A New Moon Formation Hypothesis has Emerged

A New Moon Formation Hypothesis has Emerged

(Originally posted January 10, 2017 on Blogger)

I posted a link to a paper describing a new hypothesis of how and why our moon is neither aligned with the ecliptic, nor Earth’s celestial equatorial plane. It is a fascinating read! Here's the link to my post in which the link to the paper is found for those interested:

https://plus.google.com/u/0/105142364701594866820/posts/fDTDME7LWn3?sfc=true

That paper maintained what has been the leading hypothesis as to how the moon formed; from the Theia Impact hypothesis, also known as the Giant-impact hypothesis.

Theia is the name given to a Mars-sized protoplanet that has been believed to have collided with proto-Earth 4.5 billion years ago during the Hadean eon. This impact resulted in the formation of the moon from an accretion disc ejected into an orbit beyond the Roche limit.

Księżyca Powstawanie's depiction of the Theia impact event.

Księżyca Powstawanie's depiction of the Theia impact event.

The Roche limit is the minimum distance a satellite, such as the moon, can orbit without being ripped apart by Earth's (or any host planet's) gravitational effects. Think the inverse-square law which applies to gravitation between two masses; the attraction between two masses is directly proportional to the product of their masses and inversely proportional to the square of their distance from each other. The greater the separation, the weaker the influence of gravity and vice versa.

Consider Mars' small moon, Phobos; this little moon orbits around Mars faster than Mars' rotational period, and is spiraling inward rather than outward (like our moon). Within the next 7.6 million years, Phobos will reach the Roche limit at which point Mars gravitational effects will shred the moon into billions of pieces resulting in a disc. This disc of shredded moon material will ultimately spiral into Mars.

Our moon will experience no such fate. It has formed beyond the Roche limit, and continues to distance itself from it with time. But did the moon form from a single giant impact event? A new paper has been published in the journal Nature Geoscience that posits a new hypothesis as to how our moon formed, and having read it, I have to say that it is puts forth some very strong arguments for itself while undermining the strength of the Giant-impact hypothesis. Of course, I'm just a regular schmoe, so don't take my word for it, the paper can be found here:

http://www.nature.com/ngeo/journal/vaop/ncurrent/full/ngeo2866.html

Raluca Rufu et al. from the American Technion Society, a U.S. affiliate of Israel-Technion Institute of Technology, has run 864 simulations that support an entirely new idea as to how our moon formed, and it is fascinating. Let's get started...

Rather than a single giant impact event having formed our moon, Rufu et al. suggest that our moon may have formed by multiple relatively small impacts (more than 20). The Giant-impact hypothesis suffers from what scientists have dubbed a "compositional crisis" wherein it has proven problematic to reconcile the compositional similarities of Earth and our moon without violating angular momentum constraints applied to formation sequences. The Giant-impact hypothesis, though possible, is on the grand scheme of things, quite improbable given the very restrictive set of conditions necessary for a moon our size and composition to form.

Earth and our moon are similar in ratios of isotopic oxygen, titanium, pre-veneer tungsten, and other elements. Though the ratio of isotopic oxygen (18O/16O) can be explained by a hot protoplanetary atmosphere, other more refractory elements such as titanium cannot. Refractory elements being elements that are very resistant to heat. As for a giant impactor singularly creating the moon, such an event is extremely rare, and would most likely occur very early in solar system formation. This latter possibility is undermined in that it is not consistent with recent moon formation timing estimates.

In the multiple-impact hypothesis, Rufu et al. posit that impactors the mass of 0.01 to 0.1 Earth masses collided with Earth creating debris discs from which small moonlets accrete and migrate outward controlled by tidal interactions (fast at first, then slowing with distance). This slowing migration causes the moonlets to enter their mutual Hill radii, and eventually coalesce.  Debris discs from 0.01 to 0.1 Earth mass impactors have sufficient angular momentum and mass to accrete a sub-lunar-sized moonlet, and this is supported by 1,000 Monte Carlo simulations performed by Rufu.

Where the Roche limit is the minimum distance at which a satellite must reach in order to survive the tidal effects of its host planet, the Hill radius (or sphere) is the region in which a satellite dominates the attraction of other satellites.

Mass, angular momentum, and distance are all taken into account when calculating the Hill radius.  Image source: http://www.jgiesen.de/astro/stars/roche.htm

Mass, angular momentum, and distance are all taken into account when calculating the Hill radius.

Image source: http://www.jgiesen.de/astro/stars/roche.htm

A contour plot of the effective potential of a two-body system due to gravity and inertia at one point in time. The Hill spheres are the circular regions surrounding the two large masses.  Source: Wikipedia

A contour plot of the effective potential of a two-body system due to gravity and inertia at one point in time. The Hill spheres are the circular regions surrounding the two large masses. Source: Wikipedia

In summary, there is an impact which imparts enough angular momentum to send ejecta outward beyond the Roche limit.. This results in a disc of material around Earth within days of impact. Over the course of centuries this disc accretes and migrates outward from Earth before a subsequent impact occurs. This second impact also results in a disc. This disc accretes, migrates outward, and the process continues in this fashion with variables which I'll get to momentarily. It takes centuries for moonlet mergers (or losses as we'll get to as well) to occur.

Of the 864 simulations performed by Rufu, most showed Earth's final angular momentum as being the result of several impacts, the largest of which was not necessarily the last. If I read the paper right, then it is suggested that a single giant impactor provides insufficient angular momentum relative to current measured values, further undermining its credibility.

There are important factors to consider with regard to multiple relatively smaller impactors; including direction angle relative to the mass' respective centers, impactor mass ratio, planetary rotation, and impact speed... I suppose we can couple speed and angle to simply say impact velocities.

The paper goes into detail about the different parameters involved in multiple impacts. With regard to direction angle, simulations showed that head on and low-angle impacts (slightly off from direct hits) require high speeds in order to eject material into a suitable orbit. Such impacts result in high mantle mixing and core merging with heating concentrated in Earth's upper mantle. Some low-angle impacts with high speeds produced discs with a higher degree of composition similar to Earth's, suggesting a substantial portion of the disc having been comprised of Earth material ejected into orbit.

On the other end of the scale, high-angle grazing impacts resulted in little mixing of material between the two bodies, with a large portion of the impactor's mass contributing to the disc. High speed, high-angle impactors resulted in much of the impactor material escaping the system altogether, leaving only a portion of Earth's mantle material in orbit. Low speed (relative), high-angle impactors resulted in a wide range of total disc masses, with the highest masses attributed to graze-and-merge impacts. Hit-and-run impacts resulted in about 0.2 moon mass of material in its subsequent disc. This new hypothesis really opens the door to variables that would likely best represent the chaotic nature of our early solar system.

In simulations, Earth's initial rotation prior to impacts was also a factor; head on collisions with a slow-rotating Earth resulted in low material contribution to the disc from the impactor.

Some simulations showed that high energy, high angular momentum impacts could cross the hot spin stability limit, which Rufu explains can account for our moon's enrichment in heavy potassium isotopes. The hot spin stability limit (HSSL) is where a planet (Earth in this case) cannot maintain a corotation state with a disc. Planets are significantly heated when impacted by protoplanetary objects. Initially proto-Earth may have had a rapid rotation, corotating with a disc of ejected material from an impact. HSSL is where the planet cannot maintain a corotation state; they form a continuous mantle-atmosphere disc (MAD) structure where the corotating center of the structure transitions smoothly to a sub-Keplerian outer region. A Keplerian orbit being those ellipse, parabola, hyperbola orbits that form a 2D orbital plane in 3D space. Giant impacts like the hypothesized Theia impactor would exceed the HSSL; such events require a high degree of vaporization, and sufficient angular momentum.

The hypothesized sequence of events following the Giant-impact scenario. In the multiple-impact hypothesis, high energy, high angular momentum impacts could also cross the hot spin stability limit allowing for heavy potassium isotopes to enter into the lunar mix.

A lot of the work done on HSSL simulations was done at Harvard using the HERCULES Code; a semi-analytical code designed to find equilibrium internal structure of rotating planets, and examine the dependence of the HSSL boundary on total mass, angular total momentum, and thermal profiles of planets.

Rufu et al. also found that disc composition was not significantly affected whether an impactor had retrograde sense (had opposite angular momentum of Earth) or one had a prograde sense. However, simulations did show that retrograde impactors often failed to form a disc with enough angular momentum to accrete a moonlet. Prograde impacts could have served to increase the rate of spin for an initially slow-rotating Earth, but rotation rate saturates for initial states where Earth is rotating more rapidly. This latter situation is due to angular momentum drain carried away by ejecta (conservation of energy). Rufu found that for an initial rotation rate of 5.9 h, retrograde collisions decelerate the planet, while prograde collisions had very little affect on the period. Therefore, it is concluded that acceleration beyond 5.9 h is difficult at best.

Impactor mass of course plays a role too. Medium impactor mass (0.01-0.1 Earth mass) impactors can produce sub-lunar-sized moonlets with compositions ranging from impactor material dominated to Earth material dominated. Near head-on collisions were preferred because such scenarios efficiently incorporated planetary material to the respective discs.

Our planet could have had a net gain or even net lost material from impacts, depending on the balance of impactor merger types. Net erosion could occur if a substantial portion of impacts were high energy cases. In extreme cases, simulations showed Earth could be stripped of up to half its initial mass; where the mass ratio of the impactor is 0.091, its impact velocity is 4 times the escape velocity, and its direction angle is straight on (zero degrees). Planetary erosion is more common at lower impact angles (at or near head on) than at high angles due to larger interacting mass and interacting energies.

The different discs may not have all had the same composition, but their net composition would have reflected that which is seen in observations today. Entropy, density, and vapor fraction are all necessary parameters that need to be understood in order to determine composition and moonlet accretion efficiencies.

As stated earlier, for accretion to have a chance, the disc must form beyond the Roche limit. Anything below that limit would simply fall back to Earth. Initially, disc material is hot. Getting beyond the Roche limit requires energy, and this action results in heating. According to the paper, the shockwave that accelerates material into orbit is largely responsible for heating the material. Thus, the addition of kinetic energy is intricately linked to the addition of thermal energy.

The implications of this paper could be huge. Unlike the Giant-impact hypothesis, the multiple-impact hypothesis allows for a large range of possible scenarios as to how our moon formed. There is far more leeway in impact geometries and velocities. As mentioned, most rocks on Earth exhibit similar ratios of elements, such as tungsten (182W/184W); multiple impacts could explain this phenomenon. According to the paper, they also promote the preservation of primordial heterogeneity of Earth material and possibly that of the moon, whereas a single giant impact event erases primordial heterogeneity that predated moon formation.

The multiple-impact hypothesis will now face the harsh scrutiny of the scientific community, and we will see how it fairs in the years to come. But for now, it is a fascinating new take on how our moon formed, and shows just how much there is for us to learn right here in our own backyard.

As always, thanks for reading.

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