Exoplanets: theAtmospheric Dynamics ofhot Jupiters
Adam P. Showman
University of Arizona
Collaborators: Yuan Lian, Yohai Kaspi, Lorenzo Polvani,
Jonathan Fortney, Nikole Lewis, Daniel Perez-Becker,
Mark Marley, Heather Knutson

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HAT-P-7b (Knutson et al., unpublished;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)

Perez-Becker & Showman (in preparation)

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 irradiatedcirculation regime? Can we explain lightcurves of specific hot Jupiters?
What is the mechanism for displacing the hottest regions on HD 189733b?

• Can we explain the Doppler measurements of HD 209458b? What are theexpected Doppler signatures, and what can we learn from the measurement?

• What are mechanisms for controlling the day-night temperature contrast on
hot Jupiters? Can we explain the increasing trend of day-night flux contrast
with incident stellar flux?

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.

Showman & Polvani (2011, Astrophysical Journal, 738, 71)

Forcing

Showman & Polvani (2011)

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)

Showman & Polvani (2011)

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

This dynamical theory predicts two regimes• At weak-to-moderate stellar fluxes and friction, standing planetary waves
induce zonal jets. This causes bimodal blue and redshifted velocity peaks:• Extreme stellar fluxes and/or friction damp the planetary waves, inhibiting
zonal jet formation and leading to predominant day-night flow at highaltitude. This causes a predominant blueshifted velocity peak:Showman et al. (2013), Astrophysical Journal, 762, 24

Transition between regimes should occur when damping
timescales are comparable to wave propagation time across ahemisphere:
Kelvin wave propagation speed ~ NH
Propagation time across hemisphere ~a~ 10 5 sec
NH

We now test the theory, first with idealized models, then with full3D circulation models with realistic, non-grey radiative transfer

Showman et al. (2013)

Weak damping (τrad = 10 days),
relevant to cool planetsFully nonlinear shallow-watermodels on the sphere.

Moderate damping (τrad = 1 day),relevant to warm planets

Strong damping (τrad = 0.1 days),
relevant to hot planets

Showman et al. (2013)

Dependence of flow regime on radiative anddrag time constants

0.06
Weak jets, strong
day-to-night flow

0.3

1.4
6.7
Zonal jet/eddy ratio

31
Strong, nearly zonallysymmetric zonal jets
Showman et al. (2013)

A similar transition occurs in full 3D models with realistic non-grey radiative transfer:
Blue and red
shiftedCool

GJ 436b

MediumHD 189733b

Mostly blue shifted

HotHD 209458b

Showman et al. (2013)

Detailed radiativetransfer analysisof these 3Dmodels confirms
this picture.

Showman et al. (2013)

The same shallow-water models also qualitatively explain the observationthat hotter planets have larger fractional day-night temperature differences:

Let’s now use this as a model system to understand the mechanisms that control theday-night temperature difference on synchronously rotating exoplanetsMost previous authors have assumed that
Temperature differences are small if τrad >> τadvect andTemperature differences are large if τrad << τadvect,
where τrad is the radiative time constant and τadvect is horizontal advection time fromday to night.
There are several problems with this as an explanation:•It is not predictive, since τadvect depends on the flow. You can’t even evaluate thecriterion under given external forcing conditions unless you already have a theory forthe flow itself. No such theory has ever been presented.

•While attractive, this timescale comparison neglects any role for other importanttimescales, including timescales for wave propagation, frictional drag, and planetaryrotation. These almost certainly matter.

•More generally, we seek not just a criterion for the transition between regimes but apredictive theory for the day-night temperature difference itself, valid across the fullparameter space.

Perez-Becker & Showman (in preparation)

What controls the day-night temperature difference on asynchronously rotating planet?

Background: wave adjustment as a regulator of thermal structure
Shallow-water solutions of the “dam break” problem show how wave adjustment canflatten material surfaces:•The waves cause horizontal convergence/divergence that changes the fluid thickness,allowing the topography to be flattened if the waves radiate to infinity•

The process does not require long distance horizontal advection; fluid columns movehorizontally by only a small amount if the initial topographic step is small.

•The process operates not over a horizontal advection time but rather over thehorizontal wave propagation timescale.

Kuo & Polvani (1997)•

Waves adjust isentropes up
or down in an attempt toflatten them. This erases
horizontal temperaturedifferences.

This is a key mechanism for
maintaining the small
longitudinal temperature
differences in Earth’s
tropics: the “weaktemperature gradient” orWTG regime.

Showman et al. (2013b), “Atmospheric circulation of terrestrial exoplanets,” submitted
to Comparative Climatology of TerrestrialPlanets, Univ. Arizona Press (to be published)

The same wave adjustment
process operates in 3D

Perez-Becker & Showman (in preparation)

To investigate this question, we ran shallow-water models of synchronously
rotating planets over a full grid of τrad and τdrag, which are external parametersPerez-Becker & Showman (in preparation)

Amplitude dependence

Perez-Becker & Showman (in preparation)

Analytic theory•Theory shows that transition occurs at τ wave ≈ τ rad τ dragτand τ wave ≈radΩin strong drag limit

in weak drag limit.

Perez-Becker & Showman (in preparation)

The model explains the emerging observational trend

Perez-Becker & Showman (in prep)

What about objects cooler than “classical” hot Jupiters?
• Despite the focus on hot Jupiters, known EGPs populate a continuum from~0.03-0.05 AU to > 1 AU

• Such~ “warm” Jupiters will rotate non-synchronously:
6

aQ
τ spindown ≈ 10 6  5  orb  yr
10  0.05AU • Fundamental questions also exist about how the circulation on hot Jupiters
relates to that on Jupiter and Earth

All of this motivates an investigation of how hot Jupiter circulation regimes-and observables--vary with incident stellar flux and rotation rate

Showman, Lewis, Fortney (in prep)•

Explore a regular grid of models
varying rotation rate from 0.5 to8.8 Earth days and orbital semi- 0.2 AU
major axes from 0.03 -- 0.2 AU•

Allows us to emphasize planets
amenable to transit
characterization while exploringa factor of 16 in rotation rateand ~40 in incident stellar flux
0.03 AU8.8 day

Stellar/planetary properties of
HD 189733
0.5 day•

Showman, Lewis, Fortney (in prep)

Showman, Lewis, Fortney (in prep)

Orbital distance

0.2 AU

0.03 AU0.5 day

Rotation period
8.8 dayOrbital distance

0.2 AU

0.03 AU0.5 day

Rotation period

8.8 dayMean zonal wind

Our least irradiated and most rapidly
rotating “warm Jupiter” model:
development of multiple jets in eachhemisphere due to baroclinic instability!

Potential temperature

Meridional eddy-momentum convergence

Showman, Lewis, Fortney (in prep)

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 temperaturedifference 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 futuremeasurements.

Conclusions II: hot Jupiters• At faster rotation rates and weaker stellar fluxes, the day-night heating
gradient is less important, and baroclinic instabilities emerge as a dominant
player, leading to eastward jets in the mid-latitudes, significant equator-poletemperature differences, and minimal temperature differences in longitude.

• Our most rapidly rotating and least irradiated EGP models exhibit multiple
eastward jets in each hemisphere—similar to the jets on Jupiter andSaturn—and illuminate the dynamical continuum between highly irradiated
EGPs and the weakly irradiated giant planets of our own Solar System.

Additional papers mentioned during questions and discussion•Showman & Polvani (2010, GRL 37, L18811, “The Matsuno-Gill model and equatorialsuperrotation”): Shows effect of the vertical momentum transport on equatorial superrotation
in a 1-1/2 layer shallow-water model with Gill-type forcing•

Kataria, Showman, et al. (2013, “Three dimensional atmospheric circulation of hot Jupiters onhighly eccentric orbits,” Astrophysical Journal, in press)•Liu & Showman (2013, “Atmospheric circulation of hot Jupiters: insensitivity to initialconditions”, submitted to Astrophysical Journal)