Doppler signatures of the

atmospheric circulation of hot

Jupiters

Adam Showman University of Arizona

Jonathan Fortney (UCSC), Nikole Lewis

(Univ. Arizona), Megan Shabram (Florida)

  

   

Doppler detection of winds on HD 209458b!• Snellen et al. (2010, Nature) obtained high-resolution 2 m spectra of

HD 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)

Can we explain the Doppler measurement? What are the expected Doppler signatures of hot Jupiter generally, and what can we learn from the observation?

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

Showman et al. (2009) Rauscher & Menou (2010)

Heng et al. (2010) Dobbs-Dixon & Lin (2008)

Showman & Polvani (2011) showed that these jets result from momentum transport by standing, planetary-scale

waves driven by the day-night thermal forcing

Show

man

& P

olva

ni (

2 01

1, ApJ

738

, 71)

Our 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 high altitude. This causes a predominant blueshifted velocity peak:

Transition between regimes should occur when damping timescales are comparable to wave propagation time across a hemisphere:

Kelvin wave propagation speed

Propagation time across hemisphere

We now test the theory, first with idealized models, then with full 3D circulation models with realistic, non-grey radiative transfer

€

~a

NH~ 105 sec

€

~ NH

Weak damping

Moderate damping

Strong damping

Dependence of flow regime on radiative and drag time constants

0.06 0.3 1.4 6.7 31 Zonal jet/eddy ratio

HD 189733b:Moderate stellar flux

Velocities at terminator(as seen during transit) are bimodal

HD 209458b:Stronger stellar flux

Velocities atterminator arenearly unimodaland blueshifted

The Doppler measurement allows us to estimate the strength of frictional drag in the atmosphere!

Here is a 3D model with a drag time constant drag=105 sec

Velocities atterminator areblueshifted andweaker

Drag timescales of 104-105 sec are needed to explain the measurement

This can also be understood analytically: Horizontal pressure gradient force is

If this balances drag force, , then for , we obtain

a

pTR ln

€

−u

τ drag

€

u ≈ 2 km

sec

€

drag ≈ua

RΔTΔln p≈104 sec

ConclusionsTransit spectra of HD 209458b suggest a Doppler blueshift of ~2 km/sec

caused by meteorology.

We presented a theory of the wind regime to predict and understand the Doppler behavior:

• At weak-to-moderate stellar flux and friction, standing planetary waves induce zonal jets. This causes bimodal blue- and redshifted velocity peaks in the transit spectrum.

• Strong irradiation and/or friction damp these planetary waves, inhibiting jet formation and leading to a predominant day-to-night flow at low pressure. This causes a predominantly blueshifted Doppler peak.

• The regime transition occurs for damping times of ~105 sec.

The inferred wind speeds place constraints on the strength of frictional drag. In the absence of drag, high-altitude flow equilibrates to wind speeds of 4 to 8 km/sec. Slowing down the day-night flow to speeds of ~2 km/sec requires short frictional drag times of 104-105 sec.

The same regime transition explains the observed transition from small to large day-night temperature contrast at increasing stellar irradiation.

Test of the theory with an idealized model

Adopt the shallow-water equations for a single fluid layer:

where heq-h]/rad represents thermal forcing/damping, v/drag represents drag, and where =1 when Qh>0 and =0 otherwise

€

∂h

∂t+∇ ⋅(h

r v ) =

heq (x,y) − h

τ rad

≡ Qh

€

dr v

dt+ g∇h + fk ×

r v = −

r v

τ drag

−r v

Qh

hδ

HD 189733b, solar

•

•

•

900

1500

700

1200

500

1200

Showman et al. (2009)

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

• Timescale arguments:

rad << dyn for p < 1 bar; large temperature contrasts

rad >> dyn 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

Fortney et al. (2007)

Acceleration (10-3 m/sec2)

Showman & Polvani (2011), in press arXiv 1103.3101

Theoretical estimate of jet and eddy accelerations

Jet acceleration

Day/night eddy acceleration

Regime of strong jets

Regime of weak jets (and strong eddies)

The Model

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

• Radiative transfer: plane-parallel multi-stream using correlated-k. Use 1, 5, or 10 x solar metallicity; 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.

Our 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 high altitude. This causes a predominant blueshifted velocity peak:

• Transition between regimes should occur when damping timescales are comparable to wave propagation time across a hemisphere (~105 sec)