A preliminary look into the astrophysics of Darkover by Esme n'ha Maire

FOREWORD: The following is written on the assumption that equations and all data are correct; please bear in mind that if this is not the case, then my findings will be in error! If anyone finds any errors, I would welcome an email pointing them out (esme.lancre@breathemail.net). I hope you find this of interest.

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One of the two things we know with certainty about the Sun of Darkover is that it appears red to the naked eye. The other is that it supports a cold, but human-habitable planet. Given these two facts, much can be extrapolated. In what follows, I look first at the possible characteristics of the Darkovan Sun, then at those of Darkover itself.

1.1 Overview

Red stars tend to be either very large and very luminous, or very small and very dim. Why this should be is beyond the scope of this article, but either poses problems for the possibility of human-habitable planets around them. Red giant stars are exceedingly large indeed, and if one were to replace our familiar Sun with one of them, the orbits of the planets out to Earth or even Mars would be within the surface of the star. This means that any solid planet would have to be orbiting much further away from its primary than Earth is from our Sun, which implies a longer orbit, and hence a longer year. Counteracting this, red giant stars are rather more massive than our Sun, which increases the orbital velocity for any given orbit, which shortens the orbital period. But these two effects do not exactly balance each other, and in general, habitable orbits around red giant stars will have periods of greater than one Terran Standard year.

Further, red giant stars being so huge as they are have a very high overall luminosity, despite their low surface temperature, and so can be easily seen from hundreds or even thousands of light-years away, and would likely be used as navigational beacons in interstellar travel. Cottmans star is noted in Rediscovery as being so unremarkable that it is only mentioned in an unabridged atlas, and therefore, I think we can safely rule out the possibility of its being a red giant. This leaves us with just one obvious possibility, that the Bloody Sun is a red main-sequence star, a red dwarf. Most more exotic solutions that may or may not exist can be discounted, because they would be remarkable enough that Cottmans Star would have attracted a constant stream of curious astrophysicists!

Given that our subject is a red dwarf star, the primary constraint on its characteristics is that of supporting a human-habitable planet. Essentially, the smaller - which given the way stars work also means redder- the star, the less likely it is that it can support human-habitable planets, for a number of reasons. The first is that it must be able to provide sufficient radiation to support such a planet, and the second is that it must do so at a distance such that the rotation of the planet is not tidally locked, eg. with one hemisphere always facing the sun and the other on darkness. The closer the planet is to its sun, the more likely the latter is. Also, in order to get adequate amounts of radiation from smaller stars, planets would have to be so close in that their sun would appear enormous in the sky compared to our own, something any Terranan visiting Darkover would comment on. Essentially, I feel that we should look first of all at the least difficult case, that of the biggest, warmest main-sequence star that appears definitely red to the naked eye. Hence, in what follows, I am assuming that Cottmans star is a type M0 main-sequence ("red dwarf") star.

Due to the characteristics of the physical processes within stars, massive stars have much shorter lifespans than their less massive relatives. Indeed, according to our current knowledge of the subject, some red stars are amongst the first stars that formed in the Universe. These early stars were originally composed of no more than the hydrogen and helium (and a tiny amount of lithium) created in the Big Bang. Whilst some of the original small red stars are still with us, and indeed, may outlive the lifespan of the type G yellow-dwarf star we know as our Sun, their more massive siblings have long since died in explosions which created heavier elements such as oxygen, carbon, nitrogen, iron and so on. It is important to remember that essentially all the elements with which we are familiar in everyday life here on Earth were created not in the Big Bang, but in the heart of massive stars that died billions of years ago.

Our assumption that Cottmans Star is a type M0 red dwarf, ie at the heavier end of red dwarfdom, and the fact that it has a terrestrial planet that is metal poor sit well together, therefore. Heavier red dwarfs tend to have a higher metal content than lighter ones, whilst still being metal-poor compared to yellow dwarfs like our Sun. Also, if metals are present, then so too will the lighter elements needed to create a terrestrial-type planet, although there is a question mark over whether there will be enough of them for the purpose. The two main ways in which enough of the right kind of planetary material might be acquired are through condensation of material from the nebula in which Cottmans Star was born, or through later accretion as Cottmans Star wandered through nebulae whilst orbiting the centre of the Galaxy. A third possibility - capture of planets formed elsewhere- is so extremely unlikely that it can safely be dismissed without further ado.

Frankly, I do not know enough to be able to choose which is the "best" possibility for the task in hand, that of investigating whether a planet like Darkover could potentially exist. However, the Universe has kindly arranged itself in such a way that perhaps we do not need to worry about this. W Baade proposed in 1944 that stars can be generally categorised into two Populations, type I being metal-rich highly luminous stars associated with the spiral arms of spiral galaxies (such as our own; there are other types of galaxy), and type II being old red stars found in the core and "halo" of our galaxy, as well as in a disc coexistent with the plane of our galaxy but much thicker than the main galactic disc. It is now known that in fact there is a continuum of populations shading between Baades Populations I and II. Essentially, the older the star, the more eccentric its orbit and the more highly inclined to the plane of the disc that orbit is likely to be. Also, older stars are more concentrated towards the galactic core.

This all fits rather well with other things we know of Cottmans Star from the Darkover novels; it is far from Terra, near the junction of two spiral arms, which places it well in toward the Galactic core. It has existed long enough for life to arise there (something exceedingly unlikely for a red giant star), is metal-poor, but has an orbit around the Galactic core eccentric enough to take it in and out of the plane of the discm and thus it would pass through spiral arms, with their matter-rich nebula, every now and then.

I propose, then, that Cottmans star is either a young population II or a very old population I star. Not one of the first stars to be born into our universe by any means, but still rather older than our Sun, and therefore metal-poor, with other characteristics such that it might be able to acquire suitable material with which to form at least one terrestrial type planet (ie; a rocky rather than a gaseous or iceball one), and that long enough ago that life had time to arise there. From our knowledge of stars generally, here is a set of data that might fit Cottmans Star:

Spectral type: M0V II

Bolometric magnitude: 8.25

Luminosity (Sol = 1) : .04

Surface temperature : 3,500 degrees K (subtract 273 to get degrees C)

Radius (Sol = 1) : .549

Mass (Sol = 1) : .489

The above data for an M0 dwarf star was taken from a table in Traveller Book 6, Scouts, which despite being a handbook for a role-playing game rather than a scholarly book on the subject contains a very useful and so far as I have been able to ascertain, accurate, summary of stellar characteristics, the like of which I have so far found nowhere in any serious books on astrophysics.

2.1 Overview

The main characteristic of Darkover that is of interest here is that it is human habitable, which puts constraints on how large its orbit is, and therefore, the length of its year. This is because the farther Darkover is from its sun, the colder it will be, as one might expect. However, the composition of the Darkovan atmosphere has a bearing on the matter, as does how Darkover looks from space. That is to say, the reflectivity or albedo of the planet, seen from space is important. The higher the albedo, the less energy that will be absorbed by the planet and, to a first approximation, the colder the planet will be. Matters are complicated by the fact that cloud, which has a comparitively high albedo, also traps infra-red radiation, thus helping to keep temperatures up. Similarly, the amount of certain gases, like carbon dioxide and methane, will affect the surface temperature, as they also trap infrared radiation. Collectively, this is the "greenhouse effect", and can make all the difference between habitability and non-habitability.

Finally, the very fact that Darkover had a Terran-breathable atmosphere when first discovered tells us that there must have been native life there already (which we know to be true!), as atmospheres anything like our oxygen-nitrogen one are, so far as we are aware, only produced by the action of living things on a pre-existing atmosphere of very different nature to that which we breathe today. The fact that the Darkovan atmosphere is still human breathable tells us that the biosphere is quite a healthy, robust, and sizeable one. The existence of large carnivores like the "Banshee" also argues for a well-established and relatively stable biosphere. Whilst life in the Domains may look precarious to Terrans, the planet as a whole is either teeming with life and has been for eons, or is in a slow decline from a period, not too long ago, when life was more abundant. Otherwise, there would not be so much free oxygen in the atmosphere. These matters are ones that I am not so well acquainted with as I am with things such as stellar characteristics and the celestial mechanics, and so in what follows I will have to make some assumptions that will bear further investigation by those more knowledgable in them than I.

Bearing in mind the considerations mentioned above, we can try to calculate Darkovers orbital radius about its sun. To start with, let us see how far out Earth would need to be from Cottmans Star in order to receive the same amount of radiation from Cottmans Star as we get from the Sun. This is simply calculated by noting that the luminosity of Cottmans star is just 4 percent that of our Sun. Luckily 4 per cent is one twenty-fifth, so by the inverse square rule (radiation decreases in intensity according to the square of the distance from the source of the radiation) Earth would need to orbit at one fifth the distance from Cottmans Star that ir does from the Sun in order to receive the same amount of radiation. We are now in a position to calculate the length of the "year" that such an orbit gives:

P=(D³/M)^.5 (Eqn.1)

Where P is the orbital period, in Earth years, D is the orbital radius in AU (calculated from Eqn.1), and M is the mass of the star the planet is orbiting (in Solar masses),which for Cottmans star we think is 0.489. In this case, we have

P=(.2³/.489)^.5

From this we get a value of .128 years, or about 46.7 Standard Terran days, give or take a day. From this we can see that we already have problems, as the Darkovan day and year are known to be not too dissimilar to the Terran equivalents, certainly within 50% of them. Even if we allow for the lower average temperature of Darkover compared to Earth, the orbit obtained is nothing like big enough to give a suitable year length.

The main differences between Darkover and Terra that we know of that are relevant here is that Darkover is colder, has lots of cloud cover and lots of snow (at least around the Domains), and has a similar atmosphere to Terra. For a rough guess at Darkovers albedo (the amount of incoming radiation reflected away into space by the planet) we can use the following table from Traveller Book 6 for typical albedo values:

Forest or field .10

Desert .20

Open water .02

Snow .85

Ice .55

Clouds .40 to .80

From this it can be seen that given that some 70% of Terra is open water with an albedo of .02 and an average albedo for the land surface of say .15, that for the overall albedo to be 0.39 means that cloud cover has a considerable effect. Even on Terra, somewhere around half of the surface is obscured by cloud at any given moment.

Let us assume that Darkover is, on average, some 15 degrees (Kelvin or Centigrade) cooler than Terra, on average, that is, it has a mean temperature of 273 degrees K, which is the freezing point of water. Further, let us guess the Darkovan albedo as being 0.5 These two data have conflicting effects with regard to orbital radius (and hence, orbital period). If you raise the albedo of a planet keeping its orbital radius the same, the planet will be colder. If Darkover does have an albedo as high as 0.5, then it will reflect 25% more radiation than Earth, and so by equation 1 will be in an orbit with a radius just 89% that which it would have with an albedo of 0.39. Clearly, this just makes the situation with regard to the Darkovan year length worse. Also, with such a small orbit, another effect has to be taken into account, tidal locking of the planetary rotation period. Planets too close to their primary star will have their rotation slowed by tidal effects such as to give a simple relation between the planetary rotation rate and the planetary year. In our Solar System, this is the case with Mercury, which has a year of 88 days and a day length fully two-thirds of the year length! With an orbital radius of .2 AU around a star massing over 40% that of our Sun, Darkover would surely suffer tidal locking, and thus almost certainly be rendered uninhabitable. It would certainly not seem even remotely close to Earth-normal from the surface, even if it were habitable.

Clearly Cottmans Star cannot be a red dwarf and possess a human-habitable planet. We must now look at possible alternatives, the least unpromising of which is that perhaps Cottmans Star is a small red giant. This, however, presents substantial problems in that such a star would either be a very young star still collapsing on its way to becoming a main-sequence star, or an older star in the latter phases of its life expanding and leaving the main sequence prior to almost exhausting its fuel and eventual collapse into a miniscule white dwarf.

In the former case, it is doubtful whether planets would have had time to form, let alone have life arise upon them, and the speed with which the star is developing is sufficiently rapid as to ensure that any potentially suitable planet would only receive a suitable amount of radiation for a few tens or at most hundreds of thousands of years. Before and after this period the temperature would be either too high or too low. In the latter case, any planets that may have been habitable during its main sequence phase would now be uninhabitably hot as the star expands to many times its former size, possibly engulfing some of the closer members of its planetary system.

However, this does leave us the possibility that a race living upon a habitable planet of the star during its main-sequence phase may have terraformed one of the outer planets in the same system and moved themselves there. Or perhaps Darkover is a planet terraformed by a race from another system altogether. This is not implausible, as mankind already has the capability, should it choose to use it, to terraform marginal planets, provided local conditions are not too extreme in certain ways. Mars is the prime candidate for human colonisation and terraforming in our solar system, capable of being rendered habitable to humans without special breathing equipment on a scale of only some few thousand years even with todays technology, whereas Venus has much greater problems that may necessitate tens or hundreds of thousands of years to overcome (not least of which is a very slow rotation period due to solar tidal effects). Let us now look at possible candidate star types.

The most obvious of these is a type K0V sub-giant, of luminosity 4.67, mass 2.3 and radius 3.3 times that of our Sun. Were Earth to orbit such a star, it would need to do so at a distance of 2.16 AU, and would have an orbital period of 2.09 years (about 765 Terran days). For a planet of similar albedo but 15 degrees cooler, the orbit might be some 5% larger,for an orbital period of about 823 days. However, if we assume a planet with an albeo 25% higher than Earths, then 25% more radiation is needed to obtain the same amount of radiation. Allowing for the cooler final average temperature required, this leads to:

Orbital radius: 2.03 AU

Orbital period: 1.91 Terran years (697 days)

Note that at a distance of 2.03 AU a star of 3.3 Solar radii would appear about .8 of a degree across to the naked eye, as against about .5 of a degree that our Sun appears to us, or some 60% larger across. Also, note that whilst type G sub-giants are physically smaller in both mass and radius, they are also more luminous, and yellow in colour. Type K sub-giants are the smallest sub-giants that do not look distinctly yellow/white to the eye.

Finally, sub-dwarf stars: to spare you the calculations, it transpires that for a K0 sub-dwarf of .117 Solar luminosity, .43 Solar mass and .4 Solar radius, the year-length for a Terran-type world would be about .3 Terran years, or 111 days. The Darkovan Sun would in this case appear to be just 17% larger in the sky than does our Sun. the situation is no better for other types of sub-dwarf.

Whilst it is a fairly easy to calculate the orbital radius and period given the type of star in question and the desired mean surface temperature for a broadly terrestrial planet, unfortunately matters aren't likely to be quite that simple. It isn't just the amount of radiation that a planet receives from its star that is important; the nature of it will have important effects, too, and I freely admit that at the time of writing I don't know enough about the subject to do more than point out things that bear further investigation.

For instance, a planet orbiting a bright type O star might have a habitable temperature, but it would also be deluged in far greater amounts of short-wave radiation (ultraviolet and x-rays) than Earth receives from its Sun. This may be ameliorated to some extent by the atmosphere - the more UV, the more ionisation that will occur in the upper atmosphere, ripping oxygen molecules apart to form ozone, which, of course, helps to block UV radiation. But ultimately, too much ionising radiation will render a planet uninhabitable, at least to land-based life as we know it.

Cottmans Star, on the other hand, if it were a dim type M dwarf star, would produce not only very little radiation compared to a type O star (or indeed, even compared to our own Sun), it would also produce extremely little ionising radiation, almost all of its output being in the red and infrared parts of the spectrum. This means that ionisation of the Darkovan atmosphere would be very weak, and mostly due to the background cosmic radiation levels. This, by the by, means that certain types of radio communications would be either difficult or maybe even impossible, but it also means that Darkovan life would be exposed to comparitively low levels of radiation compared to life on Terra, and therefore the mutation rate from this cause -one of the driving forces of evolution- would be low. Darkovan life might have evolved of its own accord, and possibly some considerable time before it arose on Earth, given the likely greater age of Cottmans Star. But if so, it is also likely to have evolved rather more slowly, assuming other factors affecting mutation rates are similar to those on Earth. (I should also add that Darkovers deficiency in metals also means deficiency in the most common radioactive substances, like uranium, which is considerably denser than metals like copper and iron. Thus naturally occurring background radiation from the soil will be very low, too).

If Cottmans Star is a type K sub-giant, the proportion of ionising radiation in its output would be between that from a type M and our own type G sun. And having accreted from a larger cloud of gas in the first place, the type K sub-giant would have more matter nearby from which to form planets, plus the incidenc of metals would be higher (though not so high as near a type G star).

This, of course, brings up the matter of whether life did arise of its own accord on Darkover (or indeed Terra!), or whether it arrived there from elsewhere. Certainly the fact that Chieri can interbreed with humans at all, never mind to produce viable offspring, suggests some kind of common ancestry for humans and Chieri, with all that that might imply. Perhaps the Chieri once had an interstellar civilisation and meddled with the evolution on Earth in some way before their denmise, leaving little or nothing of themselves but a small and declining population of their kind on Darkover? Perhaps the Chieri have evolved the capability of interbreeding with other reasonably similar life forms as a kind of survival trait? Less fantastically, perhaps a Lost Ship -maybe one that doesn't even set out and get lost until after the time of the later Darkover novels- got lost so far back in time that its inhabitants evolved into what we now know as Chieri? This, of course, is a matter for a novelist to settle!

That the radiation from Cottmans Star is generally at longer wavelengths than that from our own Sun has other consequences. Inagibe living in a world lit by orange or red floodlights… colour perception would be markedly affected. It isn't clear to me how strong this effect would be, I have made enquiries to find what lighting conditions would be like on an otherwise Terran-normal planet cirling a type K or M star, and have been unable to obtain a satisfactory answer. Certainly there'd be some light at the blue end of the spectrum produced by Cottmans Star, as well as a surplus (as far as humans are concerned) of red and infra-red. Whther the sky itself would still be blue, or dark blue, or maybe a rose pink, I have not been able to ascertain.

However, over sufficiently long periods of time, one might expect Terran-derived animals to adapt their eyesight to the different lighting conditions, either by evolving larger eyes, eyes sensitive to longer wavelengths, or both. And whilst the ten thousand years or so that humans have been on Darkover (due to their accicental displacement in time when their ship was lost) is short compared to the eons that life has had to evolve in on Earth, nevertheless, it is long enough for some degree of evolutionary drift and adaptation to have started. One might expect that Darkovan humans might see slightly better than Terranan at night, and also may see a little further into the red end of the spectrum -and not so far into the blue end.

Finally, plant life on Darkover would doubtless have evolved (or been bred) to make the most of the radiation they do receive (more low-energy red radiation, less harmful high-energy blue radiation), as well as adaptations to the harsh climate. Indeed, it is just possible that, barring the greater amount of snow and ice on the surface, Darkover may actually be more hospitable to life than Terra is, and its oceans could well be teeming with life (indeed, oceanic plant life would be vital in maintaining the atmospheric oxygen content) and those areas of land not either desert, rocky, or permanently or mostly under snow and ice could well have a great profusion of life of all sorts. However, it is extremely unlikely that such life would be human edible (or at least, capable of sustaining human life for long) or that native life would be able to cross-breed with Terran without fairly radical deliberate gene manipulation

When I first came across the tales of Darkover, I instinctively thought that the author had erred, and that a human-habitable planet couldn't possibly exist around a red dwarf star. This rough check of the matter indicates that sadly, this is in fact the case. However, if other factors within the stories do not rule out a year length approaching two terrestrial years, then Cottmans Star may just be a small sub-giant. However, Darkover as it currently is is then almost certainly the product of terraforming by someone. And if this is the case, it is possible that Darkover's overall albedo may be substantially higher than the .5 that I have estimated, which would reduce the orbital radius and hence the local year length. However, there is still the matter of the mix of radiation put out by such a star, and its effects on the Darkovan atmosphere. I do not know enough about the chemistry and physics of atmospheres to be sure as to whether this part of the situation may cause insuperable problems for the habitability of a Terran-like planet such as Darkover.

APPENDIX

Stellar spectra go in the sequence O,B,A,F,G,K,M, O being the hottest and M being the coolest. Gradations within these categories are numbered 0 to 9, with 0 being hotter than 9. So a type K9 is only a little hotter than a type M0. Most stars are in a grouping called the main sequence, where the hotter stars are also bigger and more massive. However, there are large massive red stars called red giants, and small hot stars called white dwarfs, as well. Astronomers recognise about half a dozen categories of stars based on their combination of mass and temperature. Main sequence stars are type V, which is why Cottmans Star, as I have initially imagined it, is a type M0V. The matter of the Population category is discussed adequately in the text, thus the full astronomical description of the star as M0V II.

Traveller Book 6; Scouts by Games Design Workshop, 1983

Macmillan Dictionary Of Astronomy, 2^nd Edition, Valerie Illingworth, 1985

Personal notes collected over many years (since about 1972) from various texts on astrophysics.

Esme n'ha Maire, Dec 2000 CE