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


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):


Viscoelasticity: Typical Results

Partial Melt Region

Response Peak Solidus

SAS Model, 15 day period, e=0.03, 1e22 Pa-s, 1ME


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


Tidal Work (T)

TSolidus



Halted Secular Cooling

TSolidus



Tidal Work (T)


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


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


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


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


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

supertidal terrestrial exoplanets wade henning goddard space flight center july 2012

Documents

fixed parameter tides3

viscoelastic form

viscoelastic method4

fixed q method

fixed q tidal solutionsearth

tidal heat

day period

mode of tidal relevance