Forbidden Worlds? Theory Clashes with Observation

Back before we knew for sure there were planets around other stars, the universe seemed likely to be ordered. If planet formation was common, then we’d see systems more or less like our own, with rocky inner worlds and gas giants in outer orbits. And if planet formation was a fluke, we’d find few planets to study. All that has, of course, been turned on its head by the abundant discoveries of exoplanets galore. And our Solar System turns out to be anything but a model for the rest of the galaxy. In today’s essay, Don Wilkins looks at several recent discoveries that challenge planet formation theory. We can bet that the more we probe the Milky Way, the more we’ll find anomalies that challenge our preconceptions.

by Don Wilkins

The past few decades have not been easy on planet formation theories. Concepts formed on the antiquated Copernican speculation, the commonality of star systems identical to the Solar System, have given way to the strangeness and variety uncovered by Kepler, Hubble, and the other space borne telescopes. The richness of the planetary arrangements defies easy explanation.

Penn State University researchers uncovered another oddity challenging current understanding of stellar system development. [1] Study of the LHS 3154 system reveals a planet so massive in comparison to its star that generally accepted theories of planet formation cannot explain the existence of the planet, Figure 1. LHS 3154, an “ultracool” star with a “chilly” surface temperature of 2,700 °K (2,430 °C; 4,400 °F), is an M-dwarf, a category that comprises three quarters of the stars in the Milky Way. Most of the light of LHS 3154 is in the infrared band. The M- dwarf star is nine times less massive than the Sun yet it hosts a planet 13 times more massive than Earth.

Figure 1. An artist rendition of the mass comparison between the Earth and Sun and the star LHS 3154, and its companion, LHS 3154b. Credit: Pennsylvania State University.

In current theories, stars form from condensing large clouds of gas and dust into smaller volumes. After the star forms, the left-over gas and dust which is a much smaller fraction of the original cloud, settles into a disk around the new star. From this much smaller mass, planets will condense, completing the star system. In these theories, the star consumes the major proportion of the progenitor clouds.

The Sun, for example, contains an estimated 99.8% of the mass of the Solar System. Only 0.2% is left over for the eight planets, various moons and asteroids.

The mass ratio comparing LHS 3154b to LHS 3154 is 117 times greater than mass ratio comparing the Earth to the Sun. LHS 3154b probably is Neptune-like in composition, completes its orbit in 3.7 Earth days and, the researchers believe, is a very rare world. Typically M-dwarves host small rocky bodies rather than gas giants.

According to current theories, once the star formed, there should not have been enough mass to form a planet as large as LHS 3154b. A young LHS 3154 disk dust-mass and dust-to-gas ratio must be ten times greater than what is typically observed surrounding an M-dwarf star to birth a giant such as LHS 3154b.

“The planet-forming disk around the low-mass star LHS 3154 is not expected to have enough solid mass to make this planet,” Suvrath Mahadevan, the Verne M. Willaman Professor of Astronomy and Astrophysics at Penn State and co-author on the paper said. “But it’s out there, so now we need to reexamine our understanding of how planets and stars form.”

Mahadevan’s team built a novel spectrograph, the Habitable Zone Planet Finder (HPF), with the intention of detecting planets orbiting the coolest of stars. Planets orbiting low temperature stars might have surfaces cool enough to support liquid water and life. In looking for planets with liquid water, the team found, as often happens in research, something new, a massive planet to challenge current theories of stellar system formation.

Another discovery, this time by a Carnegie Institution for Science team, uncovered another challenging world. [2]

Figure 2. Artist’s conception a small red dwarf star, TOI-5205, and its out-sized companion TOI-5205b. Credit: Katherine Cain, the Carnegie Institution for Science.

“The host star, TOI-5205, is just about four times the size of Jupiter, yet it has somehow managed to form a Jupiter-sized planet, which is quite surprising,” observed Shubham Kanodia, who led the team which found TOI-5205b.

When TOI-5205b crosses in front of TOI-5205, the planet blocks about seven percent of the star’s light—a dimming among the largest known exoplanet transit signals.

The rotating disk of gas and dust that surrounds a young star gives birth to its planetary companions. More massive planets require more of the gas and dust left over as the star ignites. Gas planet formation, in the accepted theories, requires about 10 Earth masses of rocky material to produce the massive rocky core of the gas giant. Once the core is formed, it gathers gas from the surrounding clouds, resulting in the mammoth atmosphere of the giant planet.

“TOI-5205b’s existence stretches what we know about the disks in which these planets are born,” Kanodia explained. “In the beginning, if there isn’t enough rocky material in the disk to form the initial core, then one cannot form a gas giant planet. And at the end, if the disk evaporates away before the massive core is formed, then one cannot form a gas giant planet. And yet TOI-5205b formed despite these guardrails. Based on our nominal current understanding of planet formation, TOI-5205b should not exist; it is a ‘forbidden’ planet.”

Not all mysteries are confined to M-dwarfs. A sun-like star, an infant of 14 million years some 360 light years from Earth, hosts a gas giant six times more massive than Jupiter, that orbits the star at a distance twenty times greater than the distance separating Jupiter and the Sun, Figure 3. [3]

Figure 3. A direct image of the exoplanet YSES 2b (bottom right) and its star (center). The star is blocked by a coronagraph. Credit: ESO/SPHERE/VLT/Bohn et al.

The large distance from YSES 2b to the star does not fit either of the two most well-known models describing large gaseous planet formation. If YSES 2b formed by means of core accretion at such an enormous distance far from the star, the planet should be much lighter than what is observed as a result of scarcity of disk material at that distant location. YSES 2b is too massive to satisfy this theory.

Gravitationally instability, the second theorized method for producing gas giants, postulates very massive protostellar disks that are unstable, splintering into large clumps from which gas giants are directly formed. YSES 2b appears not massive enough to have been formed in this fashion.

In a third possibility, YSES 2b might have formed by core accretion much closer to its host star and migrated outwards. A second planet is needed to pull YSES 2b into the outer regions of the system, but no such planet has been located.

Observations by the current generation of space-borne telescopes have upset the theories of planet formation. Hot Jupiters, worlds orbiting pulsars, odd arrangements of worlds, super Earths, and wandering worlds flung close to a star then flying back have complicated the ideas of Laplace, See, Chamberlin and Moulton. Further study by the James Webb Space Telescope and its successors will only enliven the debate surrounding the origin of the planets.

References

[1] Guðmundur Stefánsson, Suvrath Mahadevan, Yamila Miguel, et al, “A Neptune-mass exoplanet in close orbit around a very low-mass star challenges formation models,” Science, 30 Nov 2023, Vol. 382, Issue 6674, pp. 1031-1035, DOI: 10.1126/science.abo0233.

[2] Shubham Kanodia et al, “TOI-5205b: A Short-period Jovian Planet Transiting a Mid-M Dwarf,” The Astronomical Journal (2023). DOI: 10.3847/1538-3881/acabce

[3] Alexander J. Bohn et al. “Discovery of a directly imaged planet to the young solar analog YSES 2.” Accepted for publication in Astronomy & Astrophysics, www.aanda.org/10.1051/0004-6361/202140508

A Resonant Sub-Neptune Harvest at HD 110067

The ancient notion of the ‘music of the spheres’ sounds primitive until you learn something about planetary dynamics. Gravity is wondrous and can nudge planets in a given system into orbits that show an obvious mathematical ratio. Two planets in resonance can emerge, for instance, in a 2:1 ratio, where one goes around its star twice in the time it takes the second to orbit it once. Such linkages might seem almost coincidental to the casual observer until the coincidences begin to pile up.

In the exoplanet system at HD 110067, for example, resonance flourishes, so much so that we have six planets moving in a ‘resonance chain.’ No coincidence here, just gravity at work, although an actual coincidence is that just when I finished a post highlighting system dynamics in closely packed environments like TRAPPIST-1 as a ‘brake’ on inbound comets, an international team should reveal HD 110067’s resonance chain. It’s a beauty, for all six planets not only move in harmonic rhythm but also turn out to be transiting worlds. An orbital dance this complex is rare, but even more so is the ability to study such worlds thanks to the happenstance of our viewing angle.

Transits allow us to extract information, and plenty of it, including analysis of planetary atmospheres as light from the central star passes through them. Because complex resonances are in some sense ‘self-correcting,’ they tell us something about the history of the system, for planet migration during the period when the resonance is being established influences the final state of the system. In HD 110067 we have a mother lode of system harmonics around a star that, usefully enough, is fifty times brighter than TRAPPIST-1, where we have seven rocky planets in a resonant chain.

HD 110067 offers up all of this for that highly interesting category of planets called ‘sub-Neptunes,’ about which we’d like to know a lot more. 100 light years away in the constellation Coma Berenices, HD 110067’s resonance chain is obviously complex. The innermost planet makes three orbital revolutions as the second world makes two – a 3:2 resonance. But the chain continues: 3:2, 3:2, 3:2, 4:3, and 4:3, with the innermost planet making six orbits as the outermost planet completes one.

Image: A rare family of six exoplanets has been unlocked with the help of ESA’s Cheops mission. The planets in this family are all smaller than Neptune and revolve around their star HD110067 in a very precise waltz. When the closest planet to the star makes three full revolutions around it, the second one makes exactly two during the same time. This is called a 3:2 resonance. The six planets form a resonant chain in pairs of 3:2, 3:2, 3:2, 4:3, and 4:3, resulting in the closest planet completing six orbits while the outermost planet does one. CHEOPS confirmed the orbital period of the third planet in the system, which was the key to unlocking the rhythm of the entire system. This is the second planetary system in orbital resonance that CHEOPS has helped reveal. The first one is called TOI-178. Credit and copyright: ESA.

Untangling this particular chain was not easy. The astronomers used data from both ESA’s CHEOPS mission and the TESS space observatory to nail down the system architecture. Data from TESS determined the orbital periods of the innermost worlds to be 9 and 14 days. Observations from CHEOPS tagged planet d at 20.5 days and thus demonstrated that while the innermost planet revolves 9 times around the star, the second revolves six, and the third planet four times. The periods of the three outer planets could then be deduced as 31, 41 and 55 days respectively, with further analysis of the TESS data showing that no solution other than the 3:2, 3:2, 3:2, 4:3, 4:3 chain would work. Ground-based observations supplemented the TESS and CHEOPS data.

The analysis was led by Rafael Luque (University of Chicago) and published in Nature. Says Luque:

“This discovery is going to become a benchmark system to study how sub-Neptunes, the most common type of planets outside of the solar system, form, evolve, what are they made of, and if they possess the right conditions to support the existence of liquid water in their surfaces.”

TOI-178 offers a five-planet resonance chain that may include a sixth world in this system of transiting planets in the constellation Sculptor, some 200 light years out. The paper on HD 110067 takes note of the fact that resonant architectures like these imply a situation that has remained unchanged since the birth of the system, making them useful laboratories for planet formation and evolution. The planetary radii at HD 110067 range from 1.94 that of Earth to 2.85 times as large (1.94R to 2.85R), and the low densities found in the three planets whose mass has been measured point to the likelihood of large atmospheres dominated by hydrogen.

Image: Tracing a link between two neighbor planets at regular time intervals along their orbits creates a pattern unique to each couple. The six planets of the HD110067 system create together a mesmerizing geometric pattern due to their resonance-chain. © CC BY-NC-SA 4.0, Thibaut Roger/NCCR PlanetS.

Ann Egger (a graduate student at the University of Bern and a co-author of the paper on this work) notes what is ahead in the study of this system:

“The sub-Neptune planets of the HD110067 system appear to have low masses, suggesting they may be gas- or water-rich. Future observations, for example with the James Webb Space Telescope (JWST), of these planetary atmospheres could determine whether the planets have rocky or water-rich interior structures.”

The sheer beauty of the HD 110067 system comes across in the animation below:

Image: To-scale animation of the orbits of the six resonant planets in the HD110067 system. The pitch of the notes played when each planet transits matches the resonant change in orbital frequencies between each subsequent planet. The relative sizes of the planets is accurate, although their true size compared to the star is much smaller. Also available at https://www.youtube.com/watch?v=2rrODAG7nmI.

The paper is Luque et al., “A resonant sextuplet of sub-Neptunes transiting the bright star HD 110067,” Nature 623 (November 29, 2023), 932-937 (abstract).

Tightening Proxima Centauri’s Orbit (and an Intriguing Speculation)

Although I think most astronomers have assumed Proxima Centauri was bound to the central binary at Alpha Centauri, the case wasn’t definitively made until fairly recently. Here we turn to Pierre Kervella (Observatoire de Paris), Frédéric Thévenin (Côte d’Azur Observatory) and Christophe Lovis (Observatoire Astronomique de l’Université de Genève). We last saw Dr. Kervella with reference to a paper on aerographite as a sail material, but his work has appeared frequently in these pages, analyzing mission trajectories and studying the Alpha Centauri system. Here he and his colleagues use HARPS spectrographic data to demonstrate that we have at Centauri a single gravitationally bound triple system. This is important stuff; let me quote the paper on this work to explain why (italics mine):

Although statistical considerations are usually invoked to justify that Proxima is probably in a bound state, solid proof from dynamical arguments using astrometric and radial velocity (RV) measurements have never been obtained at a sufficient statistical significance level. As discussed by Worth & Sigurdsson (2016), if Proxima is indeed bound, its presence may have impacted planet formation around the main binary system.

This is a six-year old paper, but I want to return to it now because a new paper from the same team will tighten up its conclusions and slightly alter some of them. We’ve gone from resolving whether Proxima is bound to the A/B binary to pondering the issues involved in the dynamical history of this complex system. That in turn can inform the ongoing search for planets around Centauri A and B at least in terms of explaining what we might find there and how these two systems evolved. The original paper on this work lays out the challenges involved in tracing the orbit of the red dwarf. For HARPS is exquisitely sensitive to the Doppler shifts of starlight, and these data, obtained between 2004 and 2016, contain potential booby traps for analysis.

Image: Pierre Kervella, of the Observatoire de Paris/PSL.

Convective blueshift is one of these. We’re looking at the star’s spectral lines as we calculate its motion, and some of these are displaced toward the blue end of the spectrum because of the structure of its surface convection patterns. The lifting and sinking of hot internal gases has to be factored into the analysis and its effect nulled out. The spectral lines are displaced toward the blue, in effect a negative radial velocity shift, although the effect is stronger for hotter stars. In the case of Proxima, Kervella’s team finds a relatively small convective blueshift, though still one to be accounted for.

A similar though more significant issue is gravitational redshift, which occurs as photons climb out of the star’s gravity well. Here the effect is “an important source of uncertainty on the RV of Proxima” whose value can be established and corrected. How the astronomers went about making these corrections is laid out in a discussion of radial velocities that aspiring exoplanet hunters will want to read.

Image: Orbital plot of Proxima showing its position with respect to Alpha Centauri over the coming millenia (graduations in thousands of years). The large number of background stars is due to the fact that Proxima is located very close to the plane of the Milky Way. Credit: P. Kervella/ESO/Digitized Sky Survey 2/Davide De Martin/Mahdi Zamani.

Out of all this we learn that Proxima’s elliptical orbit around Centauri A and B’s barycenter extends from 800 billion kilometers when closest (periastron) to 1.9 trillion kilometers at apastron, its farthest distance, with an orbital period of approximately 550,000 years. The orbital phase is currently closest to apastron.

The Astronomy & Astrophysics site (this is the journal in which the paper above appeared) is currently down, so I’m quoting from the version of the paper on arXiv, which after noting that the escape velocity of Alpha Centauri at Proxima’s distance (545 +/- 11 m/s) is about twice as large as Proxima’s measured velocity, goes on to speculate in an intriguing way:

Proxima could have played a role in the formation and evolution of its planet (Anglada-Escudé et al. 2016). Conversely, it may also have influenced circumbinary planet formation around αCen (Worth & Sigurdsson 2016). A speculative scenario is that Proxima b formed as a distant circumbinary planet of the αCen pair, and was subsequently captured by Proxima. Proxima b could then be an ocean planet resulting from the meltdown of an icy body (Brugger et al. 2016). This would also mean that Proxima b may not have been located in the habitable zone (Ribas et al. 2016) for as long as the age of the αCen system (5 to 7 Ga; Miglio & Montalbán 2005; Eggenberger et al. 2004; Kervella et al. 2003; Thévenin et al. 2002).

The idea of Proxima b as a captured planet has not to my knowledge appeared anywhere else in the literature. I was fascinated, enough so that I dashed off a quick email to Dr. Kervella asking about this as well as the current status of the orbital calculations. And indeed, his response indicates new work in progress:

… we identified a mistake in our 2017 determination of the orbital parameters of Proxima. In the papier, they are expressed in the Galactic coordinate system, and the orbital inclination is thus not directly comparable to that of the Alpha Cen AB orbit. We are preparing a new publication with revised orbits and parameters for all three stars. The main difference is that now the orbital plane of Proxima is better aligned with that of AB. The gravitationally bound nature of Proxima with Alpha Cen AB is also strengthened, as we include new astrometry and radial velocities.

I’ll cover the new paper as soon as it appears. Dr. Kervella also observes that confirming a scenario of Proxima b as a captured planet would be difficult (Proxima b has ‘forgotten’ the history of its orbital evolution, as he puts it), meaning that working with astrometric data alone will not be sufficient. But the arrival of telescopes like the Extremely Large Telescope, now under construction in Chile’s Atacama Desert with first light planned for 2028, should signal a treasure trove of new information. A spectrum obtained by ELT could show us whether Proxima b is indeed an ocean planet.

The paper on Proxima Centauri’s orbit is Kervella, Thévenin & Lovis, “Proxima’s orbit around α Centauri,” Astronomy & Astrophysics Vol. 598 (February 2017), L7 (abstract/preprint).

The Odds on Alpha Centauri

How extraordinary that the nearest star to Earth is actually a triple system, the tight central binary visually merged as one bright object, the third star lost in the background field but still a relatively close 13000 or so AU from the others. Humans couldn’t have a better inducement to achieve interstellar flight on the grounds of these stars alone. We get three stellar types: The G-class Centauri A, the K-class Centauri B, both of which are capable of hosting planets, perhaps habitable, of their own.

And then we have Proxima Centauri, opening up M-class red dwarf stars to close investigation, and we already know of a planet in the habitable zone there, adding to the zest of the venture. If extraterrestrial beings in a system like this would have even more inducement to travel, with another star’s planets perhaps as close to them as our own system’s worlds are to us, we humans are also spurred to undertake a journey, because 4.2 light years is a mere stone’s throw in the overall galactic distribution.

Image: The central binary at Alpha Centauri, with the two stars only resolved in the x-ray image. Credit: X-ray: NASA/CXC/University of Colorado/T.Ayres; Optical: Zdenek Bardon/ESO.

I like this image, used by Dirk Schulze-Makuch to illustrate a recent popular science article, because it includes the Chandra X-Ray imagery. That’s how we can separate the central stars, which are at times nearly as close as Saturn is to the Sun while they orbit their common barycenter. Centauri Dreams readers will recognize Schulze-Makuch (Technical University Berlin and an adjunct professor at Washington State) not only as a prolific writer but the author of a host of scientific papers including many we’ve looked at in these pages. He’s played a valuable role in presenting astrobiological matters to the general public, part of the flowering of interstellar investigation that continues as we keep finding interesting worlds to explore.

If you’re wondering about Proxima Centauri’s location, the image below flags it. Credit: ESO/B. Tafreshi (twanight.org)/Digitized Sky Survey 2; Acknowledgement: Davide De Martin/Mahdi Zamani).

I like to keep an eye on what appears in the popular press from respected scientists, because they’re bringing credibility to matters that often get distorted by mainstream media attention (not to mention what happens on social media sites). We should always give a nod to scientists willing to explain their work and the broader issues involved given that kind of competition for the public’s attention. It’s interesting in this case to get Schulze-Makuch’s take on habitability at Alpha Centauri. He’s pessimistic about Proxima but is surprisingly bullish on Centauri A and B:

The other two stars in the system are believed to have planets, although they have not been confirmed. (A possible Neptune-size planet was reported in 2021 orbiting Alpha Centauri A at roughly the same distance as Earth orbits the Sun, but this could turn out to be a dust cloud instead.) The apparent lack of any brown dwarfs or gas giants close to Alpha Centauri A and B make the likelihood of terrestrial planets greater than it would be otherwise, at least in theory. The chances of a rocky, potentially habitable planet in our neighboring solar system might therefore be as high as 75 percent.

The Proxima Centauri problem is, of course, the X-ray flux, although Schulze-Makuch also considers tidal lock a distinct negative. The Chandra data (citation below) revealed a relatively benign influx of X-rays for Centauri A and B, making them fine hosts for life if it can develop there. But Proxima is deeply problematic, receiving an average dose of X-rays some 500 times greater than Earth’s, and some 50,000 times as great during periods of flare activity, which M-dwarfs are particularly prone to in their younger days.

Here the word ‘younger’ is a bit deceptive. Recall that this kind of star can live for several trillion years. That’s a bit humbling, considering that the universe itself is thought to be 13.8 billion years old. In that sense all M-dwarfs are ‘young.’

Just as we can zoom in via X-ray to see the central stars, we can also take a look at Proxima Centauri’s movements via spectroscopic data, which we’ll examine next time, along with a fascinating speculation on the origin of Proxima b.

For more on the X-ray environment at Alpha Centauri, see Ayres, “Alpha Centauri Beyond the Crossroads,” Research Notes of the AAS Vol. 2, No. 1 (January, 2018), 17 (abstract). The possibility of a ‘warm Neptune’ at Alpha Centauri is discussed in Wagner et al., “Imaging low-mass planets within the habitable zone of α Centauri,” Nature Communications 12, Article number: 922 (2021). Full text. We’ll be talking about this one a bit more in coming days.

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