I was wondering what is the smallest a terrestrial planet can be and maintain plate tectonics and generate a magnetic field, atleast to Earth's current age?
I have been browsing a few references on the subject and the parameters that are involved seem more numerous than just the size or mass of the planetary body.
Examples in the Solar System are already contradictory with the mass parameter: while Mercury has a magnetic field (around 1% of Earth's, i.e 300 nT on the surface at equator, vs. 30 µT on Earth surface - those values are order of magnitude and vary from place to place), Venus has so to speak no inner magnetic field, all of its measured magnetic field likely coming from its ionosphere.
Basically, the required conditions for a planet to have a magnetic field are a conductive liquid core layer, along with rotation and convective motions of that liquid layer. These convective motions are due to a cooling solid inner core. I did not find quantitative values regarding the minimum mass for such effects to appear, but Mars likely was around the limit, as its core likely cooled to the point where no convection exists anymore, either because its liquid core froze or its solid core is not hot enough to maintain the convectional motions.
Studies tend to show that cataclysmic events such as planetary impacts may be benefactory for plate tectonics to begin, as they would weaker the uper layers of the planet. However, I also found studies that suggest impacts may cripple the dynamo effect, i.e. the magnetic field... As well as studies hinting the contrary, which really tends to show that no conclusion can really be drawn at the moment without further data.
Sadly, due to the very few known exoplanets that have a lower mass than Earth, research regarding magnetic fields mainly address heavier planetary bodies. Factors that are usually taken into account are the temperature distribution along the planetary layers, the mass properties, the materials properties, the heat sources, incuding radioactive decay, and the presence of water, which is supposed to weaken the upper layers.
This being said, this research for example has made computation for planetary objects being 0.1 and 0.5 Earth mass. They tend to indicate that 0.1 Earth mass planets would be very unlikely to present with plates tectonics at all; 0.5 Earth mass would strongly depend on material properties, 1 Earth mass would be most likely to present with plates tectonics, while the probability decreases again as mass increases.
In conclusion, it seems that Earth is optimal regarding these factors, or maybe we lack other points of data and even a better understanding of what really is happening deep below our own feet. Objects smaller than Earth may have plates tectonics and a magnetic field, but not objects much smaller.
Plates move around because of convection in the mantle underneath them. That basically means they are floating on currents in the mantle. The mantle is liquid, though very very viscous, so as it flows hither and yon as it is heated by the core it rises then flows along the under surface of the crust then cools and sinks. There is friction between the bottom of the plate and the surface of the mantle (the asthenosphere). This is called basal drag. There are alternate theories that it is mantle plumes that are doing the moving (still transferred to the plates through basal drag) not convection current.
So theoretically, you need a hot core with a liquid mantle differentiated from the core to have plate tectonics. Well that includes just all the large objects in the solar system. Venus, Mars, Mercury, Ganymede, Titan, Callisto, Io, Luna, and Europa should all be large enough to have differentiated silicate mantle above a metallic core. Obviously, since we know very little about the mantle and core that we are standing on, we know even less about the interiors of these distant objects.
On the other hand, we haven't OBSERVED plate tectonics at work for sure on any of the other planets.
- Venus shows tectonic activity but not plate tectonics. Possible reasons include lack of water or higher viscosity of the Venusian mantle.
- Mars had plate tectonics early in its history that stopped, possibly due to cooling of the planet. Some recent evidence suggests it may have partial plates today, especially around on Tharsis Rise.
- Mercury and Luna's plate tectonics ceased 3.7 and 3 billion years ago, respectively.
- Io has lots of volcanoes and is heated from tidal stretching from Jupiter, but does not have plate tectonics.
- Europa has a structure fundamentally different from earth, since it has an ocean deeper than our crust. The ice sheets on the surface thus act like our crust, sliding over a liquid ocean instead of a mantle. Given that water is much less viscous than molten rock, it is no surprise that Europa is suspected to have plate tectonics.
- Ganymede is kind of in the same boat as the Europa, and some think that has the same ice plates over ocean thing going on...or that it used to in the past.
- Callisto always gets ignored, and I can't find anything about it. I'm the third biggest moon, why do you ignore me. Just because I don't have volcanoes, oceans, or atmosphere. Sad Face :(
- Titan may have a huge ocean like Europa and Ganymede, but I can't find anyone who thinks that this causes plate tectonics.
On to magnetic fields. This one is easier to summarize:
- Venus's magnetic field is induced by interaction between atmosphere and solar wind, not due to its core, and is thus weak. Venus's slow rotation may prevent its core from making a field.
- Mars may have had an internal dynamo in the past, but no longer.
- Mercury does have a magnetic field due to its hot core.
- Ganymede does have a self-generated field, in addition to the induced field from Jupiter due to its subsurface ocean. The self-generated field is probably generated the same way as Earth's, which makes you wonder what Ganymede is doing that Mars and Venus aren't.
- Titan and Europa have induced magnetic fields from their salty oceans. Ganymede does too, in addition to its self-generated field. Callisto is so ignored that we'll dump it in this category too.
- Luna has a very weak magnetic field, and what is there might be caused by magnetization of moon rocks during large impact events.
- Earth has both for sure
- Objects as small as the Moon may have had plate tectonics in the past
- Objects as small as Ganymede have magnetic fields to this day, for mysterious reasons.
- A different sort of ice tectonics/induced magnetic field is possible on cold moons/planets with huge salty oceans, down to the size of Europa.
- Lithospheric plate tectonics might have something to do with viscosity of the mantle, in which case a hotter mantle is better.
- The way to preserve tectonics in a smaller body is to have tidal heating of a moon to keep the mantle nice and hot. Of course, that isn't working for Io, so I guess no one knows.
So there you go, the answer is that there is no answer :)
According to NASA, the smallest planet they have discovered that functions like a planet, Tectonic plates, volcanoes etc is roughly the size of our moon.
That's not to say there can't be smaller planets out there as such, though in this instance, the smallest recorded so far is Kepler 37-b As quoted from an article:
A team of Danish astrophysicists has now made what may well be a sensational discovery. They have found the smallest planet that has ever been observed in orbit around a star other than our Sun.
With a radius of only 0.3 times that of the Earth, the planet orbits its host star once every 13 days.
Sadly however, it also states that due to the planet being so small, it cannot create enough gravity to maintain a sustainable atmosphere, meaning it wouldn't be able to harbour human life without machines, or terraformers etc.
The planet isn't known to have a magnetic field, though it is assumed so.
it could be considered terrestrial, though it's a far stretch. In terms of fiction, you could make the planet however small you wanted it.