ACTUAL TECTONIC PHYSICS AND THE FUTURE OF PROJECT PAART
THIS POST IS A CORRECTION TO MY PREVIOUS POST ON THE SUBJECT - THIS TIME USING ACTUAL SCIENCE
Some of my initial guesses were on the right track - but in general, my post is actually far from a rough guess.
The following is based of the paper Inevitability of Plate Tectonics on Super-Earths - Diana Valencia et al.
The recent discovery of super-Earths (masses≤10Me) has initiated a discussion about conditions for habitable worlds. Among these is the mode of convection, which influences a planet’s thermal evolution and surface conditions. On Earth, plate tectonics has been proposed as a necessary condition for life. Here we show that super-Earths will also have plate tectonics. We demonstrate that as planetary mass increases, the shear stress available to overcome resistance to plate motion increases while the plate thickness decreases, thereby enhancing plate weakness. These effects contribute favorably to the subduction of the lithosphere, an essential component of plate tectonics. Moreover, uncertainties in achieving plate tectonics in the 1regime disappear as mass increases: super-Earths, even if dry, will exhibit plate tectonic behavior.
What is a pretty neat discovery, but not actually what I came to talk about.
When I first started to think about how geologically active would a planet be I went through the following:
For plate tectonics to exist, there must be a thick fluid underneath to drag the plates along - the planet's mantle - and for that to be fluid, it must be either very hot, or have a light density.
The heat would be result of the internal pressure plus radiogenic heat.
And I did relate this in three formulas that despite making some little sense, are incorrect.
The internal temperature would be proportional to Earth's internal heat times it's gravity.
Ct = M/R²
The mantle activity, or how much did it move underneath, would be the temperature over pressure.
Ma = C / (density * gravity * radius)
This is actually pretty sketchy looking at now - because it does increase activity with lower pressures, and decrease activity with higher pressures, I mean, by this logic, the Moon's mantle should be a whirling turbulent sphere...
The observable tectonic activity would be mantle activity over density, again - it does favor lower densities, we know that is true to an extent, but actually, lower densities are quite of an interesting problem if you look at Venus for instance, with a lower density and lower crust density than Earth, it's seemingly impossible to have plate tectonics because the crust just mashes and mix against itself instead of floating in pieces.
Ta = Ma/density
This last point does really worry me a little - Paart's overall density is actually lower than that of Mars, about 3,8g/cm³ and 3,9g/cm respectively - I for some reason have choosen a planet with such a low mas (~0,8Me) and such a large radius (~1,05Re) that I didn't actually thought about density - I think I may had just said "heh it's denser than granite, that should work".
Paart's crust isn't as "soaked" with Xenon as Venus' is, so it might be really solid compared to the rest of the planet, but it does put it's reliability - the project's reliability - in check, and I don't like it in the slightest.
ACTUAL SCIENCE OF PLANETARY INTERNAL MOVEMENT
The table 1 of the paper does gives us some insight, even if the focus is on larger planets, we can use it as a reference for smaller ones if the relationship works along the terrestrial spectrum as whole.
Adapting some of the table, we have:
Plate thickness d = 43km * (planet mass)^(-0,45)
Plate lenght L = 1800km * (planet mass)^(0,28)
Convective time t = 70Myr * (planet mass)^(-0,91)
For Paart, the values d, L, and t, are:
Thickness = 47,6km, while before I assumed a 35km thickness.
Length = 1689,8km, so Paart's plates would be smaller than on Earth.
Convection = 85,95Myr, that's how much time it takes for rock material to circle in the mantle.
What is, surprisingly, ok? Maybe?
It does continue with convection cell sizes, the size difference of those for Earth and Super-Earths is very small (proportionally speaking), about 0,29~0,30 respectively.
C cell ~ L / planet radius
For Paart this does equate to about 0,25 (we would need Paart to be about 11.600km wide to have a 0,29 proportion).
So, we have a thicker crust, a smaller convection cell, and ~80% the Earth's plate-driving force.
We cannot, yet, say Paart would be geologically dead, the researchers believe that plate movement would still be possible with crusts 117km thick and with normal stresses of 1/10th to 60% that of Earth, if the crust is significantly weaker than the usual, as of an example, being rich in hydrated minerals, such as lime and clay, also silicates in general.
So a less dense plate/crust can move if it's weak enough, and that I at least got right on the first time - the researchers explain that tectonic activity is more common to the point of inevitability in Super-Earths because of several factors like lower density and possibly higher driving forces - Earth-mass planets are on the limit of those forces, as the materials that constitute their mantles have stresses close to the planet's best mantle flow force, example is the rock olivine, with a stress of about 5GPa - redoing the calculations, show that planets lighter than 0,5 Me may be geologically dead because the would not provide the force to overcome the mineral's resistance.
Water content, mainly lithospheric water may weaken the upper mantle rocks by hydrating then and thus reducing the effort needed to move the plate - another reason why Super-Earths would be good candidates for having plate tectonics. Venus' lithospheric hydration is between 1/10 to 1/100 that of Earth's, making it very difficult to overcome plate resistance.
IS PAART GEOLOGICALLY DEAD THEN?
I would not say that - gladly - I would hate to sit with the team and say "we either handwave it away or start again from scratch", what wouldn't be as difficult as it was to build this the first time, but certainly have to re-think how would everything relate again would be a hard time.
HOWEVER, I must admit I'm not even half-way through the calculations necessary to give precise sentence on our little red? marble.
I'm working at the moment in a Lite version of the Star System Calculator because I noticed some compatibility issues - so it now will include a planetary internal structure model page (seems those work only for terrestrial planets so ignore for other cases).
This post will have a second part to explain the model in a more - digestible - way for starters (heck, neither I can understand most of it properly atm), so stay tuned.
They also suggest that an indicative of plate tectonics would be the presence of volcanic gases such as Sulfur and Carbon dioxides in the atmosphere - as for the right amounts, it would be needed a proper modeling of it.
- M.O. Valent, 01/10/2020
RESULT
With corrections made to it, we get a convection cell that's 0,28 in size, which is acceptable for an active planet, we also get a plate movement that's about 2,3cm/yr - so we can track dates in plate movement more accurately.
- M.O. Valent, 02/10/2020
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