Earth will face its ultimate habitability crisis when the Sun leaves the Main Sequence and enters its subgiant stage in about 5 billion years. Long before that — in a billion years or less — barring technological intervention, habitability will end when the Sun brightens enough for the Earth to succumb to a runaway greenhouse. For a 1.2 Solar mass F star, the Red Giant crisis puts a conclusive end to habitability after only 5 billion years on the Main Sequence, and planets initially in the nominal habitable zone will succumb to a runaway greenhouse considerably before that. It took nearly 4 billion years (and 2 billion years after the initial rise of O₂) for complex multicellular life to arise on Earth, so if the bottlenecks faced on Earth typically take much longer to overcome, the prospects for complex life on G star planets are dim. Even if the transition to multicellularity can take place more rapidly, planets orbiting F stars do not look like likely candidates for hosting such life.

However, a red dwarf star such as our nearest neighbour, Proxima Centauri, will still be shining more or less unchanged a trillion years from now. Does this mean that, over the far future course of our Universe, habitable zone planets about such stars — assuming they can retain or regenerate a sufficient volatile inventory at the start of the main sequence — have essentially unlimited time available for complex life to emerge? In this talk, I will examine the ultimate limits on the lifespan of habitability.

The definition of the outer edge of the conventional liquid water habitable zone is defined by radiative and thermodynamic properties of CO₂, without reference to the geodynamic and geochemical processes that determine the amount of CO2 in a planet's atmosphere [1] . In reality, atmospheric CO₂ is determined by a balance between the source due to volcanic outgassing from the planetary interior and the sink due to silicate weathering. This was proposed in [2] as a potential constraint on habitability, but the subject has only recently attracted considerable interest. Studies with specified outgassing rates have shown that weathering processes can severely constrict the habitable zone (e.g [3]), and can lead to such interesting phenomena as climate limit cycles [4,5]. In reality, outgassing itself is a dynamic process, subject to constraints due to mantle chemistry and dynamics [6] and recycling of crustal carbonates, by plate tectonics or stagnant-lid processes. The collective behavior of volatile cycling, engaging both planetary interior processes, crustal processes, and atmospheric processes, ultimately determines the lifetime of habitability for a planet with given orbit, subject to the evolving instellation appropriate to the planet's host star.

In this talk, we present results from a simple model coupling planetary interior evolution to an energy-balance atmosphere and a model of the silicate weathering sink. CO₂ outgassing is represented as a function of interior temperature and heat flux out of the interior. The modeling work is very much in the spirit of models discussed in Refs. [7,8], but with a number of significant variants. Most importantly, we use the MAC weathering formulation [3], which allows for both the kinetic-limited and equilibrium-limited weathering regimes. Additionally, since we are focused on limits on habitability time, the results discussed in this talk will be given in the limit of efficient crustal recycling, as opposed to [8], which used a crustal model corresponding to a stagnant-lid regime. There are also differences in the representation of outgassing and seafloor weathering, and the effects of these will be discussed. A key planetary habitability parameter is the mass fraction of long-lived radionuclides in the planet's silicate mantle.

Some typical results are shown in the accompanying Figure. The climate model allows for ice-albedo feedback, which can allow for multiple states, bifurcations and climate oscillations. However, in order to reveal the key feeatures in their simplest form, ice-albedo feedback is suppressed in this calculation, though when global mean temperature approaches the freezing point of sea water, falling into a Snowball state would become likely in the presence of ice-albedo feedback. The mass fraction of ²³⁵U and ²³²Th is assumed the same as Earth's. Instellation L is given relative to Earth's present instellation L_e. r is the planetary radius, in units of Earth's radius. The Figure gives the evolution of surface temperature as a function of time since Zero Age Main Sequence for a low-mass K or M star that does not increase its luminosity significantly over the time period shown.

Except in the case of a large Super Earth with Earthlike instellation, the freeze-out time is 12 billion years or less, with more severe limitations for planets farther out in the nominal habitable zone. Even in the Super-Earth case the planet freezes over in under 30 billion years (not shown). It is clear that habitability is lost owing to a tectonic freeze-out crisis long before stellar evolution terminates habitability. In these calculations, seafloor weathering is represented by a small residual weathering that persists even after surface conditions become cold. This is an important effect, because in its absence weathering smoothly approaches zero as freezing conditions are approached, and the planet hovers indefinitely in near-freezing conditions. With ice-albedo feedback, such states typically enter climate oscillations, but the seafloor weathering can on its own cause a transition to globally sub-freezing conditions. These results highlight the extreme importance of seafloor weathering to habitability.

For planets in the habitable zone of low-mass stars, tidal heating can be a significant source of interior heating that can maintain tectonic recycling of carbonates into atmospheric CO₂. However, tidal dissipation for an isolated planet will quickly circularize the orbit and spin the planet down into a tide-locked state, whereafter tidal heating ceases. Gravitational interaction with a relatively nearby gas giant planet can maintain eccentricity, however, and allow sustained tidal heating. The energy available from such processes will be discussed, in comparison to the energy available from radiogenic heating.

It is interesting to note that while technological innovations a technological civilization could employ to stave off a runaway greenhouse catastrophe are very challenging (and probably completely unavailable, save for migration, for the Red Giant catastrophe), even our own civilization has the capability of preventing the tectonic freeze-out catastrophe. It takes very little energy to reverse the silicate weathering sink. Geodynamic processes accomplish this very inefficiently, but if carried out on the surface by technological processes require only a tiny fraction of the starlight reaching the planet's surface to be harnessed. As an example, the CO₂ released by worldwide cement production — counting just the chemical process of liberating CO₂ from carbonates and not the fossil fuels burned for energy — is already enough to essentially offset estimated global silicate weathering. Cement production primarily produces a complex mix of CaO with other minerals, rather than stable silicates, and if left on its own would eventually re-absorb most of the CO₂ emitted, but the process captures most of the energy requirements needed in the process of creating more weathering-resistant silicates.

Our Universe is too young for planets near the inner edge of the nominal habitable zone of M or K stars to have faced a tectonic freeze-out crisis, but even under the optimistic assumptions employed here planets further out in the nominal habitable zone are already at risk. This risk is compounded for planets with inefficient crustal recycling [8], or for planets with a lower mass mixing ratio of long-lived radionuclides than Earth. Given that uranium and thorium are currently thought to be produced primarily in rare and exotic events (merging neutron stars and collapsars) the galactic distribution of these key elements may be quite inhomogeneous despite their long lifetimes. This raises the question of whether sufficient supply of long-lived radionuclides can be a limiting factor in habitability. But even assuming a sufficient supply of such elements, the physics and geochemistry determining outgassing and weathering is rich and complex, and all existing models (including those presented here) are highly over-simplified, and just barely scratch the surface of the habitability question. This is a very fertile field for future research crossing the disciplinary boundaries of astrophysics and atmospheric physics with research capabilities most often housed in the Earth Science disciplines. As capabilities for characterizing the CO₂ content of rocky planet atmospheres develop [9], prospects for testing models of volatile cycling against astronomical data will become a key area in the study of habitability.

References

1. Kopparapu R. K. et al., 2013, ApJ, 765,131

2. Pierrehumbert R. T., 2011, ApJLett, 726, L8

3. Graham R.J. & Pierrehumbert R. T., 2020, ApJ, 896, 115

4. Haqq-Misra J et al., 2016, ApJ, 827, 120

5. Paradis A. & Menou K., 2017, ApJ, 848, 33

6. Dorn D. et al., 2018, A&A, 614, A18

7. Rushby A. et al. , 2018, Astrobio., 5, 469

8. Foley B. et al., 2018, Astrobio., 7, 873

9. Snellen I et al, 2015, A&A, 576, A59

Figure