Was Our Moon’s Formation Likely or Lucky?

Paper 1:

Paper 2: 

Cover art by Dana Berry, Source: Robin Canup, SWRI

 

Earth’s moon is peculiar in our Solar System, and in many ways it is an amazing cosmic coincidence.  Our moon is the largest known moon compared to the size of its host planet (sorry Pluto, you and Charon don’t count). Though she is creeping away from Earth a few centimeters every year, humans came about on this planet at the prime time to catch our moon at the exact distance to perfectly obscure the Sun during a solar eclipse.  And some astrobiologists posit that humans may not be here at all if it weren’t for the tide pools our oversized moon synthesized on Earth that helped to render the first forms of life a few billion years ago. But how about what our moon is made of?  Is its composition a cosmic coincidence or a likely result from the conditions of our early Solar System?  Two recent studies investigated this question, and surprisingly arrived at completely contradicting results.

The Impact of Earth

The canonical theory of how our moon came to be is the giant impact theory: about 4.5 billions years ago during the late stages of planet formation in our Solar System, a Mars-sized body (which is referred to as Theia) delivered a glancing blow to the young Earth.  The resulting debris from this collision then coalesced to form what is now our Moon.  This theory does a good job of explaining why the spin of the Earth and Moon have similar orientations and why the Moon is depleted of iron, and has been able to properly recreate the Earth-Moon system using smoothed-particle hydrodynamic simulations.

Originally, this theory was also supported by the compositional similarities between the Earth and Moon.  From analysis of lunar meteorites and lunar samples brought back by the Apollo missions, scientists have found that there are a number of stable isotopes that the Earth and Moon have nearly identical quantities of, whereas meteorites from other Solar System bodies such as Mars and Vesta have drastically different proportions of these isotopes.  This was thought to be an indication that the Earth and Moon had a common origin – the Moon formed from a plethora of material that was ejected from the early Earth when it was struck by Theia.  Studies simulating the Moon’s formation have found that this is not the case; after the impact the Moon forms primarily of the impactor Theia’s material rather than the proto-Earth’s material.  This realization puts some holes in the giant impact theory, since it requires that the protoplanet Theia formed in a part of the planetary disk compositionally identical to Earth.  Though some theories have been cooked up to explain the compositional similarity of the Earth and Moon (such as a fast-spinning Earth being struck by a large impactor, or an extremely high-velocity impactor), all so far require fine-tuning of initial conditions, which makes them unlikely scenarios.

Conflicting Conclusions

The two papers of today’s post investigated the likelihood that a planet’s last major impactor is isotopically similar to the planet it hits, as is apparently the case for Theia and Earth. Both studies used the Mercury integration package (a common software used to study Solar System dynamics) to model the planet formation and late accretion processes of the early Solar System, and used an oxygen isotope called oxygen-17 as a gauge for the how similar planetesimals are in the simulation. Oxygen-17 is one of the best measured, and strikingly similar, stable isotopes evidencing Earth-Moon similarity with a difference of less than 0.016% in terrestrial and lunar rocks.  However, the two studies came to contradictory conclusions: Kaib & Cowan (paper 1) found it very unlikely that Earth and Theia would form with similar compositions, and Mastrobuono-Battisti et. al (paper 2) concluded the opposite.  Why did they differ?  Here is a list of some of the differences between the two studies that may have led to conflicting conclusions:

1) Role of big planets?  The behemoths of our Solar System, Jupiter and Saturn, play an important role on the formation of the inner rocky planets. Since orbital characteristic such as the eccentricity of these big planets may have changed since this time in the Solar System’s history, one cannot necessarily assume the orbital characteristics we see of these planets today.  Both studies used a variety of configurations of Jupiter and Saturn that affected the accretion disk and feeding zones (the regions in the planetary disk from where developing planets grab material). Figure 1 shows how differing initial conditions of Jupiter, Saturn, and the accretion disk altered the types of planets that formed in the simulations of paper 1.

 

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Figure 1. The final mass and semi-major axis of planets created in 3 different ensembles: circular initial orbits of Jupiter and Saturn (left), eccentric initial orbits of Jupiter and Saturn (center), and circular initial orbits of Jupiter and Saturn with the planetary embryos initially confined to an annulus between 0.7 and 1.0 AU. Each ensemble was run 50 times, and the black dots represent the planets that were created throughout all 50 runs. The green, blue, and red shaded regions show Venus analogs, Earth analogs, and Mars analogs, respectively, that are selected based on their masses and orbital distances. One can see how drastically eccentric orbits of the giant planets affect the formation of inner planets in the center panel, as the planetesimal disk becomes truncated via secular resonances. Figures 1-3 in Kaib & Cowan.

 

2) Where is the oxygen?  The distribution of oxygen-17 in our Solar System’s planet-forming disk is unknown, and could potentially change the outcome of the analysis.  Both studies used a linear distribution of oxygen-17 (the amount of oxygen-17 linearly changes with distance from the Sun in the initial disk), and paper 1 also investigated other possibilities: a bimodal distribution, a step function distribution, and a random distribution, though they found that these distributions did not affect their conclusions.

3) How much of the Earth went into the Moon?  Though most simulations have the Moon being primarily composed of material from the impactor Theia, the percentage of the proto-Earth that gets mixed in is up for debate.  Paper 2 was less stringent with their criteria for the impactor’s composition, because they allowed larger percentages of the initial planet to be mixed in with the impactor to form its moon. These percentages are consistent with Moon-forming simulations.

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Figure 2. The region of contribution from the planetesimal disk for Venus (green), Earth (blue), Mars (red), and Theia (hashed) analogs in a cumulative distribution function (CDF). The solid line is the median CDF of each class of analogs, and the shaded region shows the 1-sigma uncertainty. Panels A, B, and C show the results from the circular Jupiter/Saturn, eccentric Jupiter/Saturn, and annulus simulations (see caption of figure 1 for a more detailed description of these). Figure 9 in Kaib & Cowan.

4) When is a planet the Earth?  Paper 1 also considered only planets that were deemed “Earth analogs” and impactors that were “Theia-analogs” in their conclusions.  Only planets that had a mass and orbital distance similar to Earth and impactors of Earth that were consistent with the predicted mass of Theia could lead to an Earth-Moon system. The compositional similarity of these bodies was then analyzed. Figure 2 shows the distribution of Earth and Theia analogs in the simulations of paper 1, as well as the distribution of planets deemed Venus- and Mars- analogs. Paper 2 considered all collisions between a planet and its last impactor in their conclusions, but also investigated the likelihood of collisions between Earth- and Theia-like bodies.

So what was determined by the two studies? Paper 1 found that less than ~5% of Earth-analogs were last struck by an impactor that was compositionally as similar to it as the Earth is to the Moon, and therefore the formation of a moon like Earth’s is a statistical outlier.  Paper 2 determined that ~50% of all planets were last struck by an impactor compositionally consistent with what is seen in the Moon, assuming about a fifth of the impacted planet’s material was used in the synthesis of the moon. Both studies agreed that the feeding zones of terrestrial planets aren’t exclusive but rather shared among the inner planets, yet come to shockingly different conclusions from similar studies. The drastic differences most likely came from paper 1 only considering Earth-Theia analogs in their conclusions, and paper 2 allowing the Moon to contain a significant fraction of proto-Earth material.  It seems that the origin of our nearest celestial neighbor may still be shrouded in mystery, and further analysis will need to be done to determine if our moon’s formation was a likely outcome or a cosmic coincidence.

About Michael Zevin

I am a graduate student studying Physics and Astronomy at Northwestern University. I am part of the LIGO Scientific Collaboration and work with Dr. Vicky Kalogera studying gravitational wave astrophysics, particularly parameter estimation of gravitational wave sources for the Advanced LIGO era. I received my B.S. from the University of Illinois in Astronomy, Physics, and Music. Outside of school I enjoy teaching science at Chicago’s Adler Planetarium and Kids Science Labs, playing music around the Windy City, and looking up.

20 Comments

  1. Wonderful to see exactly how our assumptions could potentially lead to such different results in a study such as this. Also, interesting to see the finer detail of what we are taught in grade school (that the moon is made up of contents of the Earth).

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    • I had very similar conclusions after reading this post – if small differences in two models lead to completely different results, how much of the universe can we really claim to know?

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  2. In spite of this, the giant impactor theory is still generally accepted, right? When you say it’s had a few holes poked in it, they’re still ones we expect to patch?

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    • Yes, this theory is still generally accepted. Certain red flags were risen when people began running simulations and seeing that the formed moon was mostly composed of the impactor’s material, but its studies like these two that are helping to investigate this scenario in much better detail!

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  3. Just some additional very important comments on the differences from one of the authors of paper II, not fully reflected in this discussion, suggesting a more comprehensive analysis by paper I, which is not the case (each paper has its advantages and disadvantages):
    1. Our paper accounted for the actual error bars arising from the simulation results. These are not considered at all by paper I, but they are crucial for calculating probabilities; some of the major differences in the conclusion simply arise from this fact. Error bars can not be ignored.
    2. We have considered a range of contributions of material coming from the Earth – from 0 to 40 %. SPH simulations actually suggest that the vast majority of collisions give rise to at least 20% contribution from the Earth – so this is actually the most likely model to consider, and not a 0%.
    3. We have considered a wide range of impactors, and checked the sensitivity of our assumptions.
    – Not any type of collisions was considered as suggested above, we focused on those with large Theia like impactors.
    – We have also considered the possibility of looking only on impacts on the third (“Earth”) planet.
    – We also considered the sensitivity of choosing the 17O calibration assumed.

    One should look into the methods section in out paper more depth when discussing our work.

    Generally we found consistent results, with the sensitivity to the assumption typically not being very large, but can affect the results up to a factor of ~2.

    Note , that a definition of what is Earth is not simple, when non of your simulations provides an exact solar system analog (true for both groups). For example should you consider the third planet (e.g as we did), or should you consider an Earth planet according to its distance from the Sun, irrespective of other planets (both have their pros and cons in respect to the evolution)

    Just taking the first two considerations into account make both groups results very similar (with at least 10-15% chances for the paper I data). We know that, because the two groups exchanged their data after the papers submissions and re-analyzed each other data. We hope to write a combined comparison paper later on.

    So yes, the assumptions matter, but once you clean the systematics the result are actually in very good agreement, without being so sensitive to the assumptions somewhat in contrast to the discussion above.

    Hagai Perets

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  4. Great piece and a salutary message. There is an article in arxiv by Kevin Heng, University of Berne, ” The nature of scientific proof in the age of simulations ” April 2014 that addresses this very issue and acts as a warning. As good as your computer and model is( and necessary) , it’s only as good as the data fed in. The more observation the better. Worryingly it has got so bad that I have seen academics get mixed up in presentations over whether their data is real or simulated.

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  5. Is it possible that the Moon could have been a protoplanet forming in the same region of the accretion disk, so it would have a similar composition to Earth, and then was pulled into orbit around earth at some point?

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    • Good question! This theory is known as the capture scenario, and is not as well accepted as the impact scenario for a variety of reasons. Some of them are that the spin axis of the Moon and Earth are really well aligned, which would be better explained if the Moon formed from a large impactor, and that the moon has a deficiency of iron. Also, I believe simulations have a hard time making this work out because the Earth is not that massive.

      However, it is definitely possible that the impactor formed in the same region of the accretion disk as the Earth, and that could definitely lead to the compositional similarity that we observe. Some studies suggest that this is unlikely, however, since the feeding zones (the regions where forming planets accrete material from in the disk) stretch quite far and are shared by other planets in the disk.

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  6. Thanks for this neat post! I have a similar question to Sam’s above — to what extent do these findings challenge the giant impact theory? Is it more likely that the giant impact theory will need to be adjusted or that we will explore entirely new models of moon formation?

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    • It is more likely that the giant impact theory just needs to be adjusted. There are lots of other pieces of evidence that support this theory than just the compositional similarity of the Earth and Moon (though this was originally a big piece of evidence FOR this theory, before simulations started recreating the collision). However, maybe the giant impact theory does not need to be adjusted that much! As evidenced by these two papers, our Moon might have just been a statistically unlikely event that ended up happening, or a likely outcome from the conditions of the early solar system.

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  7. I still find it strange how such a large scale collision can happen between Earth and Thea, would they not have reached different orbits as growing planetesimals? Perhaps I just don’t know the time scale of formation for these two masses in comparison to the time scale the the collision occurred.

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    • With the happy and stable solar system we have today, it is hard to imagine the chaotic environment of our early Solar System. However, we believe that there were many many more protoplanets forming back then than the 8 planets we have today, and interactions between these young bodies were quite common. Also, you can only squeeze so many planets into a stable system, so it is somewhat fated that only a handful of are able to stick around.

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  8. With such drastic differences in the results of these two papers, do you feel that one is more rigorous than the other? Which one should be believed?

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    • I feel that both studies are quite rigorous, and compliment each other very well! I don’t think it is as clear cut as one being right and one being wrong. Both papers had pros and cons in their analyses, and in fact agreed on certain things. I think more studies and collaboration on this will lead to better insights on this topic.

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  9. They are both excellent papers and use the same simulation. The difference is the starting point assumptions made that snowball into large differences once the simulation is allowed to run.

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  10. Interesting post!! It’s incredible how big of a difference small differences in assumptions can make!

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  11. How much can physical samples (moon rocks) support or distinguish theories? would more samples help inform this discussion or are they not that useful, leaving modeling as the best option to move forward?

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    • I’m not an expert on the Moon’s chemistry and geology, but I do not think more samples would be particularly useful. We expect the isotope ratios of lunar rocks to be mostly consistent over its surface, and rocks from different locations on the moon should match what we have already seen from lunar meteorites and rock brought back from the Apollo missions (they brought back over 800 lbs of lunar samples!!!). The physical samples are what told us that the Moon and Earth are incredibly similar in stable isotopes compared to other bodies in the Solar System. Tying this with moon forming simulations is what these studies are trying to understand.

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  12. This is really interesting. If it turns out that the probability that the moon is formed is very small, can we explain it away using the anthropic principle? The application of the principle to this problem seems somewhat laughable to me but the anthropic principle is taken very seriously in some physics circles where people are working on eternal inflation, etc.

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    • Interesting thought! I guess in some ways that depends if our Moon did in fact play a big role in creating life on Earth…

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