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Is Surface Ice Uncommon on Habitable Worlds?

The day is not far off when we’ll be able to look at a small planet in the habitable zone of its star and detect basic features on its surface: water, ice, land. The era of the 30-meter extremely large telescope approaches, so this may even be possible from the ground, and large space telescopes will be up to the challenge as well (which is why things like aperture size and starshade prospects loom large in our discussions of current policy decisions).

Consider this: On the Earth, while the atmosphere reflects a huge amount of light from the Sun, about half the total albedo at the poles comes from polar ice. It would be useful, then, to know more about the ice and land distribution that we might find on planets around other stars. This is the purpose of a new paper in the Planetary Science Journal recounting the creation of climate simulations designed to predict how surface ice will be distributed on Earth-like exoplanets. It’s a relatively simple model, the authors acknowledge, but one that allows rapid calculation of climate on a wide population of hypothetical planets.

Image: A composite of the ice cap covering Earth’s Arctic region — including the North Pole — taken 512 miles above our planet on April 12, 2018 by the NOAA-20 polar-orbiting satellite. Credit: NOAA.

Lead author Caitlyn Wilhelm (University of Washington) began the work while an undergraduate; she is now a research scientist at the university’s Virtual Planet Laboratory:

“Looking at ice coverage on an Earth-like planet can tell you a lot about whether it’s habitable. We wanted to understand all the parameters—the shape of the orbit, the axial tilt, the type of star—that affect whether you have ice on the surface, and if so, where.”

Thus we attempt to cancel out imprecision in the energy balance model (EBM) the paper deploys by sheer numbers, looking for general patterns like the fraction of planets with ice coverage and the location of their icy regions. A ‘baseline of expectations’ emerges for planets modeled to be like the Earth (which in this case means a modern Earth), worlds of similar mass, rotation, and atmospherics. The authors simulate more than 200,000 such worlds in habitable zone orbits.

What is being modeled here is the flow of energy between equator and pole as it sets off climate possibilities for the chosen population of simulated worlds over a one million year timespan. These are planets modeled to be in orbit around stars in the F-, G- and K-classes, which takes in our G-class Sun, and all of them are placed in the habitable zone of the host star. The simulations take in circular as well as eccentric orbits, and adjust axial tilt from 0 all the way to 90 degrees. By way of contrast, Earth’s axial tilt is 23.5 degrees. That of Uranus is close to 90 degrees. The choice of axial tilt obviously drives extreme variations in climate.

But let’s pause for a moment on that figure I just gave: 23.5 degrees. Because factors like this are not fixed, and Earth’s obliquity, the tilt of its spin axis, actually isn’t static. It ranges between roughly 22 degrees and 24.5 degrees over a timescale of some 20,000 years. Nor is the eccentricity of Earth’s orbit fixed at its current value. Over a longer time period, it ranges between a perfectly circular orbit (eccentricity = zero) to an eccentricity of 6 percent. While these changes seem small enough, they have serious consequences, such as the ice ages.

Image: The three main variations in Earth’s orbit linked to Milankovitch cycles. The eccentricity is the shape of Earth’s orbit; it oscillates over 100,000 years (or 100 k.y.). The obliquity is the tilt of Earth’s spin axis, and the precession is the alignment of the spin axis. Credit: Scott Rutherford. A good entry into all this is Sean Raymond’s blog planetplanet, where he offers an exploration of life-bearing worlds and the factors that influence habitability. An astrophysicist based in Bordeaux, Raymond’s name will be a familiar one to Centauri Dreams readers. I should add that he is not involved in the paper under discussion today.

Earth’s variations in orbit and axial tilt are referred to as Milankovitch cycles, after Serbian astronomer Milutin Milanković, who examined these factors in light of changing climatic conditions over long timescales back in the 1920s. These cycles can clearly bring about major variations in surface ice as their effects play out. If this is true of Earth, we would expect a wide range of climates on planets modeled this way, everything from hot, moist conditions to planet-spanning ‘snowball’ scenarios of the sort Earth once experienced.

So it’s striking that even with all the variation in orbit and axial tilt and the wide range in outcomes, only about 10 percent of the planets in this study produced even partial ice coverage. Rory Barnes (University of Washington) is a co-author of the paper:

“We essentially simulated Earth’s climate on worlds around different types of stars, and we find that in 90% of cases with liquid water on the surface, there are no ice sheets, like polar caps. When ice is present, we see that ice belts—permanent ice along the equator—are actually more likely than ice caps.”

Image. This is Figure 12 from the paper. Caption: Figure 12. Range and average ice heights of ice caps as a function of latitude for stars orbiting F (top), G (middle) and K (bottom) dwarf stars. Note the different scales of the x-axes. Light grey curves show 100 randomly selected individual simulations, while black shows the average of all simulations that concluded with an ice belt. Although the averages are all symmetric about the poles, some individual ice caps are significantly displaced. Credit: Wilhelm et al.

Breaking this down, the authors show that in their simulations, planets like Earth are most likely to be ice-free. Even oscillations in orbital eccentricity and axial tilt do not prevent, however, planets orbiting the F-, G- and K-class stars in the study from developing stable ice belts on land. Moreover, ice belts turn out to be twice as common as polar ice caps for planets around G- and K-class stars. As to size, the typical extension of an ice belt is between 10 and 30 degrees, varying with host star spectral type, and this is a signal large enough to show up in photometry and spectroscopy, making it a useful observable for future instruments.

This is a study that makes a number of assumptions in the name of taking a first cut at the ice coverage question, each of them “…made in the name of tractability as current computational software and hardware limitations prevent the broad parameter sweeps presented here to include these physics and still be completed in a reasonable amount of wallclock time. Future research that addresses these deficiencies could modify the results presented above.”

Fair enough. Among the factors that will need to be examined in continued research, all of them spelled out here, are geochemical processes like the carbonate-silicate cycle, ocean heat transport as it affects the stability of ice belts, zonal winds and cloud variability, all of this not embedded in the authors’ energy balance model, which is idealized and cannot encompass the entire range of effects. Nor do the authors simulate the frequency and location of M-dwarf planet ice sheets.

But the finding about the lack of ice in so many of the simulated planets remains a striking result. Let me quote the paper’s summation of the findings. They remove the planets ending in a moist greenhouse or snowball planet, these worlds being “by definition, uninhabitable.” We’re left with this:

…we then have 39,858 habitable F dwarf planets, 37,604 habitable G dwarf planets, and 36,921 habitable K dwarf planets in our sample. For G dwarf planets, the ice state frequencies are 92% ice free, 2.7% polar cap(s), and 4.8% ice belt. For F dwarf planets, the percentages are 96.1%, 2.9%, and 0.9%, respectively. For K dwarf planets, the percentages are 88.4%, 3.5%, and 7.6%, respectively. Thus, we predict the vast majority of habitable Earth-like planets of FGK stars will be ice free, that ice belts will be twice as common as caps for G and K dwarfs planets, and that ice caps will be three times as common as belts for Earth-like planets of F dwarfs.

And note that bit about the uninhabitability of snowball worlds, which the paper actually circles back to:

Our dynamic cases highlight the importance of considering currently ice-covered planets as potentially habitable because they may have recently possessed open surface water. Such worlds could still develop life in a manner similar to Earth, e.g. in wet/dry cycles on land, but then the dynamics of the planetary system force the planet into a snowball, which in turn forces life into the ocean under a solid ice surface. Such a process may have transpired multiple times on Earth, so we should expect similar processes to function on exoplanets.

The paper is Wilhelm et al., ”The Ice Coverage of Earth-like Planets Orbiting FGK Stars,” accepted at the Planetary Science Journal (preprint). Source code available. Scripts to generate data and figures also available.


{ 15 comments… add one }
  • Alex Tolley December 14, 2021, 11:30

    Earth has been mostly ice-free in its history. Our modern Earth is showing that even with a very modest rise in CO2 and temperature, that the North pole sea ice is declining quickly, and may even become permanently ice free. Continental ice as glaciers in Greenland and Antarctica will take longer to disappear, but they will eventually. Antarctica was inhabited by dinosaurs. Even if they were homeothermic like birds, there must have been food, and this would be scare in a frozen winter. Estimated temperatures were well above freezing suggesting a forested landscape..

    What does surprise me is the finding of equatorial ice belts. This seems so counterintuitive.

    • Richard McCormac December 15, 2021, 6:19

      “What does surprise me is the finding of equatorial ice belts. This seems so counterintuitive.”

      Yes. How is that possible? If the spin-axis and orbital-axis are aligned then the equator is closest to the sun. If the spin-axis and orbital-axis are anti-aligned (like Uranus) then while one pole should be warmest, the other would be in permanent night, until they swap for the second half of the orbit, meaning you should intuitively expect half-year seasonal ice caps at whichever pole is facing away from the sun.

      What is the mechanism at work here? Were greenhouse gases concentrated away from the poles on these ice belt planets?

    • Brett December 15, 2021, 13:43

      You beat me to it – having extensive surface ice was anomalous on our own Earth, and in the past 600 million years was mostly concentrated to the Carboniferous and the Pleistocene/Holecene periods. If Antarctica was still connected to Australia by land (blocking the Circumpolar Current from forming), and Alaska/Northeast Siberia didn’t effectively form a land barrier against warm ocean currents going into the Arctic, we might not have permanent polar ice sheets at all right now.

      The “ice belts” are on planets with a very high axial tilt. IIRC axial tilts above 60 degrees result in the poles getting more intense sunlight than the equator, and a planet tilted at 90 degrees would basically have chilly conditions year round at the equator unless its atmosphere was warm enough to make the planet ice-free.

      • Richard McCormac December 15, 2021, 18:07

        “and a planet tilted at 90 degrees would basically have chilly conditions year round at the equator unless its atmosphere was warm enough to make the planet ice-free.”

        I’m not understanding how this works. If the planet is spinning at 90 degrees relative to its orbital plane, then shouldn’t it show one pole to the sun for a portion of its orbit, then the equator, then the other pole, and finally the equator again? If it’s spinning on its side then the only way to keep that single pole pointed at the sun would be if it ALSO rotated on the other axis once a year, for a double rotation. As I understand it, this is not what happens, and Uranus shows one pole to the sun for one portion of its orbit, then the other, with a transition where it is showing its equator, either spinning “upwards” or “downwards”. This sounds like equal insolation should be hitting the entire planet averaged over its entire orbit. Or is the effect caused by the fact that when the equator faces the star a given point on the equator spins from the light side to the dark side, allowing for cooling, whereas for the halves of the orbit where one pole or another are facing the star, that entire pole always faces the sun.

  • Alex Tolley December 14, 2021, 16:35

    I see a major flaw in this analysis. The starting point is a modern Earth, with same geography, atmosphere (i.e. N2/O2, low CO2), etc.

    But the modeling assumes no changes, so the carbon cycles and geology and biology are not modeled, yet these have considerable impact on climate. The earth’s atmosphere composition alone is due to life, which changes in response to the climate. (Ice sheets reduce photosynthesis, CO2 rises, temperature rise, ice sheets retreat).

    If we assume all exoplanets are lifeless, then we should start with a different atmosphere, dominated by N2/CO2, more like Mars in composition, but as dense as Earth’s.

    This still ignores the geological carbon cycle, where volcanic outgassing increases CO2 to warm the planet, and a warm planet reduces atmospheric CO2 through reaction with the rocks, both of which stabilize the temperature.

    Without either of these 2 carbon cycling mechanisms, we don’t know whether the climate impacts the modeled outcomes. They might even reduce the ice frequency, especially as we know that the Earth has been in a cyclical Milankovitch glaciation cycle for only a fraction of his history. Prior to this modern period, there have been a few long and deep glaciations, but not the cycling we see today (although this may be partially a result of limited resolution in the sedimentary rock stratigraphy).

    Another issue is the computationally lightweight EBM model may not accurately model the climate compared to a GCM. IIRC, prior posts on CD have indicated that different modeling approaches can change the outcomes quite significantly.

    Lastly, Earth may be an anomaly. Other papers have suggested that there is a saddle-shaped distribution of water content between dry, desert planets, and water worlds. A lifeless planet of either type in a stable orbit will experience its star increasing its energy output over time. The tendency will be to heat up the planet and leave the planet ice-free, even if it started as a snowball. The exoplanets we find will be of various ages, but all of them will be subject to gradual heating, and water loss. Desert planets may have no ice, because like Mars there is insufficient surface water (although there may be subsurface glaciers that we cannot detect by spectroscopy. Water planets may have different circulations, both ensuring that temperatures have to be lower to support sea ice, but also greater heat transport to reduce cold surface water.

    We might just find that no exoplanets have any large ice caps or belts, and not even glaciers on any mountain peaks.

  • Geoffrey Hillend December 14, 2021, 17:25

    There are several flaws in this article which make it not scientific. First, looking at only a similar mass, rotation and atmosphere of an exoplanet to Earth should not be used to model the long term ice covering on an only an Earth sized exoplanet since it is not enough information so it is not applicable to our planet and Milankovitch cycles. Without the gravity of a Moon, our Moon, the stability or variation of the planets axis and obliquity would be much higher like Mars. The result is that the planets long term cycles would be different than our Milankovitch cycles. This has nothing to do with the type of star, but most K stars would be tidally locked so the exoplanet in the life belt couldn’t have a Moon. A large obliquity favors polar ice cap melt which would be the cause which is not mentioned here.

    Also Jupiter and Saturn cause the eccentricity of the Earth to vary slightly. Source Nasa. https://climate.nasa.gov/news/2948/milankovitch-orbital-cycles-and-their-role-in-earths-climate/

    The carbon cycle is not mentioned. Life is not mentioned. Photosynthesis and the carbon cycle through the Urey reaction helped remove the carbon dioxide, so we have ice ages every one hundred thousand years which include a 10,000 interglacial period. Source Google search. How often do we have ice ages. Our ice ages have only been around for three million years and our ice caps for fifteen million years. Before that there was more carbon dioxide in our atmosphere than today so the Milankovitch cycles would not cool the planet enough to make polar ice caps and the ice ages. Also there might not be any plate tectonics and continental drift without our Moon.

    The glacier on Antarctica might melt sooner than we predicted . I read a google article yesterday which says that there are cracks in the Thwaites Glacier which could cause it to collapse in five years which would result in a sea level rise of several feet afterwards. https://news.yahoo.com/doomsday-glacier-ice-shelf-could-172033562.html?fr=sycsrp_catchall

  • Geoffrey Hillend December 14, 2021, 17:30

    Oh, and without continental drift, there would not be any subduction of crust, a carbon cycle, so there will be no mild climate and no replenishing of Carbon dioxide through volcanism.

  • Robin Datta December 14, 2021, 19:44

    The Earth’s movements around the sun make our seasons and our climate. This explanatory YouTube video has more than ten million views:
    Earth’s motion around the Sun, not as simple as I thought.

  • wdk December 14, 2021, 22:05

    I look forward to becoming more familiar with this study, but one question immediately come to mind: If these terrestrial planets have
    water on them, what is the assumption about atmospheric surface pressure?
    The boiling point of water varies on Earth’s surface with altitude because the saturation temperature depends on the prevailing pressure. Consequently, vapor transport is going to be affected how thin or thick the non-hydrous atmosphere is.

    Mars, for example has a hydrosphere and a water cycle, but its surface pressure is about 7 millibar. It takes a while to transport things to the poles – and away from them on that account, but weather on Mars per temperature is usually saturated.

    It would be shooting from the hip for me to try to sort out how the Antarctic was once a home for dinosaurs – but have to wonder if the atmosphere was also thicker in the era that they roamed the Earth. Say 16 or 17 psi.An atmosphere that thick would need revised saturation temperature charts.

    Just one consideration that comes to mind as to whether ice capped worlds like Earth and Mars are the exception.

  • Geoffrey Hillend December 14, 2021, 22:09

    Robin Datta: Yes, the precession of Earth’s orbit does affect the long term climate which includes the affects of Jupiter and Saturn, that is the eccentricity which is combined with the axial tilt and precession cycle in the Milankovitch cycle. The computer simulations of this paper “Is Surface Ice Uncommon on Habitable Worlds? did not include that and also the carbon cycle as I and Alex Tolley posted and the effects of life which are large. Life also affected the Earth’s chemistry and therefore, it’s geology and climate. The Milankovitch cycles were here before the Cambrian explosion. Consequently, the loss of surface ice on Earth sized exoplanets has nothing to do with cycles of time but the lack of a stable axis like Earth which only varies a small amount, 3.5 degrees between 22.1 and 24.5 degrees. Without a Moon it would vary a lot more. Consequently, the computer model must use the effects of the Moon, Jupiter and Saturn.

  • Michael Fidler December 14, 2021, 23:40

    I disagree, No mention of super impactors and the earth becoming a snowball several times. Seems the old concept of slow changes compared to the recent concept of catastrophism or what would be called the great gamble. The odds of a major impactor hitting planets like the earth often enough to change tilt, orbit and other major changes to these planets is more like Russian Rolette. Seventy percent of the earth is newer then 250 million years and much of the continental crust washed away by snowball earth several times would seem that a lot of evidence is missing. So Don’t Look UP! ;-}

    Just wait till we pass thru the arms of are galaxy the next time, if you can….

  • torque_xtr December 15, 2021, 6:13

    What this modelling shows is that ice sheets here on Earth are precarious thing. Without enormous increase in CO2, there’s no breakout from snowball state with current Earth insolation. The chances begin at 110% which is inside inner HZ edge by some definitions.

    Maybe anthropogenic global warming is not such a bad thing, after all. Who knows, with previous long-term decrease of CO2 levels and volcanism, how close the next Snowball was without us. Of course, the reversal in current thinking and continuation of global warming still would require a whole new level at disaster and relocation mitigation.

    Re. the carbon cycle, biosphere effects and different atmospheric compositions – including this will make already enormous parameter space untractable. Axial tilt, eccentricity, insolation, rotation rate which greatly affects circulation, stellar spectral class, neutral atmospheric density, greenhouse magnitude, land/ocean ratio – that’s 8 dimensions, only 32 positions on each axis for a sample of trillion planets. No two Earth-mass planets in the Galaxy are completely similar!

    • Alex Tolley December 15, 2021, 11:37

      Maybe anthropogenic global warming is not such a bad thing, after all.

      Good or bad for what and whom? Human civilization is dependent on our interstadial climate for agriculture, and just for existing in some climes. A few degrees hotter and the tropics become unlivable, as well as populations losing their land to live on. Some species will do well, others not – like polar bears. Add in the rate of change making migration and adaptation difficult and disruption will be very bad for many species.

      My argument about the carbon cycle is not that this increases the variables to be tested, but rather that using the Earth as the baseline model is inappropriate because it has been shaped by the carbon cycles. The atmosphere alone is a result of life. If most exoplanets are lifeless, they will not have low CO2 atmospheres, and as a result will have to be farther out in the HZ to reduce the stronger greenhouse effects.

      I note the paper does have cases of hot greenhouse and snowball conditions but state that these are uninhabitable (uninhabited?). To me it is unclear what their analysis shows. Are they saying that if we situate the Earth elsewhere and change a few parameters, that ice will be a rare occurrence? If so, then looking at exoplanets will result in even lower ice occurrence of ice as most are not in any way Earthlike.

      I may have missed it, but did the authors even show that the Earth would retain polar ice when run for the last million years – a necessary test of the model emerging from a glaciation?

  • Geoffrey Hillend December 15, 2021, 18:06

    The giant impact of our Earth with Thea, a Mars sized planet gave our Earth’s the angular momentum for it’s fast rotation. It also gave our Earth the wobble in it’s axis and axial tilt which gave us the seasons. Any smaller impacts affected our axil tilt very little so our seasons are the result of the Thea’s impact which have ben stable over 4 billion years. https://www.washingtonpost.com/weather/2019/06/20/summer-is-about-here-that-you-can-thank-billion-year-old-rock/

    The gravity of our Moon helps keep the wobble or variance of the Earth’s obliquity small. Without a Moon, the variation would be large like Mars. Consequently, the astrophysics which gives us the Milankovitch cycles is unique to our Earth. It only applies to Earth sized exoplanets that have a Moon which must be close to the size of our Moon. It is logical to assume due to the laws of probability of large impacts that the percentage of Earth sized exoplanets with moons is small and those without moons high. Therefore, the Milankovitch cycles don’t have general applicability to the most of the population of Earth sized exoplanets in our galaxy. Most of them would have a high obliquity without a stabilizing Moon. The large obliquity would change quickly every 50,000 which would favor a warm climate without polar ice caps due to an increased sunlight falling on the polar regions over a short period of time. Note this is due to the fact that the cycle of a Moonless exoplanet is not the same as our Earth’s Milankovitch cycles which don’t exist with a Moonless exoplanet.

    Man made climate change has the potential to cause many extinctions of species which are on the endangered list right now. There was semi tropical plants in Antarctica in the Cretaceous period because it was much warmer then than today and there was no polar ice caps. The reason is that the carbon dioxide levels were much higher up to 1000 parts per million. Eighty million years ago, the CO2 level was roughly 650 parts per million and approximately and thirty four million years ago, the ice caps began to form at 600 ppm which is the “tipping point”. If we go past 600 ppm of atmospheric carbon dioxide, we will loose our polar ice caps and the sea level will rise over 200 feet. https://www.purdue.edu/newsroom/research/2011/111201HuberGlaciation.html

  • A. Pandy December 17, 2021, 13:13

    The extent of glacier melt depends on the warmth build up in the summer.

    In the high obliquity scenarios near the poles the sun is continuously overhead, or high in the sky, for months at a time and therefore the poles experience the greatest amount of heat build up in the summer. At the equator the sun in the summer is high in the sky for less than half the day and so the heat does not build up quite so much, and there is a cooling off in the evening and throughout the night.

    Also on top of that, the summers don’t last as long at the equator, at least in the high obliquity scenarios, because the summers there occur around the time of equinox, when the planet is rapidly swinging from one stable state to another. At the equinox the angle of the warming sun above the horizon changes very much faster day-to-day than it does during the summer or the winter, and so the summers at the equator will obviously be much the shortest on the planet, at least in the high obliquity scenarios.

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