Planet Formation and Migration

The current thinking about how planets are made from scratch revolves around the idea that the host star, in its early life, is associated with a flattened, rotating disk-like structure. The disk is made of the same stuff as the star, mostly hydrogen and helium, plus heavier elements such as carbon, nitrogen, oxygen, neon, silicon, iron, nickel and more. The elements heavier than hydrogen and helium are collectively referred to as metals in the trade, even though some of them are not metals in the traditional sense of the word. The elements that have high condensation temperatures are also referred to as refractory elements (as opposed to “volatiles”). Although the percentage of metals is tiny (in total less than 1%), it is plenty to make planets. However, the total mass required of a protoplanetary disk is uncertain but believed to be a minimum of 1 to 2% of the mass of the host star. The disk also contains compounds of various kinds and some of these are referred to by the highly technical term, “dust.” Dust can have various compositions involving some combination of the metals (for example, oxygen and iron). A common property of dust is that it reprocesses the radiation from the host star into infrared radiation and this is observable by infrared telescopes (the disk is dark in visible light because it absorbs visible light). Compounds that have been found in meteorites are thought to be direct relics of the ancient disk that was once associated with our Sun. The disk is often referred to as a “debris disk” because of the various coagulations of compounds in the disk.

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Confronting Discrepancies with Observations

Another property of the debris disks that is often touted as favoring association with planet formation is that the material in the disk rotates because the star from which it is formed spins. If planets are formed form the disk they will end up orbiting the star in the same direction as the star's rotation. However, this has now become problematic because the number of exoplanets with spin-orbit misalignment, and with outright retrograde motion, has become significant. Exoplanets that rotate in the opposite direction to the star's spin are then difficult to explain. A recent study concluded that most hot Jupiters have a spin-orbit misalignment, with as many as 25% actually showing retrograde motion. Solutions have generally focused around perturbations by unseen massive objects such as other planets or a distant star that is a member of a binary pair. There is also something known as the “Kozai effect” which is basically an “interaction” between the orbital tilt and the eccentricity of the orbit, in the sense that the latter two quantities can vary such that the orbit is able to exchange one in favor over the other, in a kind of to-and-fro “resonance.” The origin of the distribution of the eccentricity is also problematic for standard planet-formation scenarios and proposed explanations again involve planet-planet interactions after the planet-formation phase. However, the solutions to the problems presented by skewed and/or highly elliptical orbits remain speculative because the objects responsible for the perturbations have yet to be found in a single case. ⁹

Absence of Direct Observation of Key Processes

Dusty debris disks have actually been observed, but they are only found in stars that are very young, less than 10 million years old or so (compared to a typical lifetime of 10 billion years for a sunlike star). Recently a particular exoplanet was directly imaged and found to be residing in a debris disk. This is the exoplanet known as Fomalhaut b, which is a gas giant at a large distance from its host star. However, observing a planet in a debris disk does not prove that it was formed in the disk, and it does not indicate the mechanism of formation. A planet that is unambiguously in the process of formation has never been observed. In other words, there is no direct proof that planets form in the disk, it is an inference made simply from the coexistence of the planet and the disk. If you catch someone at a crime scene, you have to establish many things to prove that the person committed the crime. The same applies to a more recent case (Kraus and Ireland 2011, LkCa 15: A Young Planet Caught at Formation?). The question mark at the end of the title was conveniently omitted in a flurry of popular news stories. The paper discussed caveats pertaining to the fact the “blob” could just be a “random” chunk of matter that has nothing to do with planet formation. The authors themselves stated that further observations should be made to make conclusive deductions, but the spin in popular news stories (even those on dedicated astronomy websites) did not reflect this bottom line.

The Hurdles for Planetesimal Formation

Current planet-formation scenarios all require the production of large chunks of matter, and at least one chunk that is large enough for it to start attracting other chunks by its own gravity. These chunks can be formed either from the “bottom up” or from the “top down”. The former process starts off with the coagulation of tiny dust grains and the latter starts by gravitational instabilities in the debris disk (which is gaseous and turbulent). The bottom-up approach, known as “core accretion” is the one that is favored in the current literature. Accretion refers to the collection and aggregation of matter onto the object in question and the bottom-up scenario is known as (the) “core accretion” (theory). However, as we will see, neither approach actually works. In the core accretion scenario the chunks of matter have to reach a minimum threshold mass for gravity to kick in enough for the chunk to start growing to become what is known as a planetesimal. However, that threshold is huge. Planetesimals have to have a size of hundreds to thousands of kilometers before their mutual gravity becomes strong enough to start growing into a planet. While it is easy to get meteorite-sized objects from the coagulation of tiny dust grains and the like, once you get to boulders that are around a meter large in size, you hit a showstopper. As you know, boulders do not stick together with their own gravity. What's worse is that these boulders are theorized to be in a highly turbulent environment, traveling at very high speeds relative to each other. When these boulders collide, again as you would expect from common sense, instead of sticking together, they smash each other into smaller pieces. That's the exact opposite of what you need to build a planet. It is a showstopper.

Boulders and Rocks Do Not Stick Together

Nobody has been able to think of a way for boulders to stick together at all. As a scientist, I find what happens next deeply disturbing. Researchers admit that the problem is severe but then they simply assume that somehow boulders did manage to stick together and then they proceed to develop a sophisticated theory of planet formation assuming that the critical mass was formed. There is no known mechanism to make boulders or kilometer-sized objects stick together and prevent them from smashing each other apart so it is almost like invoking some kind of magic. It is certainly true that if there does exist a large enough core, that core will accrete material and grow larger by means of gravity. However, if the foundation of planet-formation theory is an impossibility, why should one have any reason to believe that the theory on top of that foundation is a true description of what actually takes place? If a completely different approach is required, how do we know whether that alternative mechanism continues to operate (or not) during gravitational growth? To use an analogy, the current theory of planet formation is like making a detailed budget for how you are going to spend a billion dollars when you only have a thousand dollars in the bank. It is of course possible that could run into a billion dollars tomorrow. However, shouldn't you be spending more time figuring out how to acquire a billion dollars, rather than how you are going to spend it? If you don't acquire the billion dollars, your budget will be irrelevant and wrong.

Fudging Theories by Hand

Just when you think it couldn't get any worse, it does. You see, planet-formation models are extremely complex and there are many unknowns. You have to decide what your initial conditions are, what the physical state at every point in the protoplanetary disk is, what approximations and assumptions you are going to make, and so on and so forth. There is a lot that is put in by hand. For example, in some simulations of terrestrial planet formation, Jupiter and Saturn are simply put in place by hand, with the assumption that they were somehow already formed. ¹⁰ This is because Jupiter's gravity is so strong that it affects the aggregation of mass onto a smaller object that might be very far away. In other words, Jupiter's gravity would have affected the formation of Earth. If you don't put in Jupiter by hand, things can go crazy and you might not get the answers that you want. There are many other knobs and dials that can be tweaked by hand in a planet-formation model. Obviously the more there is to tweak, the less useful the model is in giving insight into the true planet-formation mechanisms. The goal for any scientific model should be to have as few adjustable parameters as possible in order to reproduce the observables in the “real world.” Prior to the discovery of exoplanets the statistical predictions of the standard planet-formation scenarios for samples of exoplanets could not be tested. Now they can be tested and the results are already a disaster. Again, I am puzzled by expressions of surprise in the scientific literature, that the predictions of the standard model conflict with certain observational facts. Why should it be surprising? The theory is based on a hypothesis for which there is no known physical mechanism.

Further Conflicts with Observations

It was only a question of time before a conflict between theory and observation was exposed, and indeed this was concisely illustrated by a paper published in a peer-reviewed journal in 2010. ¹¹ This paper actually reveals one of the most fundamental problems with the current core accretion scenario in addition to the “no sticking” problem. The paper examines the properties of a sample of exoplanets that have an orbital period of less than 50 days and addresses how the number of exoplanets found in various mass ranges compares with the prediction of the core accretion scenario. The title of the paper is “The Occurrence and Mass Distribution of Close-in super-Earths, Neptunes, and Jupiters.” The authors studied exoplanets around 166 stars and found that, compared to the theoretical prediction, there is a statistically significant overdensity of planets in the mass range of 5 to 30 Earth masses (with orbital periods less than 50 days). The core accretion scenario actually predicts a “planet desert” in this regime, but no such deficit of planets is found. The severe conflict between the prediction and reality is heavily underplayed. The abstract states, “This region of the parameter space is in fact well populated, implying such models need substantial revision.” In other words, the paper does not state that the current models could be completely wrong, or that the current models are based on an impossible premise, requiring the need for a paradigm shift. The paper never really clarifies what is meant by “substantial revision” and stops at that. The observational result reported in the paper is robust to selection effects because the “completeness correction” that was applied to account for planets that might have been missed by observational bias increases the number of planets in a given mass range. In other words any observational bias would work in the direction of reducing the disagreement between predicted and observed planet numbers, not increasing it. The paper does not of course mention anywhere that the models that are referred to require the sticking together of boulders by hand.

Origin of the Planet Desert Prediction

Now, the reason why the core accretion scenario predicts a planet desert for the mass range of around 5 to 30 Earth masses and an orbital period of less than 50 days is very simple. A growing planet in this regime undergoes rapid evolution in only one of two ways. Either interactions with the environment result in energy loss that makes the planet rapidly spiral inwards towards its host star, or rapid runaway accretion of gaseous material grows the planet too quickly into a giant. Since planets with masses of 5 to 30 Earth masses are short-lived in the model, a snapshot survey should not find many of them. It is quite remarkable that even with a foundation that forces the sticking together of boulder-sized and mountain-sized chunks by hand, even with all the additional knobs and dials that are available to tweak, the standard model of planet formation fails in a very fundamental way. The spiraling into the host star and the runaway growth scenarios are both controlled by basic physics, and neither scenario can be made to go away by the knobs and dials in the model. This should be a big clue that something is very wrong with the current paradigm, rather than indicating that there is a problem with the details of the model. What is interesting is that both problems of planet migration and runaway accretion were known before, but the problems were never confronted with real data until recently.

Sanitization and Marginalization of the Problem

Unfortunately, school and college textbooks on science and astronomy give an extremely sanitized handwaving account of planet formation and persuade the reader that either planet formation is quite well understood, or at worst that there are some small niggling loose ends to tie up. How do research papers approach the awkward and embarrassing “no sticking” problem? There are a number of ways, but allow me to give some specific examples from a recent review paper on the subject of planet formation. ¹² In the introduction of the paper, the author states that, “The planetesimal hypothesis is widely accepted today as the basis of terrestrial planet formation.” No citation is given to back up the use of the term “widely accepted.” I don't know what fraction of scientists accept the hypothesis. If the wide acceptance is true then it is deeply troubling because it means that a large number of scientists are willing to accept a hypothesis that is currently known to be physically impossible, and their acceptance reflects the “belief” that some day someone will find a way to make boulders and mountains that are colliding at high speeds stick together instead of being smashed apart. If the “wide acceptance” statement is not true, then it is also troubling because then the implication is that the author has made a statement about the hypothesis that is not supported by fact. In any case, most of the paper discusses what happens or could happen assuming that planetesimals can, and have formed (by an unspecified mechanism).

Towards the end of the paper the author does address the “no sticking” problem directly. The author states that, “In the particle-sticking model, growth is especially difficult for boulder-sized bodies, a problem referred to as the ‘meter-size barrier’.” The author explains that these boulders could have relative speeds of several tens of miles per hour and goes on to say that, “These collisions probably lead to erosion rather than growth.” The way the problem is presented here is typical: the severity of the problem is first underplayed, and a name is invented for the problem so that one can put it aside and continue as if the problem didn't exist, on the premise that somebody will solve it. The assumption here is of course that it is solvable, but there is no basis for that assumption. The term “especially difficult” is used instead of “impossible” or “unexplained,” and the word “probably” is used to soften the fact that collisions will hinder growth. The wording implies that there may be some circumstances under which boulder-sized bodies could stick together, and some circumstances under which collisions could lead to growth. However, no citations to any study are given that demonstrate either of these two things. The wording reflects “hope” only, and that is not science. The use of the term “meter-sized barrier” implies that the barrier is in some way a property of physics, or physical conditions in the model. Where is this barrier?

There is no physical “barrier.” Really, the only barrier is in the human mind being unable to let go of a paradigm that doesn't work and come up with a new paradigm. There are only two possibilities. Either there is a regime of physical conditions that humans have not thought of that would allow meter-sized objects to aggregate into planetesimals, or the core-accretion, bottom-up scenario is completely wrong. In either case, the “barrier” is in the human mind and has nothing to do with physics. The review paper does not mention any need for a paradigm shift, and instead states that, “In the light of these problems, the hunt is on for a new mechanism for planetesimal formation that can operate in a turbulent environment.” Doesn't this statement contradict the softened, “on-the-fence” statements earlier in the review paper? Is the formation of planetesimals the only conceivable route to planet formation? The review paper described here is a state-of-the-art summary of research on the formation of terrestrial planets. It does not mention the previous paper I described that reported the conflict of observation with theory, probably because the latter was published at about the same time. This is indeed a rapidly advancing field.

How to Scrutinize Articles on Planet Formation Theory

So, how do books aimed at the layperson handle the fact that current theories about planet formation are founded upon an impossibility? Whilst scientific papers are fair game for scientific scrutiny (they should be rigorously written to defend their arguments), books aimed at the layperson are not necessarily written in a scientifically defendable form. I don't want to drag individual authors into the mud, so you will have to judge for yourself. Take a look at various books on the subject, and read them with a critical and questioning posture. There are generally two approaches that authors of such books take. One approach is to not even mention the problem, in the hope that the reader doesn't realize that gravity cannot stick together objects that are not massive enough, especially in a turbulent environment. The author typically ends with the conclusion that the core accretion theory of planet formation is acceptable. In the other approach, the gist of the arguments given is that scientists are working with some wonderful computer codes that are making dust-sized particles stick together.

The fact that rocks, boulders, and mountains coming at each other at tremendous speeds prevent any build-up of mass is marginalized (almost ignored) and the author typically moves straight on to gravitational accretion and growth of much larger masses (planetesimals). In other words, the critical failure of the entire scenario is skipped (or heavily downplayed), with the implication that people will progressively incorporate more and more complex physical processes into even more wonderful computer codes that will succeed in making the progression from dust to planetesimal.

The account usually ends with something along the lines that there certainly are problems, but the general overall picture is correct. We are nearly there. Just a few loose ends, you understand. The account is inevitably tied together with generous handwaving. Underpinning all this is a thing called hope. The hope that somebody will find a way, so that the whole theory of planet formation won't have to be rewritten from scratch. The hope that something completely different, something that nobody has yet thought of, is not at the heart of planet formation. But hope is not a scientific procedure. Nor is belief. Scientists who think that the current theory of planet formation is essentially correct, believe that the “no-sticking” problem will be solved. It is a belief that is not based on scientific facts. It is true, if the problem were solved, the theory would agree with certain observational facts, but it would still fail to explain other observational facts (such as the planet desert mentioned earlier). But nobody knows whether it can, even in principle, be solved, so until then, supposing that it can, is a belief. Ultimately, data and observation will reveal the truth, so in some sense it doesn't matter. However, it does immensely slow down progress towards that goal.

The theory of planet migration (from larger to smaller distances from the host star) is intimately tied to theories of planet formation. Planet migration is an entirely theoretical expectation from the physics of the interaction of a planet with its environment. The processes involved are very complex and the study of planet migration constitutes a subfield in itself. Of course, a planet has never been observed to migrate. However, the finding of large numbers of hot Jupiters close to their host star, combined with the expectation that most planets are created near or beyond the snow line, is taken as evidence that the gas giants created there have migrated to the close-in positions. In the current paradigm, gas giants are created by accretion of hydrogen and helium onto a rocky core that has been created by means of the standard core-accretion scenario. The evidence for planet migration is therefore circumstantial and the conclusion (that some planets have migrated) relies on assumptions that may not be true. When planet formation is finally understood, it can be expected that an understanding of planet migration will also go hand-in-hand.

Formation Theories Aside from Standard Core Accretion

The top-down scenario of planet formation is known as the “disk instability model.” In this scenario, instabilities in the protoplanetary disk cause large lumps of matter to break off and then contract under their own gravity to form planets. It is actually not straightforward to test this scenario because very complex physics is involved and correspondingly complex numerical computer codes are required to churn out the answers (with the associated large number of knobs and dials). The general conclusion appears to be that planet formation is possible under some circumstances, but only far out in the disk at tens of AU from the host star (recall that in our solar system Jupiter is nominally at about 5 AU from the Sun). There are other problems, such as the instabilities causing spiral arms to form in the disk instead of breaking up into clumps, and mass being transferred to the host star instead of going into planet formation. ¹³ The disk instability model is generally dismissed in the scientific literature. In a 2010 review paper on the topic, the authors concluded, “The ultimate fate and survivability of planets formed at such an early phase of disk evolution is unclear.”¹⁴ Then they state, “The principle of parsimonious explanations makes appeal to more than one formation mechanism for gas giants unappealing.” This is extremely bizarre. This kind of statement has no place in science, but unfortunately it is not uncommon in peer-reviewed scientific literature. The authors are essentially saying that they don't like to have two modes of planet formation, based on a completely fictitious “principle” (if their “principle” were true, the Universe need not bother to exist at all since that would be very economical indeed). If the authors are using “parsimonious” as in “Ockham's razor” and therefore don't feel the need to further justify their statement, it is important to remember that neither the “law of parsimony” nor “Ockham's razor” is a “law” of nature or physics. In any particular case, nature and physics are not obligated by such inventions of the human mind. Nevertheless, it is still true that the disk instability model is not by itself a viable scenario for planet formation.¹⁵

Some researchers have actually begun to investigate an approach that is a hybrid of the bottom-up and top-down scenarios. An oversimplified explanation of this is that a gaseous “planetary embryo” forms by fragmentation far out in the protoplanetary disk (at 100 AU or so), and dust and other heavy elements contained in the embryo sink to the core (i.e., in a process of sedimentation). Thus, a rocky core is formed without running into the “sticking together” problem. The embryo migrates towards the host star, settling to become a gas giant, or if it migrates further, the gaseous envelope is stripped off (by differential gravitational, or tidal forces and evaporation), leaving a rocky terrestrial planet. The calculations are difficult and complex and the researchers working on these models themselves state that many details have yet to be addressed in order to see if it all works. ¹⁶ In particular, why should there be a pileup of hot Jupiters very close to the host star (at a distance that can be as small as 0.04 AU), as described earlier? In other words, if giant planets come in from 100 AU or so and lose their hydrogen and helium envelopes to become “naked” terrestrial planets closer to the star, how did the hot Jupiters make it to a distance that is even closer to the host star, without losing the envelope?

I'm going to make a suggestion that is just an idea, and not even a hypothesis. What if the very close-in hot Jupiters are actually planets being born (or recently formed), instead of planets headed to their death? What if planets are formed by a mass ejection from the host star? Such ejections would have to be more massive than those observed in the Sun in our epoch but observations do not rule it out. Jupiter has only 0.1% of the Sun's mass. A blob that has a few times this mass, would, after being ejected, try to hold itself together with its own self-gravity. Depending on its size and density, it would lose the outer layers until it was either disrupted completely, or until it attained a size and mass for which its self-gravity is able to hold on to the outermost layers of its gaseous envelope. This would account for the low density of the hot Jupiters that are close-in to their host stars: these exoplanets appear to be close to tidal disruption (as discussed earlier) not because they are being torn apart, but because they are in the process of forming. At the same time, heavy elements in the blob would be sinking to the center of the planet due to gravity (sedimentation), forming a rocky core. The overall, average density could still be small if the high-density core occupies a relatively small volume. Recall that in one of the most well-known hot Jupiters (HD 209458b) a tail-like structure has been claimed to be observed, trailing from the planet. As the ejected blob moves outward, it could lose all of its hydrogen and helium envelope, to become a terrestrial planet. It would settle at a distance determined by the initial energy of the impulsive ejection (as well as other factors). Very energetic ejections could conceivably send the planet out further, and it is possible that the terrestrial planet would again start to accrete hydrogen and helium as it plunges through ices and other material in the protoplanetary disk, eventually to settle as a gas giant or an ice giant.

A paper published in Nature argued that the close-in hot Jupiters could not be formed there, near the host star, but must have migrated in from a much larger distance. ¹⁷ Two arguments are given in that paper, both of which can be dismissed after the second paragraph in the paper. The first argument is that planets form in the protoplanetary disk and the disk is predicted to be too hot at the location of the hot Jupiters for small solid particles to start sticking together. Well, it is not known that the planets we observe were formed from a disk in the manner that is supposed, and, as explained earlier, we know that the scenario of planets being built up from small particles does not work. So the first argument in the paper can be dismissed, as it is not based on facts or observational evidence. The second argument given in the paper is that evaporation of the planet would have been a problem in the past, although it appears to be small now. However, this argument does not actually provide any reason to dismiss planet formation close to the host star. There is no reason why we could not start off with a larger mass, and end up with a hot Jupiter after mass loss. So neither of the two arguments provides any reason why planets could not be formed from mass ejections from the host star. Nevertheless, there are likely to be plenty of other reasons why the ejection scenario would not work. However, some variation or modification of it might work, and it merits further investigation, considering that all of the current planet-formation scenarios are known not to work all the way (from start to finish).

As I have already mentioned, the close-in hot Jupiters present a problem for the current paradigms of planet formation and migration especially from the point-of-view of misalignment between the orbital plane and the host star's spin, not to mention the occurrence of highly eccentric orbits. ¹⁸ It is interesting that a 2010 study of the spin-orbit problem in hot Jupiters concluded that, “At present, standard disc (sic) migration cannot explain the observations without invoking at least another additional process.”¹⁹ It is also interesting that while some studies of the tidal stability of close-in hot Jupiters conclude that these exoplanets are falling in to the host star to eventually be destroyed, it has also been demonstrated that it is the youngest host stars that entertain the closest-in hot Jupiters. Given that the “falling” is not deduced from a measured direction of the motion, but simply from the fact that the star's gravity overpowers the planet's surface gravity, an alternative view is that young stars are more likely to undergo significant mass ejections, and that the hot Jupiters are freshly created and are on their way out, and are not falling in. ²⁰

A host-star ejection scenario for the creation of hot Jupiters simply does not encounter the spin-orbit misalignment problem or high eccentricity problem. The ejection does not have to occur in the plane of the protoplanetary disk so planets are not constrained to be created in that plane in the first place. On the other hand, we would have to explain why many planets are found to be close to the plane of the disk.

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(Note: superscripts in this article refer to detailed annotated references and notes which are not reproduced here but can be found in the book Exoplanets and Alien Solar Systems, by Dr. Tahir Yaqoob.)

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