What is the nature of "rock vapor" in this description of the formation of the Moon?

Question

The NPR News item MacArthur Fellow And Planetary Scientist Sarah Stewart Discusses How The Moon Was Formed and audio podcast begins:

Ari Shapiro, Host: Sarah Stewart likes to think about what happens when planets collide. She uses two actual cannons to simulate those massive impacts. Here's one firing in her lab at UC Davis.

Unidentified Person: Firing in three, two, one.

Soundbite of Cannon FIring

Ari Shapiro, Host: Her work earned her a spot in this year's class of MacArthur Fellows. Many of us call it the genius grant. For years, experts have thought that Earth's moon formed after a large collision knocked off a bunch of rock. Stewart told me her research suggests a different story.

Planetary Scientist Sarah Stewart: During planet formation, when two bodies collide, there's so much energy released that most of these bodies are vaporized. That means that a rocky planet like Earth is mostly rock vapor.

Shapiro: What is rock vapor, and what does that have to do with our moon?

Stewart: Rock vapor is taking the rocks that we stand on and heating it up to the point where it becomes a gas. And when that occurs, the Earth becomes much larger because vapor is much less dense. And it extends out into this enormous object hundreds of times larger than the Earth today. And we proposed that our moon grows within the rock vapor of the Earth after a giant impact.

Shapiro: So the moon actually came from the Earth.

Stewart: The moon grows within the rock vapor of the Earth. And that gives the moon the same chemistry as the Earth.

We don't learn about "rock vapor" in Earth Science class, but I know it's got to be a lot hotter than the lava we see in the news. A significant fraction of Earth's crust is SiO₂ based and it's boiling point is roughly 3,000°C, and I have a hunch the temperatures involved here are much much higher than that. The kinetic energy associated with say a relative velocity of 40 km/s is roughly 8 eV per AMU, over 130 eV for every oxygen atom for example.

So does "rock vapor" start out as a highly ionized "rock plasma" with almost no covalent bonds remaining, or does most of the energy of the original impactor get transferred to a much greater mass of Earth?

Is there a good place to read about her and her students' MacArthur grant-getting research described in the podcast?

Answer 1

Planetary Scientist Sarah Stewart's research is on the formation of the moon, not, as far as I can tell, as much on the chemical composition and precise temperature of the atmosphere after impact, so I don't know if plasma is all that relevant to her work, but I think she'd have to model and account for total energy and temperature, similar to what you did in your question.

If I understand you correctly, you want to know what Earth's atmosphere was like, lets say a weeks or a few weeks or maybe a year after the giant impact. Dr. Stewart's team has a word for this type of planet, a Synestia

Plasma temperature is tricky for 2 reasons. One, there's not a specific temperature where gas becomes plasma. Unlike melting points of boiling points, which happen at specific temperatures (and specific pressure for boiling points), the plasma phase of matter is closer to a dimmer switch that turns on gradually than a specific plasma point. Similar to the temperature where fusion happens, individual electrons are unpredictable, so heating a gas, it will turn into a plasma gradually.

It's also possible for a rock vapor, take SiO2 as a baseline, to retain it's double bonds as a gas and at the same time, be a low level plasma, emitting some electrons, so it can be both rock vapor and a plasma. That's not possible for water, for example, because those bonds are too weak. Water splits into Hydrogen and Oxygen a couple thousand degrees lower than when the individual molecules begin to enter the plasma state.

Another problem is pressure. The center of the Earth is plasma temperature (low level Plasma but it's in that temperature range), but people generally don't call that state of matter a plasma.

I think your 40 km/s estimate is too high, because Theia was thought to be a Trojan object before it collided with Earth, so the collision rate should be not much more than escape velocity, maybe 12 or 13 km/s because they shared the same orbit.

40 km/s meteor collisions on Earth happen because they approach at a different inclination, where the orbital directions are much less lined up, that's how you get 11 to 70 km/s for meteors, but Theia was probably on the low side of that, perhaps 14 or 15 km/s tops depending on it's eccentricity - if I can make a bad guess.

I'm sure that plasma temperature happens during giant impacts. But the temperature is highest where the two objects collide, so initially, the highest temperature corresponds with the highest pressure. After the impact you have the explosive rebound, because collisions of this magnitude are more like large explosions than anything else and after that you can model where the temperature goes as the Earth begins to settle.

Models would have to account for how the heat moves around and through the planet, how much heat ends up burred vs goes into rock vapor, heat of vaporization, heat lost due to expansion of rock vapor, how quickly heat radiates away (I would think it would be highly opaque, so radiation would be somewhat slow),

Bigger factors would be how much is lost in rebound and ejected material and how much is transferred to angular momentum. There's also the uncertainty on how massive Theia was. I think later estimates put it at 1/2 to 1/3rd the mass of Mars.

Another way to look at this question is, after formation, the synestia would have layers, similar to any gas giant, though gas giant layers aren't well understood, we could use the sun as an example. There might be convection, conduction and condensation layers, and perhaps lapse rate could be applied, and obviously gravity would be lower with the material more spread out. You might also have layers where the pressure was sufficient that different types of matter would form, like, hot enough to be liquid but enough pressure to be a solid, similar to Earth's core.

All that said, trying to calculate the lower atmospheric temperature of this theoretical, recently formed synestia is a little bit more math than I want to do, and I'd probably get it wrong anyway even if I did the math. But it seems entirely reasonable that the lower atmosphere was at plasma temperatures if much of the upper atmosphere was at rock-vapor temperature. But if you can get a temperature model, that would be a step in the direction of a plasma model. I'd guess the low level plasma temperature for rock vapor would begin somewhere in the 5,000 or 6,000 C range, but it's a hard thing to look up as different compounds have different plasma temperatures. There's even some cold plasma, like florescent bulbs work on that property, but they require an electric field.

I don't know if my long "I don't know if there was plasma" counts as an answer, but it's a fun question and I thought I'd give it a shot. I like her idea a lot and I've read a few articles that indicated problems with the more traditional giant impact models, so she may end up being right.

Answer 2

In short:

• Not every gas is a plasma. Covalent bonds can be absent in a neutral gas. Rock vapour is just vapour, silicate atoms in their gasous state. And just as oxygen can freeze, so can silicates evaporate. Of course they can thermally ionize as well at even higher temperatures, but I don't see that this is implied in the text.
• They're not the only ones investigating scenarios like that: This article for example argues that the isotopic differentiation in Moon rocks can be explained by an extended, Earth-moon spanning hot rock-vapour atmosphere just after the impact.

Answer 3

You should check out this paper called "The Vaporization of The Earth": https://iopscience.iop.org/article/10.1088/0004-637X/755/1/41 That mostly talks about composition. There are weird things at such temperatures like free radicals (e.g., neutral OH) and "molecular" forms of what are normally salts (e.g. NaCl and Na2Cl2 molecules: See the question: https://chemistry.stackexchange.com/questions/14174/what-is-sodium-chloride-like-in-gas-state ). There are also more familiar gasses non-metal like CO2 and HF.

The fact that they're molecules doesn't mean the bonds are any more covalent, and I don't see why they would be. Thus, you could imagine them as just the smallest possible crystals necessary to be electrically neutral, which IS necessary at temperatures lower than those capable of producing highly ionized plasmas. (It's important to note that the SURFACE of the Sun is actually still on the cold side for thermally ionized plasma, and I think it's MOSTLY electrically neutral, though you may want to check some other sources on that. I'm not saying temperatures in giant impacts are in any way related to the surface of the Sun, but the paper I found only goes up to 4000K, which is less than the surface of the Sun, and in the range of Red Dwarf Star surfaces.) That being said, the paper does indicate that some Na$^+$ appears above 3600K with Bulk Silicate Earth elementary composition, and some K$^+$ appears above 3400K in with Continental Crust elementary composition.

What's more interesting (or at least less obvious to me) than the fact that they're electrically neutral is the fact that unionized metals are not very common. Even at these high temperatures, MOST of the metal forming rock seems to prefer to bond to oxygen or halogens. Again, though, at the highest temperatures it shows, we do see some monotomic metals: For some reason K and Na show up first as monotomic gasses. This is strange since they're the most electropositive and so generally most likely to be bonded metals, though they might just generally be overrepresented in the gas phase in lower temperatures because they're also the most volatile (lowest boiling point) metals considered. Then, Fe and, in the Bulk Silicate Earth case, Magnesium show up as monotomic gasses at the highest temperatures considered.

We also see Oxygen and Hydrogen appear as monomic gasses, which goes along with OH and NO to indicate non-metal free radicals can be stable (or at least generated quickly enough to keep up with their destruction) at high temperatures and low pressures, though NO is stable enough to be encountered at normal (human) PT conditions as well. A slightly harder to spot free radical that appears is NaO. There are also some molecules which are not free radicals, but just less stable under normal conditions, like SiO, SO, and CO.

Again, this paper only goes up to 4000K, so it's possible you would need to consider higher temperatures, where you might start to see some plasma.

It also doesn't address high pressures, which of course are necessary to model chemistry in large parts of the volume of a planetary collision, since they already have high pressures inside them, and crashing into each other temporarily makes even higher pressures, but after a certain point (which is definitely reached in planets, whether stationary or colliding) you're really dealing with supercritical fluid, not vapor.

It should be noted that you can get gas-like supercritical fluid if the temperature is much more above the critical temperature than the pressure is above the critical pressure (I think this happens in the cores of stars), but this kind of situation doesn't happen for rocky or metallic materials in the interior of Earth-like planets, whose critical temperatures I think are mostly not even reached. (For example, the critical point of iron is estimated as 9250K$\pm$1000K in this paper I just found https://www.nature.com/articles/srep07194). Moreover, the temperatures and pressures created by sudden compression as in shock waves (or planetary collisions) follow what called "Hugeniot curves" starting at the the original pressure-temperature (PT) conditions (or follow "Rankine-Hugeniot relations"), and these curves increase density as they increase temperature. In order for a supercritical fluid to be gas-like, it has to gas-like density, so compressing rocky planets, where the rock and metal starts out denser than a gas, will not create gas-like supercritical fluids on the wave front of the impact shock wave.

On the other hand, clearly, after the shock wave passes, pressure falls faster relative to temperature than it rose during the shockwave (because the Hugeniot curve converts some of the kinetic energy of the impact into heat), otherwise we wouldn't have the low pressure high temperature conditions necessary for the rock vapor we've been talking about. Thus, MAYBE we could also have some gas-like supercritical forms of rock or metal, and we certainly could have higher pressure gasses than we've considered, but my intuition from my vague memory of all the phase diagrams I looked at a few years ago is that the rock and metal will mostly be gas, liquid, and liquid-like super critical fluid (and mostly those last two by mass, though in at least some kinds of impacts, the gas would fill a larger VOLUME, much much larger than our current atmosphere, as you can guess by looking simulations of giant planet collisions like these ones by Durham University https://icc.dur.ac.uk/giant_impacts/ . Also, technically all of space is filled with gas, so you'd need to define a minimum density or use a von-Kármán-like line or something to define the volume filled with gas.)

I'm starting this answer after having written a lot of comments, and I may edit it later after looking at those comments again. (By "starting", I mean the edit I made on March 6, 2024, when most of it was written. I'd only made a few comments when I first started and then deleted this answer on October 15 2020.)