Dynamics of Hot Jupiter Atmospheres

Adam P. ShowmanUniversity of Arizona

  

   

The transiting hot Jupiter Bestiary

• Semimajor axes 0.022 -- 0.15 AU• Periods 1.2 -- 21 days

• Radii 0.39 – 1.7 RJupiter

• Masses 0.07 – 20.2 MJupiter

• Gravities ~10 – 760 m/sec2

• Stellar fluxes of 30,000 – 4,500,000 W/m2

• Stellar metallicities [Fe/H] -0.3 to +0.45• Orbital eccentricities 0 – 0.67

The huge ranges in these parameters probably implies a huge range of behaviors!

Spitzer 8- and 24-m lightcurves for hot Jupiters

HD189733b (Knutson et al. 2007)

HD209458b (Cowan et al. 2007)

Ups And b (Harrington et al. 2006)

Zonal (east-west) winds on the giant planets

• Weather occurs in a statically stable radiative zone extending to ~100-1000 bar

• For km/sec winds, rad << advect for p < 1 bar; large temperature

contrasts

rad >> advect for p > 1 bar; temperatures homogenized

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

Iro et al. (2005)

Should the flow be be banded? What controls the sizes of flow structures?

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

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

On Jupiter/Saturn, these lengths

are << planetary radius

On most hot Jupiters, they are close to

planetary radius. Jets and vortices should

therefore be global in scale.

Banded structure results from modification of an inverse cascade by planetary rotation:

• Small-scale 2D turbulence undergoes an inverse cascade that transfers the energy to large-scale structures:

• Gradient of planetary rotation causes anisotropy, leading to east-west elongation (jets):

• Jet widths typically ~ (U/)1/2, called the Rhines scale.

Bracco et al.

(2000)

Marcus et al.

(2000)

Effect of rotation on jet widths

nominal

half nominal

twice nominal

Showman et al. (2008)

Temporal Variability?

Mechanisms for producing variability:

• Convection in the deep interior?

• Convection on the nightside?

• Shear/baroclinic instability of the jet streams?

• Clouds are a wild-card...

A range of behaviors is possible. Some hot Jupiters may exhibit steady and other may exhibit time-variable lightcurves/spectra.

Approaches

• Two-dimensional: Cho et al. (2003, 2008); Langton and Laughlin (2007, 2008); Rauscher et al. (2007, 2008)

• Two-dimensional equatorial cross-section: Burkert et al. (2005)

• Three-dimensional: Showman and Guillot (2002), Cooper and Showman (2005, 2006); Dobbs-Dixon and Lin (2008); Showman et al. (2008a, 2008b); Menou & Rauscher (2008); Fortney et al. (2006); Williams et al. (2006)

Chemistry• Dynamics implies that air parcels experience large changes in temperature/pressure

over short timescales (~ day)

• Chemical disequilibrium (e.g., quenching) is likely for any species with production/loss times exceeding the dynamical time. For example, CO and CH4 could be quenched to near-constant values above the photosphere (Cooper & Showman 2006)

• Conversely, the abundance and spatial distribution of CO, CH4, and other species contains information about the meteorology. This may probe aspects that IR lightcurves/spectra cannot directly constrain (e.g., velocities below photosphere)

• Dynamics controls patterns of cloudiness, which affects chemistry

Cooper &

S

howm

an (2006)

Coupled Radiative-Dynamical GCM simulations (Showman et al., submitted)

• We solved the full nonlinear primitive equations in the stably stratified radiative zone on the whole sphere using the MITgcm

• McKay/Marley/Fortney radiation code (plane-parallel multi-stream using correlated-k). Use 1, 5, or 10 x solar metallicity without or with TiO/VO; equilibrium chemistry; no clouds

• Thermodynamic heating rate calculated as vertical divergence of net vertical radiative flux

• Domain: 0.2 mbar – 200 bars; impermeable bottom boundary; free-slip horizontal momentum boundary conditions at top & bottom

• Assume a synchronously rotating planet with parameters for HD209458b or HD189733b. Initial temperature profile taken from 1D evolution calculations; zero initial wind.

Jupiter

Saturn

Uranus/Neptune

Lian & Showman, submitted

HD 189733b, solar, without TiO/VO

900

1500

700

1200

500

1200

Lightcurves: HD 189733b, solar

Lightcurves: HD 189733b, solar (top) and 5 x solar (bottom)

Effect of non-synchronous rotation

Spectra at many phases: HD 189733b

Temperature profiles: HD 189733b

p (bars)

1

100

0.01

0.1

0.001

10

T (K)

400 800 1200 1600

Secondary eclipse spectra: HD 189733b

Variability

HD 209458b: Spitzer secondary-eclipse spectrum suggests a hot stratosphere

Knutson et al. (2007)

HD 209458b, solar, with TiO/VO

900

1700

800

2000

600

2200

Stratosphere on HD 209458b

p (bars)

1

100

0.01

0.1

0.001

10

T (K)

500 1000 1500 2000 2500

HD 209458b

Contribution functions

ConclusionsThe intense radiation produces winds > 1 km/sec and temperature

contrasts of ~200-1000 K. All studies predict that ~3-day-period hot Jupiters should contain only a small number of wide jets. Faster rotation leads to narrower jets, consistent with Rhines length and deformation radius arguments.

The winds can distort the temperature pattern in a complex manner.

IR variability is possible, but this depends on the instability of the jets and strength of convection from below.

Our HD 189733b simulations successfully explain the modest 8-m and 24-m phase contrasts and the apparent eastward offset of the hottest regions seen in Spitzer data. However, details of the lightcurve shapes remain to be reproduced.

HD 209458b simulations with TiO and VO produce a dayside stratosphere with temperatures exceeding ~2000 K, as suggested by Spitzer dayside spectra. However, we still do not fit the spectrum in detail.