How do Rocky Planets Form?

A question in my last post raised the question of how do rocky planets form, and why is Venus so different from Earth? This will take two posts; the first covers how the planets form and why, and the second how they evolve immediately after formation and get their atmospheres.

First, a quick picture of accretion. At first, the gas cloud collapses and falls into the star, and in this stage the star the size of the sun accretes something like 2.5 x 10^20 kg per second. Call that stage 1. When the star has gobbled up most of the material, such accretion slows down, and in what I shall call stage 2 it accretes gas at least four orders of magnitude slower. The gas heats due to loss of potential energy as it falls into the star, although it also radiates heat from the dust that gets hot. (Hydrogen and helium do not radiate in the infrared easily.) In stage 1, the gas reached something like 1600 degrees C at 1 A.U. (the distance from Earth to the sun). In stage 2, because far less gas was falling in, the disk had temperatures roughly what bodies have now. Even in stage 2, standard theory has it that boulder-sized objects will fall into the star within about a hundred years due to friction with the gas.

So how did planets form? The standard explanation is that after the star had finished accreting, the dust very rapidly accreted to planetesimals (bodies about 500 km across) and these collided to form oligarchs, and in turn these collided to form planets. I have many objections to this. The reasons include the fact there is no mechanism to form the planetesimals that we assume to begin with. The calculations originally required one hundred million years (100 My) to form Earth, but we know that it had to be essentially formed well before that because the collision that formed the Moon occurred at about 50 My after formation started. Calculations solved the Moon-forming problem by saying it only took 30 My, but without clues why this time changed. Worse, there are reasons to believe Earth had to form within about 1 My of stage 2 because it has xenon and krypton that had to come from the accretion disk. Finally, in the asteroid belt there is evidence of some previous collisions between asteroids. What happens is they make families of much smaller objects. In short, the asteroids shatter into many pieces upon such collisions. There is no reason to believe that similar collisions much earlier would be any different.

The oldest objects in the solar system are either calcium aluminium inclusions or iron meteorites. Their ages can be determined by various isotope decays and both had to be formed in very hot regions. The CAIs are found in chondrites originating from the asteroid belt, but they needed much greater heat to form than was there in stage 2. Similarly, iron meteorites had to form at a temperature sufficient to melt iron. So, how did they get that hot and not fall into the sun? The only time the accretion disk got sufficiently hot at a reasonable distance from the sun was when the star was accreting in stage 1. In my opinion, this shows the calculations were wrong, presumably because they missed something. Worse, to have enough material to make the giants, about a third of the stellar mass has to be in the disk, but observation of other disks in stage 2 shows there is simply not enough mass to make the giants.

The basic argument I make is that whatever was formed in the late stages of stellar accretion stayed more or less where it was. One of the puzzles of the solar system is that most of the mass is in the star, but most of the angular momentum resides in the planets, and since angular momentum has to be conserved and since most of that was with the gas initially, my argument is any growing solids took angular momentum from the gas, which sends then mass further from the star, and it had to be taken before the star stopped accreting. (I suggest a mechanism in my ebook.)

Now to how the rocky planets formed. During primary stellar accretion, temperatures reached about 1300 degrees C where Mars would form and 1550 degrees C a little beyond where Earth would grow. This gives a possible mechanism for accretion of dust. At about 800 degrees C silicates start to get sticky, so dust can accrete into small stones there, and larger ones closer to the star. There are a number of different silicates, all of which have long polymers, but some, especially aluminosilicates are a little more mobile than others. At about 1300 degrees C, calcium silicate starts to phase separate out, and about 1500 degrees C various aluminosilicates phase separate. This happens because the longer the polymer, the more immiscible it is in another polymer melt (a consequence of the first two laws of thermodynamics, and which makes plastics recycling so difficult.) If this were the only mechanism for forming rocky planets, the size of the finished planet would diminish significantly with distance from the star. Earth, Venus and Mercury are in the wrong order. Mercury may have accreted this way, but further out, stones or boulders would be the biggest objects.

Once primary stellar accretion ends, temperatures were similar to what they are now. Stones collide, but with temperatures like now, they initially only make dust. There is no means of binding silicates through heat. However, if stones can come together, dust can fill the spaces. The key to rocky planet formation is that calcium silicate and calcium aluminosilicates could absorb water vapour from the disk gases, and when they do that, they act as cements that bind the stones together to form a concrete. The zone where the aluminosilicates start to get formed is particularly promising for absorbing water and setting cement, and because iron starts to form bodies here, lumps of iron are also accreted. This is why Earth has an iron core and plenty of water. Mars has less water because calcium silicate absorbs much less water, and its iron is mainly accreted as fine dust.

Finally, Mars is smaller because the solids density is less, and the disk is cleared before it has time to fully grow. The evidence for the short-lived disk is from the relatively small size of Jupiter compared with corresponding planets around similar sized stars that our sun cleared out the accretion disk sooner than most. This is why we have rocky planets, and not planets like the Neptune-sized planets in the so-called habitable zone around a number of stars. Venus is smaller than Earth because it was harder to get going, through the difficulty of water setting the cement, which is partly why it has very little water on its surface. However, once started it grows faster since the density of basaltic rocks is greater. Mercury is probably smaller still because it formed a slightly different way, through excessively mobile silicates in the first stage of the accretion disk, and by later being bombed by very large rocky bodies that were more likely to erode it. That is somewhat similar to the standard explanation of why Mercury is small but has a large iron core. The planets grow very quickly, and soon gravity binds all dust and small stones, then as it grows, gravity attracts objects that have grown further away, which perforce are large, but still significantly smaller than the main body in the zone.

Next post: how these rocky planets started to evolve to where they are now.

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Science that does not make sense

Occasionally in science we see reports that do not make sense. The first to be mentioned here relates to Oumuamua, the “interstellar asteroid” mentioned in my previous post. In a paper (arXiv:1901.08704v3 [astro-ph.EP] 30 Jan 2019) Sekanina suggests the object was the debris of a dwarf interstellar comet that disintegrated before perihelion. One fact that Sekanina thought to be important was that no intrinsically faint long-period comet with a perihelion distance less than about 0.25 AU, which means it comes as close or closer than about two-thirds the distance from the sun as Mercury, have ever been observed after perihelion. The reason is that if the comet gets that close to the star, the heat just disintegrates it. Sekanina proposed that such an interstellar comet entered our system and disintegrated, leaving “a monstrous fluffy dust aggregate released in the recent explosive event, ‘Oumuamua should be of strongly irregular shape, tumbling, not outgassing, and subjected to effects of solar radiation pressure, consistent with observation.” Convinced? My problem: just because comets cannot survive close encounters with the sun does not mean a rock emerging from near the sun started as a comet. This is an unfortunately common logic problem. A statement of the form “if A, then B” simply means what it says. It does NOT mean, there is B therefor there must have been A.

At this point it is of interest to consider what comets are comprised of. The usual explanation is they are formed by ices and dust accreting. The comets are formed in the very outer solar system (e.g.the Oort cloud) by the ices sticking together. The ices include gases such as nitrogen and carbon monoxide, which are easily lost once they get hot. Here, “hot” is still very cold. When the gases volatalise, they tend to blow off a lot of dust, and that dust is what we see as the tail, which is directed away from the star due to radiation pressure and solar wind. The problem with Sekanina’s interpretation is, the ice holds everything together. The paper conceded this when it said it was a monstrous fluffy aggregate, but for me as the ice vaporizes, it will push the dust apart. Further, even going around a star, it will still happen progressively. The dust should spread out, as a comet tail. It did not for Oumuamua.

The second report was from Bonomo, in Nature Astronomy(doi.org/10.1038/s41550-018-0648-9). They claimed the Kepler 107 system provided evidence of giant collisions, as described in my previous post, and the sort of thing that might make an Oumuamua. What the paper claims is there are two planets with radii about fifty per cent bigger than Earth, and the outer planet is twice as dense (relative density ~ 12.6 g/cm^3) than the inner one (relative density ~ 5.3 g/cm^3). The authors argue that this provides evidence for a giant collision that would have stripped off much of the silicates from the outer planet, thus leaving more of an iron core. In this context, that is what some people think is the reason for Mercury having a density almost approaching that of Earth so the authors are simply tagging on to a common theme.

So why do I think this does not make sense? Basically because the relative density of iron is 7.87 g/cm^3. Even if this planet is pure iron, it could not have a density significantly greater than 7.8. (There is an increase in density due to compressibility under gravity, but iron is not particularly compressible so any gain will be small.) Even solid lead would not do. Silicates and gold would be OK, so maybe we should start a rumour? Raise money for an interstellar expedition to get rich quick (at least from the raised money!) However, from the point of view of the composition of dust that forms planets, that is impossible so maybe investors will see through this scam. Maybe.

So what do I think has happened? In two words, experimental error. The mass has to be determined by the orbital interactions with something else. What the Kepler mehod does is determine the orbital characteristics by measuring the periodic times, i.e.the times between various occultations. The size is measured from the width of the occultation signal and the slope of the signal at the beginning and the end. All of these have possible errors, and they include the size of the star and the assumed position re the equator of the star, so the question now is, how big are these errors? I am starting to suspect, very big.

This is of interest to me since I wrote an ebook, “Planetary Formation and Biogenesis”. In this, I surveyed all the knowedge I could find up to the time of writing, and argued the standard theory was wrong. Why? It took several chapters to nail this, but the essence is that standard theory starts with a distribution of planetesimals and lets gravitational interactions lead to their joining up into planets. The basic problems I see with this are that collisions will lead to fragmentation, and the throwing into deep space, or the star, bits of planet. The second problem is nobody has any idea how such planetesimals form. I start by considering chemical interactions, and when I do that, after noting that what happens will depend on the temperatures around where it happens (what happens in chemistry is often highly temperature dependent) you get very selective zoes that differ from each other quite significantly. Our planets are in such zones (if you assume Jupiter formed at the “snow zone”) and have the required properties. Since I wrote that, I have been following the papers on the topic and nothing has been found that contradicts it, except, arguably things like the Kepler 107 “extremely dense planet”. I argue it is impossible, and therefore the results are in error.

Should anyone be interested in this ebook, see http://www.amazon.com/dp/B007T0QE6I

Oumuamua (1I) and Vega

Oumuamua is a small asteroidal object somewhere between 100 – 1000 meters long and is considerably longer than it is broad. Basically, it looks like a slab of rock, and is currently passing through the solar system on its way to wherever. It is our first observation of an interstellar object hence the bracketed formal name: 1 for first, I for interstellar. How do we know it came from interstellar space? Its orbit has been mapped, and its eccentricity determined. The eccentricity of a circular orbit is zero; an eccentricity greater than zero but less than one means the object is in an elliptical orbit, and the larger the eccentricity, the bigger the difference between closest and furthest approach to the sun. Oumuamua was found to have an eccentricity of 1.1995, which means, being greater than 1, it is on a hyperbolic orbit. It started somewhere where the sun’s gravity is irrelevant, and it will continue on and permanently leave the sun’s gravitational field. We shall never see it again, so the observation of it could qualify it for entry in “The Journal of Irreproducible Results”.

Its velocity in interstellar space (i.e.without the sun’s gravitational effects) was 26.3 km/s. We have no means of knowing where it came from, although if is trajectory is extrapolated backwards, it came from the direction of Vega. Of course it did not come from Vega, because when it passed through the space that Vega now occupies, Vega was somewhere else. Given there is no sign of ice on Oumuamua, which would form something like a cometary tail, it presumably came from the rocky zone closer to its system’s star, and this presumably has given rise to the web speculation that Oumuamua was some sort of alien space ship. Sorry, but no, it is not, and it does not need motors to enter interstellar space.

The way a body like Oumuamua could be thrown into interstellar space goes like this. There has to be a collision between two rocky bodies that are big enough to form fragments of the required size and the collision has to be violent enough to give the fragment a good velocity. That will also make a lot of dust. The fragments would be assumed to then go into elliptical orbits, but if there are both rocky planets and giants, the body could be ejected in the same way the Voyager space craft have left our solar system, namely through gravity assists. If the object is on the right trajectory it could get a gravity assist from an earth-like rocky planet, then another one from a giant that could give it enough impetus to leave the system. This presumably happened a long time ago, so we have no idea where the object came from.

Notwithstanding that, Oumuamua brought Vega to my attention, and it is, at least for me, an interesting star. That, of course, is because I have published a theory of planetary formation that is at odds with the generally accepted one. Vega has about twice the mass of the sun, and because it is bigger, it burns faster, and will have a life of about a billion years. It is roughly half-way through that, so it won’t have had time for planets to evolve intelligent life. The concentration of elements heavier than helium in Vega is about a third that of the sun. Vega also has an abnormally fast rate of rotation, so much so that it is about 88% of what would be required to start the star breaking up. This is significant because one of the oddities of our solar system is that the bulk of the angular momentum resides in the planets, while by far the bulk of the mass lies in the star. The implication might be that the lower level of heavier elements meant that Vega did not form cores fast enough and hence it does not have the giant planets of sufficient size to have taken up sufficient angular momentum. The situation could be like an ice skater who spins very fast, but slows the rotation by extending her arms. If the arms are very short, the spin cannot be slowed as much.

The infra-red emissions from Vega are consistent with a dust disk from about 70 – 100 A.U. out to 330 A.U. from the star (an A.U. is the distance from the sun to the Earth). This is assumed to have arisen from recent collisions of objects comparable to those in the Kuiper Belt here. There is apparently another dusty zone at 8 A.U., which would have to have originated from collisions between rocky objects. So far there is no evidence of planets around Vega, but equally there is no evidence there are none. We view Vega almost aligned with its axis of rotation, so most of the usual techniques for finding planets will not work. The transiting technique of the Kepler program requires us to be aligned with the ecliptic (which should be aligned with the equator) and the Doppler technique has similar limitations, although it has more tolerance for deviation. The Doppler technique detects the gravitational wobble of the star and if you could detect such a wobble directly, you could see it from along the polar axis. Unfortunately, we can’t, at least not yet, and worse, detecting such wobbles works best with very large planets around small stars. Here, if you follow my theory and accept the low metallicity, we expect small planets around a very large star. Direct observation has so far only worked for the first few million years of the star, where giant planets are radiating yellow to white light from their surface temperature that is so hot because of the gravitational accretion energy. These cool down reasonably quickly.

What grabbed my attention about Vega was the 8 A.U. dust zone. That can only be generated by a number of collisions because such dust zones have to be replenished. That is because solar radiation slows dust down, and it gradually falls into the star. So to have a good number of frequent collisions, you need a very large number of objects that could collide, which effectively requires a belt of boulders. So why have they not collided and formed a planet, when the standard theory of planetary formation says planets are formed by the collision of boulders to form planetesimals, and these collide to form embryos, which collide to form planets. In my ebook, “Planetary Formation and Biogenesis” I provide an answer, which is basically that to form rocky planets, the collisions have to happen in the accretion disk, and they happen very fast, and they happen because water vapour in the disk helps set cement. Once the accretion disk is removed, further accretion is impossible, other than from objects colliding with a big enough object for gravity to hold all the debris. Accordingly, collisions of boulder-sized objects or asteroids will make dust, and that would create a dust belt that would not last all that long. The equivalent of the Kuiper Belt around Vega appears to be between 3 – 6 times further out. In my theory, if the planet accreted in the same as the sun, it would be approximately 8 times further out. However, lower dust content may make it harder to radiate energy, hence accretion may be slower. If this second belt scales accordingly, it could correspond to our asteroid belt.  We know occasional collisions did occur in our asteroid belt because we see families of smaller fragments whose trajectories extrapolate back to a singe event. So maybe dust belts are tolerably common for short periods in the life of a star. It would not be a great coincidence we see one around Vega; there are a huge number of stars, we see a very large number of accretion disks, so dust belts should turn up sooner or later.

Finally, why does the star spin faster? Again, in my theory, the planets accrete from the solid and take their angular momentum, but then they also take angular momentum from the disk gas through a mechanism similar to the classical Magnus force. Vega has less dust to make planets, hence less angular momentum is taken that way, and because the planets should be smaller there is less gravity to take angular momentum from the gas, and more gas anyway. So the star retains a higher fraction of its angular momentum. All of this does not prove that my theory is right, but it is comforting that it at least has some sort of plausible support. If interested further, check out http://www.amazon.com/dp/B007T0QE6I.

What is Dark Matter?

First, I don’t know what dark matter is, or even if it is, and while they might have ideas, neither does anyone else know. However, the popular press tells us that there is at least five times more of this mysterious stuff in the Universe than ordinary matter and we cannot see it. As an aside, it is not “dark”; rather it is transparent, like perfect glass. The reason is light does not interact with it, nevertheless we also know that there are good reasons for thinking that something is there because assuming our physics are correct, certain things should happen, and they do not happen as calculated. The following is a very oversimplified attempt at explaining the problem.

All mass exerts a force on other mass called gravity. Newton produced laws on how objects move according to forces, and he outlined an equation for how gravity operates. If we think about energy, follow Aristotle as he considered throwing a stone into the air. First we give the stone kinetic energy (that is the energy of motion) but as it goes up, it slows down, stops, and then falls back down. So what happened to the original energy? Aristotle simply said it passed away, but we now say it got converted to potential energy. That permits us to say that the energy always stayed the same. Note we can never see potential energy; we say it is there because in makes the conservation of energy work. The potential energy for a mass munder the gravitational effect of a mass Mis given by V = GmM/r. Gis the gravitational constant and ris the distance between them.

When we have three bodies, we cannot solve the equations of motion, so we have a problem. However, the French mathematician Lagrange showed that any such system has a function that we call a Lagrangian, in his honour, and this states that the difference between the total kinetic and potential energies equals this term. Further, provided we know the basic function for the potential energy, we can derive the virial theorem from this Lagrangian, and for gravitational interactions, the average kinetic energy has to be half the magnitude of the potential energy.

So, to the problem. As the potential energy drops off with distance from the centre of mass, so must the kinetic energy, which means that velocity of a body orbiting a central mass must slow down as the distance from the centre increases. In our solar system Jupiter travels much more slowly than Earth, and Neptune is far slower still. However, when measurements of the velocity of stars moving in galaxies were made, there was a huge surprise: the stars moving around the galaxy have an unexpected velocity distribution, being slowest near the centre of the galaxy, then speeding up and becoming constant in the outer regions. Sometimes the outer parts are not quite constant, and a plot of speed vs distance from the centre rises, then instead of flattening, has wiggles. Thus they have far too much velocity in the outer regions of the galactic disk. Then it was found that galaxies in clusters had too much kinetic energy for any reasonable account of the gravitational potential energy. There are other reasons why things could be considered to have gone wrong, for example, gravitational lensing with which we can discover new planets, and there is a problem with the cosmic microwave background, but I shall stick mainly with galactic motion.

The obvious answer to this problem is that the equation for the potential is wrong, but where? There are three possibilities. First, we add a term Xto the right hand side, then try to work out what Xis. Xwill include the next two alternatives, plus anything else, but since it is essentially empirical at this stage, I shall ignore it in its own right. The second is to say that the inverse dependency on ris wrong, which is effectively saying we need to modify our law of gravity. The problem for this is that Newton’s gravity works very well right out to the outer extensions of the solar system. The third possibility is there is more mass there than we expect, and it is distributed as a halo around the galactic centre. None of these are very attractive, but the third option does save the problem of why gravity does not vary from Newtonian law in our solar system (apart from Mercury). We call this additional mass dark matter.

If we consider modified Newtonian gravity (MOND), this starts with the proposition that with a certain acceleration, the force takes the form where the radial dependency on the potential contained a further term that was proportional to the distance rthen it reached a maximum. MOND has the advantage that it predicts naturally the form to the velocity distribution and its seeming constancy between galaxies. It also provides a relationship for the observed mass and the rate of rotation of a galaxy, and this appears to hold. Further, MOND predicts that for a star, when its acceleration reaches a certain level, the dynamics revert to Newtonian, and this has been observed. Dark matter has a problem with this. On the other hand, something like MOND has real trouble trying to explain the wiggly structure of velocity distributions in certain galaxies, it does not explain the dynamics of galaxy clusters, it has been claimed it offers a poor fit for velocities in globular clusters, the predicted rotations of galaxies are good, but they require different values of what should be constant, and it does not apply well to colliding galaxies. Of course we can modify gravity in other ways, but however we do it, it is difficult to fit it with General Relativity without a number of ad hocadditions, and there is no real theoretical reason for the extra terms required to make it work. General Relativity is based on ten equations, and to modify it, you need ten new terms to be self-consistent; the advantage of dark matter is you only need 1.

The theory that the changes are due to dark matter has to assume that each galaxy has to incorporate dark matter roughly proportional to its mass, and possibly has to do that by chance. That is probably it biggest weakness, but it has the benefit that it assumes all our physics are more or less right, and what has gone wrong is there is a whole lot of matter we cannot see. It predicts the way the stars rotate around the galaxy, but that is circular reasoning because it was designed to do that. It naturally predicts that not all galaxies rotate the same way, and it permits the “squiggles” in the orbital speed distribution, again because in each case you assume the right amount of dark matter is in the right place. However, for a given galaxy, you can use the same dark matter distribution to determine motion of galaxy clusters, the gas temperature and densities within clusters, and gravitational lensing, and these are all in accord with the assumed amount of dark matter. The very small anisotropy of the cosmic microwave background also fits in very well with the dark matter hypothesis, and not with modified gravity.

Dark matter has some properties that limit what it could be. We cannot see it, so it cannot interact with electromagnetic radiation, at least to any significant extent. Since it does not radiate energy, it cannot “cool” itself, therefore it does not collapse to the centre of a galaxy. We can also put constraints on the mass of the dark matter particle (assuming it exists) from other parts of physics, by how it has to behave. There is some danger in this because we are assuming the dark matter actually follows those relationships, and we cannot know that. However, with that kept in mind, the usual conclusions are that it must not collide frequently, and it should have a mass larger than about 1 keV. That is not a huge constraint, as the electron has a mass of a little over 0.5 MeV, but it says the dark matter cannot simply be neutrinos. There is a similar upper limit in that because the way gravitational lensing works, it cannot really be a collection of brown dwarfs. As can be seen, so far there are no real constraints on the mass of the dark matter constituent particles.

So what is the explanation? I don’t know. Both propositions have troubles, and strong points. The simplest means of going forward would be to detect and characterize dark matter, but unfortunately our inability to do this does not mean that there is no dark matter; merely that we did not detect it with that technique. The problem in detecting it is that it does not do anything, other than interact gravitationally. In principle we might detect it when it collides with something, as we would see an effect on the something. That is how we detect neutrinos, and in principle you might think dark matter would be easier because it has a considerably higher mass. Unfortunately, that is wrong, because the neutrino usually travels at near light speed; if dark matter were much larger, but much slower, it would be equally difficult to detect, if not more so. So, for now nobody knows.

Just to finish, a long shot guess. In the late 20th century, a German physicist B Heim came up with a theory of elementary particles. This is largely ignored in favour of the standard model, but Heim’s theory produces a number of equations that are surprisingly good at calculating the masses and lifetimes of elementary particles, both of which are seemingly outside the scope of the standard model. One oddity of his results is he predicts a “neutral electron” with a mass slightly greater than the electron and with an infinite lifetime. If matter and antimatter originally annihilated and left a slight preponderance of matter, and if this neutral electron is its own antiparticle, then it would survive, and although it is very light, there would be enough of it to explain why its total mass now is so much greater than matter. In short Heim predicted a particle that is exactly like dark matter. Was he right? Who knows? Maybe this problem will be solved very soon, but for now it is a mystery.

Rocky Planet Formation

In the previous posts I have argued that the evidence strongly supports the concept that the sun eliminated its accretion disk within about 1 My after the star formed. During this 1 My, the disk would be very much cooler than while the sun was accreting, and the temperatures were probably not much different from those now at any given distance from the star in the rocky planet zone. Gas was still falling into the star, but at least ten thousand times slower. We also know (see previous posts) that small solid objects such as CAIs and iron bearing meteorites are much older than the planets and asteroids. If the heavier isotope distributions of xenon and krypton are caused by the hydrodynamic loss to space, which is the most obvious reason, then Earth had to have formed before the disk cleanout, which means Earth was more or less formed within about 1 My after the formation of the sun.

The basic problem for forming rocky planets is how does the rocky material stick together? If you are on the beach, you may note that sand does not turn into a solid mass. A further problem is the collisions of large objects involve huge energies. Glancing collisions lead to significant erosion of both objects, and even direct hits lead to local pulverization and intense heat, together with a shock wave going through the bodies. When the shock wave returns, the pulverized material is sent into space. Basically craters are formed, and a crater is a hole. Adding holes does not build up mass. Finally, if the two are large enough and about equal sized, they each tend to shatter as a consequence of the shock waves. This is why I believe the Monarchic growth makes more sense, where what collides with the major body is much smaller. Once the forming object is big enough, it accretes all small objects it collides with, due to gravity, but the problem is, how do small bodies stick together?

The mechanism I developed goes like this. While the star is accreting, we get very high temperatures and anything over 1000 degrees will lead to silicates softening and becoming sticky. This generates pebbles, stones and boulders that get increasingly big as we get closer to the star, because more of the silicates get more like liquids. At 1550 degrees C, iron melts, and the iron liquids coalesce. That is where the iron meteorites come from. By about 1750 – 1800 degrees silicates get quite soft, and it may be that Mercury formed by a whole lot of “liquids” forming a sticky mass. Behind that would be a distribution of ever decreasingly sized silicate masses, with iron cores where temperatures got over 1550. This would be the origin of the cores for Earth, Venus and Mercury. Mars has no significant iron core because the iron there was still in the very small particulate size.

The standard theory says the cores separated out with heavier liquids sinking, but what most people do not realize is that the core of the Earth does not comprise liquid silicates, at least not the mobile sort. You have no doubt heard that heat rises by convection at hot spots, but it is not a sort of kettle down there. The rate of movement has been estimated at 1 mm per year, which would mean the silicates would rise 1000 km every billion years. We are still well short of one complete turnover. Further an experiment where two different silicates were heated to 2000 degrees C under pressure of 26 Gpa showed that the silicates would only diffuse contents a few meters over the life of the Earth. They may be “liquid” but the perovskite silicates are so viscous nothing moves far in them. So how did the core form so quickly? In my opinion, the reason is the iron has already separated from the silicates, and the collision of a whole lot of small spherical objects do not pack well; there will be channels, and molten iron that already exists in larger masses will flow down them. Less-viscous aluminosilicates will flow up and form the continents.

The next part unfortunately involves some physical chemistry, and there is no way around it. I am going to argue that the silicates that formed the boulders separated into phases. An example is oil and water. Molecules tend to have an energy of association, that is all the water molecules have an energy that tends to hold them all together as a liquid as opposed to a gas, and that tends to keep phases separate because one such energy between like molecules is invariably stronger than the energy between different ones. There is also something called entropy, which favours things being mixed. Now the heat of association of polymers is proportional to the number of mers, while the entropy is (to a first approximation) proportional to the number of molecules. Accordingly, the longer the polymers, the less likely they are to blend, and the more likely to phase separate. That is one of the reasons that recycling plastics is such a problem: you cannot blend them because if the polymers are long, they tend to separate in processing, and your objects have “faults” running through them.

The reason this is important, from my point of view, is that at about 1300 degrees C, calcium silicate tends to phase separate from the rest, and about 1500 degrees C, a number of calcium aluminosilicates start to phase separate. These are good hydraulic cements, and my argument is that after cool down, collisions between boulders makes dust, and the cements are particularly brittle. Then if significant boulders come together gently, e.g. as in the postulated “rubble piles”, the cement dust works it way through them, and water vapour from the disk will set the cement. This works up to about 500 degrees C, but there are catches. Once it gets significantly over 300 degrees C, less water is absorbed, and the harder it is to set it. Calcium silicate only absorbs one molecule of water, but some aluminosilicates can absorb up to twenty molecules per mer. This lets us see why the rocky planets look like they do. Mars is smaller because only the calcium silicate cement can form at that distance, and because iron never melted it does not have an iron core. It has less water because calcium silicate can only set one molecule of water per cement molecule, and it does not have easily separable aluminosilicates so it has very little felsic material. Earth is near the optimum position. It is where the iron core material starts, and because it is further from the sun than the inner planets, there is more iron to sweep up. The separated aluminosilicates rise to the surface and form the felsic continents we walk on, and provided more water when setting the cement. Venus formed where it was a little hot, so it was a slow starter, but once going, it will have had bigger boulders to grow with. It has plenty of iron core, but less felsic material, and it started with less water than Earth. This is conditional on the Earth largely forming before the disk gases were ejected. If we accept that, we have a platform for why Earth has life, but of course that is for later.

From Whence Star-burning Planets?

This series started out with the objective of showing how life could have started, and some may be wondering why I have spent so much time talking about the cold giant planets. The answer is simple. To find the answer to a scientific problem we seldom go directly to it. The reason is that when you go directly to what you are trying to explain you will get an explanation, however for any given observation there will be many possible explanations. The real explanation will also explain every connected phenomenon, whereas the false explanations will only explain some. The ones that are seemingly not directed at the specific question you are trying to answer will nevertheless put constraints on what the eventual answer must include. I am trying to make things easier in the understanding department by considering a number of associated things. So, one more post before getting on to rocky planets.

In the previous two posts, I have outlined how I believe planets form, and why the outer parts of our solar system look like they do. An immediate objection might be, most other systems do not look like ours. Why not? One reason is I have outlined so far how the giants form, but these giants are a considerable distance from the star. We actually have rather little information about planets in other systems at these distances. However, some systems have giants very close to the star, with orbits (years) that take days and we do not. How can that be?

It becomes immediately obvious that planets cannot accrete from solids colliding that close to the star because the accretion disk get to over 10,000 degrees C that close, and there are no solids at those temperatures. The possibilities are that either there is some mechanism that so far has not been considered, which raises the question, why did it not operate here, or that the giants started somewhere else and moved there. Neither are very attractive, but the fact these star-burning giants only occur near a few stars suggests that there is no special mechanism. Physical laws are supposedly general, and it is hard to see why these rare exceptions occur. Further, we can see how they might move.

There is one immediate observation that suggests our solar system is expected to be different from many others and that is, if we look again at LkCa 15b, that planet is three times further from the star than Jupiter is from our star, which means the gas and dust there would have more than three times less concentrated, and collisions between dust over nine times rarer, yet it is five times bigger. That star is only 2 – 3 My old, and is about the same size as our star. So the question is, why did Jupiter stop growing so much earlier when it is in a more favourable spot through having denser gas? The obvious answer is Jupiter ran out of gas to accrete much sooner, and it would do that through the loss of the accretion disk. Stars blow away their accretion disks some time between 1 and 30 My after the star essentially finishes accreting. The inevitable conclusion is that our star blew out its disk of gases in the earliest part of the range, hence all the planets in our system will be, on average, somewhat smaller than their counterparts around most other stars of comparable size. Planets around small stars may also be small simply because the system ran out of material.

Given that giants keep growing as long as gas keeps being supplied, we might expect many bigger planets throughout the Universe. There is one system, around the star HR 8799 which has four giants arrayed in a similar pattern to ours, albeit the distances are proportionately scaled up and the four planets are between five and nine times bigger than Jupiter. The main reason we know about them is because they are further from the star and so much larger, hence we an see them. It is also because we do not observe then from reflected light. They are very young planets, and are yellow-white hot from gravitational accretion energy. Thus we can see how planets can get very big: they just have to keep growing, and there are planets that are up to 18 times bigger than Jupiter. If they were bigger, we would probably call them brown dwarfs, i.e. failed stars.

There are some planets that have highly elliptical orbits, so how did that situation arise? As planets grow, they get gravitationally stronger, and if they keep growing, eventually they start tugging on other planets. If they can keep this up, the orbits get more and more elliptical until eventually they start orbiting very close to each other. They do not need to collide, but if they are big enough and come close enough they exchange energy, in which case one gets thrown outwards, possibly completely out of its solar system, and one gets thrown inwards, usually with a highly elliptical orbit. There are a number of systems where planets have elliptical orbits, and it may be that most do, and if they do, they will exchange energy gravitationally with anything else they come close to. This may lead to a sort of gravitational billiards, where the system gets progressively smaller, and of course rocky planets, being smaller are more likely to get thrown out of the system, or to the outer regions, or into the star.

Planets being thrown into the star may seem excessive, nevertheless in the last week it was announced that a relatively new star, RW Aur A, over the preceding year had a 30 fold increase in the amount of iron in its spectrum. The spectrum of a star comes from whatever is on its surface, so the assumption is that something containing a lot of iron, which would be something the size of a reasonably sized asteroid at least, fell into the star. That means something else knocked it out of its orbit, and usually that means the something else was big.

If the orbit is sufficiently elliptical to bring it very close to the star one of two things happen. The first is it has its orbit circularized close to the star by tidal interactions, and you get one of the so-called star-burners, where they can orbit their star in days, and their temperatures are hideously hot. Since their orbit is prograde, they continue to orbit, and now tidal interactions with the star will actually slowly push the planet further from the star, in the same way our moon is getting further from us. The alternative is that the orbit can flip, and become retrograde. The same thing happens as with the prograde planets, except that now tidal interactions lead to the planet slowly falling into the star.

The relevance of all this is to the question, how common is life in the Universe? If we want a rocky planet in a circular orbit in the habitable zone, then we can eliminate all systems with giants on highly elliptical orbits, or in systems with star burners. However, there is a further possibility that is not advantageous to life. Suppose there are rocky planets formed but the star has yet to elimiinate its accretion disk. The rocky planet will also keep growing and in principle could also become a giant. This could be the reason why some systems have Neptune-sized planets or “superEarths” in the habitable zone. They probably do not have life, so now we have to limit the number of possible star systems to those that eliminate their accretion disk very early. That probably elimimates about 90% of them. Life on a planet like ours might be rarer than some like to think.

Monarchic Growth of Giant Planets

In the previous post, I outlined the basic mechanism of how I thought the giant planets formed, and how their mechanism of formation put them at certain distances from the sun. Given that, like everyone else, I assign Jupiter to the snow point, in which case the other planets are where they ought to be. But that raises the question, why one planet in a zone? Let’s take a closer look at this mechanism.

In the standard mechanism, dust accretes into objects by some unknown mechanism, and does this essentially based on collision probability, and so the disk progresses with a distribution of roughly equal sized objects that collide under the same rules, and eventually become what is called planetesimals, which are about the size of the classical asteroid. (I say classical because as we get better at this, we are discovering a huge number of much smaller “asteroids”, and we have the problem of what does the word asteroid mean?) This process continues, and eventually we get Mars-sized objects called oligarchs, or embryos, then these collide to get planets. The size of the planet depends on how many oligarchs collide, thus fewer collided to make Venus than Earth, and Mars is just one oligarch. I believe this is wrong for four reasons: the first is, giants cannot grow fast enough; second, the dust is still there in 30 My old disks; the collision energies should break up the bodies at any given size because collisions form craters, not hills; the system should be totally mixed up, but isotope evidence shows that bodies seem to have accreted solely from the material at roughly their own distance from the sun.

There is an alternative called monarchic growth, in which, if one body can get a hundred times bigger than any of the others, it alone grows by devouring the others. For this to work, we need initial accretion to be possible, but not extremely probable from dust collisions. Given that we see disks by their dust that are estimated to be up to 30 My old, that seems a reasonable condition. Then, once it starts, we need a mechanism that makes further accretion inevitable, that is, when dust collides, it sticks. The mechanism I consider to be most likely (caveat – I developed it so I am biased) is as follows.

As dust comes into an appropriate temperature zone, then collisions transfer their kinetic energy into heat that melts an ice at the point of contact, and when it quickly refreezes, the dust particles are fused to the larger body. So accretion occurs a little below the melting temperature, and the probability of sticking falls off as the distance from that appropriate zone increases, but there is no sharp boundary. The biggest body will be in the appropriate zone because most collisions will lead to sticking, and once the body gets to be of an appropriate size, maybe as little as a meter sized, it goes into a Keplerian orbit. The gas and dust is going slower, due to gas drag (which is why the star is accreting) so the body in the optimal zone accretes all the dust and larger objects it collides with. Until the body gets sufficiently large gravitationally, collisions have low relative velocity, so the impact energy is modest.

Once it gets gravitationally bigger, it will accrete the other bodies that are at similar radial distance. The reason is that if everything is in circular orbits, orbits slightly further from the star have longer periodic times, in part because they move slightly slower, and in part because they have slightly further to go, so the larger body catches up with them and its gravity pulls the smaller body in. Unless it has exactly the same radial distance from the star, they will pass very closely and if one has enough gravity to attract the other, they will collide. Suppose there are two bodies at the same radial distance. That too is gravitationally unstable once they get sufficiently large. All interactions do not lead to collisions, and it is possible that one can be thrown inwards while the other goes outwards, and the one going in may circularise somewhere else closer to the star. In this instance, Ceres has a density very similar to the moons of Jupiter, and it is possible that it started life in the Jovian region, came inwards, and then finished accreting material from its new zone.

The net result of this is that a major body grows, while smaller bodies form further away, trailing off with distance, then there is a zone where nothing accretes, until further out there is the next accretion zone. Such zones get further away as you get further from the star because the temperature gradient decreases. That is partly why Neptune has a Kuiper Belt outside it. The inner planets do not because with a giant on each side, the gravity causes them to be cleaned out. This means that after the system becomes settled, a lot of residues start bombing the planet. This requires what could be called a “Great Bombardment”, but it means each system gets a bombardment mainly of its own composition, and there could be no significant bombardment with bodies from another system. This means the bombardment would have the same chemical composition as the planet itself.

Accordingly, we have a prediction. Is it right? It is hard to tell on Earth because while Earth almost certainly had such a bombardment, plate tectonics has altered the surface so much. Nevertheless, the fact the Moon has the same isotopes as Earth, and Earth has been churned but the Moon has not, is at least minor support. There is, of course, a second prediction. There seem to be many who assume the interior of the Jovian satellites will have much nitrogen. I predict very little. There will be some through adsorption of ammonia onto dust, and since ammonia binds more strongly than neon, then perhaps there will be very modest levels, but the absence of such material in the atmosphere convinces me it will be very modest.