Trappist-1, and Problems for a Theoretician

In my previous post, I outlined the recently discovered planets around Trappist-1. One interesting question is, how did such planets form? My guess is, the standard theory will have a lot of trouble explaining this, because what we have is a very large number of earth-sized rocky planets around a rather insubstantial star. How did that happen? However, the alternative theory outlined in my ebook, Planetary Formation and Biogenesis, also has a problem. I gave an equation that very approximately predicts what you will get based on the size of the star, and this equation was based on the premise that chemical or physical chemical interactions that lead to accretion of planets while the star is accreting follow the temperatures in various parts of the accretion disk. In turn, the accretion disk around Trappist-1 should not have got hot enough where any of the rocky planets are, and more importantly, it should not have happened over such a wide radial distance. Worse still, the theory predicts different types of planets in different places, and while we cannot eliminate this possibility for trappist-1, it seems highly likely that all the planets located so far are rocky planets. So what went wrong?

This illustrates an interesting aspect of scientific theory. The theory was developed in part to account for our solar system, and solar systems around similar stars. The temperature in the initial accretion disk where the planets form around G type stars is dependent on two major factors. The first is the loss of potential energy as the gas falls towards the star. The temperature at a specific distance due to this is due to the gravitational potential at that point, which in turn is dependent on the mass of the star, and the rate of gas flowing through that point, which in turn, from observation, is very approximately dependent on the square of the mass of the star. So overall, that part is very approximately proportional to the cube of the stellar mass. The second dependency is on the amount of heat radiated to space, which in turn depends on the amount of dust, the disk thickness, and the turbulence in the disk. Overall, that is approximately the same for similar stars, but it is difficult to know how the Trappist-1 disk would cool. So, while the relationship is too unreliable for predicting where a planet will be, it should be somewhat better for predicting where the others will be, and what sort of planets they will be, if you can clearly identify what one of them is. Trappist-1 has far too many rocky planets. So again, what went wrong?

The answer is that in any scientific theory, very frequently we have to make approximations. In this case, because of the dust, and because of the distance, I assumed that for G type stars the heat from the star was irrelevant. For example, in the theory Earth formed from material that had been processed to at least 1550 degrees Centigrade. That is consistent with the heat relationship where Jupiter forms where water ice is beginning to think about subliming, which is also part of the standard theory. Since the dust should block much of the star’s light, the star might be adding at most a few tens of degrees to Earth’s temperature while the dust was still there at its initial concentration, and given the uncertainties elsewhere, I ignored that.

For Trappist -1 it is clear that such an omission is not valid. The planets would have accreted from material that was essentially near the outer envelope of the actual star during accretion, the star would appear large, the distance involving dust would be small, the flow through would be much more modest, and so the accreting star would now be a major source of heat.

Does this make sense? First, there are no rocky bodies of any size closer to our sun than Mercury. The reason for that, in this theory, is that by this point the dust started to get so hot it vaporized and joined the gas that flowed into the star. It never got that hot at Trappist-1. And that in turn is why Trappist-1 has so many rocky planets. The general coolness due to the small amount of mass falling inwards (relatively speaking) meant that the necessary heat for rocky planets only occurred very close to the star, but because of the relative size of the stellar envelope that temperature was further out than mass flow would predict, and furthermore the fact that the star could not be even vaguely considered as a point source meant that the zone for the rocky planets was sufficiently extended that a larger number of rocky planets was possible.

There are planets close to other stars, and they are usually giants. These almost certainly did not form there, and the usual explanation for them is that when very large planets get too close together, their orbits become unstable, and in a form of gravitational billiards, they start throwing each other around, some even being thrown from the solar system, and some end up very close to the star.

So, what does that mean for the planets of Trappist-1? From the densities quoted in the Nature paper, if they are right, and the authors give a wide range of uncertainty, the fact that the sixth one out has a density approaching that of Earth means they have surprisingly large iron cores, which may mean there is a possibility most of them accreted more or less the same way Mercury or Venus did, i.e. they accreted at relatively high temperatures, in which case they will have very little water on them. Furthermore, it has also been determined that these planets will be experiencing a rather uncomfortable amount of Xrays and extreme ultraviolet radiation. Do not book a ticket to go to them.

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