results
qualitatively match our analytic β plane solutions

Showman & Polvani(2011)

Zonal-mean zonal windAt high amplitude, nonlinearities affect thesolution, but the results
are qualitativelysimiler.
Standing Kelvin andRossby waves drive afast equatorial
superrotation.

Showman & Polvani(2011)

Acceleration (10-3 m/sec2)

Showman & Guillot (2002)

This Rossby/Kelvin wave pattern is clearly evident in
spin-up phase of 3D hot Jupiter simulations

Our dynamical theory predicts two regimes
1. At weak-to-moderate stellar fluxes and friction, planetary (Rossby andgravity) waves induce zonal jets and adjust the thermal structure, leading tosmall day-night temperature differences.

2. Extreme stellar fluxes and/or friction damp the planetary waves, inhibiting
zonal jet formation and leading to a large day-night temperature difference.

Transition between regimes should occur when damping timescales arecomparable to wave propagation time across a hemisphere:
Kelvin wave propagation speed~ NHaPropagation time across hemisphere ~~ 10 5 secNH

Weak damping (Warm)

From Warm toVery Hot Jupiters

Medium damping (Hot)Strong damping (Very Hot)

Showman et al. (2013)

Conclusions: hot Jupiters•Hot Jupiters occupy a dynamically unique regime of atmospheric circulation that
does not exist in our Solar System. The intense day-night radiative forcing produces
wind speeds >1 km/sec and temperature contrasts of ~200-1000 K. The winds candistort the temperature pattern in a complex manner, with important implications
for lightcurves and spectra.

•The day-night forcing generates planetary-scale waves that pump momentum to theequator, leading to equatorial superrotation that explains the observed hot-spot offset
on HD 189733b.

•On very hot Jupiters, the strong radiation/friction damps these waves, preventing
their ability to adjust the thermal structure and leading to large day-nighttemperature differences. On warm Jupiters, radiative damping is weaker, and thewaves efficiently mute the longitudinal thermal differences. Our models thus explain
the emerging observational trend of increasing fractional day-night temperature
difference with incident stellar flux.

•The same dynamics predicts a transition in wind regime: from zonally banded flows
at weak irradiation to a day-night flow at strong irradiation. This explains the blueshifted Doppler measurement of HD 209458b and leads to a prediction for future
measurements.