On The Death of Planets

It’s been a long time since I’ve posted here!  I am in the thick of writing my thesis and getting a job lined up for after graduation.  Still, sometimes I can sneak away and write on my own time for half an hour.  This precludes me making big, well-researched posts like the one on different schools of origin-of-life research or the astrobiological gems of the solar system I’ve been planning.  But I have time to talk briefly about something I’ve been thinking about lately.

In my post “Space and Time – Part II” I sketched out my rough calculations about our place in star and biosphere order, coming to the conclusion that our sun is in around the last fifth of all stars that will ever exist and that our biosphere is somewhere between halfway and 30% of the way through the total complement of biospheres our universe will ever have.  This, however, did not address our position in ABSOLUTE time within 15 billion years of the start of an apparently open ended universe – only our position in the order of stars and planets that will ever exist.

Our sun is large, larger than something like 90% of all stars that exist.  This has interesting implications.  The bigger a star is, the brighter it is.  Brightness increases far faster than mass – for stars in the mass range near the sun, a star twice as massive is 16 times as bright, brightness going up with the fourth power of mass.  This means that star lifetime goes down with the cube of star mass.  A star half as big as the sun will glow stably for 8 times as long.  This, combined with the fact that most stars are small, means that the vast majority of star-years that will ever happen in the universe happen around tiny stars.  The smallest stars may burn for five trillion years, the epoch of star formation we are living through the latter days of constituting the barest tiny fraction of their early history.

This has not escaped the notice of professional astronomers.  An analysis much like what I put forward in “Space and Time – Part II” was put forward in a paper by Loeb, Batista, & Sloan in the latter half of 2016, entitled “Relative likelihood for life as a function of cosmic time“.  Their numbers are a little different due to fitting different datasets but the broad conclusion about the impending end of star formation over the future history of the universe is the same.  What these authors did that I did not do, however, was to integrate the total number of star-years occurring over the history of the universe as the huge burst of star formation that is winding down now finishes and the large stars die, followed by a slower and slower rate of death of smaller and smaller stars.  According to their data, if you go by total star years that will ever happen in the universe we are in something like the first thousandth of available time with the vast majority of star-years occurring in the far distant future around dim red dwarfs.  See here for a bit in the popular press about it.  They conclude that this means that either we are exceedingly early in the universe or small stars are unsuitable for biospheres, and that the average star mass at which we find ourselves at a typical time comes to something like 0.9 solar masses.


This analysis, however, leaves out something extremely important.  This is not surprising, because what it leaves out has nothing to do with stars and everything to do with planets.  Namely, it ignores something I think is of fundamental importance to the study of astrobiology:  geology and atmospheric science, and the fact that planets can die.

What does it mean for a planet to die?  We can take our own Earth as an example.  This planet has been in a state of pretty good homeostasis for the history of the solar system so far.  We have never lost our atmosphere or hydrosphere, and we have never popped into a runaway greenhouse mode like Venus – the surface has been clement since some time deep into the Hadean all the way through to today. This is largely due to something called the carbonate-silicate cycle.  CO2, a greenhouse gas that warms the planet, is belched out of the interior of the planet through volcanoes.  On Venus, once CO2 is in the atmosphere it stays there, never to be returned to rock.  That is not the case here.  Here, there are oceans.  CO2 dissolves in water and reacts with it, interconverting with the following formula:

CO2 + H2O -> CH2O3

The product of this reaction is carbonic acid, which reacts with dissolved minerals to form carbonate rock which sequesters carbon out of the atmosphere back into the geosphere.  This is paired with another reaction, catalyzed by the protons released by acids in water solutions:

SiO3 + 2H+ -> SiO2 + H2O

In this reaction, silicate rock thrust up to the surface by geological activity reacts with acids to form silica which again returns to the geosphere.  Both of these reactions proceed overall in the forward direction at the conditions found on Earth’s surface, with CO2 becoming carbonate rock and silicate rock becoming silica.  But deep inside the Earth at high pressures and temperatures, these reactions tend to run in the opposite direction, generating the carbon dioxide and silicate rock that are pushed to the surface.  This forms the longest timescale piece of the global carbon cycle.  On geological timescales this maintains rough equilibrium of Earth’s surface temperature, as the removal of CO2 into carbonate rock runs faster at high temperatures producing a negative feedback loop that alters atmospheric composition to prevent Earth from becoming too hot or cold.

This will NOT always be the case.  Our biosphere has an expiration date.  In our case, it comes from the steadily brightening sun.  All stars brighten during their stable lifetimes – they roughly speaking double in brightness over their time in the main sequence, before going through more drastic gyrations at the end of their life.  Our sun was about 70% as bright as it is now at the dawn of the solar system, and will wind up significantly brighter than it is now before it turns the corner and shoots off into the red giant state 5+ billion years from now.  Depending on whose climate models you use, the homeostatic mechanisms that apportion carbon between methane CO2 and carbonate rock and maintain roughly even temperatures over geological timescales on Earth will reach their breaking point somewhere between 300 megayears and 2 gigayears from now – the most likely timeframe seems to be about 1.2 gigayears (see Lenton & Bloh 2001, Biotic feedback extends the life span of the biosphere).

At this time, the energy pouring in from the sun will exceed the level at which even with zero carbon in the air we could avoid our oceans starting to evaporate excessively.  Water is an even better greenhouse gas than CO2, and once enough gets into the upper atmosphere it’s all over.  A runaway feedback loop will commence in which more of the oceans evaporate, trapping more heat and evaporating more water, until all the water on Earth has become a steam atmosphere upwards of a hundred times as thick as today and quite warm all the way up to the edge of space.  Over time, the water in the upper atmosphere will be split by ultraviolet radiation and the hydrogen will escape to space, the oxygen staying behind to oxidize surface rocks and creating sulfuric acid from the sulfur exhalations of volcanoes.  The CO2 pouring out of volcanoes will have no liquid water to dissolve into and will stick around thickening as the water slowly depletes until the Earth is a twin of Venus, having gone through the exact same process its sister planet went through long ago.  Maybe a few microbes could survive, lofted up into the clouds and never plunging into the sterilizing depths; maybe not.

This is the ultimate fate of any large terrestrial planet like Earth around a star large enough to brighten rapidly.  It was certainly the fate of Venus.  Venus may have started out like Earth is today and gone through this process early in the solar system’s history or it may have always been in the runaway greenhouse state, its greater solar radiation preventing the condensation of oceans from its hot birth.  We simply can’t know with the evidence at hand, especially given that the planet’s history more than 500 megayears ago is obscured by massive lava flows that covered most of its surface then.

This is not, however, the only way a planet can die.  One needs only look at Mars to see another way.  We know that Mars used to be warm and at least intermittently wet, with an active hydrosphere and conditions that were surprisingly Earthlike.  This was back when it was getting less than a third the sunlight the Earth gets today.  But Mars is small.  Its interior is closer to its surface, and it had less primordial heat of formation.  It cooled off, its volcanic outgassing that built the atmosphere fell through the floor, its low gravity lead to high rates of atmosphere loss, and it lost its internal geological-convection-driven geodynamo and magnetic field.  Fresh nutrient minerals stopped being delivered to the surface as the atmosphere and hydrosphere were sputtered away and the planet froze over.  There are reasons that if there is any life on Mars today it is deep underground and any surface biosphere that could’ve existed in the past died long ago.  This would eventually happen to ANY  terrestrial planet, even if it were around a star that would last for five trillion years.  I am completely unprepared to determine how long a planet like Earth would last if it weren’t for the brightening sun, but it sure isn’t that long.

The biggest rocky planets that seem to exist, according to the Kepler data, look to perhaps be 1.5 Earth radii and thus about 3.3 Earth masses.  This is an upper limit based on densities of known exoplanets – almost no planets larger than 1.5 Earth radii have densities like that of rock whereas many below do.  We have no idea what the atmospheres of 1.4 Earth radius planets are like – they could be temperate places with rain or crazy 500 atmosphere hells for all we know.  But these planets would create about 3.3x the radiogenic heat of Earth with 2.25x the surface area, for a surface area to volume ratio of about 2/3 that of Earth and 1/3 that of Mars.  Eventually they too will run down, the geosphere grinding to a halt and the atmosphere hydrosphere and any biosphere slowly trickling away.  A small red dwarf may last five trillion years, but for the vast majority of that history any terrestrial planets will be dry, vaccum blasted dead husks of their former selves (barring rare catastrophic collisions between planets that might reset some clocks here and there).

Incidentally, terrestrial moons of gas giants may get around this if they are tidally heated through gravitational resonances with other moons, heating themselves internally by stealing the energy of rotation of the central planet.  However, it remains an open question if rocky as opposed to icy moons of terrestrial planet mass are even an option around gas giants – the total mass of moon systems of gas giants in our outer solar system are universally about 1/10,000 that of the mass of the central planet and have a lot of ice mass in addition to rock mass, so large rocky moons big enough to maintain atmospheres at liquid water temperatures may be pretty rare.  But places like Europa where low-energy and low-biomass biospheres are an option might last a very long time.

Anyways, if you assume that planets with biospheres die with a lifetime of say ten billion years, you no longer need to postulate a narrow range of valid star masses for us to be a typical observer.  Our absolute time becomes typical again, 5 billion years into the lifetime of a biosphere, even though our world might last a shorter time than average due to the brightening large sun.  We do wind up in the upper 10-20% of star masses hosting a biosphere that lasts this long, but this is significantly less extreme than the one in a thousand value we started with.

For all we know smaller stars could also still be nonviable for big biospheres bringing our true position in the stellar mass distribution for big biospheres closer to average.  Below something like two thirds of a solar mass you start getting into orbital regimes where a planet warm enough to have liquid water on a rock surface is close enough to the parent star that it tidally locks and we honestly don’t know if that’s a showstopper or not.  Or there could be something about planets that form close to stars in absolute distance terms (rather than radiation received terms) that makes them different and unsuitable.  Or maybe you actually need to tune the running down of a geosphere putting out less greenhouse gases over time with the brightening of a star, such that you do have a narrow population of stars that brighten at the same timescales that planets run down and the two effects balance.  More information is desperately needed, which we are only just barely starting to get by observation of exoplanets.  I look forward to the possibility of getting atmospheric information from spectra of exoplanets that transit their parent stars to help clear this up.

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Author: Tony

Cell bio/genetics grad student and astronomy enthusiast who thinks about astrobiology way too freaking much.

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