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General Epistemology        Chapter VIII-2       

 

VIII-2 Formation of the stars and planets.

 

 

This chapter addresses the first factor of the Drake equation: the formation of planets, which is the very first condition for life. Since we now have experimental confirmations of the existence of exoplanets, there is little doubt left that at least a fair proportions of stars have some. To give an idea, if only one star on 10 had planets, versus all, this would makes our closest neighbour only 2.15 times further, and a possible SETI detection only some years later.

 

But I have another specific reason for a chapter on the detailed formation of stars and planets: I find in science literature a series of theories that I do not agree for.

An ancient science hypothesis was that the formation of planets required a near encounter between two stars, which would make planets very rare. This has been disproved, and today observations show that planets are very common. But many people and even scientists are still reasoning as if planets were very rare. Or, more subtly, they say that, even if life is common on planets, mankind «must» be unique. I am sorry, but the uniqueness of mankind is a Catholic dogma, that even the Bible does not call for. There is no scientific reason for the Earth to be special and intelligence to be unique, even in the hypothesis if they are extremely rare. I suspect that this prejudice is still at the root of the general «preference» given today to special, very rare or unique processes explaining only Earth, versus general processes explaining all the cases.

A more recent hypothesis is that the formation of the Earth-Moon system resulted from a collision between a proto-Earth and a Mars sized planet. Prestigious NASA scientists invoked this to explain the differences of composition and structure between Earth and Moon, and in some years it has magically become «the generally accepted theory», without any further research or checking. Other collision models are proposed, to «explain» all the features of the planets: axis tilt, rotation speed, satellites, etc. I am sorry, but all these features and compositions can be explained in a number of other ways, such as with the model which follows. So, until today, we do not really need such improbable collisions. We even have recent compelling evidences that such major collisions never happened in our solar system, and they even seem to be rare in other systems.

Many also invoke a planet accretion process which would involve the formation of «planetesimals», asteroid-sized bodies, which would gather into planets by collisions. I do not agree either, as we have a counter-example: this is what happened in the asteroid belts, and several collisions here resulted in more disorder, not In accretion. In more, gaseous planetesimals cannot exist, so planets like Jupiter cannot form by this process. The model which follows does not require planetesimals, and it easily accounts for all the variety of sizes, composition and orbits into our solar system and into the others.

Some also invoke planets spiraling around their sun, in order to explain some composition discrepancies with the standard model. I do not believe this too much either: to move Jupiter from its orbit to, say, Mars orbit, would require a huge energy. This can happen only if we add to it large amounts of matter. Problem, matter available to do so already has nearby the same orbit than the proto-Jupiter! So, moving Jupiter in this way would require adding much more matter that it had in the beginning: it would become a dwarf star. Or the contrary, the proto-Jupiter would be smaller than Earth, and unable to retain gasses. In both cases, the resulting body would have the composition of the matter absorbed, and the original body would be completely diluted, contributing only marginally to the overall composition. So the idea of planets spiraling cannot be the explanation of their composition or position.

Another disturbing fact is planetary rotation resonances: Mercury has its daily rotation locked on Earth orbit, and another resonance exists with Venus. This is commonly explained by tidal effect. However the Moon was unable to tidally lock Earth, so how could Earth lock Mercury, while exerting on it a 100000 times weaker gravitational force? The locking necessarily happened otherwise, and this is the subject of this chapter. On the other hand, many orbit resonances visible in the solar system can be explained by current theories.

Please note that this is a classical science debate: there is no General Epistemology involved in this chapter. This is simply different theories based on the same known physics and the same astronomy observation facts. I just don't like that someone writes a sensational paper, and 10 years after this paper has become «the generally recognized theory» without any further checking, or even against contradictory evidences.

But now I need to explain why I disagree, and for this discuss the formation of stars and planets, in details.

Simple model of a spherical non-rotating cloud.

It is well known today that solar systems formed by condensation of interstellar gas and dust clouds. However many details are missing. Let this chapter fill some.

 

So let us suppose first a simple model of an interstellar cloud of uniform density, immobile, cold, and not rotating. I did a small finite elements model of this, only inertial (non-hydrodynamic), assuming a spherical symmetry (One dimension). The result was a bit unexpected: while the core matter remains relatively immobile, we see a wave of compression, starting from the edge, reaching this inner matter and pushing it down to the centre. At this point, of course, the inertial approximation is no longer valid, but the behaviour of hydrodynamic shock waves is well known.

A more realistic simulation with density decreasing regularly from the centre to the border, still shows this behaviour: a compression wave, but now it starts from an intermediate position. The outer shell of leftover matter falls much more slowly, without wave, and it arrives later to the centre, as a small but continuous stream, when this centre is already compressed. We shall see that this late fall will play an important role in the formation of planets.

 

So what about real interstellar clouds, with complicated shapes? Such clouds could form when smaller clouds meet, or a stellar wind compresses diffuse clouds. So diluted clouds can gather under many external influences, from the simple play of non-gravitational forces. Until somewhere gravitational forces become greater than the mechanical dispersion forces, and a gravitational collapse starts. The faster this condition is met, the more mass will be taken in the collapse (this is why shock waves from nearby supernovae play an important role of collapse starters. At least two supernovae events could be dated in the millions years preceding the formation of Earth). But as the simulation shows, some of the most peripheral matter will escape the brutal shock wave process, while being still gravitationally caught in the system. This matter will fall later, and more slowly.

 

It is important to understand here that the compression takes places under many orders of magnitude, from 10,000 billions of kms (the cloud) to 100 thousands of kms (a star). So we can see the same phenomena reproducing at different scales, several times. But each time, we have denser and denser clouds, smaller and smaller, so that each time compression happens in a shorter and shorter time scale. So all the phenomena that we describe here can happen at very different scales, from a huge interstellar cloud to a comet core of some tens of kilometres. And they happen faster and faster when the scale is smaller.

In an interstellar cloud, the sound velocity is very low, compared to the km/s easily sustained by space bodies. So the compression wave will quickly turn to a shock wave. As the starting cloud is likely very asymmetrical, these shock waves will make of it a chaotic object, where parts are collapsing, others are bouncing, etc.

 

At this point, the cloud is still entirely transparent to its own infrared thermal radiation, so that the heat generated by compression with disperse into space, and temperature will not rise much. But an important transition will occur when the cloud becomes dense enough to be opaque to its own thermal radiation. Then, the heat of the compression can no more leave the core of the cloud, and the temperature rises. This creates a pressure which opposes the compression. So, now, compression is limited, and it occurs only in the extent in which the cloud is able to radiate its heat outside. This relatively quiet process will damp and dissipate the shock waves and irregularities: we now have a Bok globule (a proplyd after the most recent vocabulary), which is a spherical object with a relatively smooth shape.

A noteworthy point here is that dust is much more efficient than gas to emit heat and dissipate it. So a dust-bearing cloud will compress faster. A pure gas cloud, such as it existed in the very beginning of the universe, will emit less heat, exert more pressure, and fall more slowly. This may allow it to gather more matter, explaining why the very first stars were (probably) much larger than the subsequent generations of stars.

 

At this point, we can start to see something spherical resembling a star, but larger, with a blurred surface, like a red giant with a hazy surface, and no dense core. And heat is radiated only by this surface. The compression is still taking place, but now it is only at the rate of the thermodynamic cooling of the object. So the late compression is slow and quasistatic, involving only slow movements, slow shift of an equilibrium point, and a slow decrease in diameter. This is very different of the shock-wave collapse of the beginning.

This compression continues until we get a star or a planet.

 

Added in January 2015: A highly unclear point in science popularisation articles is how we pass from a fuzzy cloud without core, to a star with a defined surface and a dense core. But the slow compression points at a reply: the whole cloud is in a thermodynamic equilibrium with its own gravitational field. The equation of its density versus its radius then follows a power law (to simplify). The fuzzy appearance and the clear cut surface appearance are then just two different cases of the same power law. In the fuzzy case, the cloud is little dense, and mostly transparent, so that it is fuzzy, as it also happens in red giant stars. In a more condensed case, like in a star or a giant planet, the fuzzy zone is still here, but very thin compared to the overall diameter, giving an apparent clear cut surface. So a cloud progressively but entirely passes from the fuzzy aspect to the clear cut aspect, simply by varying its size. And there is no moment where we have a star embryo mysteriously forming inside a cloud. Instead it is the whole cloud which changes aspect, progressively polishing its surface, and increasing its density, progressively changing as a whole into a star.

 

This is what would happen if the cloud was not rotating. However real clouds always rotate, so that their appearance is somewhat different:

Rotating cloud model.

The simplified model above, although physically sound, cannot explain things like two dwarf stars orbiting circularly around each other, at less than one million of kilometres: even if two interstellar clouds were already orbiting around each other, they are much too big to orbit at such a close distance. But these interstellar clouds are chaotic objects, with clumps of matter moving in every direction. So, when the compression wave starts, it is very likely asymmetrical. Different sides may not arrive at the centre in the same time, etc. The result is then a chaotic object: at every scale of the compression, we have new faster smaller-scale compression waves starting even before the larger scale slow waves die. And in a squeezed cloud, it may easily happen that the new compression waves break it in two or more objects. This is one of the ways to form multiple stars, which will more often have very elliptic orbits of medium to large size.

 

But there is still another factor: the rotation of the cloud. When a cloud is caught in a compression process, all its chaotic internal movements are doomed to be cancelled, from rubbing on each other. All, save one: the overall rotation, which has nothing to rub on. On the contrary, the rotation speed will increase with the crushing of the cloud. This may strongly influence the behaviour of the compression waves too, through Coriolis forces. Probably these waves more or less end up rotating around the central body, a bit like squalls in a cyclone. This is a bit too complicated for human intuition to visualise how it behaves, we need a computer simulation. But all this happens with only common mechanics, without any need for special or rare conditions.

However, at a moment, the cloud rotates so fast that its equator is at orbital speed. But only the equator! At this stage, if the cloud continues to compress, this equator ringlet will be simply left in orbit, while the central body continues to dwindle. And the proto-star (still dark at this stage) will decrease and decrease, leaving a Saturn-like disk in orbit around it, made of concentric ringlets of matter. When the compression ends, we now have a ring system around a star: the accretion disk. This is how a good share of the excess rotation energy is left out of the central body. It is important to understand here that, in this case, each ringlet is necessarily circular, and each is similar to the previous, but on a smaller scale, from a huge one which was formed first (the Oort cloud) to the smallest ringlet touching the star.

We clearly see here that several features of a planetary system are already in place: circular orbits, in the same plane, in a Titus-Bode-like exponential scale. Let us call this disk the primary accretion disk.

And, contrarily to a common view, this primary disk is not formed from matter falling on the star, but pulled out of the star itself.

The primary accretion disk is a second way to form double or multiple star systems with circular orbits, from medium to small size.

The problem of excess rotation momentum and jets

But with this, all stars should be flat ellipses, with their equator rotating at orbital speed. We need another process to slow down this mad rotation and bring real stars, which rotate much slower. The most common hypothesis (2011) is the formation of polar jets, which kinetic energy would evacuate the rotation momentum of the proto-star.

It is not clear how these jets are formed, and even not where: at the poles of the central sphere, of by a larger part of the accretion disk? We just know that these jets are common, as we see them in all new born stars, quasars, micro-quasars, everywhere where we have active accretion disks. In the case of stars in formation, they are called Herbig Haro objects, and they can extend as far as one light-year.

The most accepted explanation for these jets is a magnetic phenomenon, converting rotation energy into linear energy. I am not aware of any detailed explanation on how it works, but such a phenomenon implies high enough temperature to ionise matter, and a powerful magnetic field occupying a lot of space. Today the sun would be totally unable to brake its own rotation with its remaining magnetic field. It however necessarily did, at a time, as its rotation speed is much smaller than the orbital speed at its equator. Same goes for all know stars and planets.

We have a hint that the process is magnetic: old pulsars, which have lost their magnetic field, are unable to brake when they start accreting matter again, into binary systems. So they rotate at insane speeds, close to the limit imposed by centrifugal force. Many asteroids also do this. On the other hand, it is likely that the accretion disk and newly born stars have a very strong magnetic field, concentrated from the interstellar cloud. «Strong» here does not necessarily mean a large number of Teslas, but rather more extended in space. Also, remember that no matter can remain in orbit at the poles of a black hole, so, contrarily to many images, the jets are likely emanating from somewhere else, from its equator, see from the accretion disk.

 

Let us try to describe how it works. As soon as the accretion disk is hot enough to conduce electricity, a dynamo process starts to create currents into it. Most probably these currents are circular, along the ringlets of the accretion disk, or the equator of the central body. But we can imagine more complex patterns, with for instance eddies rotating along the disk, or ringlets with current rotating the same way, alternating with ringlets where the current circulates in the other way, or even tokamak-like current patterns. Only sure thing, most emerging magnetic lines will be perpendicular to the accretion disk, through the central hole, or through eddies, or between ringlets. So these magnetic lines will escape toward the infinite on each side. Then it is not hard to guess that any plasma ripped off the disk can only escape following these magnetic lines, toward the infinite. And this plasma has a rotating helicoidal movement along the magnetic lines... close from the rotating current of the disk. So, Lorentz forces will push the rotating plasma strongly away, just as two spires of a transformer are pushed apart. This high energy ejection would form the jets.

Another popular description entails Birkeland currents, ropes of plasma which also follow the magnetic lines. Complex electromagnetic phenomena within them can accelerate particles at a very high speed, forming the jets. This process does not necessarily involve very high magnetic fields or temperatures.

But in both cases, the power required for this ejection is taken from the magneto energy of the rotating disk, so that it comes to brake the rotation of this disk. So the disk is slowed, and this makes that its matter spirals in. We can even have the innermost ringlet of matter free falling toward the central body. But the braking is most likely to be more efficient on the central body itself, which is the hottest and the fastest spinning. So this process can well explain how hot accretion disks rotating at orbital speed can produce powerful jets and a central body rotating much slower than orbital speed. Just that, contrarily to common science popularisation images, the jets may pick up matter from all over the disk, not just the poles of the central body.

 

In the case of our solar system, this process would be responsible of the «central hole» inside Mercury orbit. This hole probably marks the limit where the disc became conductive of electricity, and was braked enough to spiral down to the sun. The future Mercury and beyond were not braked.

 

However, we can hardly see hot plasmas involved into the formation of such small icy bodies like Enceladus, see of comets. These small bodies have to brake their excess rotation energy only under a cold accretion process, otherwise their ice would just vaporize and disperse into space. We can suppose weak magnetic fields and atoms ionised by ultra-violet light, or electricity-bearing dust behaving like a plasma (as supposed in Unexplained Lunar Events, chapter VII-5). Another possibility for these bodies to form, is a purely mechanical jets formation process, without requiring ionization (high temperature).

On the other hand, we see many asteroids rotating so fast that they have an elliptic or peanut shape, proof that rotation braking does not work much for them. But these asteroids were accreted from blocks, not from dust. Indirect evidence that the braking process can work as well with dust as with gasses.

The role of the late fall.

However it is classically recognized that an accretion disk forms around a star, in a very different way, from matter falling on it.

We noted that a fair amount of the total collapsing mass is left over by the cloud collapse process, and falls only much later. This makes that we can have a lot of matter arriving after the primary accretion disk is formed. This late falls happens under the form of streams coming from several directions, continuously or by clumps.

Let us reason as if there was no primary disk, and see how this late fall can form an accretion disk from scrap. And why should it be a disk, in first? We can think at two particles orbiting in different planes. If they happen to meet, they will lose relative energy, and their new orbits will be closer from each other. If they collide again and again, they will end cancelling any relative speed, and get on two very similar orbits: circular, same plane, same size. Many particles will do the same thing, and gather into an accretion disk, flat and with a circular rotation, the average of all their movements. So this is how such regular feature as a circular disc can appear from chaotic movements.

So we have clumps of matter falling from every direction, on parabolic trajectories, heading toward our new born star. They will hit the primary accretion disk, or hit each other anyway if there is no accretion disk. But what if they move in opposite directions? They will cancel their speed. And then, being no longer on their orbit, they will quasi-free fall closer to the star. But in doing so, they are likely to hit another clump, and from the dynamic of accretion seen above, they will end up to gather in a more or less circular orbit. Many clumps of matter falling at random on the disk will produce this phenomenon again and again, until the late fall stops. Each time, a substantial portion of the accretion disk will fall down closer from the star, and meet another ringlet. It will either settle on this new orbit, or demolish the ringlet, making it fall still closer from the star, etc. This Dantesque view of successive downward demolitions and reconstruction of the accretion disk will lead to a complete renewal of the matter of the disk, and eventually to a very different geometry. The final result may have several rings with different angles, be eccentric, or show large differences of composition and mass along its radius. Let us call the resulting disk the secondary accretion disk. This is the one we use to see around the quasars.

 

And we have an evidence that this irregular process is actually taking place: quasar jets and star jets often appear wriggling and shooting in different directions. This tells us that their accretion disk is permanently destroyed and reconstructed, eventually in a different plane, by clumps of matter arriving from random directions. The «eruptions» of a quasar would happen when a part of its disk collapses toward the black hole on a free fall trajectory, after being hit by some arriving matter.

 

At a pinch, the idea of a spiralling accretion disk would be false. Accretion disks would nearby not spiral from their own dynamics, but under the destructive fire of arriving clumps of matter. Without new arrivals, an accretion disk would be relatively stable, until it condenses in planets or it dissipates.

 

These processes of chaotic late arrival on the accretion disk explains very well a lot of otherwise incredible features of newly found exoplanets:

-Well circular systems with a Titus-Bode law and regular thermal differentiation appear when the primary accretion disk was little or not disturbed.

-Heavily remodelled disks (secondary accretion disk) give irregular systems.

-That a star may have counter-rotating planets, and even counter-rotating accretion disks.

-That planets may have very elliptic or very inclined orbits: a clump of matter cancelled most of its orbital speed hitting the accretion disk, and took this elliptic orbit. (probably the accretion disk was heavily damaged at this level, and no planet could form here).

-That matter may spiral down into the disk, without invoking an impossible spiralling down of the planets.

-That Jupiter-like planets can form very close to a star, in a place where thermal differentiation should dissipate their gas. Some heavy clump of matter fell here, and swiftly collapsed into a planet, before the light dispersed it. Very likely they can be large enough to become stars, explaining multiple stars with very close and eccentric orbits. This is the third process to form multiple stars.

-That comets have very elliptical orbits, which would be last remnants of the late fall.

Composition of the raw accretion ring

Reminder: The thermal differentiation model explains that the heat of the sun chases out the volatile elements (gases, water) from the closest planets, while farther planets keep their ice, and the farthest some very volatile gasses like methane. This model works well for our solar system, where we have rocky planets near the sun, and gaseous giants with icy moons further away. But it is challenged by the discovery of large gas giants too close to their sun, called «hot Jupiters», which after this model should not exist here. After my model, these planets can form here during the late fall and the chaotic accretion process it produces.

 

The model I am presenting here can better explain the varied compositions of the planets, and especially all the departures from the thermal differentiation model. These varied compositions can easily result from the late fall of clumps of matter with very different compositions, including pure ejections of a close supernova, not already mixed with the average clouds around. This makes that, besides the common types of planets we have in our system (rocky/silicate, gaseous, watery/icy), we can expect very different types: helium planets, carbon planets (like Phoebe around Saturn), iron planets, metal oxide planets, sulphide planets, and even organic matter CHON planets or oxygen planets (that we need not to confuse with life-bearing planets).

 

For instance, Mars, Venus and Mercury are very dry, from the thermal differentiation which evaporated their water. So, after the thermal differentiation model, Earth should be as dry as Mars and Venus, as it formed from the same disk and was submitted to the same evaporation. Comet falls were proposed to explain this difference, but if so Venus should be wet too, as it captured as many comets. (Added in 2014: anyway the Rosetta mission found a different water in comets, so that the Earth's water cannot come from comets.) What likely happened is that the proto-Earth cloud probably received in the last moment a clump of fresh supernova matter, rich in hydrogen or in water. This necessarily happened before this proto-Earth cloud condensed, while it still had enough cross section to intercept the late fall, but not too long before it condensed, so that the sun light had no time to chase out this hydrogen or water.

 

Dynamics of the raw accretion ring

Another thing with the accretion disk is that, when the late arrival stops, it does no more evolve, save of course with the condensation in planets that we describe further. Its overall geometry is now definitively frozen: circular or elliptic orbits, density and composition versus distance from the sun.

A general view in science vulgarisation reviews is that the accretion ring «spirals in». My view here is that precisely, it does not. For matter to come closer to the sun, requires events which allow for the cancellation of its orbital speed, such as encounters of late fall clumps. (Added January 2015: this is confirmed by recent papers and simulations on rings with several parts, tilted or even counter-rotating: the cancellation of orbital speed happens at the points where different matter flows encounter. But a regular disk precisely does not have such points, so that it is much more stable).

 

But an important feature of an accretion disk is that the ringlets which are to form each future planets still have a much stronger interaction than today. The reason of this is that clouds and ringlets are much larger than a condensed planet, so that they can encounter, while planets don't. It is said that they have a much larger cross-section. This makes that we can have some weird things, such as a small but dense proto-Pluto stream of matter passing through a larger but thinner proto-Neptune stream, exchanging some inertia and rotation momentum. As a result, this warped part of Neptune’s accretion disk, giving it its unique retrograde moon. (January 2015: The common theory is that Triton was captured. However this capture, precisely, is much more easy to explain if Triton results of an exchange of matter between two clouds. The following also fits much better:) We also have a similar composition between Pluto and Triton, and the Pluto-Neptune resonance. Only later these bodies condensed, and their much smaller sizes forbid any such interactions since then.

 

So, all these kind of features can be expected, without sensational encounters of the planets themselves. A catastrophic encounter between two solid planets would never give any resonance anyway.

From the accretion disk to one ringlet per future planet

Now we need to know how planets can form from the calm accretion disk. I assume that this formation is automatic, save if parts of the disk are under the Roche limit, as it happened with Saturn. Under the Roche limit, the accretion disk is indefinitely stable and it becomes very thin (cold, or minimal energy state, in thermodynamics terms). But, contrarily to a common view, it does not either spiral in, save from some marginal processes. (dispersion may cause the rings to spread, and indeed the innermost rings seem to be falling on Saturn. But there does not seem to be any global spiralling)

 

I see three very different processes for collapsing a disk into planets.

The first process is astrodynamic: the orbital interactions lead to the depletion of some orbits. An accretion disk will often have clumps and other irregularities, which mass may be larger than a big planet. And their gravitation pushes other matter off some resonance orbits, and force it in others. This reinforces the original clump. Once we have a large enough clump, it may initiate the partition of the disk into ringlets, and this partition process will quickly propagate into the whole disk. Ideally, an unique clump into a perfectly regular disk will break it into evenly spaced ringlets, which size grows exponentially from the centre to the outer reaches, in a perfect Titus Bode law. But of course, irregularities in discs lead to many departures from the Titus Bode law, explaining it is not rigorous, and even often false.

 

The second process would be convective. The ring is an hydrodynamic object, submitted to gravitational and orbital forces, but also to gas thermodynamics. So we can think of it as having a surface (equipotential), which would look «horizontal» for a local observer, with space «above» and matter «under». But instead of a sphere, it is a doughnut shaped object, which section would look like a triangular wedge (thin near the star, larger far away). And it is in an hydrostatic equilibrium, just as a star is. Just that, contrarily to a planet, where the horizontal surfaces show places which all have similar densities, we have here very different densities depending on the distance of the sun.

However the section near the centre is hot, while the outermost parts are cold. So we shall have convection currents evacuating this heat along the surface of the doughnut.

In an immobile disk, these convection currents would flow away from the central hole, in a radial pattern, along one or both of the outer surfaces, while cooler matter would flow back toward the centre. But in a rotating disk, these currents will be submitted to the Coriolis force. So they instead organise in a series of toroidal flows, each toroidal vortex being of an increasing diameter and lowering density. These vortexes will create a zonal circulation, like bands on Jupiter, but instead of bands around a planet, they will make ringlets of increasing diameter in the accretion disk. This will make some zones rotate a bit faster than their orbital speed, while others will rotate move slower, like wind zones going east on west on a planet. This makes orbital mechanics enter on stage here: if ringlets change their orbital speed, they will increase or decrease the diameter of their orbit... So some zones will be depleted, and others filled and compressed... This is how we get well separate ringlets, each for one future planet! Here again, the zoning can explain the Titus-Bode law, and also its departures, since it is a far from perfect process. It also explains that these ringlets lead to planets with well individualised orbits, not easily allowing for collisions later.

I claim precedence for this convective model in January 2015.

 

 

The third process is the magnetohydrodynamic process seen above about the formation of the jets. If it is powerful enough to brake the whole disk and make it fall on the star, it can have lesser effects such as gathering and separating ringlets, or eddies. If eddies rotate around the disk, they are obvious seeds for planets, and in more they have their own jets to brake their own rotation.

 

It is hard to guess without simulations which of the three processes actually works. It may depend on conditions, or we may get a mixture of both. Also, the exact pattern of convection current is hard to predict from just intuition, without a complex multi-scale numerical simulation. It may also lead to non-cylindrical solutions, in which the disk would show eddies rotating around the star. These three completely different process may however give the same final result: planets in fairly circular orbits, more or less obeying the Titus-Bode law.

 

The interesting fact with the convective mechanism breaking the disk into ringlets, is that it involves the whole accretion disk as a single hydrodynamic object, where all the parts are linked and strongly interact with each other. This can easily cause the resonances found into planetary orbits, like Mercury and Earth. These resonances can be established only at this moment, when the proto-planets are still interacting into an unique hydrodynamic object. Today they would require thousands billions years to establish. The basic cause of these orbit resonances into an unique hydrodynamic object is not unlike the regular Benard cells in a pan of water. Each cell interacts with all the others.

 

At last, these processes create clearly individualized regions in the accretion disk, that I now call ringlets, with stable and clearly separated movements, if not in clearly separated zones of space. Since it spends some time in this situation, the unstable solutions are eliminated, by «collision» (mixing) of streams, without catastrophic explosions. So it is clear now that each of these ringlets will condensate in a planet, and that the movements of these planets are already organized in a stable system where collisions are not likely to happen, and even not orbit shifts. These orbits already have all the odd characteristics which cannot appear later, such as the resonances, the composition discrepancies, tilted orbits, retrograde moons, hot Jupiters, etc. even if they do not yet appear as individualized objects.

 

To be noted that, in the astrodynamic process seen above, the condensation of a ringlet into a planet may start the fragmentation of the whole accretion disk into ringlet. We then have a single process producing both results simultaneously.

 

The Titus Bode Law?

(Added February 2016)

The Titus Bode Law says that planets or moons orbiting a central body do it after a regular series of orbit sizes. Today astronomer do not give a great value to this law, since there are many irregularities and even frank departures. Moreover, the ratio of the series is different for each known system (accounting with this is called the Dermott's law, and I should therefore use this name throughout this chapter. But it is little known, so that I keep to the well known term)

The three processes described above for the separation of an accretion disk into ringlets, the astrodynamical process, the hydrodynamical process, the magnetohydrodynamical process, or any mixture of the three, provide a satisfying explanation to the Titus Bode law. I would even add that the ratio of the series would be a function of the density of the disk: the denser the disk, the higher the ratio. This is well visible with the main satellites of Jupiter, probably the denser moon system in our solar system, which shows the highest ratio. On the other extreme, the asteroids in the Asteroid Belt and the Kuyper belt, and the external moons of Pluto, both have a very low mass, with a low ratio. This relationship between density and ratio is a strong evidence for the hydrodynamical process.

A proof of the astrodynamical process appeared recently: the many small objects beyond Neptune are not dispersed at random, but clearly show groupings, which are a continuation of the Titus Bode series of the whole solar system, beyond Neptune. Astronomers say that these groups (or families) are the result of resonances with Neptune. This is well consistent with the idea of a first body to form (probably Jupiter) inducing the cutting of the continuous accretion disk into ringlets, by resonance, until well beyond the orbit of Neptune. But the bodies beyond Neptune have a very low mass, and, in the hydrodynamical process, could not influence Neptune in return, and neither gathered in only one body per ring. This proves that the disc cutting beyond Neptune was more astrodynamical.

At last, Pluto and its family are a frank exception to the Titus Bode Law. The explanation is very likely that the accretion disk here was damaged by a current of matter from the late fall, which impacted the main disk, disturbing Neptune's moon system and forming a separate inclined ringlet of its own. This ringlet later condensed in the Pluto family. A similar situation probably happened with the hot Jupiters and other eccentric exoplanets. In regard to this, our own system looks quite regular. But even so, the small departures from the Titus Bode law are well explained by small irregularities in the accretion disk.

Changing symmetry, from a ringlet to a spherical cloud

 

Now that we have individualized ringlets, or at least individualized streams in the accretion disk, we need to condense them into planets. This secondary compression will change the ringlet from a «O» to a «C», then to a «(», then a «,», and at last to a «.». It is clear that there must be some strong mechanism involving the whole ringlet, and fast changing it into a spherical cloud, before the planet itself condenses. This can be a quasistatic hydrodynamic process, involving the whole ringlet as an unique object linked by gravitation. A strong evidence of this is that we never find two planets on a single orbit, each one in the Lagrange point of the other: this configuration is however stable, and it would happen often if we had only local or independent processes into different parts of the ringlet. But we never find such couples of planets or stars on a single orbit.

From the remark above, I even wondered if it is possible to have a stable string of planets all around a star, each on the Lagrange point of the others. Is such a solution stable? How many planets could cohabit in this way? Six? Or can we have only two planets at 60° on the same orbit? The question is fascinating, even if such a structure cannot happen naturally. But it could be created in artificially modified solar systems, allowing for much more living space for its inhabitants. See chapter VIII-10 on bioforming planets.

I actually tried two times to do a numerical simulation of multiple bodies on the same circular orbit. Unfortunately, this is much more difficult than it looks, due to the accumulation of numerical errors and other simulation issues which cannot be solved with current PC software. Others tackled the problem, using numerical or analytic methods, and found «choreographies» which are stable solutions for the n-bodies problem. We can see some amazing regular orbits videos. Unfortunately, they are very unpractical, since the distance to the sun varies widely. I did not found any mentioned with n bodies on the same circular orbit.

 

The process of changing from a toroidal ringlet to a spherical object can be explained in this way: while the whole ringlet is in weightlessness relative to the central star, each part of it still attracts the others. In a perfect ringlet, the attraction of the different points cancel each other, and the ring is stable. But the least irregularity starts a flow toward it, along the orbit. Thus irregularities reinforce themselves. This process is much similar to the formation of dew drops along a spider wire: instead of forming a constant thickness sheath of water around the wire, surface tension forces water into drops. However surface tension has a short range, and has to work against other forces, resulting in a stable string of dew drops along the wire. On the contrary, gravitation has a potentially infinite reach: instead of forming droplets around the ringlet, the clumps will quickly gather into only one. So that we never have several planets on the same orbit, where they will collide later: these collisions take place well before the planets form, and they involve the quiet coalescence of diffuse clouds, instead of a catastrophic collision of hard bodies ejecting debris everywhere.

By the way, in the case of an artificial Dyson ring orbiting a star, this process is a serious risk of having it all collapse back in a planet. Thus such a ring must be carefully balanced and actively maintained. If abandoned, it would probably collapse in a relatively short time.

 

From cloud to planet

The final compression of a planet plays again all the steps of the formation of a star: accretion disk, with all the oddities leading to irregular moon systems, compositions differences, tilted rotation axis, retrograde orbits, double planets (Earth-Moon), etc. And the formation of the planets too requires jets, to stop the mad rotation. If not, all the planets would have a flying saucer shape, and space travel would be possible by foot, from the equator!

 

Resonances in the Asteroid belt and in the Kuyper Belt can appear from the astrodynamic process, either at the disk stage, or much later (we have an evidence of this: most of the asteroids in the today belt formed recently, from collision between parent bodies. But they already show resonances with Jupiter, that is empty or crowded orbits).

In these belts, the total available mass was much lower than with the other planets (about 1/1000th of Mars in the Asteroids Belts), so that this ringlet was unable to condense in a single body (from lack of gravitational force). So it formed an irregular string of a dozen of small bodies, like with the dew drops seen above. These parent bodies collided since to give the numerous asteroids we have today. A similar process worked in the Kuyper Belt, but objects here are so far away of each other that seemingly none collided.

Still further, in the Oort cloud, the density is so low and the time scale so huge that the accretion was never able to give any large body, forming numerous comets instead. Here the relative speeds are so slow, that when an ice dust hits another, or a comet, it melts, and stick to the comet, rather than exploding. More, the slowness of the process makes that a rotating comet nucleus will gather new dust from random directions, statistically cancelling their rotational impulse. So this accretion will not produce accelerated rotation as in a star accretion. This is checkable: the inner limit of formation of comets would be where impacting grains vaporise, and the outer limit would be when they just bounce apart without sticking together. This can be predicted precisely.

 

That our solar system is relatively regular implies that in our case the late fall little disturbed the primary accretion disk. However such disturbances seem to have happened in the outer parts of it, where we find comets with very elliptic orbits and very inclined dwarf planets. Probably our late fall was weak, unable to break the central part of the disk, having only influenced the diffuse outer parts. However it was probably the main player in all the systems where we find very elliptic planets, or hot Jupiters which should not be here.

The nearby free fall orbits of the comets intrigued me since maybe the 1970 years. It was an evidence that several very different processes were working in the formation of a solar system. But it is the discovery of hot Jupiters which really put me on the track and finally allowed me to assemble the puzzle presented here.

Final touches

This relatively complex model, especially with the late fall, explains very well all the solar systems we know, with circular orbits or elliptic orbits, with a regular Titus Bode law or without, with flat or inclined orbit, resonances, double bodies, composition differences, departures from the thermal differentiation, and probably a lot of other oddities waiting to be discovered. It does this without supposing any rare event like collisions.

 

After, when the solar system is cleared of all the remaining dust and gas, the planets may slowly modify their orbits, from astrodynamical reasons. This may at times lead to close encounters and abrupt changes in orbits. However, none of these is required to explain the features of our Solar System. Collisions too are not required to explain the evolution of the moon systems around the giant planets. The ring dynamics I propose was able to clear up any condition for such collisions, producing a clean solar system free of all the meteorites we have today.

 

Final point, we had, in our own solar system, a late heavy meteorites bombardment by unusually large bodies, from 4.2 to 3.8 billions years ago, which created many extra large craters on all planets and moons, including the ones we see with the naked eye on the Moon. It is hard to guess what produced this, and several reasons are possible:

-A collision between asteroids. This happened several times in the asteroid belt. If the two culprits had very different orbits, the debris cancel part of their speed, and spread many large bodies into very elliptic orbits, able of reaching the Moon and Mercury as well.

-A brutal flip of some planet’s or moon’s trajectory, expelling many large bodies of their orbit.

-A special population of extra large comets formed when the latest solidification of bodies took place in the Kuyper Belt or Oort Cloud.

-A close encounter of our solar system with another system, or with a planetary nebulae, or with a supernova remnant, or with a dense interstellar cloud, bringing extra large exocomets.

-A galaxy merger event, disturbing a lot of things or bringing our solar system into unusual regions of space.

-It is discussed if this was not simply a statistical effect: if meteorites were more numerous, large ones were too more numerous in the same proportion.

-Probably several small bodies were left over by the formation of the main planets, in low density zones between the main ringlets. Not being on stable orbits, they collided each other, or they formed the late heavy bombardment. In this category of explanations, it was supposed that Earth had a second smaller moon, which broke apart from tidal effects an the pieces fell on the Moon.

No planetesimals.

(Added in January 2015)

Another common re-hash in science vulgarisation reviews is that the dust would have gathered in small bodies called planetesimals, which would then gather in small planets, and then in large planets, by successive collisions and aggregation. For the media, they like the k-bomm-boom aspect, as usual. For scientists, they probably wrote this in a time where it was not yet understood that a cloud of dust behaves just like a cloud of gas (with the same thermodynamic and hydrodynamic laws). We have numerous examples on Earth, such as volcanic pyroclastic clouds, or mud currents in some valleys of the ocean.

Reasoning about grains of dusts in terms of independent orbiting objects was conceptually inducing this idea of hierarchical collisions. However we know that collisions lead to fragmentation, as observed in our Asteroids Belt. For these fragmented objects, to end into gathering would entail several cycles of coalescence and destruction, until they have exhausted all their relative energy. Indeed, asteroids are often mere piles of rubble. However after 4.5 billions years they are still not accreted in a single body.

Reasoning about grains of dust in terms of gas thermodynamics leads to a very different conclusion: these grains are already coordinated by streams of similar energy, well before these streams appear as separated objects in distinct regions of space. And when they do, they can gather as a whole, by a quasistatic compression of a cloud of dust, without entailing collisions of large blocs. A «collidable» solid state appears only at the very end of the process. This process is even observable on Earth, when pyroclastic clouds settle on the ground, passing nearby continuously from a «gas» state to a «solid» state. One of the moons of Saturn, Methone, exhibits this astonishing «liquid» intermediate state between dust cloud and solid, where hydrostatic activity gives it a perfectly smooth oval shape, like an egg, without craters.

 

If collisions between large bodies were needed, we would need dozens of them to explain all the moon and planets composition discrepancies in our solar system. But then, to produce regular circular orbits for all these moons requires so many ad-hoc parameters for the impactors, that we can more safely invoke the direct action of angels using billiard cues. This is why I keep the planetesimal model as false, even against the majority of astronomers and astrophysicists.

Final accretion of the Earth-Moon system

I explain the final accretion of planets on this example, since it is the most well known, and it shows an interesting feature: a double planet. The discovery of Charon around Pluto showed that such bodies are not rare, and even that they should appear regularly when specific conditions are gathered.

(Added February 2016) It appeared since that the astronomers restrict the use of the term «double planet» to the case where the centre of mass is between the two bodies (no known example). However I shall keep using the definition of the double stars, to outline the similarity between the formation processes.

 

So let us see this final process in details. Indeed several important transitions happen, into the process leading from a ringlet to a solid planet.

 

The first transition is the quasistatic hydrodynamic compression of a C shaped ringlet into a spherical cloud. It may happen relatively quickly. But this necessarily leads to an object which is tidally locked with the central star or planet. The reason is, in such a non-spherical object, any rotation relative to its mass centre necessarily leads to strong friction, so it is quickly dampened, automatically leading to a tidally locked object. Let us call this rotation cancellation process the tidal cloud braking. And, since it acts on fluid bodies still much larger than planets, it can be much stronger, and give a quick tidal lock on any future planet. So that the result of the tidal cloud braking is an object rotating on itself in one year, in about the same direction and plane than its orbit.

However, at a moment, when compression continues and the cloud becomes spherical, the tidal cloud braking stops operating, and the residual rotation will increase again, due to further compression, up to the today daily rotation rate of the condensed planet. Here is the explanation of these common properties of planets: rotation axis parallel to the star axis, into the same direction, but faster that the yearly rotation. Today, most astronomers suppose that tidal braking can operate on the solid planets themselves; however it is far less efficient than the cloud braking, so that most ratios and locks in our solar system appeared well before the planets went solid, still in the cloud stage.

 

 

The second transition is physico-chemical processes starting to happen into the cloud when it becomes hot enough.

In rocky planets close from their star, like Earth, very likely most of the gas (mainly hydrogen and helium) is chased out of the cloud while it is still transparent. This is the classical thermal differentiation process. We see how this happens in comet tails, where gas and dust are separated in a matter of hours, often creating a double tail for comets. The only remaining gasses and water are those which are adsorbed into the grains of dust.

Exceptions may happen when the late fall provokes an important disturbance in the accretion ring, and brings huge masses of dust and gas close to the star. In this case gasses have not enough time to be ejected, and we get a «hot Jupiter». Smaller clumps, but formed from fresh supernova matter, may not disturb the accretion disk, but they may bring a composition discrepancy or isotopic discrepancy where they hit.

 

But now let us see what may happen in a spherical dust of cloud, in a quasistatic thermodynamic equilibrium with its own gravitational field.

Simulations have shown that, in a fully gaseous spherical planet, convection occurs under the form of thin vortexes, which axis is parallel to the rotation axis of the planet, going all through the planet like huge needle in a pin cushion. These tornadoes however are hampered by the solid core, so that they gather in a squirrel cage structure, tangent to the core. In this way they emerge on the surface at a given latitude, forming the storm alleys on Jupiter and Saturn. So these storms are not meteorological storms, but the equivalent of volcanoes in a gaseous planet, which evacuate its internal heat.

In a body without solid core, such a system will more likely form a single tornado on the rotation axis, and emerging at both poles, one absorbing matter like a whirlpool, and the other belching hot matter from the depth. And we notice easily that all the matter of the body will pass many times through this tornado! And in doing so, heavier or denser particles are more likely to be ejected out of the tornado, like in a cyclone separator. So this is may be a very effective process for separating iron grains and gather them into a core, so that differentiation may be started, and even mostly complete, well before the planet starts to become liquid or solid! So, when the Earth-Moon system separated, this iron was logically not available to form the Moon. This is just one among the many simple and common processes explaining that we do not need rare events like a collision of planets to explain the differences in composition even between the two members of a double planet like the Earth-Moon system. I even see this discrepancy as an evidence that some degree of differentiation already happened well before the Earth was solid.

We find the same scheme in the Pluto-Charon couple. Charon is less dense, since it received less rocky materials from the common source. In more, the presence of no less than four other moons, on well circular and well coplanar orbits, clearly shows that the system formed from a single nebula, not from a capture or a collision.

 

When the cloud becomes hot enough for the particles to melt, phenomena of coalescence of molten droplets will appear, changing the properties of the dust «gas». It is not clear how this happens, and how the properties of the pseudo-gas will be changed. We have little studies on this, as experiments can be performed only in weightlessness. However, a general rule in gas thermodynamics states that reducing the number of particles makes a gas oppose less resistance to compression, so that it can be collapsed with little energy. So, when the centre of the cloud reaches melting temperature, and droplets coalesce, the cloud will engage into a runaway collapse process, since collapse melts still more dust.

Most probably, this process starts in the warmer nucleus, creating a liquid nucleus, and it propagates outward. Depending on the size of the body, it will result in an entirely molten planet, or with some residual layer of dust on its surface. If the body is too small, though, there will be no runaway stage, since no particles can melt. This probably happened in the comets, and in the smallest asteroids where the chondrules which formed them are still visible.

A peculiar case would be a carbon planet large enough for melting: since carbon can be liquid only at a high pressure, the planet must surround itself in an atmosphere of gaseous carbon. But the later, while cooling, would fall again at once, under the form of soot. So such a planet would have an hyper-violent convection, quickly lowering the temperature until a thick enough solid surface can contain the pressure of the liquid.

 

 

 

Also, we may too have more subtle chemical processes, much like in a volcano lava chamber. For instance even a very low pressure of free oxygen gas in the cloud, (or steam), in thermochemical equilibrium with the grains, may bring the whole system to a chemical equilibrium, oxidising the most reactive metals until there is not enough oxygen left to oxidise all the available iron. These oxides will further combine with silica to form silicates, and form the mantle of the planet, while the remaining metallic iron will sink into the core. So, it is not the quantity or iron which dictates the size of the iron core, but the quantity of available oxygen! This process may be still operating today at the contact between the mantle and the core of Earth, especially in the ultra low seismic waves velocity zones, where oxidizing of the core iron seems to be still taking place at a much lower rate, slowly enriching the mantle in iron.

 

 

A third transition would happen, in the collapsing proto-Earth, at the moment where Earth and Moon separated. Let us see what may have happened, when the cloud reached the diameter of the Moon orbit (which was likely much smaller in this time, let us say 100,000kms diameter). We have an opaque and cold object which much resembles Jupiter, but 1000 times less dense, and without a solid core. At this moment this cloud may still be dark, and surprisingly look like a Bok globule, but with a more solid-looking surface. This surface probably exhibited bands like Jupiter, and cyclone alleys like Jupiter or Saturn, formed by the convection of inner layers. Although we most likely have a single cyclone piercing this whole object from pole to pole, as we do not yet have a solid core to hamper the inner convection. Red glow will however appear soon, into the upwelling cyclones.

However, at a stage or rapid compression, the proto-Earth will rotate so fast that it gets the shape of a flattened ellipse, until the equator reaches orbital speed. But this equatorial belt, being in weightlessness relative to the bulk of the object, becomes unstable: each part of it is still attracting the others. So any minimum disturbance will be amplified: the equatorial belt will soon become a bulge at a given longitude. So we have now a peanut shaped object. Of course, this peanut object will continue to contract around the two centres, but without these two centres get closer anymore. So they form two distinct objects, the Earth and the Moon, leaving the later on a very circular orbit. This is how the Moon took birth, natively tidally locked. And, as the proto-Earth cloud was already somewhat differentiated, the proto-Moon received in its share only the external less dense matter.

The final jets braking

Many planets have moons, evidence that they once rotated much faster than today. If so, their equator should be still at orbital speed. However their today rotation speeds are always ten to hundred times slower. This is a clear evidence that a final process efficiently cancelled most of the remaining rotational speed.

In a general way, nearby all the bodies in the solar system rotate slowly, telling that some very common process cancelled the rotation momentum of the cloud which formed them. The only exceptions are the asteroids which were formed recently from coalescence of collision debris, and which often rotate fast, showing elongated shapes and even peanut shapes. The same process could not take place with them.

This was already discussed this in the formation of stars, and probably this process is magnetic, producing polar jets and braking.

This requires however that the magnetic field was much larger than it is today. This is likely, since the condensing dust cloud will concentrate the ambient magnetic field while collapsing. (this could not happen in those recent asteroids)

But this also requires that the dust cloud conduces electricity. This seems less likely, but we can invoke a hot gas background, or the strange idea of a cold dust plasma: grains of dust bearing electric charges. We can see such dust plasmas in volcano plumes (where they form lightning) and maybe in the TLE (Transient Lunar Phenomena, see chapter VII-5).

Added in January 2015: measures in the disk of HL Tauri showed that its particles are magnetized. In such conditions, we do not need a powerful field to make them react in a way to produce jets.

Or quite simply this magnetic field would arise when a liquid iron core starts to form. Since it rotates very fast, it would yield a powerful field.

But the idea of a cold dust plasma is very appealing, when we come to the final braking of very small ice bodies like Enceladus or the comets. Such bodies would not survive any hot gas plasma, while they still undergone some form of braking.

 

Curiously, some of our today magnetosphere processes are still surprisingly resembling the jets-bearing processes involved into the latest stages of the accretion of a planet, when they produce the jets. Of course, in this time, the rotation was much faster, and the magnetic field much greater, resulting in strong jets and efficient braking, as described above. But today these processes are totally insignificant.

However, this tells that our today magnetosphere should still produce polar ejections! This would be nice, we would have a pico-quasar at hand to study and understand how the big ones work. Incredible? Well, the previous sentence is a prediction I made independently in 2012, thinking that nothing even loosely related was ever found, and that scientists would dismiss this as weird. However, just some days later, while searching about documentation on this part, I found that such Earth polar jets were actually observed by the Themis satellites. In facts, what Themis found is a bit more complicated, as the Earth magnetosphere plasmas are mostly powered by the solar wind, rather than the Earth rotation. However Birkeland currents were found (a complicated phenomenon where a plasma «rope» and a current move all together along a magnetic flux line: the helicoid movements of the plasma particles reinforce the magnetic flux, and the later tends to constrict this rope, thus reinforcing itself and keeping the rope shape). Such Birkeland currents form the auroras when they fall down to Earth. But others fly outwards. Themis even found current ropes linking each pole of the Earth to the sun! So we really have polar ejections. In more, Birkeland currents can produce intense electrical fields, accelerating particles to very high energies, to the point that they are invoked in the ultra-violent processes which produce quasar jets and very high energy cosmic particles. All this makes Earth magnetosphere somewhat resembling a quasar, with jets and fast particles, although with an external energy source instead of its own rotation.

For these phenomena being efficiently able to brake the ultra fast rotation of the new born Earth however required a magnetic field of many orders of magnitude larger than today. And, to be able to absorb the huge energy of the proto-Earth rotation in a short enough time, the braking would be so violent that the forces applied to the proto-Earth would have produced terrifying processes, such as supersonic winds, hundred kilometres lava waves, super heating, etc. We may even have an exponential process: Earth heating increases braking, which in turn increases heating... The braking force was more likely applied to the equator, flattening the equatorial bulge, explaining why planets (and stars) at this stage no longer form moons with any of the processes described above. At an extreme, Earth probably had a spindle shape just before becoming solid. The tips of the spindle can easily provide a lot of matter for the formation of the jets.

Synthesis

We cannot know without calculus and simulations in which order the three transitions described above will happen. Just the third will logically happen after the first. But what is interesting to see is that many phenomena can happen, explaining the geometry of the Earth-Moon system, including differences in composition, even from an unique and homogenous source of matter.

However, for increasing planet sizes, the peanut process will happen sooner and sooner, relative to the end of the collapse. So this predicts that rocky planets larger than Earth have more and more chances to be double planets like Earth and Moon. Larger planets like Jupiter and Saturn will have moons from a primary or secondary accretion disk, while Uranus and Neptune are possibly intermediate cases, where both accretion disk and peanut process may have worked. On the contrary, smaller planets like Mercury, Mars, and even Venus, were unable to get moons, probably because the final jets braking happened before, or their rotation was too slow, so that the peanut division process never happened.

However, small bodies like Pluto, and many Kuiper objects, have moons. Things may happen a bit differently here, due to the fact that they are mostly formed of ice, which is much easier to melt. So melting of ice dust will thermodynamically release the pressure opposing the condensation of the proto-planetary cloud, much sooner than the melting of rock. So this cloud may collapse faster, making the peanut division process more likely. So there may be a link between the peanut division process and the melting of solid dust, probably because compression is much faster at this time, and the rotation braking process cannot absorb the sudden excess of rotation due to fast compression.

The high ice content of Uranus and Neptune may also have favoured the peanut division process here, as for Pluto. However, in this case, it stopped playing when all the ice was molten, explaining why Uranus and Neptune have their major moons in far orbits, and only small ones nearby. Their low eccentricity however shows that these small close moons are true moons, and not captured asteroids.

 

A remark here is that, it is often said that the Moon favoured life on Earth, with stabilizing the rotation axis, and thus the climate. This argument is considered to make life rarer. However, it is cancelled by the fact that Earth sized planets are more likely to have one moon by the peanut division process. So our «Earth-only» view of the Moon eclipsing exactly the Sun may not be so rare, after all.

 

We note that this peanut division process of a quasistatic cloud is different of the fragmentation process of a turbulent cloud described above for the stars. It is also slightly different of the formation of a primary accretion disk (forming a large central body with tiny planets or moons on circular orbits) and very different of the late fall accretion disk (forming hot Jupiters and elliptic orbits). It is not sure which process happens in which case, but this peanut separation process may also be a fourth way to have multiple star systems, giving close stars with circular orbits, close enough to exchange matter later. A good indication of this is the statistically preferred ratio of mass between very close stars, indicating that they may form in a peanut division process, at a stage where they compress fast.

 

The difference before the primary accretion disk and the peanut division process is dynamic: the peanut process happens when a Roche lobe is formed, while when there is not enough matter it cannot form a Roche lobe and it remains under the form of a primary accretion disk. So the peanut process directly gives spherical bodies, while the primary disk will do this only later. But maybe in practice there are some intermediate cases.

The chondrules

Chondrules are tiny grains of sand which are the basic compositions of the most primitive asteroids in our solar system. Their datation show that they formed mostly before the solar system, of which they were the most basic components.

I take this composition of the asteroids as an evidence that these asteroids did not formed through collisions of planetesimals, but by a quieter process of dust compression or coalescence. If there was collisions, we would observe impact breccia, random assemblies of blocks, melts and fractures. But the only melting we observe is in the asteroids which were large enough to form lava, and even to differentiate, from the heat generated by aluminium 26. (I am not speaking here of the collisions which happened much more recently in the Asteroid Belt. I am speaking of the planetesimal encounters which are supposed to happen in the beginning of our solar system).

 

Chondrules come in a large variety of compositions. But they can be classified in three categories:

-calcium-aluminium, which can be as large as 1cm, and undergone a temperature of 1300°C. Their age is 4567.30 million years.

-silicates, often enriched in oxides, sulfides and phosphates, which undergone one or several short heating event at 1000°C, followed by a fast cooling, both in some minutes. Their age ranges from 4567.30 to 4564.70 million years.

-carbonaceous, rich in carbon, organic matter and often iron, which experienced temperatures of 200°C.

In asteroids they use to be embedded in a matrix of much finer dust (1 micron) which is believed to be raw supernova material.

For information, Earth formed 4,540 millions years ago, with an uncertainty of ±40 millions years. So that the chondrules are likely older than Earth.

 

There is today no clear explanation on how and where the chondrules formed, although it is generally assumed that they formed in the accretion disk of our solar system, before the planets formed, from raw mixed interstellar dust. The first category may even point at a specific supernova event. The most puzzling is the short duration of heating events, which rather points at explosions, as it would happen with planetesimal collisions. But again we find no other traces of these explosions.

 

In the above model of toroidal convection patterns in the accretion disc, material would be brought near the sun, and moved back. However the closest loop (the one of Mercury) would still take days to go through it, not minutes. This makes that the chondrules-forming events may be probably shock waves from the late fall, solar flares, etc. An original hypothesis would be storm-like surges in the toroidal flow, suddenly bringing cold material out of the shadow of the disk, into the bright heat of the sun, and back. I would even consider the possibility of lightning in the dust cloud, a common phenomenon in Earth's volcanoes. And a relatively simple experiment to do, with an electric arc in a low pressure chamber.

Observational evidences

(added in January 2015, from data available since the original writing of this chapter)

 

The Stardust probe found material of the original accretion disk mixed in its whole volume, from close to the sun to the farthest reaches. Actually Stardust found both olivine, which can be formed only at 1027°C, and very volatile organic materials which can exist only beyond the orbit of Jupiter. This strong mixing in the whole accretion disk can be an evidence of the toroidal convection model. (although other solutions were proposed, such as weak polar jets falling back on the disk).

 

We now have observational evidences that collisions between large planets never happened in our system. It was recently found a very clear signature of such a large planets collision in HD 172555, a 12 millions years old solar system in formation. This system exhibits a Moon worth mass of obsidian dust, flash-frozen magma (tektites) and vaporized rock (silicon monoxide gas), formed in the fantastic heat of the explosion. So indeed it is statistically expectable, but rare. Only one was found, pointing at a good efficiency of the processes I describe above, to form clearly individualized orbits which do not collide after.

The point here is that we find no silicon monoxide in our system, thus disproving that Earth and Moon formed from such a collision, and none of the other supposed collision event (Venus, Neptune, Mars, etc). Especially, the impact velocity required to form silica fumes (silicon monoxide) is something like 10km/s, while an Earth-sized body and a Mars-sized body cannot encounter at less than 16km/s. So we are sure that no such collision ever happened, and the Earth-Moon system must be explained by the accretion process alone.

Note: the temperature reached in an hypersonic collision does not much depends on the size or composition of the bodies, but mostly of the speed.

Note: It is well established that we had several more recent collisions in the asteroids belt. However these collisions resulted in the fragmentation of the parent bodies, and never in accretion or large regular systems.

The most fantastic evidence however came from this History-making image of HL Tauri, taken by the Atacama millimetre telescope and published in 2014.

This is the first accretion disk photographed in details, and it much surprised the astronomers. The reason is that they think that the dark lanes are formed by planets, and the luminous rings are only leftovers. That planets are already formed in a one million years old only system, is quite astonishing and goes against current models.

But I am not at all surprised by this image, which shows exactly what I expected. After the model of the toroidal convection in the accretion disk, the planets are not yet formed. But each toroidal convection ringlet is already well individualised and separated, ready to evolve each one into a planet. This disk even much resembles our own solar system: the outer parts will give many Kuyper-like dwarf planets. The large dark gaps will give asteroid belts, and the denser part in the middle will give rocky planets.

Still about this image, the millimetre emission allowed to find a complex magnetic field, partly polar, partly following the ringlets. My explanation is that charged particles of dust or ice produce the magnetic field while moving. This magnetic field is then available for the final braking. The article explains that most grains of dust tend to move along magnetic lines. This magnetic field was predicted above in this chapter, as a mean to explain the final braking of cold accreting objects, by the same magnetic phenomena than the hot objects.

 

Added on June 22, 2016: For evidence, a new category of stars recently came in the attention: the Fu Orionis type, or Fuors in short. These stars are very young stars showing large variations of luminosity, caused by episodes of strong accretion of matter. I think this fits well the model I propose, in the extreme case where the successive demolishing and reconstruction of a secondary accretion disk reaches the surface of the star. The point is that these stars are rare, a very small proportions of the stars of this age (only six known), still more rare than older stars with «hot Jupiters». This confirms the general rule as what the accretion disk does not spiral in of its own, unless some external flow of matter makes it crumble nearer from the star.

 

(Added on September 19, 2017). The recent discovery of the solar system around the Trappist-1 star, the first known in details, confirms the views of this chapter, by showing a Titus-Bode law. Better, this system went further, with exact integer ratios. Given the very close relations of the different planets, it is possible that these exact ratios appeared after the formation of the system, by tidal effect. But that such a regularity exists for seven planets in a row, tells that at least an approximate Titus-Bode law already existed in the accretion disk, as explained in this chapter. Otherwise, tidal braking would have led this system to a chaos.

Conclusions

So this model is not a simple model, it involves several different and competing mechanisms, some never described before, working to produce a variety of solar systems, showing small or large departures from a basic regular scheme. But it is difficult to go further using only deduction and intuition: calculus and intensive simulations are needed too, especially for the complex dynamic of an active hydrodynamic accretion disk, of which we have very few observation data today, and only very recent simulations (2014). Simulations are needed too for the late stage of the condensation of a planet, especially for all the chemical interactions. But this job is far beyond the capacities of a lonely person with only an insultingly low allowance to survive with.

It is especially difficult to guess which of the mechanisms described here actually takes place: primary disk or peanut separation, late arrival secondary disk, astrophysical or hydrodynamic separation, toroidal convection or eddies, magnetic braking or mechanical braking, thermal differentiation, dust cyclone separation, etc. Most probably one or two dominate, on a case to case basis

Much more accurate knowledge of other solar systems is needed too. Today (2011) we know only the most exotic cases. It is as doing a statistic of stars using only the stars visible to the naked eye: it does not show any structure, even not the main Hertzprung Russel sequence.

 

However a practical conclusion of this chapter is that we do not need extraordinary events to explain all the features of planets and orbits. Our solar system is quite ordinary, totally devoid of any special or unique feature. But even extraordinary features do not preclude inhabitable planets to form. This makes that the conditions for the appearance of life can also happen about anywhere, in a huge variety of places, some looking like Earth, some eventually very different.

 

Last remark is that exoplanets were found on very old stars, which however had only 1% of the solid matter of our solar system. The probable explanation is that the size of the planets does not depends on the amount of solid elements, provided there are some of them. This is a very interesting contribution, since we now know that inhabitable planets may exist since much longer than Earth, allowing for a much longer evolution of life here.

First term of the Drake equation

We are now fairly sure, from the statistics of exoplanets already discovered in 2015, that the extraordinary cases already found are just the tip of a much larger distribution, making stable planets almost certain in the large majority of stars. Let us say a conservative value of 80%, although I am fairly sure it is in the 98% or so.

The only disputed case is about double stars. It was until recently estimated that double star systems could not have planets, due to the irregular orbits they would have. However there is no essential difference between systems with small planets like ours, and systems with large planets with moons, and even systems with large enough bodies to form orbiting stars with their own planets. Such systems are perfectly able to bear planets around any of their components. But still more recently it was found that even double stars of equal size can have planets, close enough from each star, or much further away of the couple.

The statistics on known exoplanets is still not enough to make clear conclusions on the probability of planets around double stars. Since half of the stars are double, assuming that none has planets brings a pessimistic factor of 2 in the first term of the Drake equation, which only increases the distance of our closest neighbour of 25%

This makes a very conservative value of 0.4 for fp the first term of the Drake equation. If we assume that our closest neighbour is at 4.3 light-years, then statistically we should find the closest exoplanet at 6 light-years.

The closest sure exoplanet actually found (January 2015) is at 11.9 light years, making a minimum value of 0.05 for fp. A very pessimistic estimate, since we can still expect a lot of closer discoveries.

(Added June 2015) Indeed, today the most popular method for finding exoplanets is the one of occultations. For extraterrestrials to discover one planet in our solar system with this method, they need to be in a narrow zone of about 3° around our ecliptic, where most planets are. There is about one odd on 60 they do so. This factor, applied on the observed value of 0.05 for fp, makes our theoretical closest neighbour at only 3 Light years! So that we can pose with a great certainty fp is close to 1.

 

(Added in June 2015) The database of Exoplanets shows an earth sized planet around Proxima centauri B, that is our closest neighbour. This brillantly confirms the previous estimate from 0,4 to 1 for fp.

 

 

 

 

 

 

General Epistemology        Chapter VIII-2       

 

 

 

 

 

 

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