Lecture IV: Terrestrial Planets
1.
2.
3.
4.
From Lecture III: Atmospheres
Earth as a planet: interior & tectonics.
Dynamics of the mantle
Modeling terrestrial planets
Observations for Reflected Light
• Sudarsky Planet types
– I : Ammonia Clouds
– II : Water Clouds
– III : Clear
– IV : Alkali Metal
– V : Silicate Clouds
• Predicted Albedos:
– IV : 0.03
– V : 0.50
Picture of class IV planet generated using
Celestia Software
Sudarsky et al. 2000
Lunar Transit of Earth
• Compare the albedo of
the Moon to the
Earth’s features, e.g.,
the Sahara desert.
NASA EPOXI spacecraft (2008)
HD 209458b: Albedos
New upper
limit on Ag
(Rowe et al. 2008)
Rowe et al.(2006)
Models Constraints
Different atmospheres
Equilibrium Temperature
blackbody
model
Spitzer Limit
best fit
2004 1 sigma limit – or ~2005 3 sigma limit
Rowe et al. 2006
Rowe et al. (in prep)
The Close-in Extrasolar Giant Planets
• Type and size of condensate is important
• Possibly large reflected light in the optical
• Thermal emission in the infrared
Scattered Light
Need to consider:
• phase function
• multiple scattering
Scattering Phase Functions and Polar Plots
MgSiO3 (solid), Al2O3 (dashed), and Fe(s)
Forward throwing & “glory”
Seager, Whitney, & Sasselov 2000
MOST at a glance
Mission
 Microvariability and
Oscillations of STars /
Microvariabilité et
Oscillations STellaire
 First space satellite dedicated
to stellar seismology
 Small optical telescope &
ultraprecise photometer
 goal:
~few ppm = few micromag
Canadian Space Agency (CSA)
MOST at a glance
Orbit
 circular polar orbit
 altitude h = 820 km
 period P = 101 min
 inclination i = 98.6º
 Sun-synchronous
 stays over terminator
 CVZ ~ 54° wide
 -18º < Decl. < +36º
 stars visible for up to 8 wks
 Ground station network
 Toronto, Vancouver, Vienna
CVZ =
Continuous
Viewing Zone
MOST
• Relative depths
– transit: 2%
– eclipse: 0.005%
• Duration
– 3 hours
• Phase changes of
planet
Relative Flux
Lightcurve Model for HD 209458b
Eclipse
Transit
Phase
Lecture IV: Terrestrial Planets
1. Earth as a planet: interior & tectonics.
2. Dynamics of the mantle
3. Modeling terrestrial planets
Earth’s interior
PREM = Preliminary
Reference Earth Model
Earth as a planet - tectonics
Earth as a planet - tectonics
Earth - plate collision & subduction
Evidence from seismic
tomography for the
subduction of the plate
under Japan.
Variations in shear-wave
velocity: dvS/vS
Earth - the Core-Mantle Boundary
QuickTime™ and a
YUV420 codec decompressor
are needed to see this picture.
Labrosse & Sotin (2002)
Earth mantle convection simulation
Earth interior - mantle plumes
Earth interior - cooling
Super-Earths
Super-Earths:
planets in the mass range of ~1 to 10 ME
1. Mass range is now somewhat arbitrary
•
Upper range corresponds approx to a core that
can accrete H2 gas from the disk.
2. Two generic families - depending on H2O content.
3. No such planets in our Solar System.
(Discussed at Nantes Workshop - June 16-18, 2008)
Interiors of Super-Earths
Formation and survival of large
terrestrial planets:
All evidence
is that they
should be
around:
Ida & Lin (2004)
The “Tree of super-Earths”
Super-Earths
Terrestrial
Planets /
Dry, Rocky
Planets
Fe -rich
mantle
?
H2O -rich
mantle
Ocean
Planets /
Aqua
Planets
Mini-Neptunes
?
?
?
?
Super-Earth Model
Input: M, Psurf, Tsurf, guess R, gsurf, composition
Output: R, ρ(r), P(r), g(r), m(r), phase transitions, D, ...
Interior
Models:
the Mass
Dependence
Zero-temperature
spheres
Zapolsky & Salpeter (1969);
Stevenson (1982);
Fortney et al. (2007);
Seager et al. (2007)
(GJ 436b: Gillon et al. 2007)
Interior Structure of Super-Earths
Interior Structure: Radius & Composition
Valencia, Sasselov, O’Connell (2007)
Phase Diagram of H2O
Super-Earths
“Confusion region”
Mass range:
~1 - 10 Earth mass
‘Toblerone’ Diagram
M±ΔM
Valencia et al. 2007b
A tool to infer which compositions fit M and R with uncertainties
Degeneracy is important
dRP
Valencia, Sasselov, O’Connell (2007)
Models vs. Kepler observations
Earth is a ‘perovskite’ planet
(Fe, Mg) SiO3
- enstatite
- perovskite (Pv)
40% of Earth is Pv !
- post-perovskite (pPv)
Pv
pPv at ~125 GPa
Tiny amount of post-perovskite
at the CMB (the thin D” region)
Super-Earths are
‘post-perovskite’ planets.
Super-Earths as post-Perovskite planets
T-P curves for 7.5 ME models
< Note: all mantles
have pressures that
reach 1000 GPa
(Valencia, Sasselov,
O’Connell 2007)
Super-Earths: very high pressures
Post-Perovskite
Super-Earths as post-Perovskite planets
pPv
(Oganov 2006)
Pv
Does post-perovskite incorporate more Fe ?
Is there a post-post perovskite, e.g. like GGG ?
Are there analogs to the Pv lower mantle ‘oxygen pump’ ?
Post- Post-Perovskite ?
Expectation that all
(Si, Al, Mg, Fe) oxides
will collapse to an
O12 perovskite structure,
like Gd3Ga5O12 (GGG)
does at >120 GPa.
< above 150 GPa becomes
less compressible than
diamond !
(Mashimo, Nellis, et al. 2006)
New high-P experiments needed
(2008)
Z-Beamlet target chamber of 10TWcm-2 setup at SNL
(J.Remo, S.Jacobsen, M.Petaev, DDS)
(Remo et al. 2008)
T-P: Experimental Results
We measure 10-50x Fe, Cr, Al -enrichments of
the silicate melts
(Rightley et al. 1996)
Strong mixing occurs due to a Richtmeyer-Meshkov
instability behind the shock
- is it scalable & relevant to giant impacts ?
Interiors of Super-Earths
Earth-like
Ocean Planet
Interiors of Super-Earths
Mass-Radius relations for 11 different
mineral compositions (Earth-like):
Valencia, O’Connell, Sasselov (2005)
1ME
2ME
5ME
10ME
Theoretical Error Budget:
Planet Radius Errors:




New high-P phases, e.g. ice-XI:
EOS extrapolations (V vs. BM):
Iron core alloys (Fe vs. FeS):
Viscosity, f(T ) vs. const.:
-0.4%
+0.9%
-0.8%
+0.2%
 Overall the uncertainties are below 2%
(at least, that’s what is known now)
20,000
7.5 ME
12,000
4,000
2,000
6,000
RADIUS (km)
10,000
Valencia, Sasselov, O’Connell (2006)
DENSITY (kg/m3)
Interior Structure of GJ 876d
Interior Structure of GJ 876d
What would we look for
and could we measure it ?
Could we measure the difference? - YES:
We need at least 5% in Radius,
and at least 10% in Mass.
Work on tables for use with Kepler
underway - masses 0.4 to 15 ME
Degeneracy - solution: samples
H2O
All you need to constrain planet formation models!
- sample with radii to 5% and masses to 10%.
QuickTime™ and a
decompressor
are needed to see this picture.
Valencia, Sasselov, O’Connell (2007)
Dry vs. Ocean super-Earths