supertidal terrestrial exoplanets wade henning goddard space flight center july 2012
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Supertidal Terrestrial Exoplanets
Wade Henning Goddard Space Flight Center
July 2012
Tidal Overview• Motivation & Orbits• Fixed Parameter Tides• Viscoelastic Tides• Subtopics & Discussion
1. Orbital Environment 2. Fixed Parameter Tides 3. Viscoelastic Method 4. Effects
Eccentricity Heating Melting EquilibriumVolcanism
Habitability
Melt Transport
Resonances& Perturbations
Exoplanet Eccentricities• Motivation & Orbits• Fixed Parameter Tides• Viscoelastic Tides• Subtopics & Discussion
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0.00 1.00 2.00 3.00 4.00 5.00
Semi Major Axis (AU)E
cce
ntr
icity
.
Out to 0.5 AU Out to 5.0 AU
- Data c. 2010 exoplanet.eu (Schneider, 2010). - Subject to change, and includes a number of e<x values.
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0.00 0.10 0.20 0.30 0.40 0.50
Semi Major Axis (AU)
Ecc
en
tric
ity
.
Fixed Parameter Form:
Viscoelastic Form:
Internal Terms: Uncertainty
Peale & Cassen, 1978; Peale et al., 1979
Tidal Heat: Two Models• Motivation & Orbits• Fixed Parameter Tides• Viscoelastic Tides• Subtopics & Discussion
External Terms: Knowable, but high powers
Segatz et al., 1988
Fixed Q Tidal Solutions
Earth ~44TW
• Motivation & Orbits• Fixed Parameter Tides• Viscoelastic Tides• Subtopics & Discussion
?
Extreme Volcanism
Modest Impact Negligible
Impact
Computed for: e = 0.05, 1ME, 1MSol, Q = 50, k2 = 0.3
1.E-06
1.E-03
1.E+00
1.E+03
1.E+06
1.E+09
0 5 10 15 20 25 30 35 40
Hot Earth Orbital Period (days)
Hea
t R
ate
Rat
io
.
TIDES DOMINATE SURFACEPeriod < ~2
TIDES DOMINATE INTERIOR
Period < ~25
ETidal / ERadio
ETidal / EInsol
. .
. .
EXTREME SOLUTIONS
QUESTIONABLE
GJ 876 cx
GJ 876 bx
HIP 57050 bx
GJ 581 dx
GJ 581 cx
HD285968 bx
e=0.1M=1ME
k2 = 0.3Q = 50A = 0.3
Based on data from Exoplanet.eu, Jean Schneider, Mid-2010
Heat Rate RatiosHeating Ratios suggest the region and mode of tidal relevance for earthlike planets
• Motivation & Orbits• Fixed Parameter Tides• Viscoelastic Tides• Subtopics & Discussion
Viscoelastic Method: Four Models
Voigt-Kelvin
η J
S.A.S.
ηδJ
Ju
Burgers
ηA δJ
MB
ηB
Step Response:
Time
Dis
pla
cem
en
tMaxwell
M
η
Model:
Period
Wo
rk
Diffusion Creep &Grain Boundary Slip
e.g. Cooper, 2002
Freq. Response (Applied Strain):
• Motivation & Orbits• Fixed Parameter Tides• Viscoelastic Tides• Subtopics & Discussion
Viscoelasticity: Typical Results
Partial Melt Region
Response Peak Solidus
SAS Model, 15 day period, e=0.03, 1e22 Pa-s, 1ME
• Motivation & Orbits• Fixed Parameter Tides• Viscoelastic Tides• Subtopics & Discussion
Convection Heat Flow (T)
Tidal Work (T)
TSolidus
O’Connell and Hager, 1980Fischer and Spohn, 1990
Moore, 2003
SAS Model, 15 day period, e=0.03
Stable Planetary Equilibrium
Ein = Eout
Tidal Equilibria• Motivation & Orbits• Fixed Parameter Tides• Viscoelastic Tides• Subtopics & Discussion
δ=(d/2a2)(Ra/Rac) -1/4
Ra =αgρd4qBL
η(T) κ ktherm
Sudden Heating
Convection Heat Flow (T)
Tidal Work (T)
TSolidus
SAS Model, 15 day period, e=0.03
Tidal Equilibria• Motivation & Orbits• Fixed Parameter Tides• Viscoelastic Tides• Subtopics & Discussion
Halted Secular Cooling
TSolidus
SAS Model, 15 day period, e=0.03
Convection Heat Flow (T)
Tidal Work (T)
Tidal Equilibria• Motivation & Orbits• Fixed Parameter Tides• Viscoelastic Tides• Subtopics & Discussion
Burgers Model, 15 day period, e=0.03
Burgers: Double Response Peak• Motivation & Orbits• Fixed Parameter Tides• Viscoelastic Tides• Subtopics & Discussion
ShiftingEquilibrium
Points
Tidal Forcing (e.g. e or a)
Heating
Cooling
Secular Cooling Uninterrupted by Tides
StableBranch
UnstableBranch
Bifurcation Point
Temperature
Migration
TSolidus
Heat Rate (TW)
Increasing Tidal Forcing
(e.g. eccentricity)
TSolidusTemperature
Bifurcation Diagram
Mapping Behaviors via Equilibria• Motivation & Orbits• Fixed Parameter Tides• Viscoelastic Tides• Subtopics & Discussion
1200 1300 1400 1500 1600 1700 1800 1900 2000
100
102
104
106
108
Hea
t R
ate
(TW
)
Mantle Temperature (K)
Tsolidus
Tbreakdown
Tidal Input (Maxwell)
Convective Output
Circularization Extension
Wade Henning, Departmental Seminar, Feb. 2009
• Motivation & Orbits• Fixed Parameter Tides• Viscoelastic Tides• Subtopics & Discussion
GJ 876d, M sin(i) = 6.3 ME, Period = 1.937 days, e: using 0.139 (Correia et al. 2010)
Fixed Q Method: Q=100 → τcirc = 4 Ma → H = 80 million TW!
With Heating and Melting: H=80,000 TW → Q =100,000 → τcirc = 4Ga
GMpriMsece2
(1-e2)aEtidal
τcirc =Therefore, try to check using the form:
55 Cnc e
Wade Henning, Departmental Seminar, Feb. 2009
• Motivation & Orbits• Fixed Parameter Tides• Viscoelastic Tides• Subtopics & Discussion
1100 1200 1300 1400 1500 1600 1700 1800 1900 200010
-1
100
101
102
103
104
105
106
107
108
Hea
t R
ate
(log
TW
)
Mantle Temperature (K)
Tsolidus T
breakdown
Tidal Input (Maxwell)
Tidal Input (Burgers)
Convective Output
Peak ~ 1e8 TWEquilibrium ~ 40000TW
55 Cnc e, Msin(i) = 7.6 ME, Period = 2.82 days, e: using 0.07, 1.03 MSol
Simple Fixed Q Method: Q=100 → τcirc = 10 Ma → H = 20 million TW
But With Heating and Melting: H=40,000 TW → Q =60,000 → τcirc = 7Ga
Circularization: Exomoons• Motivation & Orbits• Fixed Parameter Tides• Viscoelastic Tides• Subtopics & Discussion
• Consider a silicate exomoon analog of Triton, recently captured into a highly eccentric orbit.
EXAMPLE: 1ME moon around a 1MJ host, P = 8 days, eintial = 0.9
Q = 100 → τcric ~70 Ma → H ~ 250,000 TW
H = 25,000 TW → Q = 1000 → τcric ~700 Ma
At 25000 TW, potential to resurface up to ~60% of a 1RE surface per year
• With traditional circularization, τcric is often independent of the starting eccentricity.(If e starts higher, dissipation is just more intense). But with Heat-limited behavior, e inital
suddenly matters far more.
Ice Silicate Hybrid: H(r), H(t)• Motivation & Orbits• Fixed Parameter Tides• Viscoelastic Tides• Subtopics & Discussion
Multilayer Comparisons• Motivation & Orbits• Fixed Parameter Tides• Viscoelastic Tides• Subtopics & Discussion
Homogeneous Silicate: H = 0.63 TW
Multilayer Earth Model: H = 0.82 TW
Ice Silicate Hybrid: H = 26.72 TW
Tidal Shutdown
SupertidalEarthlikePartial melt regions
eventually expand into the mantle despite high
pressures.
Tidal-Advective Equilibrium: Balance between the volume well coupled to tidal heating, and volume of melt percolating to the surface.
High partial melt zones rob the mantle of volume to
couple into tides
• Motivation & Orbits• Fixed Parameter Tides• Viscoelastic Tides• Subtopics & Discussion
Will depend on: permeability, grain sizes, melt storage, bulk geometry
Focusing and Amplification?
Regions of partial melt
Regions of partial melt
Magma Oceans Worlds:
Surface magma ocean initiation:
~4000 TW: Resurfacing 10% of dry Earth surface to 1m per year
Magma Lakes:
Requires ~500,000 TW
Subsurface, set up by insolation, giant impacts, or primordial
Fluid Planet Love Number:
• Response peak ~seconds • In short highly eccentric orbits tides may exceed
radionuclides• Magma slosh in partially melted oceans
~8m global resurfacing depth per year
Magma Ocean Worlds• Motivation & Orbits• Fixed Parameter Tides• Viscoelastic Tides• Subtopics & Discussion
• Near G class stars:– Tides have minimal impact on surface
temperatures
• Near K stars:– Still too bright for the tidal and habitable zone to
overlap
• Near M-Dwarf stars:– Can help get the habitable zone further away from
UV radiation kill zone, synchronization zone, and superflares
• Habitable planets/moons far from or without luminous primaries:
– Habitable zone not just defined by LStar and aPlanet – Has more to do with the distribution in nature of
eccentricities and the frequency of occurrence of mean-motion resonances. Statistically much harder to quantify
HZ
Tidal Zone
Habitable Zone
Hab Zone
HZ
Tidal Zone
Reduction
Shifting & Reduction
HZ
Tidal Zone
Shifting & Reduction
or Expansion
Habitable Zone Modification• Motivation & Orbits• Fixed Parameter Tides• Viscoelastic Tides• Subtopics & Discussion
Tidal Zone
Tidal Zone
Assuming: LStar = 0.124 LSol, A = 0.3, and “Ideal Viscoelastic Tuning”
Habitable Zone Widths• Motivation & Orbits• Fixed Parameter Tides• Viscoelastic Tides• Subtopics & Discussion
H.Z. Separation occurs Preferential Reduction occurs
At 0.012 LSol (~M3.5V) At 0.02 LSol (~M3V)
Assuming: A = 0.3, and Q=50/Ideal Viscoelastic Tuning
Habitable Zone Modification by Mass• Motivation & Orbits• Fixed Parameter Tides• Viscoelastic Tides• Subtopics & Discussion
aIo = 0.00283 AU
Tides Matter Most Where Insolation is Weak
• Based on achieving surface temp. of 273 to 373 K• Negligible insolation
• 30 - 40 K contribution from Earthlike radiogenic+ bkgd. heat• Changing MPri alters zones in a but not in T.
e.g. @ Ultracool Dwarfs: Eduardo Martín et al. 1999 Ejected planets: Renu Malhotra et al. 2005
Exomoon Tidal Habitable Zones• Motivation & Orbits• Fixed Parameter Tides• Viscoelastic Tides• Subtopics & Discussion
Detecting Extrasolar Volcanism• Motivation & Orbits• Fixed Parameter Tides• Viscoelastic Tides• Subtopics & Discussion
Image: Clark Air Force Base Staff, 1991
Mt. Pinatubo, June 14, 1991Sulfur Dioxide: spectral proxy for extrasolar volcanism
H2O 63.6 250-500 Too CommonCO2 20.6 82-104 Too CommonSO2 9.49 15-19 Best signalH2S 0.91 1.2-1.6 Good secondary signalH2 4.91 0.2-0.5 Too Common, Too littleHCl - 0-3.0 Washed outHF - - Too littleCO 0.92 - Too littleOCS 0.0007 - Converts to SO2
Volume, AveRift. Zone
(mol%)
Pinatubo,Total mass
(Mt)Gas
Kaltenegger Henning and Sasselov 2010 & refs therein
- Explosive Events: Stratospheric deposition best for observablity and reduced washout- Pinatubo: Best measured stratospheric event-Tidal Volcanism: Competing effects
More overall activityLower viscosities, MOR/OI style eruptionsMagma lakes & oceansDevolitization – less water/steamLIP style eruptions?
Kaltenegger Henning and Sasselov, 2010
Emission/Reflection (Direct Imaging)
• Motivation & Orbits• Fixed Parameter Tides• Viscoelastic Tides• Subtopics & DiscussionExtrasolar Volcanism, Methods
Secondary Eclipse
Transmission (Primary Eclipse) Spectrum via L. Kaltenegger: Black: no SO2
Red: 10x Pinatubo Eruption
Blue 100x Pinatubo Eruption
NASA, JWST
Extreme Tidal Volcanism
Earthlike rates of large explosive Plinean volcanism, and the number of # of observations needed for detection
• Motivation & Orbits• Fixed Parameter Tides• Viscoelastic Tides• Subtopics & Discussion
El Chichón Pinatubo Krakatau Tambora Taupo Toba Yellowstone
0.5x 1x 2x 10x 100x 500x 1000x
1982 1991 1883 1815 23500 y.a. 73000 y.a. 600000 y.a.
5 6 7 7 8.1* 8.8* 8.7-8.9*
7-8 17 30-50 ~200 est. ~2000 est. ~10,000 est. ~20,000 est.
0.05-0.2** 0.03 0.002 0.001 1e-4-1e-6** 1e-6-1e-8** 1e-6-1e-8**
1% 1 1 6 11 1e2-1e4 1e5-1e6 1e5-1e6
10% 1-3 4 53 106 1e3-1e5 1e6-1e7 1e6-1e7
90% 11-45 76 1151 2302 2e4-2e6 2e7-2e8 2e7-2e8
n/a 2 30 170 170 170 170
1% n/a 183 73 24 2e2-2e4 2e5-2e6 2e5-2e6
10% n/a 730 645 228 2e3-2e5 2e6-2e7 2e5-2e6
90% n/a 13870 14003 4943 5e5-5e6 5e7-5e8 5e7-5e8
Signal Duration, Nd (days)
# Observations to achieve P =
VEI/Mag
Stratosphereic SO2 (Mt)
Frequency Estimate, f (1/yr)
# Planet-years to achieve P =
Name
~ x Baseline
Year
Detecting Extrasolar Volcanism
e.g: ~10% chance of seeing a Tambora class event after watching 106 Earths for 1 year, 50 Earths for 2 years, or 10 Earths for 10 years.
Probabilities enhanced for moderate tidal worlds, younger planets
Tides and Disks?• Motivation & Orbits• Fixed Parameter Tides• Viscoelastic Tides• Subtopics & Discussion
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