Geodynamics of terrestrial exoplanets

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Artistic sketch of Kepler-22b, a recently discovered exoplanet with comparable mass (within 10 Earth masses) of the planet Earth. Kepler22b-artwork.jpg
Artistic sketch of Kepler-22b, a recently discovered exoplanet with comparable mass (within 10 Earth masses) of the planet Earth.

The discovery of extrasolar Earth-sized planets has encouraged research into their potential for habitability. One of the generally agreed [1] requirements for a life-sustaining planet is a mobile, fractured lithosphere cyclically recycled into a vigorously convecting mantle, in a process commonly known as plate tectonics. Plate tectonics provide a means of geochemical regulation of atmospheric particulates, as well as removal of carbon from the atmosphere. This prevents a “runaway greenhouse” effect that can result in inhospitable surface temperatures and vaporization of liquid surface water. [2] Planetary scientists have not reached a consensus on whether Earth-like exoplanets have plate tectonics, but it is widely thought that the likelihood of plate tectonics on an Earth-like exoplanet is a function of planetary radius, initial temperature upon coalescence, insolation, and presence or absence of liquid-phase surface water. [3] [4] [5] [6]

Contents

Potential exoplanet geodynamic regimes

In order to characterize the geodynamic regime of an Earth-like exoplanet, the basic assumption is made that such a planet is Earth-like or “rocky”. This implies a three-layer stratigraphy of (from center to surface) a partially molten iron core, a silicate mantle that convects over geologic timescales, and a relatively cold, brittle silicate lithosphere. Within these parameters, the geodynamic regime at a given time point in the planet's history is likely to fall within one of three categories:

Plate tectonics

The mantle of a planet with plate tectonics has driving forces that exceed the yield strength of the brittle lithosphere, causing the lithosphere to fracture into plates that move relative to each other. [3] [4] A critical element of the plate tectonic system is these lithospheric plates become negatively buoyant at some point in their evolution, sinking into the mantle. The surface mass deficit is balanced by new plate being formed elsewhere through upwelling mantle plumes. Plate tectonics is an efficient method of heat transfer from the interior of the planet to the surface. Earth is the only planet plate tectonics is known to occur on, [6] although evidence has been presented for Jupiter's moon Europa undergoing a form of plate tectonics analogous to Earth's. [7]

Stagnant lid

A stagnant lid regime occurs when mantle driving forces do not exceed the lithospheric yield strength, resulting in a single, continuous rigid plate overlying the mantle. Stagnant lids only develop when the viscosity contrast between the surface and planetary interior exceeds about four orders of magnitude. [8]

Episodic tectonics

Episodic tectonics is a general term for a geodynamic regime that possesses aspects of both plate tectonics and stagnant lid dynamics. Planets with episodic tectonic regimes will have immobile surface lids for geologically long spans of time, until a shift in equilibrium conditions is precipitated by either weakening lithosphere or increasing mantle driving forces. When this occurs, the shift to plate tectonics is usually catastrophic in nature and can involve resurfacing of the entire planet. [9] After such a resurfacing event (or period of resurfacing events), stagnant lid equilibrium conditions are regained, resulting in a quiescent, immobile lid.

Methods of predicting exoplanet geodynamic regimes

Exoplanets have been directly observed and remotely sensed, [10] but due to their great distance and proximity to obscuring energy sources (the stars they orbit), there is little concrete knowledge of their composition and geodynamic regime. Therefore, the majority of information and conjectures made about them come from alternative sources.

Solar system analogues

All the rocky planets in the solar system except Earth are generally believed to be in the stagnant lid geodynamic regime. [8] [9] Mars and particularly Venus have evidence of prior resurfacing events, but appear to be tectonically quiescent today. Geodynamic inferences about solar system planets have been extrapolated to exoplanets in order to constrain what kind of geodynamic regimes can be expected given a set of physical criterion such as planetary radius, presence of surface water, and insolation. In particular, the planet Venus has been intensely studied due to its general physical similarities to Earth yet completely different geodynamic regime. Proposed explanations include a lack of surface water, [9] the lack of a magnetic geodynamo, [11] or large-scale evacuation of interior heat shortly after planetary coalescence. [8]

Another source of insight within our solar system is the history of the planet Earth, which may have had several episodes of stagnant lid geodynamics during its history. [12] These stagnant-lid periods were not necessarily planet-wide; when supercontinents such as Gondwanaland existed, their presence may have shut off plate motion over large expanses of the Earth's surface until mantle heat buildup underneath the superplate was sufficient to break them apart. [13]

Observation of exoplanets

Three identified exoplanets around the roughly sun-sized star HR8799, imaged through a vector vortex coronagraph on a 1.5m section of the Hale telescope. 444226main exoplanet20100414-a-full.jpg
Three identified exoplanets around the roughly sun-sized star HR8799, imaged through a vector vortex coronagraph on a 1.5m section of the Hale telescope.

Indirect and direct observation methods such as radial velocity and coronagraphs can give envelope estimates of exoplanet parameters such as mass, planetary radius, and orbital radius/eccentricity. Since distance from the host star and planetary size are generally believed to influence exoplanet geodynamic regime, inferences can be drawn from such information. For example, an exoplanet close enough to its host star to be tidally locked may have drastically different "dark" and "light" side temperatures and correspondingly bipolar geodynamic regimes (see insolation section below).

Spectroscopy has been used to characterize extrasolar gas giants, but has not yet been used on rocky exoplanets. However, numerical modeling has demonstrated that spectroscopy could detect atmospheric sulfur dioxide levels as low as 1 ppm; presence of sulfur dioxide at this concentration may be indicative of a planet without surface water and with volcanism 1500–80000 times higher than Earth. [2]

Numerical modeling

Since real data on exoplanets is currently limited, a large amount of the dialogue regarding rocky exoplanet tectonics has been driven by the results of numerical modeling studies. In such models, different planetary physical parameters are manipulated (i.e. mantle viscosity, core-mantle boundary temperature, insolation, “wetness” or hydration of subducting lithosphere) and the resultant impact on the geodynamic regime is reported. Due to computational limitations the large amount of variables that control planet geodynamics in real life cannot be accounted for; models therefore ignore certain parameters believed to be less important and emphasize others to try to isolate disproportionately important driving factors. Some of these parameters include:

Scaling parameters

Bar chart showing the size distribution of observed Kepler planet candidates (terrestrial exoplanets in the habitable zone of their host star). Data set is 2,740 planets orbiting 2,036 stars. The Earth-size and Super Earth-size (leftmost) columns represent potential terrestrial exoplanets. Size of Kepler Planet Candidates.jpg
Bar chart showing the size distribution of observed Kepler planet candidates (terrestrial exoplanets in the habitable zone of their host star). Data set is 2,740 planets orbiting 2,036 stars. The Earth-size and Super Earth-size (leftmost) columns represent potential terrestrial exoplanets.

Early models of rocky exoplanets scaled different factors (namely mantle viscosity, lithospheric yield strength, and planetary size) up and down to predict the geodynamic regime of an exoplanet with given parameters. Two scaling studies of exoplanet size published in 2007 came to fundamentally different conclusions: O’Neill and Lenardic (2007) [3] showed that a planet of 1.1 Earth mass would have Earth-like lithospheric yield stress but reduced mantle driving stresses, resulting in a stagnant lid regime. Conversely, Valencia et al. (2007) [4] concluded the increase in mantle velocity (driving force) is large compared to the gravitationally-forced increase of plate viscosity as planets increase beyond one Earth mass, increasing the likelihood of plate tectonics with planet size.

Viscoelastic-plastic rheology

Most models simulate lithospheric plates with a viscoelastic-plastic rheology. In this simulation, plates deform viscoelastically up to a threshold level of stress, at which point they deform in a plastic manner. The lithospheric yield stress is a function of pressure, stress, composition, but temperature has a disproportionate effect on it. [9] Therefore, changes to the lithospheric temperature, whether from external sources (insolation) or internal (mantle heating) will increase or decrease the likelihood of plate tectonics in viscoelastic-plastic models. Models with different modes of mantle heating (heat originating from the core-mantle boundary versus in-situ mantle heating) can produce dramatically different geodynamic regimes. [14]

Time-dependent versus quasi-steady states

For computational purposes, early exoplanet mantle convection models assumed the planet was in a quasi-steady state, that is, the heat input from the core-mantle boundary or internal mantle heating remained constant throughout the model run. Later studies such as that of Noack and Breuer (2014) [1] show that this assumption may have important implications, resulting in a gradual increase of the temperature differential between the core and mantle. A planet modeled with realistic decrease of internal heating throughout time had a lower likelihood of entering a plate tectonic regime compared to the quasi-steady state model.

Damage theory

A flaw of viscoelastic-plastic models of exoplanet geodynamics is in order for plate tectonics to be initiated, unrealistically low yield stress values are required. Additionally, plates in viscoelastic-plastic models have no deformation memory, i.e. as soon as the stress on a lithospheric plate drops below its yield stress it returns to its pre-deformation strength. This stands in contrast to Earth-based observations, which show that plates preferentially break along preexisting areas of deformation. [15]

Damage theory attempts to address this model flaw by simulating voids created in areas of strain, representing the mechanical pulverization of coarse grains of rock into finer grains. In such models, damage is balanced by “healing”, or the temperature and pressure-driven dynamic recrystallization of smaller grains into larger ones. If the reduction of grain size (damage) is intensely localized in a stagnant lid, an incipient crack in the mantle can turn into a full-blown rift, initiating plate tectonics. [16] Conversely, a high surface temperature will have more efficient lithospheric healing, which is another potential explanation for why Venus has a stagnant lid and Earth does not. [15]

Potential determining factors for Earth-like exoplanet geodynamic regimes

Initial temperature

For rocky exoplanets larger than Earth, the initial interior temperature after planetary convalescence may be an important controlling factor of surface motion. Noack and Breuer (2014) [1] demonstrated that a core-mantle boundary initial temperature of 6100 K would likely form a stagnant lid, while a planet of the same dimensions with an initial core-mantle boundary 2000 K hotter will likely eventually evolve plate tectonics. This effect is diminished on planets smaller than Earth, because their smaller planetary interiors efficiently redistribute heat, reducing core-mantle heat gradients that drive mantle convection.

Insolation

Conceptual plot of the effect of distance from a host star vs. planetary age on terrestrial exoplanet geodynamics. Example planets not drawn to scale. Exoplanet wiki figure.jpg
Conceptual plot of the effect of distance from a host star vs. planetary age on terrestrial exoplanet geodynamics. Example planets not drawn to scale.

External sources of planetary heat (namely, radiation from a planet's host star) can have drastic effects on geodynamic regime. With all other variables held constant, an Earth-sized exoplanet with a surface temperature of 273 K will evolve over its geological lifetime from a plate tectonic regime, to episodic periods of plate tectonics interspersed with stagnant lid geodynamics, to a terminal stagnant lid phase as interior heat is exhausted. Meanwhile, a "hot" planet (759 K surface temperature) under the same initial conditions will have an amorphous surface (due to lithospheric yield stress being constantly exceeded) to a stagnant lid as interior heat is exhausted, with no plate tectonics observed. [5]

Planets closer than 0.5 astronomical units from their star are likely to be tidally locked; these planets are expected to have drastically different temperature regimes on their "day" and "night" sides. When this scenario is modeled, the day side displays mobile lid convection with diffuse surface deformation flowing toward the night side, while the night side has a plate tectonic regime of downwelling plates and a deep mantle return flow in the direction of the night side. A temperature contrast of 400 K between day and night sides is required to create such a stable system. [5]

Presence of surface water

While early modeling studies emphasized the size of a given exoplanet as a critical factor of geodynamic regime, [3] [4] later studies showed that the influence of size may be small to the point of irrelevance compared to the presence of surface water. For plate tectonics to be a sustained, rather than episodic process, the friction coefficient at the upper boundary layer (the mantle-lithosphere interface) must be below a critical value; while some models arrive at a critically low friction coefficient via increased upper boundary layer temperature (and subsequent decreased viscosity), Korenaga (2010) demonstrates high pore fluid content can lower the coefficient of friction below the critical value as well. [6]

Implications of exoplanet geodynamic regime

A planet in a stagnant lid regime has a much lower likelihood of being habitable than one with active surface recycling. The outgassing of mantle-derived carbon and sulfur that occurs along plate margins is critical for producing and maintaining an atmosphere, which insulates a planet from solar radiation and wind. [11] The same atmosphere also regulates surface temperature, providing a clement condition for biological activity. It is for these reasons the search for exoplanets will be steered largely towards finding ones with a plate tectonic geodynamic regime, since they are better candidates for human habitation.

Related Research Articles

<span class="mw-page-title-main">Plate tectonics</span> Movement of Earths lithosphere

Plate tectonics is the scientific theory that Earth's lithosphere comprises a number of large tectonic plates which have been slowly moving since about 3.4 billion years ago. The model builds on the concept of continental drift, an idea developed during the first decades of the 20th century. Plate tectonics came to be accepted by geoscientists after seafloor spreading was validated in the mid-to-late 1960s.

<span class="mw-page-title-main">Lithosphere</span> Outermost shell of a terrestrial-type planet or natural satellite

A lithosphere is the rigid, outermost rocky shell of a terrestrial planet or natural satellite. On Earth, it is composed of the crust and the lithospheric mantle, the topmost portion of the upper mantle that behaves elastically on time scales of up to thousands of years or more. The crust and upper mantle are distinguished on the basis of chemistry and mineralogy.

<span class="mw-page-title-main">Asthenosphere</span> Highly viscous, mechanically weak, and ductile region of Earths mantle

The asthenosphere is the mechanically weak and ductile region of the upper mantle of Earth. It lies below the lithosphere, at a depth between ~80 and 200 km below the surface, and extends as deep as 700 km (430 mi). However, the lower boundary of the asthenosphere is not well defined.

<span class="mw-page-title-main">Mantle plume</span> Upwelling of abnormally hot rock within Earths mantle

A mantle plume is a proposed mechanism of convection within the Earth's mantle, hypothesized to explain anomalous volcanism. Because the plume head partially melts on reaching shallow depths, a plume is often invoked as the cause of volcanic hotspots, such as Hawaii or Iceland, and large igneous provinces such as the Deccan and Siberian Traps. Some such volcanic regions lie far from tectonic plate boundaries, while others represent unusually large-volume volcanism near plate boundaries.

<span class="mw-page-title-main">Mountain formation</span> Geological processes that underlie the formation of mountains

Mountain formation refers to the geological processes that underlie the formation of mountains. These processes are associated with large-scale movements of the Earth's crust. Folding, faulting, volcanic activity, igneous intrusion and metamorphism can all be parts of the orogenic process of mountain building. The formation of mountains is not necessarily related to the geological structures found on it.

<span class="mw-page-title-main">Geothermal gradient</span> Rate of temperature increase with depth in Earths interior

Geothermal gradient is the rate of change in temperature with respect to increasing depth in Earth's interior. As a general rule, the crust temperature rises with depth due to the heat flow from the much hotter mantle; away from tectonic plate boundaries, temperature rises in about 25–30 °C/km (72–87 °F/mi) of depth near the surface in most of the world. However, in some cases the temperature may drop with increasing depth, especially near the surface, a phenomenon known as inverse or negative geothermal gradient. The effects of weather, the Sun, and season only reach a depth of roughly 10–20 m (33–66 ft).

<span class="mw-page-title-main">Mantle convection</span> Gradual movement of the planets mantle

Mantle convection is the very slow creeping motion of Earth's solid silicate mantle as convection currents carry heat from the interior to the planet's surface.

<span class="mw-page-title-main">Geodynamics</span> Study of dynamics of the Earth

Geodynamics is a subfield of geophysics dealing with dynamics of the Earth. It applies physics, chemistry and mathematics to the understanding of how mantle convection leads to plate tectonics and geologic phenomena such as seafloor spreading, mountain building, volcanoes, earthquakes, faulting. It also attempts to probe the internal activity by measuring magnetic fields, gravity, and seismic waves, as well as the mineralogy of rocks and their isotopic composition. Methods of geodynamics are also applied to exploration of other planets.

<span class="mw-page-title-main">Slab (geology)</span> The portion of a tectonic plate that is being subducted

In geology, the slab is a significant constituent of subduction zones.

<span class="mw-page-title-main">Large low-shear-velocity provinces</span> Structures of the Earths mantle

Large low-shear-velocity provinces, LLSVPs, also called LLVPs or superplumes, are characteristic structures of parts of the lowermost mantle of Earth. These provinces are characterized by slow shear wave velocities and were discovered by seismic tomography of deep Earth. There are two main provinces: the African LLSVP and the Pacific LLSVP. Both extend laterally for thousands of kilometers and possibly up to 1,000 kilometres vertically from the core–mantle boundary. The Pacific LLSVP is 3,000 kilometers across, and underlies four hotspots that suggest multiple mantle plumes underneath. These zones represent around 8% of the volume of the mantle. Other names for LLSVPs include "superswells", "thermo-chemical piles", or "hidden reservoirs". Most of these names, however, are more interpretive of their proposed geodynamical or geochemical effects. For example, the name "thermo-chemical pile" interprets LLSVPs as lower-mantle piles of thermally hot and/or chemically distinct material. LLSVPs are still relatively mysterious, and many questions remain about their nature, origin, and geodynamic effects.

<span class="mw-page-title-main">Earth's internal heat budget</span> Accounting of the energy flows at and below the planets crust

Earth's internal heat budget is fundamental to the thermal history of the Earth. The flow of heat from Earth's interior to the surface is estimated at 47±2 terawatts (TW) and comes from two main sources in roughly equal amounts: the radiogenic heat produced by the radioactive decay of isotopes in the mantle and crust, and the primordial heat left over from the formation of Earth.

<span class="mw-page-title-main">Geodynamics of Venus</span>

NASA's Magellan spacecraft mission discovered that Venus has a geologically young surface with a relatively uniform age of 500±200 Ma. The age of Venus was revealed by the observation of over 900 impact craters on the surface of the planet. These impact craters are nearly uniformly distributed over the surface of Venus and less than 10% have been modified by plains of volcanism or deformation. These observations indicate that a catastrophic resurfacing event took place on Venus around 500 Ma, and was followed by a dramatic decline in resurfacing rate. The radar images from the Magellan missions revealed that the terrestrial style of plate tectonics is not active on Venus and the surface appears to be immobile at the present time. Despite these surface observations, there are numerous surface features that indicate an actively convecting interior. The Soviet Venera landings revealed that the surface of Venus is essentially basaltic in composition based on geochemical measurements and morphology of volcanic flows. The surface of Venus is dominated by patterns of basaltic volcanism, and by compressional and extensional tectonic deformation, such as the highly deformed tesserae terrain and the pancake like volcano-tectonic features known as coronae. The planet's surface can be broadly characterized by its low lying plains, which cover about 80% of the surface, 'continental' plateaus and volcanic swells. There is also an abundance of small and large shield volcanoes distributed over the planet's surface. Based on its surface features, it appears that Venus is tectonically and convectively alive but has a lithosphere that is static.

<span class="mw-page-title-main">Lithosphere–asthenosphere boundary</span> Level representing a mechanical difference between layers in Earth’s inner structure

The lithosphere–asthenosphere boundary represents a mechanical difference between layers in Earth's inner structure. Earth's inner structure can be described both chemically and mechanically. The lithosphere–asthenosphere boundary lies between Earth's cooler, rigid lithosphere and the warmer, ductile asthenosphere. The actual depth of the boundary is still a topic of debate and study, although it is known to vary according to the environment.

Lid tectonics, commonly thought of as stagnant lid tectonics or single lid tectonics, is the type of tectonics that is believed to exist on several silicate planets and moons in the Solar System, and possibly existed on Earth during the very early part of its history. The lid is the equivalent of the lithosphere, formed of solid silicate minerals. The relative stability and immobility of the strong cooler lids leads to stagnant lid tectonics, which has greatly reduced amounts of horizontal tectonics compared with plate tectonics. The presence of a stagnant lid above a convecting mantle was recognised as a possible stable regime for convection on Earth, in contrast to the well-attested mobile plate tectonics of the current eon.

<span class="mw-page-title-main">Earth's crustal evolution</span>

Earth's crustal evolution involves the formation, destruction and renewal of the rocky outer shell at that planet's surface.

Ridge push is a proposed driving force for plate motion in plate tectonics that occurs at mid-ocean ridges as the result of the rigid lithosphere sliding down the hot, raised asthenosphere below mid-ocean ridges. Although it is called ridge push, the term is somewhat misleading; it is actually a body force that acts throughout an ocean plate, not just at the ridge, as a result of gravitational pull. The name comes from earlier models of plate tectonics in which ridge push was primarily ascribed to upwelling magma at mid-ocean ridges pushing or wedging the plates apart.

Heat-pipe tectonics is a cooling mode of terrestrial planets and moons in which the main heat transport mechanism in the planet is volcanism through the outer hard shell, also called the lithosphere. Heat-pipe tectonics initiates when volcanism becomes the dominant surface heat transfer process. Melted rocks and other more volatile planetary materials are transferred from the mantle to surface via localised vents. Melts cool down and solidify forming layers of cool volcanic materials. Newly erupted materials deposit on top of and bury older layers. The accumulation of volcanic layers on the shell and the corresponding evacuation of materials at depth cause the downward transfer of superficial materials such that the shell materials continuously descend toward the planet's interior.

Anne Davaille is a French geophysicist and director of research at the CNRS, France in the field of Earth Sciences. Davaille is known for her innovative experiments using thermochemical convection in fluids to simulate the mantles of planets. She uses these experiments to analyze fluid mechanics that create a new understanding of convective regimes in Earth and other planets.

Intraplate volcanism is volcanism that takes place away from the margins of tectonic plates. Most volcanic activity takes place on plate margins, and there is broad consensus among geologists that this activity is explained well by the theory of plate tectonics. However, the origins of volcanic activity within plates remains controversial.

David A. Bercovici is an American geophysicist. He is primarily known for his theoretical explanations of why planet Earth has plate tectonics. He is also known for his development of models of how the Earth's mantle recycles and stores water and how such hydrological processes are involved in Earth's geochemical history.

References

  1. 1 2 3 Noack, L.; Breuer, D. (August 2014). "Plate tectonics on rocky exoplanets: Influence of initial conditions and mantle rheology". Planetary and Space Science. 98: 41–49. Bibcode:2014P&SS...98...41N. doi:10.1016/j.pss.2013.06.020.
  2. 1 2 Kaltenegger, L.; Sasselov, D. (10 January 2010). "Detecting Planetary Geochemical Cycles on Exoplanets: Atmospheric Signatures and the Case of So2". The Astrophysical Journal. 708 (2): 1162–1167. arXiv: 0906.2193 . Bibcode:2010ApJ...708.1162K. doi:10.1088/0004-637X/708/2/1162.
  3. 1 2 3 4 O'Neill, C.; Lenardic, A. (11 October 2007). "Geological consequences of super-sized Earths". Geophysical Research Letters. 34 (19): L19204. Bibcode:2007GeoRL..3419204O. doi: 10.1029/2007GL030598 .
  4. 1 2 3 4 Valencia, D.; O'Connell, R.J.; Sasselov, D. (20 November 2007). "Inevitability of Plate Tectonics on Super-Earths". The Astrophysical Journal. 670 (1): 45–48. arXiv: 0710.0699 . Bibcode:2007ApJ...670L..45V. doi:10.1086/524012.
  5. 1 2 3 Van Summeren, J.; Conrad, C.P.; Gaidos, E. (20 July 2011). "Mantle convection, plate tectonics, and volcanism on hot exo-earths". The Astrophysical Journal Letters. 736 (1): L15. arXiv: 1106.4341 . Bibcode:2011ApJ...736L..15V. doi:10.1088/2041-8205/736/1/L15.
  6. 1 2 3 Korenaga, J. (10 December 2010). "On the Likelihood of Plate Tectonics on Super-Earths: Does Size Matter?". The Astrophysical Journal Letters. 725 (1): 43–46. Bibcode:2010ApJ...725L..43K. doi: 10.1088/2041-8205/725/1/L43 .
  7. Katterhorn, Simon; Prockter, Louise (September 7, 2014). "Evidence for subduction in the ice shell of Europa". Nature Geoscience. 7 (10): 762–767. Bibcode:2014NatGe...7..762K. doi:10.1038/ngeo2245.
  8. 1 2 3 Reese, C.C.; Solomatov, V.S.; Moresi, L.-N. (25 June 1998). "Heat transport efficiency for stagnant lid convection with dislocation viscosity: Application to Mars and Venus". Journal of Geophysical Research. 103 (E6): 13643–13657. Bibcode:1998JGR...10313643R. doi: 10.1029/98JE01047 .
  9. 1 2 3 4 Moresi, L.; Solomatov, V. (2 December 1997). "Mantle convection with a brittle lithosphere: thoughts on the global tectonic styles of the Earth and Venus". Geophysical Journal International. 133 (3): 669–682. Bibcode:1998GeoJI.133..669M. doi: 10.1046/j.1365-246X.1998.00521.x . Retrieved 10 October 2014.
  10. Mayor, M.; Udry, S.; Lovis, C.; Pepe, F.; Queloz, D.; Benz, W.; Bertaux, J.-L.; Bouchy, F.; Mordasini, C.; Segransan, D. (1 August 2008). "The HARPS search for southern extra-solar planets XIII. A planetary system with 3 super-Earths (4.2, 6.9, and 9.2 Earth masses)". Astronomy and Astrophysics. 493 (2): 639–644. arXiv: 0806.4587 . Bibcode:2009A&A...493..639M. doi:10.1051/0004-6361:200810451.
  11. 1 2 Van Summeren, J.; Gaidos, E.; Conrad, C.P. (16 May 2013). "Magnetodynamo lifetimes for rocky, Earth-mass exoplanets with contrasting mantle convection regimes". Journal of Geophysical Research: Planets. 118 (5): 938–951. arXiv: 1304.2437 . Bibcode:2013JGRE..118..938V. doi:10.1002/jgre.20077.
  12. Stern, R.J. (14 August 2007). "Modern-style plate tectonics began in neoproterozoic time: an alternative interpretation of Earth's tectonic history". In Condie, Kent C.; Pease, Victoria (eds.). When did plate tectonics begin on planet Earth?. Geological Society of America Special Paper. Vol. 440. pp. 265–280. doi:10.1130/2008.2440(13). ISBN   978-0-8137-2440-9.
  13. Ernst, W.G. (13 July 2008). "Archean plate tectonics, rise of Proterozoic supercontinentality and onset of regional, episodic stagnant-lid behavior". Gondwana Research. 15 (3–4): 243–253. Bibcode:2009GondR..15..243E. doi:10.1016/j.gr.2008.06.010.
  14. Dumoulin, C.; Doin, M.-P.; Fleitout, L. (10 June 1999). "Heat transport in stagnant lid convection with temperature- and pressure-dependent Newtonian or non-Newtonian rheology" (PDF). Journal of Geophysical Research. 104 (B6): 12759–12777. Bibcode:1999JGR...10412759D. doi: 10.1029/1999JB900110 .
  15. 1 2 Foley, B.J.; Bercovici, D.; Landuyt, W. (15 May 2012). "The conditions for plate tectonics on super-Earths: Inferences from convection models with damage". Earth and Planetary Science Letters. 331–332: 281–290. Bibcode:2012E&PSL.331..281F. doi:10.1016/j.epsl.2012.03.028.
  16. Landuyt, W.; Bercovici, D.; Ricard, Y. (6 May 2008). "Plate generation and two-phase damage theory in a model of mantle convection". Geophysical Journal International. 174 (3): 1065–1080. Bibcode:2008GeoJI.174.1065L. doi: 10.1111/j.1365-246X.2008.03844.x . Retrieved 10 October 2014.