Sharrukin's Palace

Before we get started with this step in the design sequence, be aware that the modeling here is even more pragmatic and “rule-of-thumb” than usual. I think the following material will work properly, but it’s going to need some rigorous testing and tweaking before I’m satisfied with it.

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In this step, we will determine some of the geological history of the world under development. In particular, we will estimate the world’s internal heat budget, characterize the presence and degree of active plate tectonics, and estimate the level of vulcanism.

A world’s internal heat will normally derive from three different sources:

• The primordial heat of the world’s formation
• Radiogenic heat derived from the decay of radioactive isotopes
• Tidal heat generated by friction due to any tidal forces acting on the world

The structure and behavior of the world’s lithosphere will be strongly determined by the amount of heat remaining in the world’s deep interior. The hotter the world’s mantle and core, the more likely it is that heat will escape to and through the world’s surface, softening or melting surface rocks and possibly giving rise to volcanic eruptions.

Procedure

Primordial and Radiogenic Heat Budget

Begin by estimating the primordial and radiogenic heat budget of the world under development.

Evaluate the following quantity for all worlds:

Here, K is the density of the world compared to Earth, R is the world’s radius in kilometers, M is the metallicity of the star system (as determined in Step Five), and A is the age of the star system in billions of years. H_P is a rough measure of the total amount of primordial heat and radiogenic heat a world possesses, on a logarithmic scale. On this scale, Earth had an H_P value of about 90 immediately after its formation (and has an H_P value of about 54 today).

Tidal Heat Budget

Not all worlds will have a significant budget of internal heat due to tidal friction. Or each world under development, check to see whether the world falls into any of the following two cases. If so, compute the quantity H_T according to the formula given.

First Case: Major Satellites of Gas Giants

A major satellite of a gas giant planet only (not a Leftover Oligarch, Terrestrial Planet, or Failed Core) will experience significant tidal heating if and only if:

• There is at least one other major moon in the next outward orbit from the gas giant, as established in Step Fourteen, the first case, and
• That “next outward” major moon is in a stable resonance with the moon being developed (that is, the ratio of their two orbital radii was derived from the Stable Resonant Orbit Spacing Table in Step Eleven).

In this case, the resonance between the two orbital periods will tend to maintain a small degree of eccentricity in the first moon’s orbit. This in turn will cause tidal forces imposed by the gas giant to increase and decrease slightly during the moon’s orbital period, causing the moon’s body to “flex” and create friction. In our own planetary system, two of the satellites of Jupiter fall into this case (Io and Europa).

If a moon falls into this case, evaluate the following:

Here, M is the mass of the gas giant in Earth-masses, D is the moon’s radius in kilometers, and R is the moon’s orbital radius in kilometers. H_T is a rough estimate of the moon’s tidal heat budget, on the same logarithmic scale as H_P.

Second Case: Spin-Resonant Planets Without Major Satellites

A Leftover Oligarch, Terrestrial Planet, or Failed Core which has no major satellite may experience significant tidal heating due to its primary star, if and only if the planet is in a spin-orbit resonance with its primary star, as determined in Step Sixteen, and at least one of the two following cases is correct:

• The spin-orbit resonance is not 1:1 (that is, the planet is not tide-locked to its primary star), or
• Both of the following are true:
  • There is at least one other planet in the next outward orbit from the primary star, as established in Step Eleven, and
  • That “next outward” planet is in a stable resonance with the planet being developed (that is, the ratio of their two orbital radii was derived from the Stable Resonant Orbit Spacing Table).

In either case, tidal forces imposed by the primary star will cause the planet’s body to flex slightly during its orbital period, giving rise to internal friction and heat. In practice, the effect is likely to be minimal unless the planet orbits very close to its primary star.

If a planet falls into this case, evaluate the following:

Here, M is the mass of the primary star in solar masses, D is the planet’s radius in kilometers, and R is the planet’s orbital radius in AU. H_T is a rough estimate of the planet’s tidal heat budget, on the same logarithmic scale as H_P.

Once you have computed H_P and (possibly) H_T, make a note of the greater of the two – that is, the heat budget associated with the source that is currently providing more internal heat for the world – for use in the rest of this step.

Status of Lithosphere

The lithosphere of a world is the top layer of its rocky structure. A world’s lithosphere usually begins as a global sea of magma, but it will soon cool, forming a solid crust that provides a (more or less) stable surface. Over time, as the world cools, the crust will tend to become thicker and more rigid, eventually forming a single immobile plate that covers the entire sphere.

Note that on a world with Massive prevalence of water, the lithosphere is effectively inaccessible, submerged beneath deep ice sheets or liquid-water oceans. In this case, the actual surface of the world will be atop the water layers (the hydrosphere). Determine the status of the lithosphere in any case since it will still affect several other properties of the world.

The possible cases will be sorted into six categories: Molten, Soft, Early Plate, Mature Plate, Ancient Plate, and Solid. These categories are defined as follows.

• Molten Lithosphere: Large portions of the world’s lithosphere are still covered by magma oceans. A thin solid crust may form in specific regions. Active volcanoes are extremely common and may appear anywhere on the lithosphere. Examples: Earth in the Hadean Eon.
• Soft Lithosphere: A solid lithosphere has formed, and no magma oceans remain. However, the lithosphere is not strong enough to resist the upwelling of magma from the world’s mantle, so active volcanoes remain very common and continue to appear anywhere on the lithosphere. Examples: Earth in the early Archean Eon.
• Early Plate Lithosphere: The lithosphere is becoming strong enough to resist the upwelling of magma from the mantle. The crust is organizing into solid plates. Volcanoes remain common, but (depending on the presence of active plate tectonics) may be limited to certain locations. Examples: Earth in the later Archean Eon.
• Mature Plate Lithosphere: The organization of the crust into solid plates is complete, with most or all of the crust now integrated into the system. Some of the crustal plates are now thicker and more durable. Volcanoes are less common. Examples: Earth today.
• Ancient Plate Lithosphere: The lithosphere is becoming thick and rigid, and the system of crustal plates is becoming stagnant. Vulcanism is increasingly rare. Examples: Earth billions of years from now, Mars today.
• Solid Lithosphere: The lithosphere is solid and completely stagnant. Vulcanism is vanishingly rare or extinct. Examples: Earth’s moon.

To determine the current status of a world’s lithosphere, roll 3d6 and add H_P or H_T, whichever is greater. Then refer to the Lithosphere Table.

Lithosphere Table
Modified Roll (3d6)	Lithosphere Status
96 or higher	Molten Lithosphere
88-95	Soft Lithosphere
79-87	Early Plate Lithosphere
45-79	Mature Plate Lithosphere
31-44	Ancient Plate Lithosphere
30 or less	Solid Lithosphere

Plate Tectonics

Even if a world’s crust is organized into solid plates, those plates may or may not be able to move and interact in an active system of plate tectonics. In our own planetary system, several worlds show some sign of plate tectonics. However, only on Earth is the entire crust arranged into a clear set of plates that move across the mantle and actively recycle crust material. The decisive factor seems to be Earth’s extensive prevalence of water, which permeates the crustal rocks and reduces friction among the tectonic plates.

Determine the status of the world’s plate tectonics only if its lithosphere is in an Early Plate, Mature Plate, or Ancient Plate status as determined above.

The possible cases will be sorted into two categories: Mobile Plate Tectonics and Fixed Plate Tectonics, defined as follows.

• Mobile Plate Tectonics: The crust’s tectonic plates are able to move freely past or against one another. As tectonic plates collide, some of them experience subduction, moving down into the mantle and recycling the crustal material. Orogeny, or the formation of mountain ranges, takes place in such areas as well. Volcanic activity is likely to take place at plate boundaries. Volcanoes may also appear in plate interiors, at the top of magma plumes rising from the deep mantle.  Such shield volcanoes will tend to form arcs or chains, as the tectonic plate moves across the top of the plume.
• Fixed Plate Tectonics: The crust’s tectonic plates are unable to move freely. Little or no subduction takes place to recycle crustal material. Orogeny is rare. As with Mobile Plate Tectonics, volcanoes are likely to appear at plate boundaries. Shield volcanoes are also possible, but since the tectonic plates are nearly immobile, such volcanoes can grow very large over time.

In general, a world is likely to have Mobile Plate Tectonics if it is younger (and therefore still has a hot mantle and core) and has plenty of surface water to reduce friction among the plates. To determine the status of a world’s plate tectonics at random, roll 3d6 and modify the result as follows:

• +6 if the world has Extensive or Massive prevalence of water
• -6 if the world has Minimal or Trace prevalence of water
• +2 if the world has an Early Plate Lithosphere
• -2 if the world has an Ancient Plate Lithosphere

A world will have Mobile Plate Tectonics on a modified roll of 11 or greater, and Fixed Plate Tectonics otherwise.

Special Case: Episodic Resurfacing

If a world has an Early Plate or Mature Plate Lithosphere, and has Fixed Plate Tectonics, then vulcanism will follow an unusual pattern of episodic resurfacing.

In this case, the lithosphere is too strong to permit magma to reach the surface under normal conditions. Since any tectonic plates are fixed in place, subduction and orogeny are very rare. Active volcanoes are also uncommon. However, heat built up in the mantle periodically breaks through, causing massive volcanic outbursts that “resurface” large portions of the lithosphere before the situation restabilizes.

For an Early Plate Lithosphere, these resurfacing events will take place millions of years apart. For a Mature Plate Lithosphere, resurfacing becomes much less frequent, tens or even hundreds of millions of years apart. In our own planetary system, Venus is an example of this case.

Examples

Both Arcadia IV and Arcadia V are planets without major satellites, and both of them are at a significant distance from the primary star, so Alice assumes that tidal heating will be insignificant for both of them. She evaluates H_P for both. The star system is 5.6 billion years old and has metallicity of 0.63.

Arcadia IV has density of 1.04 and radius of 6450 kilometers, and so has H_P of 41 (rounded to the nearest integer). With a 3d6 roll of 9, the total is 50. Arcadia IV has a Mature Plate Lithosphere.

Arcadia V has density of 0.92 and radius of 5670 kilometers, and so has H_P of 34 (rounded to the nearest integer). With a 3d6 roll of 13, the total is 47. Arcadia V also has a Mature Plate Lithosphere. Notice that both of these planets have total scores fairly low in the range for a Mature Plate result, indicating that they have rather “old” geology and may be transitioning to an Ancient Plate configuration.

Arcadia IV has Extensive water, so Alice rolls 3d6+6 for a result of 15. Arcadia IV has Mobile Plate Tectonics, resembling Earth in this respect.

Arcadia V only has Moderate water, so Alice makes an unmodified roll of 3d6 for a result of 7. Arcadia V has Fixed Plate Tectonics and exhibits episodic resurfacing on a timescale of tens or hundreds of millions of years.