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.

Trappist-1

By now, I suspect everybody has heard of Trappist-1, a totally non-spectacular star about 39 light years from Earth, and in terms of astronomy, a really close neighbour. I have seen a number of people on the web speculating about going there some time in the not too distant future. Suppose you could average a speed of 50,000 kilometers per hr, by my calculation (hopefully not hopelessly wrong) it would take about 850,000 years to get there. Since chemical rockets cannot get significantly more velocity, don’t book your ticket. Is it possible for a person to get to such stars? It would be if you could get to a speed sufficiently close to light speed. Relativity tells us that as you approach light speed your aging process slows down, and if you went at light speed (theoretically impossible if you have mass) you would not age, even though it would take 39 years as seen by an observer on earth. (Of course, assuming an observer could see your craft, it would seem to take 78 years at light speed because the signal has to get back.) It is not just aging; everything you do slows down the same way, so if you were travelling at light speed you would think the star was surprisingly close.

The chances are you will also have seen the comment that Trappist-1 is only a little bit bigger than Jupiter. In terms of mass, Trappist-1 is about 8% the mass of the sun, and that certainly makes it a small star as stars go, but it is about 84 times the mass of Jupiter. In my book, 84 times as big is not exactly “a little bit bigger”. Trappist-1 is certainly not as hot as the sun; its surface temperature is about 40% that of the sun. The power output of the star is also much lower, because power radiated per unit area is proportional to the fourth power of the temperature, and of course the area is much less. In this context, there are a lot of planets bigger than Jupiter, many of them about 18 times as big, but they are also too small to ignite thermonuclear reactions.

Nevertheless the system has three “earth-sized” planets in the “habitable” zone, and one that would be too hot for water to be in the liquid state, with a surface temperature predicted to be about 127 degree Centigrade provided it is simply in equilibrium with incoming stellar radiation. Of course, polar temperatures could be significantly cooler. The next three out would have surface temperatures of about 68 degrees C, 15 degrees C (which is rather earth-like) and minus 22 degrees C. Such temperatures do not take into account any greenhouse effect from any atmosphere, and it may be that the planet with a temperature of 68 degrees could equally end up something like a Venus. Interestingly, in the Nature paper describing them, it is argued that it is the planets e, f and g that could have water oceans, despite having temperatures without any greenhouse effect of minus 22, minus 54, and minus 74 degrees C. This arises from certain modeling, which I find unexpected. The planets are likely to be tidally locked, i.e. like the moon, the same face will always be directed towards the star.

So, there is excitement: here we have potential habitable planets. Or do we?

In terms of size, yes we do. The planetary radii for many are quite close to Earth’s, although d, the one with the most earth-like temperatures has a radius of about 0.77 Earth’s. Most of the others are a shade larger than earth, at least in terms of radius.

Another interesting thing is there are estimates of the planetary masses. How they get these is interesting, given the complexity of the system. The planets were detected by their transiting over the face of the star, and such transits have a periodic time, or what we would call a year, i.e how long it takes to get the next transit. Thus the closest, b, has a periodic time of 1.51087081 days. The furthest out has a period of 20 days. Now, the masses can be determined by mutual gravitational effects. Thus since the planets are close, suppose one is being chased by the other around transit time. The one behind will be pulled along a bit and the one in front retarded a bit, and that will lead to the transits being not quite on time. Unfortunately, the data set meant that because of the rather significant uncertainties in just about every variable, the masses are somewhat uncertain, thus the mass of the inner one is 0.85 + 0.72 earth masses. The second one is calculated to have a density of 1.17 times that of earth, which means it has a huge iron core. However, with the exception of the outer one, they all have densities that strongly suggest rocky planets, most with iron cores.

Suppose we went there. On our most “earth-like” planet we might have trouble growing plants. The reason is the light intensity is very low, and is more like on earth just after sunset. The reason the temperatures are adequate is that the star puts out much of its energy in the form of infrared radiation, and in general that is not adequate to power any obvious photochemistry, although it is good for warming things. The web informs us that astronomers are excited by this discovery because they give us the best chance of analyzing the atmospheres of an alien planet.

The reason is the planets orbit in a plane that means they pass in front of the star from our observation point, and that gives us an excellent chance to measure their size, but eventually also to analyse their atmospheres if they have certain sorts of gases. The reason for this is that as infrared radiation passes through material, the energies corresponding to the energies of molecular vibrations get absorbed. So, if we record the spectrum of the stellar radiation, when a planet passes in front of it, besides the main part of the planet lowering the intensity of all the radiation, where there is an energy corresponding to a molecular vibration, there would be a further absorption, so there would be little spikes on the overall dip. Such absorption spectra are often used by chemists to help identify what they have. It only identifies the class of compounds, because all compounds with the same functional group will absorb the same sort of radiation, but as far as gases go, there are not very many of them and we should be able to identify the with quite a degree of confidence, with one exception. Gases such as nitrogen and oxygen do not absorb in the infrared.

So, where does that leave us? We have a system that in principle lets us analyze things in greater detail than for most other planetary systems. However, I suspect this might also be misleading. This system is quite unlike others we have seen, mainly because it is around a much smaller star, and the planets may also be different due to the different conditions around a smaller star during planetary formation.