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?

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    I should have said angular kinetic energy not momentum. Fair enough. – userLTK Oct 7 at 11:52
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    @userLTK got it! ~100 eV per atom is a phenomenal amount of energy to start with. In that particular part of that sentence, I'm making some attempt to think about how the initial kinetic energy is partitioned amongst the final products. I'm sure there's some upper limit to what fraction can be converted to rotational energy and I'm just guessing it's less than half. I'll do some more reading on this in the next few days. Thanks! – uhoh Oct 7 at 11:59
  • Small sidebar, but highly ionized rock vapor is unlikely because high-ionization would also undo any chemical bonds. Partially or weakly ionized rock vapor may be possible but high ionization tends to split most gas molecules into atoms. en.wikipedia.org/wiki/… – userLTK Oct 8 at 18:07
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    I tracked down her publication though it appears you have to pay for it: agupubs.onlinelibrary.wiley.com/doi/abs/10.1002/2017JE005333 and here's a more detailed article on her research. ucdavis.edu/news/… I'll also add a short answer: – userLTK Nov 6 at 4:39
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    @userLTK same title and dates: arxiv.org/abs/1802.10223 and researchgate.net/publication/… – uhoh Nov 6 at 4:42

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.

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    I'm really enjoying this answer, thank you! I'm also happy to see others express how interesting this problem really is. Matter in a range of conditions that are complex, transient, and unusual, with no handy analogs on Earth. – uhoh Nov 6 at 6:50
  • I think Figure 18 in arxiv.org/abs/1802.10223 is really helpful to begin to envision the nature and scale of the proposed synestia. – uhoh Nov 6 at 7:00
  • Why is sulfur dioxide relevant, or did you mean SiO2? Also, what does "heat ends up burred" mean? I guess it's a typo, but I just can't decode it. ;) – PM 2Ring Nov 6 at 11:08
  • @PM2Ring I meant SiO2 - typo. Thanks for catching that. – userLTK Nov 6 at 11:24

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.
  • -1 "Not every gas is a plasma" is almost tautological, and "silicate atoms in their gaseous state" is obfuscatory and circular relabeling. Can you describe "...the nature of 'rock vapor' in this description..." more clearly? Also, are you sure that Stewart's model does not take into account ionization? – uhoh Oct 6 at 12:30
  • @uhoh: ...and the usage of fancy english vocabulary doesn't help other people help you in your understanding of the issue at hand. Your comment essentially says "i still don't get it", which is fine, but other than that I don't know how to help you. Is it basic plasma physics that you lack? What is it about the concept of solids evaporating that you don't get? – AtmosphericPrisonEscape Oct 7 at 6:57
  • I lack an answer to the question as written. – uhoh Oct 7 at 7:11
  • @uhoh: Funny that you would think so. I answered your question precisely. – AtmosphericPrisonEscape Nov 1 at 15:03

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