Rarely-Done Planets

This is a guest post by David Waltham, Reader in Mathematical Geology at Royal Holloway, University of London. David’s new book, Lucky Planet, is out in April 2014. Visit his ‘Strange Worlds Catalogue‘ for more exoplanet oddities. 


One of the unlucky planets?

The issue of manmade global-warming seems far removed from questions of exoplanet habitability but there is a close link.  A planet whose climate is highly sensitive to greenhouse-gas changes is also a planet that responds strongly to increasing heat from its aging star; and it’s hard for such a world to remain habitable for long. The Earth seems to be one such world (that’s why global warming is such a threat) but it has never-the-less remained habitable for billions of years.  How it managed pull off this trick is an intriguing, but not particularly new, mystery.

In 1972 Carl Sagan and George Mullen recognized that, since our Sun produced 30% less heat when she was young, surface temperatures on the early Earth should have been far below freezing. However, geological evidence showed running water when our world was just a few hundred million years old.   Sagan and Mullen called this the faint young Sun paradox and, forty years later, there is still no consensus on how to resolve it.  However the concept of climate sensitivity, an idea refined over the last thirty years by climate scientists interested in anthropogenic global-warming, now gives us a clear framework for discussing the issues.

Climate sensitivity tells us how much warmer a planet becomes for a given increase in the heat it receives.  It’s a bit like going from gas-mark 5 to gas-mark 6; how much hotter does this make an oven?  At gas-mark 6 more gas is being burnt and temperature rises but, in a badly insulated oven for example, the increase would be less than expected.  Similarly, different planets warm up by different amounts for a given increase in heating and this difference in climate sensitivity depends upon the relative strengths of positive and negative feedbacks in the climate system.  As I’ll show below, the faint young Sun paradox occurs because Earth’s high climate sensitivity is incompatible with the flowing of liquid water on her surface when she was young.

Climate sensitivity is usually expressed by how much warmer the Earth becomes if carbon dioxide concentrations are doubled.  Doubling of CO2 is expected by the end of the current century and so this is a very concrete way of expressing the expected impact.  The best guess is that climate sensitivity is in the range 1.5-4.5 °C .  This range is largely based upon computer models of the present-day climate system but it is backed up by simulations of Earth’s past climate which only match observations when similar climate sensitivities are used .  If anything, these geological studies suggest that the computer estimates are too low but let’s be conservative and stick with the computer models.  What does a climate sensitivity of 3 °C predict concerning temperature changes over the life time of our planet?

To calculate this we need to re-express climate sensitivity in a slightly different way.  Doubling CO2 increases heating at the Earth’s surface by 3.7 Wm-2 but, to produce an equivalent amount of heating at ground level, solar radiation must go up by 5.3 Wm-2 because some is reflected back into space.  Thus, temperatures go up 3 °C if solar heating increases by 5.3 Wm-2.  Earth’s climate sensitivity is therefore 0.6 °C per Wm-2.  Heat from the Sun has actually gone up 90 Wm-2 over the last 4 billion years and so temperatures should have risen more than 50 °C.  This implies a young Earth that endured average temperatures near -40 °C and that is inconsistent with liquid water anywhere on our planet’s surface.

An obvious objection to this analysis is that the ancient climate system was very different to that of the modern Earth and so the present-day climate sensitivity may not be relevant.  That’s a fair point but we can get around it by concentrating instead on the Phanerozoic Eon (i.e. the last 542 million years) when there is no reason to think that climate sensitivity would have been massively different to today.  Solar heating has increased 15 Wm-2 over this time and so temperatures should have risen by about 10 °C but there is no evidence whatsoever for such a rise.  Analysis of oxygen isotopes in ancient marine organisms suggest that Phanerozoic temperatures have fluctuated around a steady mean or perhaps even dropped a little.  Thus, whether we look at the whole of Earth’s history or just the last half-billion years, there is no evidence for the expected overall warming despite the steadily increasing luminosity of our Sun.  What’s going on?

Tropical Sea Surface Temperatures over the Phanerozoic ()

Tropical Sea Surface Temperatures over the Phanerozoic (after Vizier et al., 1999)

The missing part of the puzzle is that Earth itself has evolved, both geologically and biologically, during its long history.  For example, the slow growth of the continents and the biological evolution of more effective rock-fragmenters (e.g. lichens and trees) has steadily increased the efficiency with which CO2 is removed from the atmosphere by the chemical reaction of acid-rain on volcanic rock.  Another greenhouse gas, methane, has also greatly declined through time as oxygen levels have grown following the evolution of photosynthesis.  Furthermore, land, especially plant-covered land, is more reflective than sea and so, as the continents grew and as they became colonized by life, more of the Sun’s heat has been reflected into space.  These processes, and perhaps others, cooled our planet as the Sun tried to warm it.

Two opposing forces therefore fought for dominance of climate trends and, coincidentally, roughly cancelled out.  But what produced this coincidence?  Some would ascribe it to the Gaia hypothesis that a sufficiently complex bio-geochemical system will inherently produce environmental stability.  However there’s no credible mechanism for this and, in any case, Gaia may have confused cause and effect: Earth’s complex biosphere didn’t produce a stable climate; rather a stable climate was a necessary precondition for a complex biosphere.  If this is right, then biospheres whose complexity and beauty rival that of the Earth will be rare in the Universe.  On the majority of those few worlds where life arises, it will all-too-soon be frozen by bio-geochemistry or roasted by its sun.  However a few worlds will, purely by chance, walk the fine line between these fates long enough for intelligent life to arise.  We live on one of those rare, lucky planets.

A Multiplicity of Worlds [RSS]

Earth-like planet (Image credit: Sean McMahon)

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.

Enough Time for Life: Part II

We are like butterflies who flutter for a day and think it’s forever.

 -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 figure plots the results as a function of star mass, running along the horizontal axis. The vertical axis is in units of billions of years, and is on a logarithmic scale. The dashed line running through the middle (‘mean habitable period’) represents the habitable period that would be expected if a planet was located right in the centre of the habitable zone at the beginning of the star’s lifetime. I’ve included it to highlight the fact that lower mass stars have longer habitable periods. I’ve also included the Earth and Mars, as well as the four habitable exoplanet candidates mentioned in the preceding post.

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

Like as the waves make towards the pebbl’d shore,
So do our minutes hasten to their end

 -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.

What Earth may look like 5-7 billion years from now – after the Sun swells and becomes a Red Giant. (Wikipedia)

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.

Enough Time for Life: Part I

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 habitable zone for stars of different masses at the point of entry on to the ‘main sequence’. The horizontal axis shows the distance from the star in astronomical units (AU) on a logarithmic scale. The dashed boundaries illustrate the uncertainty of the HZ when cloud cover is taken into account.


The habitable zone for stars of differing masses at the end of their main sequence evolution.

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.