Select Page

## Exoplanet Detection: Nudging Into the Rayleigh Limit

We’re building some remarkably large telescopes these days. Witness the Giant Magellan Telescope now under construction in Chile’s Atacama desert. It’s to be 200 times more powerful than any research telescope currently in use, with 368 square meters of light collection area. It incorporates seven enormous 8.5 meter mirrors. That makes exoplanet work from the Earth’s surface a viable proposition, but look at the size of the light bucket we need to make it work. Three mirrors like that shown below are now in place, and the University of Arizona’s Mirror Lab is building number 6 now.

Image: University of Arizona Richard F. Caris Mirror Lab staff members Damon Jackson (left) and Conrad Vogel (right) in the foreground looking up at the back of primary mirror segment five, April 2019. Credit: Damien Jemison; Giant Magellan Telescope – GMTO Corporation. CC BY-NC-ND 4.0.

Imaging an exoplanet from the Earth’s surface is complicated by the Rayleigh Limit, which governs the resolution of our optical systems and their ability to separate two point sources. Stephen Fleming showed the equation in his talk on super-resolution imaging at the Interstellar Research Group’s recent meeting in Montreal. I use few equations on this site but I’ll show this one because it’s straightforward and short:

θ = 1.22 * (λ / D)

Here λ is the wavelength and D is the diameter of the mirror. What this says is that there is a minimum angular separation (θ) that allows two point sources to be clearly distinguishable, which in terms of astronomy means we can’t pull useful information out of the image when they are closer than this. I’ve pulled the image below out of Wikipedia (in the public domain, submitted by Spencer Bliven).

Image: Two Airy disks at various spacings: (top) twice the distance to the first minimum, (middle) exactly the distance to the first minimum (the Rayleigh criterion), and (bottom) half the distance. This image uses a nonlinear color scale (specifically, the fourth root) in order to better show the minima and maxima.

Here we have another useful term: An Airy disk is a diffraction pattern that is produced when light moves through the aperture of a telescope system. Light diffracts – it’s in the nature of the physics – and the Airy disk is the best focused spot of light that a perfect lens with a circular aperture can make. We’re looking at light interfering with itself, so in the image, we have a central bright spot with surrounding rings of light and dark. The diffraction pattern depends upon the wavelength being observed and the aperture itself. This diffraction can be described as a point spread function (PSF) for any optical system, and essentially governs how tightly that system can be focused.

Bigger apertures matter as we try to deal with these limitations, and the Giant Magellan Telescope will doubtless make many discoveries, as will all of the coming generation of Extremely Large Telescopes. But when we want to see ever smaller objects at astronomical distances, we run into a practical problem. Nothing in the physics prevents us from building a ground-based telescope that could see an Earth-class planet at Alpha Centauri, but if we want details, Fleming notes, we would need a mirror 1.8 kilometers in diameter to retrieve a 40 X 40 pixel image.

The point of Fleming’s talk, however, was that we can use quantum technologies to nudge into the Rayleigh limitations and extract information about amplitude and phase from the light we do collect. That, in turn, would allow us to distinguish between point sources that are closer than what the limit would imply. The operative term is super-resolution, a topic that is growing in importance in the literature of optics, though to this point not so much in the astronomical community. This may be about to change.

Counter-intuitively (at least insofar as my own intuitions run), a multi-aperture telescope does a better job with this than a large single-aperture. Instead of a 3-meter mirror you use three 1.7 meter mirrors that are spaced out over, perhaps, an acre. This hits at mirror economics as well, because the costs of these enormous mirrors goes up more than exponentially. The more you can break the monolithic mirror into an array of smaller mirrors, you can add to the data gain but also sharply reduce the expense.

In terms of the science, Fleming noted that the point spread function spreads out when multiple smaller mirrors are used, and objects become detectable that would not be with a monolithic single mirror instrument. The technique in play is called Binary Spatial Mode Demultiplexing. Here the idea is to extract quantum modes of light in the imaging system and process them separately. The central mode – aligned with the point spread function of the central star – is the on-axis light. The off-axis photons, sorted into a separate detector, are from what surrounds the star.

So in a way we’re nudging inside the Rayleigh Limit by processing the light, nulling out or dimming the star’s light while intensifying the signal of anything surrounding the star. I’m reminded, of course, of all the work that has gone into coronagraphs and starshades in the attempt to darken the star while revealing the planets around it. In fact, some of the earliest research that convinced me to write my Centauri Dreams book was the work of Webster Cash out at the University of Colorado on starshades for this purpose, with the goal of seeing continents and oceans on an exoplanet. I later learned as well of Sara Seager’s immense contributions to the concept.

Thus far the simulations that have been run at the University of Arizona by Fleming’s colleagues have shown far higher detection rates for an exoplanet around a star using multi-aperture telescopes. In fact, there is a 100x increase in sensitivity for multi-aperture methods. This early work indicates it should be possible to identify the presence of an exoplanet in a given system with this ground-based detection method.

Can we go further? The prospect of direct imaging using off-axis photons is conceivable if futuristic. If we could create an image like this one, we would be able to study this hypothetical world over time, watching the change of seasons and mining data on the land masses and oceans as the world rotates. The possibility of doing this from Earth’s surface is startling. No wonder super-resolution is a growing field of study, and one now being addressed within the astronomical community as well as elsewhere.

## Atmospheric Types and the Results from K2-18b

The exoplanet K2-18b has been all over the news lately, with provocative headlines suggesting a life detection because of the possible presence of dimethyl sulfide (DMS), a molecule produced by life on our own planet. Is this a ‘Hycean’ world, covered with oceans under a hydrogen-rich atmosphere? Almost nine times as massive as Earth, K2-18b is certainly noteworthy, but just how likely are these speculations? Centauri Dreams regular Dave Moore has some thoughts on the matter, and as he has done before in deeply researched articles here, he now zeroes in on the evidence and the limitations of the analysis. This is one exoplanet that turns out to be provocative in a number of ways, some of which will move the search for life forward.

by Dave Moore

124 light years away in the constellation of Leo lies an undistinguished M3V red dwarf, K2-18. Two planets are known to orbit this star: K2-18c, a 5.6 Earth mass planet orbiting 6 million miles out, and K2-18b, an 8.6 Earth mass planet orbiting 16 million miles out. The latter planet transits its primary, so from its mass and size (2.6 x Earth’s), we have its density (2.7 g/cm2), which class the planet as a sub-Neptune. The planet’s relatively large radius and its primary’s low luminosity make it a good target to get its atmospheric spectra, but what also makes this planet of special interest to astronomers is that its estimated irradiance of 1368 watts/m2 is almost the same as Earth’s (1380 watts/m2).

Determining an exosolar planet’s atmospheric constituents, even with the help of the James Webb telescope, is no easy matter. For a detectable infrared spectrum, molecules like H2O, CH4, CO2 and CO generally need to have a concentration above 100 ppm. The presence of O3 can function as a stand-in for O2, but molecules such as H2, N2, with no permanent dipole moment, are much harder to detect.

The Hubble telescope got a spectrum of K2-18b in 2019. Water vapor and H2 were detected, and it was assumed to have a deep H2/He/steam atmosphere above a high pressure ice layer over an iron/rocky core, much like Neptune. On September 11 of this year, the results of spectral studies by the James Webb telescope were announced: CH4 and CO2 were found as well as possible traces of DMS (Dimethyl sulfide). No signal of NH3 was found. Nor was there any sign of water vapor. The feature thought to be water vapor turned out to be a methane line of the same frequency.

Figure 1: Spectra of K2-18b obtained by the James Webb telescope

This announcement resulted in considerable excitement and speculation by the popular press. K2-18b was called a Hycean planet. It was speculated that it had an ocean, and the possible presence of DMS was taken as an indication of life because oceanic algae produce this chemical. But that was not what intrigued me. What caught my attention was the seemingly anomalous combination of CH4 and CO2in the planet’s atmosphere. How could a planet have CH4, a highly reduced form of carbon, in equilibrium with CO2, the oxidized form of carbon? A search turned up a paper from February 2021: “Coexistence of CH4, CO2, and H20 in exoplanet atmospheres,” by Woitke, Herbort, Helling, Stüeken, Dominik, Barth and Samra.

The authors’ purpose for this paper was to help with the detection of biosignatures. To quote:

The identification of spectral signatures of biological activity needs to proceed via two steps: first, identify combinations of molecules which cannot co-exist in chemical equilibrium (“non-equilibrium markers”). Second, find biological processes that cause such disequilibria, which cannot be explained by other physical non-equilibrium processes like photo-dissociation. […] The aim of this letter is to propose a robust criterion for step one…

The paper presents an exhaustive study for the lowest energy state (Gibbs free energy) composition of exoplanet atmospheres for all possible abundances of Hydrogen, Carbon, Oxygen, and Nitrogen in chemical equilibrium. To do that, they ran thermodynamic simulations of varying mixtures of the above atoms and looked at the resulting molecular ratios. At low temperatures (T ≤ 600K), they found that the only molecular species you get in any abundance are H2, H20, CH4, NH3, N2, CO2, O2. At higher temperature, the equilibrium shifts towards more H2, and CO begins to appear.

Some examples of their results:

If O > 0.5 x H + 2 x C ––> O2-rich atmosphere, no CH4
If H > 2 x O + 4 x C ––> H2-rich atmosphere, no CO2
If C > 0.25 x H + 0.5 x O ––> Graphite condensation, no H20

They also used the equations to tell what partial pressures of the elemental mixture will produce equal pressures of the various molecules:

If H = 2 x O then the CO2 level will equal CH4
If 12 C = 2 x O + 3 x H then the CO2level will equal H20
If 12 C = 6 x O + H then the H20 level will equal CH4

To summarize, I quote from their abstract:

We propose a classification of exoplanet atmospheres based on their H, C, O, and N element abundances below about 600 K. Chemical equilibrium models were run for all combinations of H, C, O, and N abundances, and three types of solutions were found, which are robust against variations of temperature, pressure, and nitrogen abundance.

Type A atmospheres[which] contain H20, CH4, NH3, and either H2 or N2, but only traces of CO2 and O2.

Type B atmospheres [which] contain O2, H20, CO2, and N2, but only traces of CH4, NH3, and H2.

Type C atmospheres [which] contain H20, CO2, CH4, and N2, but only traces of NH3, H2, and O2

Type A atmospheres are found in the giant planets of our outer solar system. Type B atmospheres occur in our inner solar system. Earth, Venus and Mars fall under this classification, but we don’t see any planets with Type C atmospheres.

Below is a series of charts showing the results for each of the six main molecular species over a range of mixtures.

Figure 2: The vertical axis is the ratio of Hydrogen to Oxygen, starting at 100% Hydrogen at the bottom and running to 100% Oxygen at the top. The horizontal axis shows the proportion of Carbon in the total mixture (The ratio runs up to 35%.) Molecular concentrations are in chemical equilibrium as a function of Hydrogen, Carbon, and Oxygen element abundances, calculated for T = 400 K and p = 1 bar. The blank regions are concentrations of < 10−4.

The central grey triangle marks the region in which H20, CH4, and CO2 can coexist in chemical equilibrium. The thin grey lines bisecting the triangle indicate where two of the constituents are at an equal concentration. These lines are hard to discern unless you can magnify the original image. For H20 and CO2 at equal concentration, it’s the dashed line (the near vertical line running upwards from 0.2 on the horizontal scale.) For CO2 and CH4, it’s the horizontal line. And for H20 and CH4, it’s the dotted line swooping upwards toward the top right-hand corner.)

The color bars at the right-hand side of the charts are both a color representation of the concentration and show the proportion of Nitrogen tied up as N2, i.e. that which is not NH3. Not surprisingly, the more Hydrogen there is in the mix, the higher the proportion of NH3 there is.

Other Results from the Paper

In the area around the stoichiometric ratio for water you get maximum H20 production and supersaturation occurs. Clouds form and the water rains out. Therefore, you cannot get an atmosphere with very high concentrations of water vapor unless the temperature is over 650°K, the critical point of water. Precipitation results in the atmospheric composition moving out of the area that gives CO2/CH4 mixtures.

Atmospheres with high carbon concentrations and having Hydrogen and Oxygen near their stoichiometric ratio have most of the atmospheric constituents tied up as water, so at a certain point carbon forms neither CO2 nor CH4 but rains out as soot. This, however, only precludes mixtures in the very right hand side of the CO2/CH4 Triangle.

Full-equilibrium condensation models show that the outgassing from warm rock, such as mid-oceanic ridge basalt can naturally produce Type C atmospheres.

Thoughts and Speculations

i) While it is difficult to argue with the man who coined the term, I still think Madhusudhan’s description of K2-18b as Hycean is too broad. Watching Madhusudhan in a Youtube interview, he refers to his paper “Habitability and Biosignatures of Hycean Worlds,’ which suggests that ocean covered planets under a Hydrogen atmosphere can exists within a zone that reaches into a level of irradiance slightly greater than Earth’s; however, he doesn’t mention the work by Lous et al in their paper, “Potential long-term habitable conditions on planets with primordial H–He atmospheres,” that showed that inside irradiance levels equivalent to 2 au from our Sun or greater, the Hydrogen atmosphere required to maintain Earthlike temperatures and not cook it is so thin that it is lost quickly over geological timescales. (You can see this in more detail in my article Super Earths/Hycean Worlds.) I would therefore define a Hycean planet as a rocky world with a radius up to 1.8 x Earth’s outside the irradiance equivalent of 2 au from our sun. K2-18b, being both larger than this and less dense than a rocky world, would fall, in my mind, firmly into the category of sub-Neptune.

ii) Another way of thinking of Type A, Type B and Type C atmospheres is to denote them as Hydrogen dominated, Oxygen dominated and Carbon dominated. Carbon dominated atmospheres may have by far the bulk of their constituents being Hydrogen and Oxygen; but because the enthalpy of the Hydrogen-Oxygen reaction is so much greater than the other reactions, when Hydrogen and Oxygen are close to their stoichiometric ratio, they preferentially remove themselves from the mix leaving Carbon as the dominant constituent. There is no Nitrogen dominated atmosphere because for most of its range Nitrogen sticks to itself forming N2 and is inert.

iii) The lack of H20 spectral lines is puzzling. Madhusudhan in his interview suggests that the spectra was a shot of the high-dry stratosphere. To cross-check the plausibility of this, I looked up the physical data on DMS. Dimethyl Sulfide vaporizes at 37°C and freezes at -98°C, which is lower than CO2’s freezing point. It also has a much higher vapor pressure than water at below freezing temperatures, so this does not contradict the assumption.

iv) I’m surprised this paper is not more widely known as not only does it provide a powerful tool for the analysis of exosolar planets’ atmospheric spectra, but it can also point to other aspects of a planet.

After the Hubble results came out in 2017, papers were published to model the formation of K2-18b, and while a range of possibilities could match the planet’s characteristics, they all came from the assumption that the planet began via the formation of a rocky/iron core followed by the gas accretion of large amounts of H2, Helium, and H20. According to the coexistence paper though, you cannot have large amounts of H2 and get a CO2/CH4 mix with no NH3. So to arrive at this state, this planet must never have had much gas accretion in the first place, or lost large amounts of Hydrogen after it formed. This latter scenario would require the planet to gain a Hydrogen envelope while at less than full mass in a hot nebula and then at full mass, in a cooler environment, lose most of its Hydrogen.

It is much easier to explain the planet’s characteristics by assuming it formed outside the snowline, never gained much of a gas envelope in the first place and spiraled into its present position. If it was formed from icy bodies like Ganymede and Titan (density ~ 1.9 gm/cc), this would give a good match for its density (2.7 gm/cc) allowing for gravitational contraction. The snow line is also the zone where carbonaceous chondrites form, so this would give the planet a higher carbon content than a pure rocky/iron one.

v) Madhusudhan, again from his interview, seems to think that K2-18b is an ocean planet, but I’m dubious about this for two reasons:

The first is that from the work done on Hycean planets by Lous et al, any depth of atmosphere especially with the potent greenhouse mix of CO2 and CH4 is likely to result in a runaway-greenhouse steam atmosphere inside the classically defined habitable zone (inside 2 au. for our sun).

The planet’s CO2/CH4 mix also points against this. From the paper, if there is a slight excess of Hydrogen over the stoichiometric ratio for water, then condensing H20 out, as either water or high pressure ice, pushes the planet’s atmosphere towards a Type A Hydrogen excess with no CO2 and NH3 lines appearing.

All of this would point towards a planet with a rocky/iron core overlaid by high pressure ice, which would, at about the megabar level, transition to a gas atmosphere composed mainly of super-critical steam. This would make up a significant volume of the planet. At the top of this atmosphere, the water, now in the form of steam, would condense out as virago rain leaving a dry stratosphere consisting mainly of CO2, CH4, H2 and N2.

To test my assumption, I did a rough back of the envelope calculation using online calculators, and looked at the wet adiabatic lapse rate (the rate of increase in temperature when saturated air is compressed) per atm. pressure doubling starting from 1 bar at 20°C. This rate (1.5°C/1000 ft) is considerably less than the rate for dry gases (3°C/1000 ft).

It was all very ad hoc, but the first thing I noted was that for each pressure doubling, the boiling point of water goes up significantly–at 100 bar, water boils at 300°C–until its temperature approaches its critical point (374°C) where it levels off. So the lapse rate increase in temperature chases the boiling point of water as you go deeper and deeper into the atmosphere; however, from my calculations, it catches water’s boiling point at 270°C and 64 bar. The calculations are arbitrary—I was using Earth’s atmospheric composition and gravity–and small changes in the parameters can result in big changes in the crossover point; but what this does point to is that if the planet has an ocean, it could be a rather hot one under a dense atmosphere, and if the atmosphere has any great depth then the ocean is likely to be a supercritical fluid.

Also, for the atmosphere to be thin, the planet’s ratio of CO2, CH4 and H2 must be less than 1/10,000 that of H20, which is not something I regard as likely, given what we know about the outer solar system.

I’ll leave you with a phase diagram of water with (red line) the dry adiabat of Venus moved 25°C cooler to represent a dry Earth and the wet adiabat (blue line) the one I calculated out. It’s also a handy diagram to play with as it gives you an idea of how deep the ocean or critical fluid layer will be at a given temperature before it turns into a layer of high pressure ice.

vi) One final point, and this reinforces the purpose of the paper: that we need to thoroughly understand planetary chemistry to eliminate false bio-markers. DMS is widely touted as a biomarker, but if we look at the most thermodynamically stable forms of sulfur: In a Type A reducing atmosphere, it’s H2S; and in a wet, oxidizing, Type B atmosphere, it’s the Sulfate (SO42-) ion. Unfortunately, the authors of the paper did not extend their thermodynamic analysis to Sulfur, but if we look at DMS’s formula (CH3)2S, it looks an awful lot like a good candidate for the most thermodynamically stable form of Sulfur for a Type C atmosphere, not a biomarker.

References

Wikipedia: K2-18b
https://en.wikipedia.org/wiki/K2-18b

N. Madhusudhan, S. Sarkar, S. Constantinou, M Holmberg, A. Piette, and J. Moses, Carbon-bearing Molecules in a Possible Hycean Atmosphere, Preprint, arXiv: 2309.05566v2, Oct 2023
https://esawebb.org/media/archives/releases/sciencepapers/weic2321/weic2321a.pdf

P. Woitke, O. Herbort, Ch. Helling, E. Stüeken, M. Dominik, P. Barth and D. Samra, Coexistence of CH4, CO2, and H2O in exoplanet atmospheres, Astronomy & Astrophysics, Vol. 646, A43, Feb 2021
https://doi.org/10.1051/0004-6361/202038870

N. Madhusudhan, M. Nixon, L. Welbanks, A. Piette and R. Booth, The Interior and Atmosphere of the Habitable-zone Exoplanet K2-18b, The Astrophysical Journal Letters, 891:L7 (6pp), 2020 March 1
https://doi.org/10.3847/2041-8213/ab7229

Super Earths/Hycean Worlds, Centauri Dreams 11 November, 2022

Youtube interview of Nikku Madhusudhan, Is K2-18b a Hycean Exoworld? on Colin Michael Godier’s Event Horizon

## Tidal Lock or Sporadic Rotation? New Questions re Proxima and TRAPPIST-1

Centauri Dreams regular Dave Moore just passed along a paper of considerable interest for those of us intrigued by planetary systems around red dwarf stars. The nearest known exoplanet of roughly Earth’s mass is Proxima Centauri b, adding emphasis to the question of whether planets in an M-dwarf’s habitable zone can indeed support life. From the standpoint of system dynamics, that often comes down to asking whether such a planet is not so close to its star that it will become tidally locked, and whether habitable climates could persist in those conditions. The topic remains controversial.

But there are wide variations between M-dwarf scenarios. We might compare what happens at TRAPPIST-1 to the situation around Proxima Centauri. We have an incomplete view of the Proxima system, there being no transits known, and while we have radial velocity evidence of a second and perhaps a third planet there, the situation is far from fully characterized. But TRAPPIST-1’s superb transit orientation means we see seven small, rocky worlds moving across the face of the star, and therein lies a tale.

The paper Dave sent, by Cody Shakespeare (University of Nevada Las Vegas) and colleague Jason Steffen, picks up on earlier work Shakespeare undertook that probes the differences between such scenarios. We know that conditions are right for a solitary planet, unperturbed by neighbors, to orbit with a spin rate synchronous with its orbital rate, the familiar ‘tidal lock.’ On such a world, we probe questions of climate, heat transport, the effects of an ocean and so on, to see if a planet with a star stationary in its sky could sustain life.

Image: This illustration shows what the TRAPPIST-1 system might look like from a vantage point near planet TRAPPIST-1f (at right). Credit: NASA/JPL-Caltech.

But as TRAPPIST-1 shows us in exhilarating detail, multi planet systems are not uncommon around this type of star, and now we have to factor in mean motion resonance (MMR), where the very proximity of the planets (all well within a fraction of Mercury’s orbit of our Sun) means that these effects can perturb a particular planet out of its otherwise spin-orbit synchronization. Call this ‘orbital forcing,’ which breaks what would have been, in a single-planet system, a system architecture that would inevitably lead to permanent tidal lock.

The results of this breakage produce the interesting possibility that planets like TRAPPIST-1 e and f may retain tidal lock but exhibit sporadic rotation (TLSR). Indeed, another recent paper referenced by the authors, written by Howard Chen (NASA GSFC) and colleagues, makes the case that this state can produce permanent snowball states in the outer regions of an M-dwarf planetary system. What is particularly striking about TLSR is the time frame that emerges from the calculations. Consider this, from the Shakespeare paper:

The TLSR spin state is unique in that the spin behavior is often not consistently tidally locked nor is it consistently rotating. Instead, the planet may suddenly switch between spin behaviors that have lasted for only a few years or up to hundreds of millennia. The spin behavior can occasionally be tidally locked with small or large librations in the longitude of the substellar point. The planet may flip between stable tidally locked positions by spinning 180°so that the previous substellar longitude is now located at the new antistellar point, and vice versa. The planet may also spin with respect to the star, having many consecutive full rotations. The spin direction can also change, causing prograde and retrograde spins.

Not exactly a quiescent tidal lock! Note the term libration, which refers to oscillations around the rotational axis of a planet. What Shakespeare and Steffen are analyzing is the space between long-lasting rotation and pure tidal lock. Indeed, the authors identify a spin scenario within the TLSR domain they describe as prolonged transient behavior, or PTB. Here the planet moves back and forth in a ‘spin regime’ that is essentially chaotic, so that questions of habitability become fraught indeed. Instead of a persistent climate, which we usually assume when assessing these matters, we may be looking at multiple states of climate determined by present and past spin regimes, and their necessary adaptation to the ever changing spin state.

Such global changes are reminiscent, though for different reasons, of Asimov’s fabled story “Nightfall,” in which scientists on a world in a system with six stars must face the social consequences of a ‘night’ that only appears every few thousand years. For here’s what Shakespeare and Steffen say about a scenario in which TSLR effects kick in, a world that had been tidally locked long enough for the climate to have become stable. The scenario again involves TRAPPIST-1:

Such a planet in the habitable zone around a TRAPPIST-1-like star could have an orbital period of around 4-12 Earth days – the approximate orbital periods of T-1d and T-1g, respectively. Due to the TLSR spin state, this planet may, rather abruptly, start to rotate, albeit slowly – on the order of one rotation every few Earth years. The previous night side of the planet, which had not seen starlight for many Earth years, will now suddenly be subjected to variable heat with a day-night cycle lasting a few years. The day side would receive a similar abrupt change and the climate state that prevailed for centuries would suddenly be a spinning engine with momentum but spark plugs that now fire out-of-sync with the pistons. In this analogy, the spark plugs and the subsequent ignition of fuel correspond to the input of energy from starlight. The response of ocean currents, prevailing winds, and weather patterns may be quite dramatic.

Not an easy outcome to model in terms of climate and habitability. The authors use a modified version of an energy release modeling software called 1D EBM HEXTOR as well as a model called the Hab1 TRAPPIST-1 Habitable Atmosphere Intercomparison (THAI) Protocol as they analyze these matters. I send you to the paper for the details.

Science fiction writers take note – here is rich material for new exoplanet environments. Notice that the TLSR spin state is different from the one-way change that occurs when a rotating planet gradually becomes tidally locked over large timescales. This is a regime of sudden change, or at least it can be. The authors consider spin regimes lasting less than 100 Earth years, with the longest regimes (these are classified as ‘quasi-stable’) lasting for 900 years or more and perhaps reaching durations of hundreds of thousands of years. The point is that “TLSR planets are able to be in both long-term persistent regimes and PTB regimes -– where frequent transitions between behaviors are present.”

We learn that all tidally locked bodies experience libration to some degree even if no other bodies are found in the system being examined. Four spin regimes are found within the broader spin state TLSR. Tidal lock with libration can occur around the substellar point, as well as around the substellar or antistellar point, or as noted a planet may be induced into a slow persistent rotation. Much depends upon how long any one of these ‘continuous’ states lasts; given enough time, a stable climate could develop. The chaotic behavior of the fourth state, prolonged transient behavior (PTB), induces frequent transitions in spin. Such transitions would be expected to produce extreme changes in climate.

The spin history of a given system will depend upon that system’s architecture and the key parameters of each individual planet, an indication of the complexity of the analysis. What particularly strikes me here is how fast some of these changes can occur. Here’s a science fiction scenario indeed:

The more extreme change is in the temperature of different longitudes as the planet transitions from a tidally locked regime to a Spinning regime or after the planet flips 180 and remains tidally locked. Rotating planets experience temperature changes at the equator of 50K or more over a single rotation period. The exact effects require more robust climate models, like 3D GCMs [Global Circulation Model], to properly examine. However, using comparisons with climate changes on Earth, it is likely that erosion of land masses would increase and major climate systems would experience significant changes.

As if the issue of habitability were not complex enough…

The paper is Shakespeare & Steffen, “Day and Night: Habitability of Tidally Locked Planets with Sporadic Rotation,” in process at Monthly Notices of the Royal Astronomical Society and available as a preprint. The Chen paper referenced above is “Sporadic Spin-Orbit Variations in Compact Multi-planet Systems and their Influence on Exoplanet Climate,” accepted at Astrophysical Journal Letters (preprint).

## A Liquid Water Mechanism for Cold M-dwarf Planets

A search for liquid water on a planetary surface may be too confining when it comes to the wide range of possibilities for supporting life. We see that in our own Solar System. Consider the growing interest in icy moons like Europa and Enceladus, where there is no possibility of surface water but a potentially rich environment under a thick layer of ice. Extending these thoughts into the realm of exoplanets reminds us that our calculations about how many life-bearing worlds are out there may be in need of revision.

This is the thrust of work by Lujendra Ojha (Rutgers University) and colleagues, as developed in a paper in Nature Communications and presented at the recent Goldschmidt geochemistry conference in Lyon. What Ojha and team point out is that radiogenic heating can maintain liquid water below the surface of planets in M-dwarf systems, and that added into our astrobiological catalog, such worlds, orbiting a population of stars that takes in 75 percent or more of all stars in the galaxy, dramatically increase the chances of life elsewhere. The effect is striking. Says Ojha:

“We modeled the feasibility of generating and sustaining liquid water on exoplanets orbiting M-dwarfs by only considering the heat generated by the planet. We found that when one considers the possibility of liquid water generated by radioactivity, it is likely that a high percentage of these exoplanets can have sufficient heat to sustain liquid water – many more than we had thought. Before we started to consider this sub-surface water, it was estimated that around 1 rocky planet every 100 stars would have liquid water. The new model shows that if the conditions are right, this could approach 1 planet per star. So we are a hundred times more likely to find liquid water than we thought. There are around 100 billion stars in the Milky Way Galaxy. That represents really good odds for the origin of life elsewhere in the universe.”

Image: This is Figure 2 from the paper. Caption: Schematic of a basal melting model for icy exo-Earths. a Due to the high surface gravity of super-Earths, ice sheets may undergo numerous phase transformations. Liquid water may form within the ice layers and at the base via basal melting with sufficient geothermal heat. If high-pressure ices are present, meltwater will be buoyant and migrate upward, feeding the main ocean. The red arrows show geothermal heat input from the planet’s rocky interior. b Pure water phase diagram from the SeaFreeze representation illustrating the variety of phases possible in a thick exo-Earth ice sheet. Density differences between the ice phases lead to a divergence from a linear relationship between pressure and ice-thickness. Credit: Ohja et al.

The effect is robust. Indeed, water can be maintained above freezing even when planets are subject to as little as 0.1 Earth’s geothermal heat produced by radiogenic elements. The paper models the formation of ice sheets on such worlds and implies that the circumstellar region that can support life should be widened, which would take in colder planets outside what we have normally considered the habitable zone.

But the work goes further still, for it implies that planets closer to their host star than the inner boundaries of the traditional habitable zone may also support subglacial liquid water. We also recall that the sheer ubiquity of M-dwarfs in the galaxy helps us, for if water from an internal ocean does reach the surface, perhaps through cracks venting plumes and geysers, we may find numerous venues relatively close to the Sun on which to search for biosignatures.

The key factor here is subglacial melting through geothermal heat, for oceans and lakes of liquid water should be able to form under the ice on Earth-sized planets even when temperatures are as low as 200 K, as we find, for example, on TRAPPIST-1g, which is the coldest of the exoplanets for which Ojha’s team runs calculations.

Such water is found to be buoyant and can migrate through this ‘basal melting,’ a term used, explain the authors, for “any situation where the local geothermal heat flux, as well as any frictional heat produced by glacial sliding, is sufficient to raise the temperature at the base of an ice sheet to its melting point.” Subglacial ice sheets are found on Earth in the West Antarctic Ice Sheet, Greenland and possibly the Canadian Arctic, and the paper points out the possibility of the mechanism at work at the south pole of Mars.

The authors’ modeling uses a software tool called SeaFreeze along with a heat transport model to investigate the thermodynamic and elastic properties of water and ice at a wide range of temperatures and pressures. Given the high surface gravity of worlds like Proxima Centauri b, LHS 1140 b and some of the planets in the TRAPPIST-1 system, water ice should be subjected to extreme pressures and temperatures, and as the paper points out, may evolve into high-pressure ice phases. In such conditions, the meltwater migrates upward to form lakes or oceans. Indeed, this kind of melting and migration of water is more likely to occur on planets where the ice sheets are thicker and there is both higher surface gravity as well as higher surface temperatures.

Image: A frozen world heated from within, as envisioned by the paper’s lead author, Lujendra Ojha.

Beyond radiogenic heating, tidal effects are an interesting question, given the potential tidal lock of planets in close orbits around M-dwarfs. Yet planets further out in the system could still benefit from tidal activity, as the paper notes about TRAPPIST-1:

…the age of the TRAPPIST-1 system is estimated to be 7.6 ± 2.2 Gyr; thus, if geothermal heating has waned more than predicted by the age-dependent heat production rate assumed here, tidal heating could be an additional source of heat for basal melting on the TRAPPIST-1 system. On planets e and f of the TRAPPIST-1 system, tidal heating is estimated to contribute heat flow between 160 and 180 mW m−2. Thus, even if geothermal heating were to be negligible on these bodies, basal melting could still occur via tidal heating alone. However, for TRAPPIST-1 g, the mean tidal heat flow estimate from N-body simulation is less than 90 mW m−2. Thus, ice sheets thinner than a few kilometers are unlikely to undergo basal melting on TRAPPIST-1 g.

So we have two mechanisms in play to maintain lakes or oceans beneath surface ice on M-dwarf planets. The finding is encouraging given that one of the key objections to life in these environments is the time needed for life to evolve given that the young planet should be bombarded by ultraviolet and X-ray radiation, a common issue for these stars. We put in place what Amri Wandel (Hebrew University of Jerusalem), who writes a commentary on this work for Nature Communications, calls ‘a safe neighborhood,’ and one for which forms of biosignature detection relying on plume activity will doubtless emerge building on our experience at Enceladus and Europa.

The paper is Ojha et al., “Liquid water on cold exo-Earths via basal melting of ice sheets,” Nature Communications 13, Article number: 7521 (6 December, 2022). Full text. Wandel’s excellent commentary is “Habitability and sub glacial liquid water on planets of M-dwarf stars,” Nature Communications 14, Article number: 2125 (14 April 2023). Full text.

## Earth in Formation: The Accretion of Terrestrial Worlds

It would be useful to have a better handle on how and when water appeared on the early Earth. We know that comets and asteroids can bring water from beyond the ‘snowline,’ that zone demarcated by temperatures beyond which volatiles like water, ammonia or carbon dioxide are cold enough to condense into ice grains. For our Solar System, that distance in our era is 5 AU, roughly the orbital distance of Jupiter, although the snowline would have been somewhat closer to the Sun during the period of planet formation. So we have a mechanism to bring ices into the inner Solar System but don’t know just how large a role incoming ices played in Earth’s development.

Knowing more about the emergence of volatiles on Earth would help us frame what we see in other stellar systems, as we evaluate whether or not a given planet may be habitable. Usefully, there are ways to study our planet’s formation that can drill down to its accretion from the materials in the original circumstellar disk. A new study from Caltech goes to work on the magmas that emerge from the planetary interior, finding that water could only have arrived later in the history of Earth’s formation.

Published in Science Advances, the paper involves an international team working in laboratories at Caltech as well as the University of the Chinese Academy of Sciences, with Caltech grad student Weiyi Liu as first author. When I think about studying magma, zircon comes first to mind. It appears in crystalline form as magma cools and solidifies. I’m no geologist, but I’m told that the chemistry of melt inclusions can identify factors such as volatile content and broader chemical composition of the original magma itself. Feldspar crystals are likewise useful, and the isotopic analysis of a variety of rocks and minerals can tell us much about their origin.

So it’s no surprise to learn that the Caltech paper uses isotopes, in this case the changing ratio of isotopes of xenon (Xe) as found in mid-ocean ridge basalt vs. ocean island basalt. Specifically, 129Xe* comes from the radioactive decay of the extinct volatile 129I, whose half-life is 15.7 million years, while 136Xe*Pu comes from the extinction of 244Pu, with a halflife of 80 million years. So the 129Xe*/136Xe*Pu ratio is a useful tool. As the paper notes, this ratio:

…evolves as a function of both time and reservoirs compositions (i.e., I/Pu ratio) early in Earth’s history. Hence, the study of the 129Xe*/136Xe*Pu in silicate reservoirs of Earth has the potential to place strong constraints on Earth’s accretion and evolution.

The ocean island basalt samples, originating as far down as the core/mantle boundary, reveal this ratio to be low by a factor of 2.8 as compared to mid-ocean ridge basalts, which have their origin in the upper mantle. Using computationally intensive simulations drawing on what is known as first-principles molecular dynamics (FPMD), the authors find that the low I/Pu levels were established in the first 80 to 100 million years of the Solar System (thus before 129I extinction), and have been preserved for the past 4.45 billion years. Their calculations assess the I/Pu findings under different accretion scenarios, drawing on simulated magmas from the lower mantle, which runs from 680 kilometers below the surface, to the core-mantle boundary (2,900 kilometers), and also from the upper mantle beginning at 15 kilometers and extending downward to 680 kilometers.

The result: The lower mantle reveals an early Earth composed primarily of dry, rocky materials, with a distinct lack of volatiles, with the later-forming upper mantle numbers showing three times the amount of volatiles found below. The volatiles essential for life seem to have emerged only within the last 15 percent, and perhaps less, of Earth’s formation. In the caption below, the italics are mine.

Image: This is Figure 4 from the paper. Caption: Schematic representation of the heterogeneous accretion history of Earth that is consistent with the more siderophile behavior of I and Pu at high P-T [pressure-temperature] conditions (this work). As core formation alone does not result in I/Pu fractionations sufficient to explain the ~3 times lower 129Xe*/136Xe*Pu ratio observed in OIBs [ocean island basalt] compared to MORBs [mid-ocean ridge basalt], a scenario of heterogeneous accretion has to be invoked in which volatile-depleted differentiated planetesimals constitute the main building blocks of Earth for most of its accretion history (phase 1), before addition of, comparatively, volatile-rich undifferentiated materials (chondrite and possibly comet) during the last stages of accretion (phase 2).Isolation and preservation, at the CMB [core mantle boundary], of a small portion of the proto-Earth’s mantle before addition of volatile-rich material would explain the lower I/Pu ratio of plume mantle, while the mantle involved in the last stages of the accretion would have higher, MORB-like, I/Pu ratios. Because the low I/Pu mantle would also have an inherently lower Mg/Si, its higher viscosity could help to be preserved at the CMB until today. Credit: Liu et al.

We’re a long way from knowing in just what proportions Earth’s water has derived from incoming materials from beyond the snowline. But we’re making progress:

…our model sheds light on the origin of Earth’s water, as it requires that chondrites represent the main material delivered to Earth in the last 1 to 15% of its accretion. Independent constraints from Mo [molybdenum] nucleosynthetic anomalies require these late accreted materials to come from the carbonaceous supergroup. Together, these results indicate that carbonaceous chondrites [the most primitive class of meoteorites, containing a high proportion of carbon along with water and minerals] must have represented a non-negligible fraction of the volatile-enriched materials in phase 2 and, thus, play a substantial role in the water delivery to Earth.

All this from the observation that mid-ocean ridge basalts had roughly three times higher iodine/plutonium ratios (inferred from xenon isotopes) as compared to ocean island basalts. The key to this paper, though, is the demonstration that the ratio difference is likely from a history of accretion that began with dry planetesimals followed by a secondary accretion phase driven by infalling materials rich in volatiles.

Thus Earth presents us with a model of planet formation from dry, rocky materials, one that presumably would apply to other terrestrial worlds, though we’d like to know more. To push the inquiry forward, Caltech’s Francois Tissot, a co-author on the paper, advocates looking at rocky worlds within our own Solar System:

“Space exploration to the outer planets is really important because a water world is probably the best place to look for extraterrestrial life. But the inner solar system shouldn’t be forgotten. There hasn’t been a mission that’s touched Venus’ surface for nearly 40 years, and there has never been a mission to the surface of Mercury. We need to be able to study those worlds to better understand how terrestrial planets such as Earth formed.”

And indeed, to better measure the impact of ices brought from far beyond the snowline to the infant worlds of the inner system. Tissot’s work demonstrates how deeply we are now delving into the transition between planetary nebulae and fully formed planets. working across the entire spectrum of what he calls ‘geochemical problematics,’ which includes studying the isotopic makeup of meteorites and their inclusions, the reconstruction of the earliest redox conditions in the Earth’s ocean and atmosphere, and the analysis of isotopes to investigate ancient magmas. At Caltech, he has created the Isotoparium, a state-of-the-art facility for high-precision isotope studies.

That we are now probing our planet’s very accretion is likely not news to many of my readers, but it stuns me as another example of extraordinary methodologies driving theory forward through simulation and laboratory work. And as we don’t often consider work on the geological front in these pages, it seems a good time to point this out.

The paper is Weiyi Liu et al., “I/Pu reveals Earth mainly accreted from volatile-poor differentiated planetesimals,” Science Advances Vol. 9, No. 27 (5 July 2023) (full text).

## Tightening our Understanding of Circumbinary Worlds

I’m collecting a number of documents on gravitational wave detection and unusual concepts regarding their use by advanced civilizations. It’s going to take a while for me to go through all these, but as I mentioned in the last post, I plan to zero in on the intriguing notion that civilizations with abilities far beyond our own might use gravitational waves rather than the electromagnetic spectrum to serve as the backbone of their communication system. It’s a science fictional concept for sure, though there may be ways it could be imagined for a sufficiently advanced culture.

For today, though, let’s look at a new survey that targets highly unusual planets. Binaries Escorted by Orbiting Planets has an acronym I can get into: BEBOP. It awakens the Charlie Parker in me; I can almost smell the smoky air of a mid-20th century jazz club and hear the clinking of glasses above Parker’s stunning alto work. I was thinking about the great sax player because I had just watched, for about the fifth time, Clint Eastwood’s superb 1988 film Bird, whose soundtrack is, of course, fabulous.

On the astronomy front, the BEBOP survey is a radial velocity sweep for circumbinary planets, those intriguing worlds, rare but definitely out there, that orbit around two stars in tight binary systems. Beginning in 2013, BEBOP targeted 47 eclipsing binaries, using data from the CORALIE spectrograph on the Swiss Euler Telescope at La Silla, Chile. This is intriguing because what we know about circumbinary planets has largely come from detections based on transit analysis. Radial velocity work has uncovered planets orbiting one star in a wide binary configuration but until now, not both.

Image: Artist’s visualization of a circumbinary planet. Credit: Ohio State University / Getty Images.

The new work adds data from the HARPS spectrograph at La Silla and the ESPRESSO spectrograph at Paranal to confirm one of two planets at TOI-1338/BEBOP-1. Thus we have radial velocity evidence for the gas giant BEBOP-1 c, massing in the range of 65 Earth masses, in an orbit around the binary of 215 days. A second world, referenced as TOI-1338 b because it shows up only in transit data from TESS, complements the RV find, making this only the second circumbinary system known to host multiple planets. TOI-1338 b is 21.8 times as massive as the Earth and as a transiting world could well be a candidate for atmospheric studies by the James Webb Space Telescope.

But BEBOP-1 c is the planet that stands out. I think I am safe in calling a co-author on this paper, David Martin (Ohio State University), a master of understatement when he describes the problems in extracting radial velocity data on a circumbinary world. After all, we’re relying on the tiniest gravitational effects flagged by minute changes in wavelength, and now we have to factor in multiple sets of stellar spectra. Here’s Martin:

“When a planet orbits two stars, it can be a bit more complicated to find because both of its stars are also moving through space. So how we can detect these stars’ exoplanets, and the way in which they are formed, are all quite different. Whereas people were previously able to find planets around single stars using radial velocities pretty easily, this technique was not being successfully used to search for binaries.”

Nice work indeed. Circumbinary planets are what the paper describes as ‘harsh environments’ for planet formation given the gravitational matrix in which such formation occurs, and thus we should be able to use the growing number of such systems (now 14 including this one) in the study of how planets form and also migrate. BEBOP should be a useful survey in providing accurate masses for planets in systems we’ve already discovered with the transit method.

Image: This is Figure 3 from the paper, offering an overview of the BEBOP-1 system. Caption: The BEBOP-1 system is shown along with the extent of the system’s habitable zone (HZ) calculated using the Multiple Star HZ website. The conservative habitable zone is shown by the dark green region, while the optimistic habitable zone is shown by the light green region. The binary stars are marked by the blue star symbols in the centre. The red shaded region denotes the instability region surrounding the binary stars as described by Holman and Wiegert. BEBOP-1 c’s orbit is shown by the red orbit models…shaded from the 50th to 99th percentiles. TOI-1338 b’s orbit is shown by the yellow models, and is also based on 500 random samples drawn from the posterior in its discovery paper. Credit: Standing et al.

Learning more about how planets in such perturbed environments emerge should advance the study of planet growth around single stars. It’s likely that the increased transit probabilities of circumbinary planets should play into our efforts to study planetary atmospheres as well. And while transits should provide the bulk of new discoveries in this space, radial velocity follow-ups should expand our knowledge of individual systems, being less dependent on orbital periods and inclination. BEBOP presages a productive use of these complementary observing methods.

The paper is Standing et al., “Radial-velocity discovery of a second planet in the TOI-1338/BEBOP-1 circumbinary system,” Nature Astronomy 12 June 2023 (full text). See also Martin et al., “The BEBOP radial-velocity survey for circumbinary planets I. Eight years of CORALIE observations of 47 single-line eclipsing binaries and abundance constraints on the masses of circumbinary planets,” Astronomy & Astrophysics Vol. 624, A68 (April 2019), 45 pp. Abstract.