That Was 2017, That Was

With 2017 coming to a close, I can’t resist the urge to look back and see what happened from my point of view. I had plenty of time to contemplate because the first seven months were largely spent getting over various surgery. I had thought the recovery periods would be good for creativity. With nothing else to do, I could write and advance some of my theoretical work, but it did not work but like that. What I found was that painkillers also seemed to kill originality. However, I did manage one e-novel through the year (The Manganese Dilemma), which is about hacking, Russians and espionage. That was obviously initially inspired by the claims of Russian hacking in the Trump election, but I left that alone. It was clearly better to invent my own scenario than to go down that turgid path. Even though that is designed essentially as just a thriller, I did manage to insert a little scientific thinking into the background, and hopefully the interested potential reader will guess that from the “manganese” in the title.

On the space front, I am sort of pleased to report that there was nothing that contradicted my theory of planetary formation found in the literature, but of course that may be because there is a certain plasticity in it. The information on Pluto, apart from the images and the signs of geological action, were well in accord with what I had written, but that is not exactly a triumph because apart from those images, there was surprisingly little new information. Some of which might have previously been considered “probable” was confirmed, and details added, but that was all. The number of planets around TRAPPIST 1 was a little surprising, and there is limited evidence that some of them are indeed rocky. The theory I expounded would not predict that many, however the theory depended on temperatures, and for simplicity and generality, it considered the star as a point. That will work for system like ours, where the gravitational heating is the major source of heat during primary stellar accretion, and radiation for the star is most likely to be scattered by the intervening gas. Thus closer to our star than Mercury, much of the material, and even silicates, had reached temperatures where it formed a gas. That would not happen around a red dwarf because the gravitational heating necessary to do that is very near the surface of the star (because there is so much less falling more slowly into a far smaller gravitational field) so now the heat from the star becomes more relevant. My guess is the outer rocky planets here are made the same way our asteroids were, but with lower orbital velocities and slower infall, there was more time for them to grow, which is why they are bigger. The inner ones may even have formed closer to the star, and then moved out due to tidal interactions.

The more interesting question for me is, do any of these rocky planets in the habitable zone have an atmosphere? If so, what are the gases? I am reasonably certain I am not the only one waiting to get clues on this.

On another personal level, as some might know, I have published an ebook (Guidance Waves) that offers an alternative interpretation of quantum mechanics that, like de Broglie and Bohm, assumes there is a wave, but there are two major differences, one of which is that the wave transmits energy (which is what all other waves do). The wave still reflects probability, because energy density is proportional to mass density, but it is not the cause. The advantage of this is that for the stationary state, such as in molecules, that the wave transmits energy means the bond properties of molecules should be able to be represented as stationary waves, and this greatly simplifies the calculations. The good news is, I have made what I consider good progress on expanding the concept to more complicated molecules than outlined in Guidance Waves and I expect to archive this sometime next year.

Apart from that, my view of the world scene has not got more optimistic. The US seems determined to try to tear itself apart, at least politically. ISIS has had severe defeats, which is good, but the political futures of the mid-east still remains unclear, and there is still plenty of room for that part of the world to fracture itself again. As far as global warming goes, the politicians have set ambitious goals for 2050, but have done nothing significant up to the end of 2017. A thirty-year target is silly, because it leaves the politicians with twenty years to do nothing, and then it would be too late anyway.

So this will be my last post for 2017, and because this is approaching the holiday season in New Zealand, I shall have a small holiday, and resume half-way through January. In the meantime, I wish all my readers a very Merry Christmas, and a prosperous and healthy 2018.

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Ross 128b a Habitable Planet?

Recently the news has been full of excitement that there may be a habitable planet around the red dwarf Ross 128. What we know about the star is that it has a mass of about 0.168 that of the sun, it has a surface temperature of about 3200 degrees K, it is about 9.4 billion years old (about twice as old as the sun) and consequently it is very short of heavy elements, because there had not been enough supernovae that long ago. The planet is about 1.38 the mass of Earth, and it is about 0.05 times as far from its star as Earth is. It also orbits its star every 9.9 days, so Christmas and birthdays would be a continual problem. Because it is so close to the star it gets almost 40% more irradiation than Earth does, so it is classified as being in the inner part of the so-called habitable zone. However, the “light” is mainly at the red end of the spectrum, and in the infrared. Even more bizarrely, in May this year the radio telescope at Arecibo appeared to pick up a radio signal from the star. Aliens? Er, not so fast. Everybody now seems to believe that the signal came from a geostationary satellite. Apparently here is yet another source of electromagnetic pollution. So could it have life?

The first question is, what sort of a planet is it? A lot of commentators have said that since it is about the size of Earth it will be a rocky planet. I don’t think so. In my ebook “Planetary Formation and Biogenesis” I argued that the composition of a planet depends on the temperature at which the object formed, because various things only stick together in a narrow temperature range, but there are many such zones, each giving planets of different composition. I gave a formula that very roughly argues at what distance from the star a given type of body starts forming, and if that is applied here, the planet would be a Saturn core. However, the formula was very approximate and made a number of assumptions, such as the gas all started at a uniform low temperature, and the loss of temperature as it migrated inwards was the same for every star. That is known to be wrong, but equally, we don’t know what causes the known variations, and once the star is formed, there is no way of knowing what happened so that was something that had to be ignored. What I did was to take the average of observed temperature distributions.

Another problem was that I modelled the centre of the accretion as a point. The size of the star is probably not that important for a G type star like the sun, but it will be very important for a red dwarf where everything happens so close to it. The forming star gives off radiation well before the thermonuclear reactions start through the heat of matter falling into it, and that radiation may move the snow point out. I discounted that largely because at the key time there would be a lot of dust between the planet and the star that would screen out most of the central heat, hence any effect from the star would be small. That is more questionable for a red dwarf. On the other hand, in the recently discovered TRAPPIST system, we have an estimate of the masses of the bodies, and a measurement of their size, and they have to have either a good water/ice content or they are very porous. So the planet could be a Jupiter core.

However, I think it is most unlikely to be a rocky planet because even apart from my mechanism, the rocky planets need silicates and iron to form (and other heavier elements) and Ross 128 is a very heavy metal deficient star, and it formed from a small gas cloud. It is hard to see how there would be enough material to form such a large planet from rocks. However, carbon, oxygen and nitrogen are the easiest elements to form, and are by far the most common elements other than hydrogen and helium. So in my theory, the most likely nature of Ross 128b is a very much larger and warmer version of Titan. It would be a water world because the ice would have melted. However, the planet is probably tidally locked, which means one side would be a large ocean and the other an ice world. What then should happen is that the water should evaporate, form clouds, go around the other side and snow out. That should lead to the planet eventually becoming metastable, and there might be climate crises there as the planet flips around.

So, could there be life? If it were a planet with a Saturn core composition, it should have many of the necessary chemicals from which life could start, although because of the water/ice live would be limited to aquatic life. Also, because of the age of the planet, it may well have been and gone. However, leaving that aside, the question is, could life form there? There is one restriction (Ranjan, Wordsworth and Sasselov, 2017. arXiv:1705.02350v2) and that is if life requires photochemistry to get started, then the intensity of the high energy photons required to get many photochemical processes started can be two to four orders of magnitude less than what occurred on Earth. At that point, it depends on how fast everything that follows happens, and how fast the reactions that degrade them happen. The authors of that paper suggest that the UV intensity is just too low to get life started. Since we do not know exactly how life started yet, that assessment might be premature, nevertheless it is a cautionary point.

A Giant Planet Around a Dwarf Star

The news here, at least, has made much of the discovery of NGTS-1b, described as a giant planet orbiting a dwarf star. It is supposed to be the biggest planet ever found around such a small star, and it is supposed to be inexplicable how such a big planet could form. One key point that presumably everyone will agree with is, a small star forms because there is less gas and dust in the cloud that will form the star than in the cloud that forms a big star. Accordingly there is less total material to form a planet. Missing from that statement is the fact that in all systems the amount of mass in the planets is trivial compared to the mass of the star. Accordingly, there is nothing at all obscure about an unexpectedly big planet if the planet was just a bit more efficient at taking material that would otherwise go into the star.

So, a quick reality check: the star is supposed to be about 60% the size of the sun, and the planet is about 80% the mass of Jupiter, but has a somewhat larger radius. Planets up to twenty times the size of Jupiter are known around stars that are not more than about three times the size of our sun, so perhaps there is more being made of this “big planet” than is reasonable.

Now, why is it inexplicable how such a large planet could form around a small star, at least in standard theory? The mechanism of formation of planets in the standard theory is that first gas pours in, forms the star, and leaves a residual disk (the planetary accretion disk), in which gas is essentially no longer moving towards the star. That is not true; the star continues to accrete, but several orders or magnitude more slowly. The argument then is that this planetary accretion disk has to contain all the material needed to form the planets, and they have to form fast enough to get as big as they end up before the star ejects all dust and gas, which can take somewhere up to 10 million years (10 My), with a mean of about 3 My. There is some evidence that some disks last at least 30 My. Now the dust collides, sticks (although why or how is always left out in the standard theory) and forms planetesimals, which are bodies of asteroid size. These collide and form bigger bodies, and so on. This is called oligarchic growth. The problem is, as the bodies get larger, the distance between them increases and collision probability falls away, not helped by the fact that the smaller the star, the slower the orbiting bodies move, the less turbulent it will be, so the rate of collisions slows dramatically. For perspective purposes, collisions in the asteroid belt are very rare, and when they occur, they usually lead to the bodies getting smaller, not bigger. There are a modest number of such families of detritus asteroids.

The further out the lower the concentration of matter, simply because there is a lot more space. A Jupiter-sized body has to grow fast because it has to get big enough for its gravity to hold hydrogen, and then actually hold it, before the disk gases disappear. Even accreting gas is not as simple as it might sound, because as the gas falls down the planetary gravitational field, it gets hot, and that leads to some gas boiling off back to space. To get going quickly, it needs more material, and hence a Jupiter type body is argued (correctly, in my opinion) to form above the snow line of water ice. (For the purposes of discussion, I shall call material higher up the gravitational potential “above”, in which case “below” is closer to the star.) It is also held that the snow line is not particularly dependent on stellar mass, in which case various planetary systems should scale similarly. With less material around the red dwarf, and as much space to put it in, everything will go a lot slower and the gas will be eliminated before a planet is big enough to handle it. Accordingly, it seems that according to standard theory, this planet should not form, let alone be 0.036 A.U. from the star.

The distance from the star is simply explained in any theory: it started somewhere else and moved there. The temperature at that distance is about 520 degrees C, and with solar wind it would be impossible for a small core to accrete that much gas. (The planet has a density of less than 1, so like Saturn it would float if put in a big enough tub of water.) How would it move? The simplest way would be if we imagined a Jupiter and a Saturn formed close enough together, when they could play gravitational billiards, whereby one moves close to the star and the other is ejected from the system. There are other plausible ways.

That leaves the question of how the planet forms in the first place. To get so big, it has to form fast, and there is evidence to support such rapid growth. The planet LkCa 15b is around a star that is slightly smaller than the sun, it is three times further out than Jupiter, and it is five times bigger than Jupiter. I believe this makes our sun special – the accretion disk must have been ejected maybe as quickly as 1 My. Simulations indicate that oligarchic growth should not have led to any such oligarchic growth that far out. My explanation (given in my ebook “Planetary Formation and Biogenesis”) is that the growth was actually monarchic. This is a mechanism once postulated by Weidenschilling, in 2004 (Weidenschilling, S., 2004. Formation of the cores of the outer planets. Space Science Rev. 116: 53-56.) In this mechanism, provided other bodies do not grow at a sufficient rate to modify significantly the feed density, a single body will grow proportionately to its cross-sectional area by taking all dust that is in its feed zone, which is augmented by gravitation. The second key way to get a bigger planet is to have the planetary accretion disk last longer. The third is, in my theory, the initial accretion is chemical, and the Jupiter core forms like a snowball, by water ice compression fusing. Further, I argue it will start even while the star is accreting. That only occurs tolerably close to the melting point, so it is temperature dependent. The temperatures are reached very much closer to the star for a dwarf. Finally, the planet forming around a dwarf has one final growth advantage: because the star has a lower gravity, the gas will be drifting towards the star more slowly, so the growing planet, while having a less dense feed, also receives a higher fraction of the feed.

So, in my opinion, apart from the fact the planet is so lose to the star, so far there is nothing surprising about it at all, and the mechanisms for getting it close to the star are there, and there are plenty of other “star-burning” planets that have been found.

Why has the monarchic growth concept not taken hold? In my opinion, this is a question of fashion. The oligarchic growth mechanism has several advantages for the preparation of scientific papers. You can postulate all sorts of initial conditions and run computer simulations, then report those that make any sense as well as those that don’t (so others don’t waste time.) Monarchic growth leaves no real room for scientific papers.

The Fermi Paradox and Are We Alone in the Universe?

The Fermi paradox is something like this. The Universe is enormous, and there are an astronomical number of planets. Accordingly, the potential for intelligent life somewhere should be enormous, but we find no evidence of anything. The Seti program has been searching for decades and has found nothing. So where are these aliens?

What is fascinating about this is an argument from Daniel Whitmire, who teaches mathematics at the University of Arkansas and has published a paper in the International Journal of Astrobiology (doi:10.1017/S1473550417000271 ). In it, he concludes that technological societies rapidly exterminate themselves. So, how does he come to this conclusion. The argument is fascinating relating to the power of mathematics, and particularly statistics, to show or mislead.

He first resorts to a statistical concept called the Principle of Mediocrity, which states that, in the absence of any evidence to the contrary, any observation should be regarded as typical. If so, we observe our own presence. If we assume we are typical, and we have been technological for 100 years (he defines being technological as using electricity, but you can change this) then it follows that our being average means that after a further 200 years we are no longer technological. We can extend this to about 500 years on the basis that in terms of age a Bell curve is skewed (you cannot have negative age). To be non-technological we have to exterminate ourselves, therefore he concludes that technological societies exterminate themselves rather quickly. We may scoff at that, but then again, watching the antics over North Korea can we be sure?

He makes a further conclusion: since we are the first on our planet, other civilizations should also be the first. I really don’t follow this because he has also calculated that there could be up to 23 opportunities for further species to develop technologies once we are gone, so surely that follows elsewhere. It seems to me to be a rather mediocre use of this principle of mediocrity.

Now, at this point, I shall diverge and consider the German tank problem, because this shows what you can do with statistics. The allies wanted to know the production rate of German tanks, and they got this from a simple formula, and from taking down the serial numbers of captured or destroyed tanks. The formula is

N = m + m/n – 1

Where N is the number you are seeking, m is the highest sampled serial number and n is the sample size (the number of tanks). Apparently this was highly successful, and their estimations were far superior to intelligence gathering, which always seriously overestimated.

That leaves the question of whether that success means anything for the current problem. The first thing we note is the Germans conveniently numbered their tanks, and in sequence, the sample size was a tolerable fraction of the required answer (it was about 5%), and finally it was known that the Germans were making tanks and sending them to the front as regularly as they could manage. There were no causative aspects that would modify the results. With Whitmire’s analysis, there is a very bad aspect of the reasoning: this question of whether we are alone is raised as soon as we have some capability to answer it. Thus we ask it within fifty years of having reasonable electronics; for all we know they may still be asking it a million years in the future, so the age of technological society, which is used to base the lifetime reasoning, is put into the equation as soon as it is asked. That means it is not a random sample, but causative sample. Then on top of that, we have a sample of one, which is not exactly a good statistical sample. Of course if there were more samples than one, the question would answer itself and there would be no need for statistics. In this case, statistics are only used when they should not be used.

So what do I make of that? For me, there is a lack of logic. By definition, to publish original work, you have to be the first to do it. So, any statistical conclusion from asking the question is ridiculous because by definition it is not a random sample; it is the first. It is like trying to estimate German tank production from a sample of 1 and when that tank had the serial number 1. So, is there anything we can take from this?

In my opinion, the first thing we could argue from this Principle of Mediocrity is that the odds of finding aliens are strongest on earth-sized planets around G type stars about this far from the star, simply because we know it is at least possible. Further, we can argue the star should be at least about 4.5 billion years old, to give evolution time to generate such technological life. We are reasonably sure it could not have happened much earlier on Earth. One of my science fiction novels is based on the concept that Cretaceous raptors could have managed it, given time, but that still only buys a few tens of millions of years, and we don’t know how long they would have taken, had they been able. They had to evolve considerably larger brains, and who knows how long that would take? Possibly almost as long as mammals took.

Since there are older stars out there, why haven’t we found evidence? That question should be rephrased into, how would we? The Seti program assumes that aliens would try to send us messages, but why would they? Unless they were directed, to send meaningful signals over such huge distances would require immense energy expenditures. And why would they direct signals here? They could have tried 2,000 years ago, persisted for a few hundred years, and given us up. Alternatively, it is cheaper to listen. As I noted in a different novel, the concept falls down on economic grounds because everyone is listening and nobody is sending. And, of course, for strategic reasons, why tell more powerful aliens where you live? For me, the so-called Fermi paradox is no paradox at all; if there are aliens out there, they will be following their own logical best interests, and they don’t include us. Another thing it tells me is this is evidence you can indeed “prove” anything with statistics, if nobody is thinking.

Star and Planetary Formation: Where and When?

Two posts ago, as a result of questions, I promised to write a post outlining the concept of planetary accretion, based on the current evidence. Before starting that, I should explain something about the terms used. When I say something is observed, I do not mean necessarily with direct eyesight. The large telescopes record the light signals electronically, similarly to how a digital camera works. An observation in physics means that a signal is received that can be interpreted in one only certain way, assuming the laws of physics hold. Thus in the famous two-slit experiment, if you fire one electron through the slits, you get one point impact, which is of too low an energy for the human eye to see. Photomultipliers, however, can record this as a pixel. We have to assume that the “observer” uses laws of physics competently.

The accretion of a star almost certainly starts with the collapse of a cloud of gas. What starts that is unknown, but it is probably some sort of shock wave, such as a cloud of debris from a nearby supernova. Another cause appears to be the collision of galaxies, since we can see the remains of such collisions that are accompanied by a large number of new stars forming. The gas then collapses and forms an accretion disk, and these have been observed many times. The gas has a centre of mass, and this acts as the centre of a gravitational field, and as such, the gas tries to circulate at an orbital velocity, which is where the rate of falling into the star is countered by the material moving sideways, at a rate that takes it away from the star so that the distance from the centre remains the same. If they do this, angular momentum is also conserved, which is a fundamental requirement of physics. (Conservation of angular momentum is why the ice skater spins slowly with arms outstretched; when she tucks her arms in, she spins faster.

The closer to the centre, the strnger gravity requires faster orbital velocity. Thus a stream of gas is moving faster than the stream just further from the centre, and slower than the stream just closer. That leads to turbulence and friction. Friction slows the gas, meaning it starts to fall starwards, while the friction converts kinetic energy to heat. Thus gas drifts towards the centre, getting hotter and hotter, where it forms a star. This has been observed many times, and the rate of stellar accretion is such that a star takes about a million years to form. When it has finished growing, there remains a dust-filled gas cloud of much lower gas density around it that is circulating in roughly orbital velocities. Gas still falls into the star, but the rate of gas falling into the star is at least a thousand times less than during primary stellar accretion. This stage lasts between 1 to 30 million years, at which point the star sends out extreme solar winds, which blow the gas and dust away.

However, the new star cannot spin fast enough to conserve angular momentum. The usual explanation is that gas is thrown out from near the centre, and there is evidence in favour of this in that comets appear to have small grains of silicates that could only be formed in very hot regions. The stellar outburst noted above will also take away some of the star’s angular momentum. However, in our system, the bulk of the angular momentum actually resides in the planets, while the bulk of the mass is in the star. It would seem that somehow, some angular momentum must have been transferred from the gas to the planets.

Planets are usually considered to form by what is called oligarchic growth, which occurs after primary stellar accretion. This involves the dust aggregating into lumps that stick together by some undisclosed mechanism, to make first, stone-sized objects, then these collide to form larger masses, until eventually you get planetesimals (asteroid-sized objects) that are spread throughout the solar system. These then collide to form larger bodies, and so on, at each stage collisions getting bigger until eventually Mars-sized bodies collide to form planets. If the planet gets big enough, it then starts accreting gas from the disk, and provided the heat can be taken away, if left long enough you get a gas giant.

In my opinion, there are a number of things wrong with this. The first is, the angular momentum of the planets should correspond roughly to the angular momentum of the dust, which had velocity of the gas around it, but there is at least a hundred thousand times more gas than dust, so why did the planets end up with so much more angular momentum than the star? Then there is timing. Calculations indicate that to get the core of Jupiter, it would take something approaching 10 million years, and that assumes a fairly generous amount of solids, bearing in mind the solid to gas ratio. At that point, it probably accretes gas very quickly. Get twice as far away from the star, and collisions are much slower. Now obviously this depends on how many planetesimals there are, but on any reasonable estimate, something like Neptune should not have formed. Within current theory, this is answered by having Neptune and Uranus being formed somewhere near Saturn, and then moved out. To do that, while conserving angular momentum, they had to throw similar masses back towards the star. I suppose it is possible, but where are the signs of the residues? Further, if every planet is made from the same material, the same sort of planet should have the same composition, but they don’t. The Neptune is about the same size as Uranus, but it is about 70% denser. Of the rocky planets, Earth alone has massive granitic/feldsic continents.

Stronger evidence comes from the star called LkCa 15 that apparently has a gas giant forming that is already about five times bigger than Jupiter and about three times further away. The star is only 3 million years old. There is no time for that to have formed by this current theory, particularly since any solid body forming during the primary stellar accretion is supposed to be swept into the star very quickly.

Is there any way around this? In my opinion, yes. I shall put up my answer in a later post, although for those who cannot wait, it is there in my ebook, “Planetary Formation and Biogenesis”.

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.