I wrote an article for the October edition of the Royal Statistical Society’s Significance magazine about statistics and exoplanets. You can download a .pdf copy here.
-Carl Sagan. Cosmos
In my last post I discussed how it was possible to make tentative estimates about the total amount of time that a planet spends in the habitable zone, also known as its habitable period, and why this is important. In this post, I’d like to put numbers to those estimates.
This simple model, the results of which are outlined in the image above, estimates the Earth’s total habitable period to be approximately 4.91 billion years, meaning that it will end about 370 million years from now. That sounds like a long time, and in the context of human time-scales, it certainly is. Even geologically, the world of 370 million years ago was a very different place. It was the height of the Late Devonian period, and a full 172 million years after the Cambrian explosion saw the rapid diversification and speciation of some the earliest complex eukaryote life. The first forests were in the process of transforming the landscape of the supercontinent Gondwana, unconstrained by the lack of large herbivorous animals, and the first tetrapods were appearing in the fossil record. Who knows what transformations the world and life will undergo during the next 370 million years?
I should note that the error bars for these numbers are high, and I’m making no concrete predictions here for the inhabitants of the world 369 million years from now to call me out on. The habitable zone as a theory itself is fraught with assumptions that are, at this stage of understanding, regrettably necessary and regularly challenged and amended.
The Clock is Ticking
-William Shakespeare, Sonnet LX
It remains intrinsically unsettling to consider the fact that at some point our lovely blue-green home planet will eventually lose its ability to support life. It is certain that, whether after 4.91 billion years or not, the edge of the gradually advancing theoretical boundary of habitability will near planet Earth; now an apocalyptic world of blistering heat and desolation, unrecognisable from today’s lush, watery paradise. As Sol’s mass, radiative output and surface temperature steadily increase, the Earth’s climate will eventually become scorching. The fundamental biogeochemical mechanisms that help to regulate the Earth’s climate will break down, buckling under the strain of the ever encroaching Sun, and a ‘runaway greenhouse‘ crisis will result. Caused by the evaporation of the oceans and the initiation of a irreversible water vapour/temperature feedback mechanism, the runaway greenhouse is thought to be responsible for the of climate of Venus today. High temperatures result in more water vapour in the air and higher humidity, which in turns boosts the temperature further causing more evaporation and more humidity. Eventually the Earth will become enveloped in thick, impenetrable cloud, insulating the surface and acting like an planet-wide pressure cooker, undoubtedly heralding the end of life on the Earth as we know it.
As the Sun grows larger and hotter, high energy particles from the solar wind will eventually strip away this thick atmosphere which will be forever lost to space. The parched, molten husk of the Earth, former home to countless organisms and every human ever to exist, as well as the stage to every single event, from the minuscule to the revolutionary that took place for nearly 5 billion years, will probably be devoured by the Sun long after it has become inhospitable for life, an incomprehensibly distant 7 billion years from now.
The Earth, my friends, is lost. But fear not, perhaps we could move out to Mars? Our dusty neighbour will move into the habitable zone approximately 1.7 billion years from now, and stay there for the remainder of the Sun’s main sequence lifetime. The Sun in it’s death throes will make for an incredible sight in the Martian sky. However, Mars has a very chaotic orbit, making it difficult to determine exactly where it will be in the distant future. On top of all this, it’s hard to predict what conditions will be like around the ageing Sun.
Well, so much for the Earth and Mars. Let’s hope that in the preceding 370 million years our descendants make it to a better world.
The Lives of Planets
The Super-Earth Gliese 581d (top left of plot) has an approximate habitable period of over 50 billion years. I don’t know about you, but I have real difficultly grasping the truly unfathomable immensity of that amount of time. Research suggests that its star, red dwarf Gliese 581, is approximately 8 billion years old, and therefore the habitable zone has been home to Gliese 581d for 1.4 times as long as the Earth has existed for, yet it is only 13% of the way through its total habitable period. Still, this isn’t to say that it’s ‘habitable’; there are plenty of other factors (its large mass for example) that suggests that it’s not a place where life would thrive. Although, given 50 billion years who knows what evolution could throw up?
Gliese 667Cc, also orbiting a red dwarf star, will be in the habitable zone for 1.8 billion years because it formed straddling the inner edge – it won’t be (relatively) long until the heat of its star overwhelms its ability to maintain a habitable environment, if it has one at all. It’s a similar story for the Super-Earth HD 85512 b. Despite it’s location in the habitable zone, it’s still too close to be habitable for any considerable length of time – a mere 603 million years which, if we draw on Earth’s evolutionary history for comparison, is barely enough time for the denizens of the Cambrian to make themselves comfortable, if we extrapolate backwards (and ignore the ~3.5 billion years that it took to get to this stage in the first place).
Kepler 22b is another excellent candidate for a habitable planet, orbiting well within the habitable zone and remaining there for 3.4 billion years. On Earth, 3.4 billion years ago, it is thought that the first primitive organisms had emerged and were building reefs (stromatolites) and going about their daily business of dividing and multiplying – the kind of stuff that modern bacteria tend to fill their lives with. From these humble beginnings we emerged eons later; perhaps the same can be true on Kepler 22b?
In the End…
I realise this has been quite a long article, and I appreciate you sticking it out to the end. I hope that you found it as interesting to read as I did to write. The concept of habitability through time hasn’t been explored in great detail, and I hope to refine these numbers and tweak the model and its assumptions to improve the accuracy of the estimates in the future. Nevertheless, I found it an interesting, and rather humbling, thought experiment if nothing else.
Perspective is important, and yet always in short supply. We’re currently 92% of the way through our planet’s habitable period, enjoying the twilight years of its habitable lifetime. We have to remember that the Earth isn’t going to be able to shelter us indefinitely and that all planets’ lives come to an end at some point. It’s worth bearing that mind when considering that despite our delusions of grandeur, our brief residence on this planet has been a fleeting blip in its long and tumultuous history. Our future may well be too.
As you may know if you frequent this blog often, I spend a fair amount of time writing about planets that astronomers spend a lot more time discovering. My main interest in these worlds lies with their ‘habitability’, a rather esoteric and loosely defined term that is primarily concerned with describing how broadly livable these planets are, in a very Earthcentric way. Planetary habitability is an extremely complex recipe that turns climatic, planetary and geological ingredients, added in just the right quantities, into a warm, salty, non-toxic broth. Perhaps life on other planets, if it exists, has completely different requirements, but without a good sample of inhabited planets teeming with life we can’t really be sure and have to make this assumption for now.
A reasonably good place to start looking for planets hosting these conditions is the ‘habitable zone‘ of stars, a concept that I’ve discussed before. The habitable zone describes an area around a star where a planet, if it was discovered to be orbiting within this area, could have liquid water on its surface. Stars of different masses and classifications have different habitable zone distances, and not all planets in the habitable zone are habitable: some may be too massive, others too small, many wouldn’t have the correct mix of atmospheric constituents, others may have no atmosphere at all. In fact, there are more reasons to think that planets, whether inside or outside the habitable zone, are more likely to be completely unsuitable for (Earth-like) life than there are to consider the opposite.
However, whilst habitability is variable in space, it is almost certainly variable in time as well. The habitable zone isn’t a fixed distance: its boundaries move outwards as the star undergoes main-sequence evolution, growing larger and hotter over time. More massive stars (classifications F, G and K) have the shortest main sequence lifetimes and therefore the habitable zone boundaries around these stars migrate outwards at a proportionally more rapid rate. Low mass stars, M-stars for example, have extensive lifetimes on the order of tens or hundreds of billions of (Earth) years, and therefore their habitable zones are relatively more static in time.
The Habitable Period: A Measure of Habitability Through Time
The time that a planet spends within the habitable zone can be considered its ‘habitable period‘. The habitable period of a planet is an important factor when considering the possibility of life on these worlds. A planet with a long habitable period is perhaps more likely to host complex organisms that require more time to evolve, if we make the assumption that evolution by natural selection is a universal constant, operating in a similar way in potential exobiological systems as it does on Earth. An alternative means of speciation has not been discovered on Earth, and natural selection has withstood 200 years of intense scientific scrutiny and analysis relatively unscathed. As before, with a sample of one assumptions have to be made.
Building on this idea, if it is possible to determine the extent of the habitable zone at the beginning and end of the star’s main sequence lifetime using modelling techniques, and estimate the approximate age of the star, then a rate of outward migration of the boundaries of the habitable zone can be derived and quantifying the habitable periods of these planets becomes a possibility.
The figures above go some what to illustrating this point: the image on the left shows the extent of the habitable zone of different stars at the stage at which the star enters the ‘main sequence‘ – the beginning of its hydrogen-burning life. I’ve included the Earth, Mars and the confirmed habitable zone exoplanets from the Habitable Exoplanet Catalog and plotted them at their semi-major axes. Note that the Earth and Kepler 22b are comfortably within the warming embrace of their respective suns’ habitable zone at this stage, whilst the other planets remain fairly peripheral. The figure on the right shows the same planets in the same relative orbital locations, but at the end of their star’s lives. Earth, Kepler 22b and most of the other planets, with the welcome exception of Mars (not likely to be at this location in the future anyway because of its chaotic orbit), have all been relegated to the dangerous and inhospitable ‘hot zone’ nearest the star as the boundaries of the habitable zone migrated past their positions at some point during stellar evolution. The rate at which the imaginary boundaries move outwards is proportional to the mass of the star, as discussed above.
I used a very simple model to estimate exactly how long these planets will spend in the habitable zone and I’ll post the results in the coming days.
Undoubtedly the most exciting exoplanet news of the past week is the discovery of a star system with a total of 9 potential planets, surpassing even our own Solar System in terms of planetary diversity. University of Hertfordshire astronomer Mikko Tuomi discovered the bustling planetopolis around the enigmatic star HD 10180, a Sun-like G-type main sequence star 127 light years distant, using a probabilistic Bayesian analysis technique.
HD 10180 has been known as a multi-planet system since 2010, but the last analysis of the HARPS data available for the star, carried out by Christopher Lovis last year, seemed to indicate a 6 or 7-planet system was most likely. However, the novel probabilistic methods used by Tuomi are more computationally intense than those previously applied, and confirm the findings of Lovis whilst also adding a further two planets to the planetary inventory of HD 10180.
Tuomi’s Bayesian method, which seeks to evaluate a number of possible scenarios to determine which is most consistent with the observations, finds that an orbital configuration including an eighth and ninth planet, with masses 5.1 and 1.9 times that of the Earth respectively, returns a 99.7% probability.
The planets themselves, denoted HD 10180 b through h, are a diverse bunch, including two Earth-mass terran planets, one superterran, five neptunian and one jovian-sized planet, and all are contained within 3.5 AU – roughly the distance of the asteroid belt between Mars and Jupiter in our Solar System. Despite their proximity, the orbits are predicted to be stable over astronomical time.
The image above, from the Habitable Exoplanets Catalog, provides a visualisation of the orbital system and a comparison of the sizes of the planets. Note that one neptunian, HD 10180 g, is within the habitable zone but is unlikely to be habitable given its large mass, at least not by our definition.
That’s an extraordinary array of sizes and shapes crammed into a comparatively small area, and unseats our Solar System, with a certain 8 planets (excluding trans-neputunian objects, asteroids and dwarf planets – sorry Pluto fans!), from atop the pile of planetary richness, all the while adding to our understanding of the mechanisms of planetary system formation.
Whilst this is certainly an exciting discovery, should we be surprised by the apparent ubiquity of multi-planetary systems? It would be more unusual if this architecture wasn’t the norm, given model predictions. Writing for his Scientific American blog Life, Unbounded, astrobiologist Caleb Scharf notes that the combined masses of the HD 10180 planets would only amount to roughly half that of Jupiter, and given the star’s similarity to our own Sun, its proto-planetary circumstellar disk should have contained a similar amount of material. Therefore, it wouldn’t be surprising if more planets lurked in the HD 10180 system somewhere!
In fact, the same could be said for any of the planetary systems we have detected so far as well as those that we find in the future. Our detection techniques remain biased towards massive, short-period planets that produce readily identifiable signals, particularly when using the radial velocity method, and we suffer from the fact that we have only been collecting data for a few years and so may have missed more orbitally distant, longer period planets.
However, as with most exoplanet discoveries, the detection of this diverse family of worlds serves to put our planet into some wider perspective – to challenge the notion that Earth and this solar system are particularly unique, at least in an astronomical sense.
Solar systems, it seems, are everywhere.
Given that 80% of the stars in the Universe are M-type ‘red dwarfs’, research into the habitability of planets in these stars’ orbits has received relatively little attention in the past as they were generally considered unsuitable for hosting habitable planets due to their low mass and temperatures, as well as the propensity for planets in their orbit to be ‘tidally locked’. However, this trend has shown signs of reversal over the past few years, and habitability assessments have generally returned favourable reviews of M-star planets. The issue of tidal locking, where one hemisphere of a planet constantly faces the star, doesn’t seem to be resolved yet, but more research is being carried out and a definitive assessment may be forthcoming soon.
A paper published in Astrobiology this month has bolstered the habitability assessment of red dwarf systems even further. Manoj Joshi, now at the University of East Anglia, and Robert Haberle at the NASA Ames Research Center, have considered the effect that the longer wavelength spectra of M-stars may have on the ice-albedo feedback operating on planets within their habitable zones. Albedo describes the fractional reflectivity of a given surface, from 0 (nothing reflected, a hypothetical ‘black-body’ ) to 1 (all light reflected). On Earth, the albedo of ice is ~0.5 (50% of light reflected), whilst snow has an albedo of ~0.8.
The ice-albedo feedback is a fundamentally important abiotic feedback mechanism that has a powerful control over the planetary climate: it describes the ability of ice and snow to reflect light away from the surface, thereby cooling it further and causing more ice/snow to form, which continues to exacerbate the effect in what is termed a ‘positive’ or destabilising feedback loop. More ice, more light reflected away, cooler temperatures, more ice and so on.
The ice-albedo feedback is thought to have been at least partially responsible for the ‘Snowball’ or ‘Slushball’ Earth events that occurred in the late Proterozoic eon, approximately 600 million years ago, which saw the Earth frozen from pole to pole, with possible refugia at the equator. This interpretation is still rather contentious within the geosciences, but most researchers agree that the Earth experienced a period of extreme glaciation around this time, but its full extent, and how the Earth emerged from this deep-freeze, is still not fully understood.
The amount of incident light, as well as atmospheric greenhouse effects, exhibit a strong control on the ability of the ice-albedo feedback to enter a ‘runaway’ state by preventing temperatures from falling below a critical level of ice cover. Accordingly, this mechanism is often considered a controlling factor on the outer boundary of the habitable zone because of its very powerful ability to destabilise the planetary environment into an irreversible state of complete glaciation.
Joshi and Haberle constructed a simple model to test how the the ice-albedo feedback would operate on planets within the habitable zones of M-stars when considering the longer wavelength, lower energy emissions of these stars. Red dwarfs, as their name suggests, emit much of their radiation in the red and near-infrared portion of the electromagnetic spectrum. Observations from the red dwarfs Gliese 436 and GJ 1214 mentioned by the authors show that they emit much of their radiation at wavelengths greater than 0.7 μm, and significantly more in the 3 to 10 μm region than would be expected from a ‘black-body’ hypothesised M-type of a similar temperature. The albedo of ice and snow begins to decrease at wavelengths greater than 1 μm, and therefore the albedo of snow and ice covered surfaces on planets in the orbit of red dwarfs would be proportionally lower than that of the same surface on Earth (or any other planet in orbit around a G- or K-type star), meaning they reflect less radiation away from the surface, and that the ice-albedo feedback mechanism is weakened. For example, the authors show that snow or ice covered surfaces on planets orbiting GJ1214 may have albedos of 0.43 and 0.23 respectively, representing a significant decrease in the amount of incident light reflected from the surface and a dampening of the ice-albedo feedback mechanism.
Because of the diminished effect of the ice-albedo feedback mechanism around red dwarfs, the authors propose that their habitable zone may be 10-30% further from the star than was previously considered. This finding has a significant impact on the search for habitable exoplanets and for astrobiology, and, as is often the case with good science, has been drawn from a relatively simple experiment – in this case, by analysing the reflectivity of frozen or snowy surfaces under the observed radiative regime of red dwarfs. It seems that the tide really is turning in terms of our understanding of the habitability of planets in the orbits of red dwarfs, and that these numerous and ubiquitous stars should receive renewed research and observational attention.
Click here for the Astrobiology article (requires subscription).
Manoj M. Joshi and Robert M. Haberle (2012). Suppression of the water ice and snow albedo feedback on planets orbiting red dwarf stars and the subsequent widening of the habitable zone Astrobiology, 12 (1) DOI: http://arxiv.org/abs/1110.4525
So, more exciting news from the Kepler team: Kepler 20, a planetary system of five planets orbiting an Earth-like star 946 light years away in the constellation Lyra was announced at a NASA press conference yesterday. This time, none of the planets, from Kepler 20b through -f, were estimated to be orbiting within the habitable zone of Kepler 20 but instead had very short orbital periods of between 3 and 77 days, putting them all within the orbit of Mercury if superimposed onto our Solar System. The importance of the Kepler 20 system is that two of the planets (-e and -f) are Earth-sized, or possibly even smaller, making them the smallest extrasolar planets yet discovered. The remaining three planets -b,-c and -d are sub-Neptune sized. I’ve done my best to illustrate their orbital configurations here (click for a better view):
In terms of habitability, there is not much we can garner from the Kepler 20 planets. They are all in the ‘hot zone’ in very close proximity to the star. Their equilibrium temperatures are likely to range from 1014 °K (Kepler 20b) to 369 °K (Kepler 20d) – much too hot to host terrestrial biology within our current experience and understanding. It is possible, within ‘theoretical considerations‘ (i.e. planet formation model output), that Kepler 20e and -f are rocky, and that Kepler 20d may have a thick water-vapour atmosphere.
The larger Kepler 20 b, -c and -d were detected using a combination of photometry and astrometry, but due to their relatively small photometric and/or gravitational effect, the smaller Kepler 20 planets were uncovered using a statistical method that excluded the possibility that the detected signal was caused by a binary star eclipsing Kepler 20. The Kepler team have now provided proof that they are able to detect Earth-sized planets, even in very short period orbits. Coupled with the discovery of Kepler 22b in the habitable zone a few weeks ago, their brief of discovering Earth-like planets with the habitable zone of distant stars is partially complete – all we need now is to find an Earth-sized planet, like Kepler 20e, in the habitable zone, like Kepler 22b. It really is only a matter of time now.