supertidal terrestrial exoplanets wade henning goddard space flight center july 2012

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