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 b! Snellen et al. (2010, Nature) obtained high-resolution 2  m spectra of HD b during transit with the CRIRES spectrograph on the VLT Tentative detection of ~2 km/sec blueshift in CO lines during transit of HD b Interpreted as winds flowing from day to night at high altitude (~ 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 Showman & Polvani (2 011, 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

Weak damping Moderate damping Strong damping

Dependence of flow regime on radiative and drag time constants Zonal jet/eddy ratio

HD b: Moderate stellar flux Velocities at terminator (as seen during transit) are bimodal

HD b: Stronger stellar flux Velocities at terminator are nearly unimodal and 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 =10 5 sec Velocities at terminator are blueshifted and weaker Drag timescales of 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

Conclusions Transit spectra of HD b 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 ~10 5 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 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  h eq -h]/  rad represents thermal forcing/damping,  v/  drag represents drag, and where  =1 when Q h >0 and  =0 otherwise

HD b, solar Showman et al. (2009)

Weather occurs in a statically stable radiative zone extending to ~ 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: ~10 5 W/m 2 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/sec 2 ) Showman & Polvani (2011), in press arXiv

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 (~10 5 sec)