Supertidal Terrestrial Exoplanets Wade Henning Goddard Space Flight

Supertidal Terrestrial Exoplanets Wade Henning Goddard Space Flight Center July 2012

• Motivation & Orbits • Fixed Parameter Tides • Viscoelastic Tides • Subtopics & Discussion Tidal Overview Habitability Resonances & Perturbations Eccentricity Heating Melting Equilibrium Volcanism Melt Transport 1. Orbital Environment 2. Fixed Parameter Tides 3. Viscoelastic Method 4. Effects

Exoplanet Eccentricities Out to 0. 5 AU - Data c. 2010 exoplanet. eu (Schneider, 2010). - Subject to change, and includes a number of e<x values. Out to 5. 0 AU • Motivation & Orbits • Fixed Parameter Tides • Viscoelastic Tides • Subtopics & Discussion

• Motivation & Orbits • Fixed Parameter Tides • Viscoelastic Tides • Subtopics & Discussion Tidal Heat: Two Models Fixed Parameter Form: External Terms: Knowable, but high powers Internal Terms: Uncertainty Peale & Cassen, 1978; Peale et al. , 1979 Viscoelastic Form: Segatz et al. , 1988

Fixed Q Tidal Solutions • Motivation & Orbits • Fixed Parameter Tides • Viscoelastic Tides • Subtopics & Discussion ? Extreme Volcanism Modest Impact Earth ~44 TW Computed for: e = 0. 05, 1 ME, 1 MSol, Q = 50, k 2 = 0. 3 Negligible Impact

Heat Rate Ratios • Motivation & Orbits • Fixed Parameter Tides • Viscoelastic Tides • Subtopics & Discussion Heating Ratios suggest the region and mode of tidal relevance for earthlike planets e=0. 1 M=1 ME k 2 = 0. 3 Q = 50 A = 0. 3 Based on data from Exoplanet. eu, Jean Schneider, Mid-2010

Viscoelastic Method: Four Models Maxwell Voigt-Kelvin S. A. S. • Motivation & Orbits • Fixed Parameter Tides • Viscoelastic Tides • Subtopics & Discussion Burgers Model: η M δJ J η η δJ ηA ηB Ju MB Displacement Step Response: Time Work Freq. Response (Applied Strain): Period Diffusion Creep & Grain Boundary Slip e. g. Cooper, 2002

Viscoelasticity: Typical Results Response Peak • Motivation & Orbits • Fixed Parameter Tides • Viscoelastic Tides • Subtopics & Discussion Solidus Partial Melt Region SAS Model, 15 day period, e=0. 03, 1 e 22 Pa-s, 1 ME

• Motivation & Orbits • Fixed Parameter Tides • Viscoelastic Tides • Subtopics & Discussion Tidal Equilibria Convection Heat Flow (T) Tidal Work (T) δ=(d/2 a 2)(Ra/Rac) -1/4 αgρd 4 q. BL Ra = η(T) κ ktherm Stable Planetary Equilibrium Ein = Eout TSolidus SAS Model, 15 day period, e=0. 03 O’Connell and Hager, 1980 Fischer and Spohn, 1990 Moore, 2003

• Motivation & Orbits • Fixed Parameter Tides • Viscoelastic Tides • Subtopics & Discussion Tidal Equilibria Convection Heat Flow (T) Tidal Work (T) Sudden Heating TSolidus SAS Model, 15 day period, e=0. 03

• Motivation & Orbits • Fixed Parameter Tides • Viscoelastic Tides • Subtopics & Discussion Tidal Equilibria Convection Heat Flow (T) Tidal Work (T) Halted Secular Cooling TSolidus SAS Model, 15 day period, e=0. 03

Burgers: Double Response Peak Burgers Model, 15 day period, e=0. 03 • Motivation & Orbits • Fixed Parameter Tides • Viscoelastic Tides • Subtopics & Discussion

• Motivation & Orbits • Fixed Parameter Tides • Viscoelastic Tides • Subtopics & Discussion Mapping Behaviors via Equilibria Increasing Tidal Forcing Heat Rate (e. g. eccentricity) (TW) Bifurcation Diagram Tidal Forcing (e. g. e or a) Heating Shifting Equilibrium Points Unstable Branch Stable Branch Migration Cooling Bifurcation Point Secular Cooling Uninterrupted by Tides Temperature TSolidus

Circularization Extension • Motivation & Orbits • Fixed Parameter Tides • Viscoelastic Tides • Subtopics & Discussion GJ 876 d, 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 = 4 Ga Therefore, try to check using the form: τcirc = Wade Henning, Departmental Seminar, Feb. 2009 GMpri. Msece 2 (1 -e 2)a. Etidal

• Motivation & Orbits • Fixed Parameter Tides • Viscoelastic Tides • Subtopics & Discussion 55 Cnc e Peak ~ 1 e 8 TW Equilibrium ~ 40000 TW 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 = 7 Ga Wade Henning, Departmental Seminar, Feb. 2009

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: 1 ME moon around a 1 MJ host, P = 8 days, eintial = 0. 9 Q = 100 → H = 25, 000 TW τcric ~70 Ma → → Q = 1000 H ~ 250, 000 TW → τcric ~700 Ma At 25000 TW, potential to resurface up to ~60% of a 1 RE 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, einital 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 • Motivation & Orbits • Fixed Parameter Tides • Viscoelastic Tides • Subtopics & Discussion Supertidal Earthlike Partial melt regions eventually expand into the mantle despite high pressures. High partial melt zones rob the mantle of volume to couple into tides Focusing and Amplification? Regions of partial melt Tidal-Advective Equilibrium: Balance between the volume well coupled to tidal heating, and volume of melt percolating to the surface. Will depend on: permeability, grain sizes, melt storage, bulk geometry

Magma Ocean Worlds Magma Oceans Worlds: 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 Surface magma ocean initiation: Requires ~500, 000 TW ~8 m global resurfacing depth per year Magma Lakes: ~4000 TW: Resurfacing 10% of dry Earth surface to 1 m per year • Motivation & Orbits • Fixed Parameter Tides • Viscoelastic Tides • Subtopics & Discussion

• Motivation & Orbits • Fixed Parameter Tides • Viscoelastic Tides • Subtopics & Discussion Habitable Zone Modification • Near G class stars: – Tides have minimal impact on surface temperatures • Tidal Zone Near M-Dwarf stars: – Can help get the habitable zone further away from UV radiation kill zone, synchronization zone, and superflares • Habitable Zone Near K stars: – Still too bright for the tidal and habitable zone to overlap • Tidal Zone Habitable planets/moons far from or without luminous primaries: – Habitable zone not just defined by LStar and a. Planet – 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 Hab Zone HZ Tidal Zone Reduction Shifting & Reduction or Expansion

Habitable Zone Widths Assuming: LStar = 0. 124 LSol, A = 0. 3, and “Ideal Viscoelastic Tuning” • Motivation & Orbits • Fixed Parameter Tides • Viscoelastic Tides • Subtopics & Discussion

Habitable Zone Modification by Mass At 0. 012 LSol (~M 3. 5 V) H. Z. Separation occurs • Motivation & Orbits • Fixed Parameter Tides • Viscoelastic Tides • Subtopics & Discussion At 0. 02 LSol (~M 3 V) Preferential Reduction occurs Assuming: A = 0. 3, and Q=50/Ideal Viscoelastic Tuning

Exomoon Tidal Habitable Zones • Motivation & Orbits • Fixed Parameter Tides • Viscoelastic Tides • Subtopics & Discussion Tides Matter Most Where Insolation is Weak a. Io = 0. 00283 AU • 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

Detecting Extrasolar Volcanism • Motivation & Orbits • Fixed Parameter Tides • Viscoelastic Tides • Subtopics & Discussion Sulfur Dioxide: spectral proxy for extrasolar volcanism Mt. Pinatubo, June 14, 1991 Gas H 2 O CO 2 SO 2 H 2 S H 2 HCl HF CO OCS Volume, Ave Rift. Zone (mol%) Pinatubo, Total mass (Mt) 63. 6 20. 6 9. 49 0. 91 4. 91 0. 92 0. 0007 250 -500 82 -104 15 -19 1. 2 -1. 6 0. 2 -0. 5 0 -3. 0 - Too Common Best signal Good secondary signal Too Common, Too little Washed out Too little Converts to SO 2 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 activity Lower viscosities, MOR/OI style eruptions Magma lakes & oceans Devolitization – less water/steam LIP style eruptions? Image: Clark Air Force Base Staff, 1991

Extrasolar Volcanism, Methods • Motivation & Orbits • Fixed Parameter Tides • Viscoelastic Tides • Subtopics & Discussion Spectrum via L. Kaltenegger: Transmission (Primary Eclipse) Black: no SO 2 Red: 10 x Pinatubo Eruption Blue 100 x Pinatubo Eruption Secondary Eclipse Emission/Reflection (Direct Imaging) Kaltenegger Henning and Sasselov, 2010 NASA, JWST

Detecting Extrasolar Extreme Tidal. Volcanism • Motivation & Orbits • Fixed Parameter Tides • Viscoelastic Tides • Subtopics & Discussion Earthlike rates of large explosive Plinean volcanism, and the number of # of observations needed for detection 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