The Four Elements: It’s all in the Record

This time I will talk about terrestrial planet interiors and geological activity. It turned out another lengthy post, but there are a lot of things to mention.

Geological activity is defined as the expression of the internal and external processes and events that affect a planetary body. It has been proposed that plate tectonics during a long period of time, say, at least a few billion years, is a necessary condition for life. For complex life to evolve, as in Earth’s example, more than 3 Gyrs are required. However, once tectonics shuts down, that might not be the end of the story. Both Earth and Mars are geologically active (and Mars now is thought to be at a primitive stage of plate tectonics), just operating in different convection regimes. So Mars still can be a good choice, if eventually terraformed. It will require a lot of work and a lot of new awesome technology to get things spinning, though.

Well, for a Mars-like body there is a second chance to possibly get plate tectonics and magnetic shielding going if something big strikes and melts it again, and adds considerably more mass. Maybe your system had some instability and another small planet smashed into similar half-dead fish. Chances of this happening in the more or less stable system are very, very small, almost improbable. But if this had happened to our Mars, the afterglow would have been a spectacular sight from Earth, and so is the flying debris. When things have cooled down, the terraforming can begin. Of course, it will be a VERY lengthy process. However, if you are interested in a short-term and a quicker project, Mars isn’t any better than any space station in terms of life support. And with current interior processes it wouldn’t get any better with age.

What exactly powers a planet?

In case of Earth 75% comes from radioactive element decay and the rest is the remnant heat (the trapped potential energy) from accretion times. Then, there’s another question: How old can a terrestrial planet be? According to BB theory, the universe is about 14 billion years old (well, 13.75 to be exact, but that is irrelevant here), and most elements are much younger. Even if galaxies appeared early in Universe history, I doubt there would be a habitable planet that old. Primordial gas giants? Perhaps, plenty. Primordial rocky objects? Not a chance.

After the Universe became more and more enriched in elements, the possibility for rocky planets to form eventually appeared. However, a planet, say, 7 billion years old (or older) would be powered by a different ratio of radioactive isotopes than an earth-aged planet. The age of chemical elements can be estimated using radioactive decay to determine how old a given mixture of atoms is.

The long-term thermal evolution of rocky planets depends on the abundance of the long-lived radioisotopes Th-232, U-235, and U-238 at the time of planet formation, and those are produced only during explosive nucleosynthesis (r-process) in stars with at least 8 to 20 solar masses (Chen et al. 2006).

Since we are talking about terrestrial planets, we are looking for silicates. In contrast to the abovementioned isotopes, silicon (Si) is produced by the whole range of massive stars. Thorium (Th) and uranium (U) are difficult to detect, but there is another element, europium (Eu), which is produced in the same reaction type (r-process) as Th and U, and can be measured. All r-process elements scale closely with solar values (Frebel 2008). This means that the average abundance of Th-232, U-235, and U-238 can be predicted from the europium trend with metallicity, the age-metallicity relationship and the star formation history of the Galaxy, and the half-life of each isotope. The average abundance of Eu to Si decreases by a factor of 0.63 as the metallicity increases by a factor of 100 to a solar value (Cescutti 2008).

An overwhelmingly large proportion of uranium on Earth is U-238. This makes it the heaviest atom commonly found in nature. U-238 and Th-232 have half-lives of 4.468 and 14.05 Gyrs respectively, but the uranium is underabundant in the Solar System compared to the expected production ratio in supernovae. This is not surprising since the U-238 has a shorter half-life.

Planets forming early in the history of the Galaxy would have 50% more U-238, but six times more U-235, than Earth. The higher abundance is because the amount of radioisotopes in the interstellar medium only reflects massive star formation over a few half-lives, whereas Si-28 and other stable isotopes accumulate over the history of the Galaxy. Therefore, these systems are silicon-poor. However, the high abundance of U-235 could have an important role in the early thermal history of such planets.

Heat transfer

Thermal energy from the hot interior of the planet flows out of the surface into space. When an object is at a different temperature than its surroundings, heat will transfer from the region of higher temperature to the region of colder temperature to achieve thermal equilibrium. The mantle transfers heat from the hot core at the planet’s center to the colder surface. When an upward heat flux passes through a fluid, the thermal energy is transported in two ways: conduction and convection. The control parameter that selects between the two regimes is the Rayleigh number.

In conduction the energy transfer occurs from hot vibrating atoms and molecules to neighboring atoms and molecules, while the fluid stays put, as if it were a solid. In a gravitational field, if temperature gradients in the mantle are large enough, instability due to buoyancy will cause convection.

Convection is heat transfer by the movement of fluid. The increase in temperature produces a reduction in density and the warm, buoyant material begins to rise, while colder, denser material near the surface is displaced and sinks. Convection transports heat more efficiently than conduction due to mass transport.

Mantles are predominantly solid rocky shells (getting more solid with depth), yet over very long time scales (tens to hundreds of millions of years) mantle rocks under extreme pressure and temperature slowly deform like a viscous fluid, moving in circular currents called convection cells.

Mantle convection ultimately drives all geological events, such as volcanoes, earthquakes, and plate tectonics. It moves continents to new positions. The continents, in turn, modify the flow inside the mantle due to “thermal blanketing”, acting like perfect thermal insulators. Thus, continental growth strongly affects mantle cooling.

Plate tectonics

Plate tectonics is a model in which the outer shell of a planet is broken into a number of thin rigid plates that move with respect to one another. The relative velocities of plates are of the order of a few tens of millimeters per year. Volcanism and tectonism are concentrated at plate boundaries. Much of Earth’s internal heat is relieved through this process and many of Earth’s large structural and topographic features are consequently formed.

Continental drift is cyclic and the main reason for this is the movement in convection cells. Ocean basins open and close, forming supercontinents, which later break apart again during another opening of the ocean; this process is known as the Wilson cycle.

Continental collision is one of the primary mechanisms for the creation of mountains in the continents; the other is subduction, the process when one tectonic plate moves under another, sinking into the mantle, as the plates converge. The Himalayas and the Alps are examples of mountain belts caused by continental collisions, and the Andes are associated with subduction. That’s the awesome power of Earth’s convection mode and gravity combined. In contrast, the extreme height of the Martian volcanoes can be attributed to the low surface gravity and the lack of relative motion between the lithosphere and the magma source.

Implications to climate

Continents are not just a fancy decoration for your maps. Continent cycle is a major player in the global geochemistry and climate of a planet.

During continental dispersal the sea level is high, and warm and humid maritime climate is dominant. The level of ocean floor spreading is high and relatively large amounts of carbon dioxide are produced at oceanic rifting zones. Seafloor spreading centers cycle seawater through hydrothermal vents, reducing the ratio of magnesium to calcium in the seawater through metamorphism of calcium-rich minerals in basalt to magnesium-rich clays (Wilkinson and Given, 1986; Lowenstein et al., 2001). This reduction in the Mg/Ca ratio favors the precipitation of calcite over aragonite, thus the seawater chemistry is that of a calcite sea.

During continental aggregation the ocean level drops due to lack of seafloor production. The cooler and arid continental climate dominates, corresponding with severe desert environments and frequent continental glaciations. The seawater chemistry is that of an aragonite sea, with high magnesium content.

The continental shelf has a very low slope and a small increase in sea level will result in a large change in the amount of flooded land. With averagely young world ocean the seafloor will be relatively shallow, making the sea level high with more landmass flooded. The old world ocean is relatively deep and more land will be exposed due to low sea level.

When continents are dispersed, the plate tectonic flux is high and Andean-type volcanism is extensive. With a single supercontinent and a low plate flux (the huge plate is a “blanket”) the mantle heats up due to the decay of radioactive isotopes. The increase in mantle temperature and the warming near the core–mantle boundary leads to an increase in the plume flux and the breakup of the supercontinent.

Implications to life

Continental spreads stimulate life diversity on evolutionary scale. Not only that, continental cycle influences the size of the species. According to Bergmann’s rule most mammals tend to be larger in cold climates and smaller in hot ones. The study by Smith et al.(2010) also shows that the colder the environment and the bigger the land surface, the bigger the large mammals become.

Tectonic environments and humans

Tectonic activity, as earthquakes and volcanoes, has a great influence on the course of development of civilizations and other complex cultures. Beside the obvious destruction, tectonism apparently accelerated cultural development. How this happened (and happens) exactly, is discussed in great detail in Tectonic Environments of Ancient Cultures blog by Eric Force.

A matter of mass

The mass of a planet is probably one of the most important properties regarding convection mode. Adding more mass can add troubles similar to that of reducing it (Venus, Mars). Earth might be a neat borderline case here, when things operate smoothly. Well, no one really knows for sure yet if plate tectonics will operate on massive planets, and regarding that there is a disagreement in the scientific community. Several studies were carried out and the results are quite interesting in all cases.

For my personal designs I have chosen a condition that plate tectonics does indeed operate on larger worlds (but not extremely large, though, because of several other factors). However, I take things from the other models into account as well.

There is also another thing worth mentioning here, a paper by Martyn Fogg (I have mentioned it in one of my previous posts). There, in section 3.2, page 7, is a formula (14) for estimating the duration of viable volcanic/tectonic recycling of volatiles on a given planet – basically, the timescale for plate tectonics. As the continent cycle goes on, increasing continental area would eventually initiate a transition between plate tectonics and a stagnant lid mode of mantle convection.

Plate tectonics is the primary mechanism through which Earth (and any planet with the same regime) loses its heat. Lenardic et al.(2005) suggests a potential constraint on continental surface area at which continental growth will stop. This critical point is predicted as a function of mantle heat flow. For the Earth’s current global heat flux, the critical continental surface area is estimated to be 35-50% to allow plate tectonics to initiate, and present day Earth’s continent crust area is about 40%.

So, how would things work on bigger planets?

There are several conditions necessary for plate tectonics to operate (Martin et al.,2008). First of all, the planet must have cooled enough so that it is too cold to sustain magma ocean. Second, its interiors must be hot enough to maintain convection within the upper layers of the body to prevent the existence of stagnant lid. Third, its lithosphere needs to be cool enough, strong enough, dense enough and thin enough to allow subduction. Fourth, liquid water on the surface is probably the most vital ingredient for successful plate tectonics.

Magnetic field lifetime is also tightly related to the thermal evolution of a planet. To drive dynamo action, a liquid metallic core must be in an active convection state.

Valencia et al. (2006), (2007) used planetary parameter scaling to argue that higher gravity favors subduction and plate tectonics are inevitable on larger terrestrial worlds. Nearly at the same time O’Neill and Lenardic (2007) proposed that super-sized Earths are likely to be in an episodic or stagnant lid regime.

As planet mass increases, it poses an increasingly severe problem for plate tectonics. Middle-aged super-Earths may suffer from continental spread, which could choke off plate tectonics, placing a planet in stagnant lid mode. Provided that crustal flow limits continental thickness, it was shown that continents will spread out to coat the surface of a terrestrial planet with more than three Earth masses in much less time than the age of the Earth (Kite et al., 2009).

More recent studies show that there might be another severe problem to plate tectonics on super-sized “Earths”. The convective pattern and the heat transport in a terrestrial planet depends on the viscosity of the mantle material. The viscosity, on the other hand, depends strongly on temperature and pressure, i.e., the viscosity decreases with increasing temperature but increases with increasing pressure. Thus, the larger the planet the stronger is the influence of the pressure on the viscosity and flowability of material. This dependence becomes an important factor for the mantle convection of planets with masses larger than one Earth mass. With more mass, planets are subject to sluggish convection regime in the lower mantle and formation of a conductive lid over the core-mantle boundary. Eventually convection stops and heat is transported only due conduction. Thermally induced magnetic field generation is suppressed as well. Compositional dynamos might also become suppressed due to small cooling rate of the inner core; such planets will end up with small surface magnetic fields, higher radiation environment and stronger atmospheric loss (Stamenkovic et al., 2010).

The results of another study using 2D spherical mantle convection model (Noack & Breuer, 2011) show that the propensity of plate tectonics has a peak at a specific mass: assuming viscosity increases with pressure, the peak occurs between one and five Earth masses. However, the variation of viscosity with pressure is strongly debated and might as well decrease with pressure (Karato, 2011, Icarus; Armann et al., 2010, Nature).

Tidally locked planets

This is another interesting case. If a planet lacks an atmosphere thick enough to balance the surface temperature, it will be in a stagnant lid convection regime at the night side and in a mobile regime at the day side. The reason for such difference is the upper convective mantle, which is sensitive to temperature variations on the surface (Noack et al., 2010).

The habitability of planets in synchronous rotation about their star may lie well outside the Habitable Zone (Gelman et.al 2011). Such world may still support liquid water on its surface, or shallow subsurface, in certain regions of the planet. Thus, tidally locked mantle and climate patterns must be combined and assessed to determine the surface environment, keeping in mind this may vary greatly from the substellar to antistellar regions.

# Well, this is it for now; maybe something will be added later.