Lecture 4: Giant planetsand brown dwarfs

Adam P. Showman
University of Arizonaon sabbatical at Peking University

Latitude (deg)Zonal winds on the giant planets

Sukoriansky et al. (2002)

Eastward wind (m/sec)

Kaspi et al. (2013)

•Earth (to scale)•Rotation (hours)•Mean radius (km)•Max. wind velocity (m/s)•Obliquity•Rossby number, u/ΩL

•Jupiter•Saturn•Uranus•Neptune•9.92•69,911
•140
•3°
•0.02

•10.57•58,232
•480
•27°
•0.04

•17.24•25,362
•240
•98°
•0.1

•16.11•24,622
•380
•28°
•0.1

•Small Rossby number• u/ΩL<<1

implies geostrophic balance – a balance between
Coriolis accelerations and pressure-gradient forces at large scaleTemperatures are relatively homogeneous:

Ingersoll (1990)

Energy budgets
Internal heat fluxes are substantial compared tosolar flux on Jupiter, Saturn and Neptune

Internal structure:Jupiter and Saturn’s temperatures and cloudsJupiter’s Zonal Winds

Limaye (1986), Porco et al. (2003)

Saturn’s zonal winds at the dawn of Cassini

Sanchez-Lavega et al. (2004, 2007); Porco et al. (2005)

Latitude (deg)Cassini confirmed strong vertical shear at the equator with aslowdown in the upper troposphere (relative to Voyager).

Zonal wind speed (m/sec)

Choi et al. (2009), GarciaMelendo et al. (2010, 2011)

Thermal and jet structure above the clouds

Read et al. (2009);
Flasar et al. (2005);
Li et al. (2008)

Stratospheric equatorial jet oscillations

Guerlet et al. (2011),
Orton et al. (2008);
Fouchet et al. (2008);
Schinder et al. (2011);
Li et al. (2011)

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 baroclinic
instabilities)– Deep: Convective plumes penetrating
the molecular envelope

These are among the most important
unsolved problems in planetaryatmospheres.
Note that the issues of structure andforcing are distinct!

Rotation also causes alignment of convection atlarge scalesEvidence for eddy-momentum convergences into the jets at cloud level
Jupiter

SaturnThese measurements demonstrate that the jets are being driven at cloud level.
Salyk et al. (2006), Del Genio et al. (2007), Del Genio & Barbara (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

Gravitational signature of internal dynamics
Gravitational potential represented as

On the giant planets, thedynamics may involve a
considerable fraction of themass, and therefore density
fluctuations due to dynamics
may be detectable in thegravity field.

nùGM é ¥ æ a ö
V (r ) =ê1- åç ÷ J n Pn (m)úr ë n= 2è r øûwhere Jn are the gravitational harmonics,
defined as

Jn = -

1
n
3
r
P
(
m
)
r
(r,
m
,
f
)
d
r
ò
n
Man

r is density, Pn are Legendre polynomials,
a is planetary radius, r is radial distance, f
is longitude, m is cosine of angle fromrotation axis, and M is total mass.
(See Hubbard 1984 for a review.)u r , 

idealized interior vertical structure with adecay length H.

u  ucyl e a r 


 H 

H  aH a• Calculate corresponding density structurefrom thermal wind equation.

r ' r , 

Kaspi, Hubbard, Showman, & Flierl (2010)• Use the observed winds and assume an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.

Odd gravity harmonics are a very sensitive probe ofdeep dynamics
Hemispheric (N minus S)
difference in Saturn zonal winds

Gravity spectrum under various assumptions
for how deep the jets penetrate

Latitude (deg)

90

60

30

0
Zonal wind difference (m/sec)

Kaspi (2013)

Kaspi et al. (2013)

What about Uranus and Neptune?

Observed jets are broad, and winds are fast. Thus, winds cause a large perturbation
to low gravity harmonics like J4. This suggests that we can constrain depth of jets on
Uranus and Neptune now with current data—namely, J2 and J4—unlike the case of
Jupiter where we need a close flying orbiter like Juno.

Procedure to infer depth of jets from J4• Calculate the full suite of static, wind-free interior models that match all
data—mass, radius, J2, and atmospheric density—but without using J4 as aconstraint.

• Determine the J4 values that these wind-free interior models imply.
• If the J4 calculated for these wind-free models is consistent withobservations, then winds are not needed to explain the data (i.e., winds are
not strong enough to influence the gravity, implying jets are shallow).

• But if the J4 calculated for these wind-free models differs significantly fromthe observed J4, then the discrepancy must be explained by dynamics(which would require that the jets extend deep into the interior).

Atmospheric confinement of jets on Uranus and Neptune!

If winds extend too deeply, the meteorological perturbation to J4 would exceed the
maximum possible difference between the observed J4 and the allowable J4 fromstatic, wind-free models. This implies that:––On Neptune, winds confined to outermost ~1000 km (~3000 bars, 0.2% of planetary mass)
On Uranus, winds confined to outermost ~1500 km (~4000 bars, 0.35% of planetary mass)

Kaspi, Showman, et al. (2013)

Storms and lightning

Vasavada & Showman (2005)

Vortex behavior

Jupiter

Neptune
MacLow & Ingersoll (1986)

Vasavada et al. (2006), Choi et al. (2009)

Local features on Saturn

Spots cluster at a certain size (~500-1000 km),putting constraints on the deformation radius

The White Ovals formed in 1938-40 during an
instability on a jet:

There were 3, but 2 merged in 1998 and theremaining 2 merged in 2000, leaving only one left:Models support the idea that large Jovian ovals formed by
jet instability:

Williams (2002); Dowling & Ingersoll (1989), Read & Hide (1983, 1984),
Sommeria et al. (1988)

A new frontier: directly imaged planets andbrown dwarfs

Brown dwarf basics•

Brown dwarfs are fluid hydrogen objects intermediate in mass between giant planetsand stars. They are often free floating, though many also orbit stars.

•

Presumed to form like stars (i.e., directly collapsing from a hydrogen cloud) but havemasses too low to fuse hydrogen. Generally defined as objects with masses of 13 to~80 Jupiter masses.

•

Since they cannot fuse hydrogen, they cool off over time (like Jupiter). But massive
brown dwarfs cool slowly and can still have surface temperatures >1000 K even after
many billions of years
Evolution tracks: luminosity versus time•

Over a wide mass range (~0.3 to ~80
Jupiter masses), brown dwarfs andgiant planets have radii very close to
Jupiter’s.

•>1000 brown dwarfs have been
discovered, mostly with hightemperature (>700 K) but now
including objects as cool as ~300 K.

Burrows et al. (2001)

M
L
T
Jupiter

Burgasser (2009, “The brown-dwarf exoplanet connection”)

Typical brown dwarf infrared spectra

Brown dwarfs are classified according to their IR spectra into M, L, T, and Y (from hot tocold). Unlike most stars, their spectra are dominated by molecular features. Dust (i.e.,silicate clouds) affects the spectrum of M and L dwarfs, but not T dwarfs.

datamodel with clouds

Saumon et al. (2006)

T dwarfs are generally cloud free:This behavior is explained by the factthat condensate levels lie in theatmosphere for hot objects (M, L
dwarfs) but sink into the interior forcool objects (T dwarfs):

Burrows et al. (2001)

model without clouds

Tsuji et al. (2004)

Brown dwarfs show evidence for condensate (dust) clouds
L dwarfs are cloudy, leading to flat spectral features:bright

M
Saumon & Marley (2008)

Magnitude (brightness) in J band, which isa spectral window

Color-magnitude diagrams are useful for understanding
overall trends among brown dwarfs

L

T
dim

blue

red
Color

The change in color across the L/T transition is due to the loss of clouds, which opens
the spectral windows. This occurs better in J than K, causing a shift to the blue as theclouds disappear.

bright

M
Saumon & Marley (2008)

Magnitude (brightness) in J band, which isa spectral window

Color-magnitude diagrams are useful for understanding
overall trends among brown dwarfs“J-band bump”
L

T
dim

blue

red
Color

The change in color across the L/T transition is due to the loss of clouds, which opens
the spectral windows. This occurs better in J than K, causing a shift to the blue as theclouds disappear.

•Although the loss of clouds across the L/Ttransition makes sense, the details are apuzzle: the transition occurs too fast.
–

1D models of uniform cloud decks sinking
into the interior predict that the J-band flux
continually dims across the transition:–

But in reality the J-band flux actually
increases temporarily across the transition(the “J-band bump”), despite the fact that T
dwarfs are cooler than L dwarfs–

This suggests that the cloud decks are notsimply disappearing from view, but
becoming patchy or getting thin as they do so

1D models that assume the cloud deck gets
patchy across the transition do a much betterjob of reproducing the “J-band bump”

This suggests a strong role formeteorology in controlling the transition

Marley et al. (2010)•

Burrows et al. (2006)

The L/T transition

Chemical disequilibrium
In cool giant planets and brown dwarfs, the equilibrium form of carbon and nitrogenat the top are CH4 and NH3. The equilibrium form at depth are CO and N2.

•

In the absence of dynamics, equilibrium would prevail. But vertical mixing candredge CO-rich, CH4-poor, and NH3-poor air from depth and mix it into theatmosphere.

•

This will result in an excess of CO, and a deficit of CH4 and NH3, in the atmosphere•

Just such excesses and deficits are observed, and are interpreted as the result ofvertical mixing. The observed abundances can be used to constrain the mixing rates
Saumon et al. (2006)•

Thus, dynamics is required to explain the chemical disequilibrium

T2.5 brown dwarf SIMP 0136 shows weather
variability

Artigau et al. (2009); see also Radigan et al. (2012), Buenzli et al. (2012), andmany upcoming papers by Apai, Metchev, Radigan, Flateau, ….

Light Curves

Artigau et al. (2009)

Apai et al. (2013)

Doppler imaging technique: a method to map thesurface patchiness of brown dwarfs

Showman (2014); see also Rice (2002)

Maps of Luhman 16B, the closest known brown dwarf to Earth

Crossfield et al. (2014, Nature), see also Showman (2014, Nature)Summary of evidence for dynamics/weather on brown dwarfs
1) Existence of clouds is required to explain spectra of many brown dwarfs.
2) Explaining the L/T transition requires change in cloud dynamics/physics, e.g.,
opening of holes in the clouds, as objects cool off over time.
3) Disequilibrium chemistry (quenching of CO, CH4, NH3) implies mixing frombelow, and allows mixing rate to be inferred if chemical kinetics are understood.
4) IR variability implies cloudy and cloud-free patches rotating in and out of view.
Shape of lightcurves vary over time, implying that the spatial pattern of cloud
patchiness evolves rapidly.

5) Doppler imaging allows global maps of surface patchiness to be inferred for thebrightest brown dwarfs.

Dynamical Regime of brown dwarfs•

Rapid rotation (Period ~ 1.5-12 hours) implies
rotational domination (Rossby numbers << 1)•

Stably stratified atmosphere overlies vigorously
convecting interior•

No external irradiation
no imposed
horizontal gradients in heating or temperature(unlike solar system planets or transiting
exoplanets)

Þ• Wave generation will play a

Burrows et al. (2006)

key role. Atmospheres may bemechanically driven, likestratospheres of Earth and Jupiter

Freytag et al. (2010)

Some questions• What is the atmospheric circulation like on brown dwarfs? Are there zonal
jets? Large vortices? Fluctuating turbulence? What are the wind speeds,
temperature fluctuations, and key length scales?

• How does the circulation work? What types of waves are generated by theconvection, and by what mechanisms might they drive a circulation? How
coupled is the atmosphere to the interior?

• What are the vertical mixing rates? To what extent is the mixing dominatedby breaking gravity waves rather than large-scale overturning?

• How do clouds couple to the circulation? How patchy are the cloud layers?

Jupiter at many wavelengths

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(p.7) https://wisp.physics.wisc.edu/astro104/homework/homework7_soln.html(p.8左) http://photojournal.jpl.nasa.gov/catalog/PIA02873(p.9左) http://apod.nasa.gov/apod/ap140413.html(p.13上) http://lasp.colorado.edu/~bagenal/3720/CLASS18/TaylorColumns.jpg(p.13下) http://slideplayer.es/slide/5327635/(p.17) https://www.nasa.gov/feature/jpl/nasas-juno-spacecraft-breaks-solar-powerdistance-record(p.25左上) http://spaceflightnow.com/news/n0012/30flyby/lightning.jpg(p.25左下) http://cdn.newsapi.com.au/image/v1/bb374edc2dedbb9829c47076061ae243(p.26右) http://www.jpl.nasa.gov/spaceimages/images/largesize/PIA00045_hires.jpg(p.28下) http://photojournal.jpl.nasa.gov/catalog/PIA02823(p.30)
http://newsroom.ucla.edu/portal/ucla/artwork/8/6/4/4/6/186446/Benjamin_Zuckerman_HR_8799_planets_image_Dec._2010_.jpg(p.45) http://www.astrobio.net/also-in-news/brown-dwarfs-reveal-exoplanets-secrets/(p.48) http://www.ehu.eus/iopw/jupiter01_images.htm(p.48右下) http://spacetelescope.org/images/opo9632b/