Super Earths/Hycean Worlds

Dave Moore is a Centauri Dreams regular who has long pursued an interest in the observation and exploration of deep space. He was born and raised in New Zealand, spent time in Australia, and now runs a small business in Klamath Falls, Oregon. He counts Arthur C. Clarke as a childhood hero, and science fiction as an impetus for his acquiring a degree in biology and chemistry. Dave has kept up an active interest in SETI (see If Loud Aliens Explain Human Earliness, Quiet Aliens Are Also Rare) as well as the exoplanet hunt, and today examines an unusual class of planets that is just now emerging as an active field of study.

by Dave Moore

Let me draw your attention to a paper with interesting implications for exoplanet habitability. The paper is “Potential long-term habitable conditions on planets with primordial H–He atmospheres,” by Marit Mol Lous, Ravit Helled and Christoph Mordasini. Published in Nature Astronomy, this paper is a follow-on to Madhusudhan et al’s paper on Hycean worlds. Paul’s article Hycean Worlds: A New Candidate for Biosignatures caught my imagination and led to this further look.

Both papers cover Super-Earths, planets larger than 120% of Earth’s radius, but smaller than the Sub-Neptunes, which are generally considered to start at twice Earth’s radius. Super-Earths occur around 40% of M-dwarf stars examined and are projected to constitute 30% of all planets, making them the most common type in the galaxy. Hycean planets are a postulated subgroup of Super-Earths that have a particular geology and chemistry; that is, they have a water layer above a rocky core below a hydrogen–helium primordial atmosphere.

We’ll be hearing a lot more about these worlds in the future. They are similar enough to Earth to be regarded as a good target for biomarkers, but being larger than Earth, they are easier to detect via stellar Doppler shift or stellar transit, and their deep atmospheres make obtaining their spectra easier than with terrestrial worlds. The James Webb telescope is marginal for this purpose, but getting detailed atmospheric spectra is well within the range of the next generation of giant, ground-based telescopes: the 39-meter Extremely Large Telescope and the 24.5-meter Giant Magellan Telescope, both of which are under construction and set to start collecting data by the end of the decade (the status of the Thirty Meter Telescope is still problematic).

Earth quickly lost its primordial hydrogen-helium atmosphere, but once a planet’s mass reaches 150% of Earth’s, this process slows considerably and planets more massive than that can retain their primordial atmosphere for gigayears. Hydrogen, being a simple molecule, does not have a lot of absorption lines in the infrared, but under pressure, the pressure-broadening of these lines makes it a passable greenhouse gas.

If the atmosphere is of the correct depth, this will allow surface water to persist over a much wider range of insolation than with Earth-like planets. With enough atmosphere, the insulating effect is sufficient to maintain temperate conditions over geological lengths of time from the planet’s internal heat flow alone, meaning these planets, with a sufficiently dense atmosphere, can have temperate surface conditions even if they have been ejected from planetary systems and wander the depths of space.

Figure 1: This is a chart from Madhusudhan et al’s paper showing the range where Hycean planets maintain surface temperatures suitable for liquid water, compared with the habitable zone for terrestrial planets as derived by Kopparapu et al. ‘Cold Hycean’ refers to planets where stellar insolation plays a negligible part in heating the surface. Keep in mind, that Lous et al regard the inner part of this zone as unviable due to atmospheric loss.

Madhusudhan et al’s models were a series of static snapshots under a variety of conditions. Lous et al’s paper builds on this by modeling the surface conditions of these planets over time. The authors take a star of solar luminosity with a solar evolutionary track and, using 1.5, 3 and 8 Earth mass planets, model the surface temperature over time at various distances and hydrogen overpressures, also calculating in the heat flow from radiogenic decay.

Typically, a planet will start off too hot. Its steam atmosphere will condense, leaving the planet with oceans; and after some period, the surface temperature will fall below freezing. The chart below shows the length of time a planet has a surface temperature that allows liquid water. (Note that, because of higher surface pressures, water in these scenarios has a boiling point well over 100°C, so the oceans may be considered inhospitable to life for parts of their range.)

Planets with small envelope masses have liquid water conditions relatively early on, while planets with more massive envelopes reach liquid water conditions later in their evolution. Out to 10 au, stellar insolation is the dominant factor in determining the surface temperature, but further out than that, the heat of radiogenic decay takes over. The authors use log M(atm)/log M(Earth) on their Y axis, which I didn’t find very helpful. To convert this to an approximate surface pressure in bars, make the following conversions: 10-6 = 1 bar, 10-5 = 10 bar, 10-4 = 100 bar and so on.

Figure 2: Charts a-c are for core masses of 1.5 (a), 3 (b) and 8 M? (c). The duration of the total evolution is 8 Gyr. The color of a grid point indicates how long there were continuous surface pressures and temperatures allowing liquid water, ?lqw. These range from 10 Myr (purple) to over 5 Gyr (yellow). Gray crosses correspond to cases with no liquid water conditions lasting longer than 10 Myr. Atmospheric loss is not considered in these simulations. d is the results for planets with a core mass of 3 M?, but including the constraint that the surface temperature must remain between 270 and 400 K. Every panel contains an ‘unbound’ case where the distance is set to 106 AU and solar insolation has become negligible.

The authors then ran their model adjusted for hydrodynamic escape (Jeans escape is negligible). This loss of atmosphere mainly affects the less massive, closer in planets with thinner atmospheres.

To quote:

The results when the hydrodynamic escape model is included are shown in Fig. 3. In this case, we find that there are no long-term liquid water conditions possible on planets with a primordial atmosphere within 2au. Madhusudhan et al. found that for planets around Sun-like stars, liquid water conditions are allowed at a distance of ~1 au. We find that the pressures required for liquid water conditions between 1 and 2au are too low to be resistant against atmospheric escape, assuming that the planet does not migrate at a late evolutionary stage.

Figure 3: Charts a-c are for core masses of 1.5 (a), 3 (b) and 8 M? (c). d is the results for planets with a core mass of 3 M?, but including the constraint that the surface temperature must remain between 270 and 400 K. Note: escape inhibits liquid water conditions by removing the atmosphere for close-in planets with low initial envelope masses. Lower core masses are more affected.

The authors also note that their simulations indicate that, unlike terrestrial planets which require climatic negative feedback loops to retain temperate conditions, Hycean worlds are naturally stable over very long periods of time.

The authors then go on to discuss the possibility of life, pointing out that the surface pressures required are frequently in the 100 to 1000 bar range, which is the level of the deep ocean and with similar light levels, so photosynthesis is out. This is a problem searching for biomarkers because photosynthesis produces chemical disequilibria, which are considered a sign of biological activity, whereas chemotrophs, the sort of life forms you would expect to find, make their living by destroying chemical disequilibria.

The authors hope to do a similar analysis with red dwarf stars as these are the stars where Super-Earths occur most frequently. Also, they are the stars where the contrast between stellar and planetary luminosity gives the best signal.

Thoughts and Speculations

The exotic nature of these planets lead me to examine their properties, so here are some points I came up with that you may want to consider:

i) The Fulton Gap—also called the small planet mass-radius valley. Small planets around stars have a distinctly bimodal distribution with peaks at 1.3 Earth radii and 2.4 Earth radii with a minimum at 1.8 Earth radii. Density measurements align with this distribution. Super-Earth densities peak, on average, at 1.4 Earth radii with a steady fall off above that. Planets smaller than about 1.5 Earth radii are thought to contain a solid core with shallow atmospheres, whereas planets above 1.8 Earth radii are thought to have deep atmospheres of volatiles and a composition like an Ice-Giant (i.e. they are Sub-Neptunes.)

Taking Lous et al’s planets, a 3 Earth mass planet would have an approximate radius of 1.3 Earth radii. An 8 Earth mass planet would have an approximate radius of 1.8 Earth radii (assuming similar densities to Earth.) This would point towards the 8 Earth mass planets having an atmosphere too deep to make a Hycean world. The atmosphere would probably transition into a supercritical fluid.

ii) I compared the liquid water atmospheric pressures from our solar system’s giant planets with the expectations of the paper. I had trouble finding good figures, as the pressure temperature charts peter out at water ice cloud level, but here are the approximate figures for the giant planets compared with the range on the 270°K-400°K graph that Lous et al produced:

Jupiter: 7-11 bar / 8-30 bar

Saturn: 10-20 bar / 25-100 bar

Neptune: 50+ Bar (50 bar is the level at which ice clouds form) / 200-500 bar

Our giant planets appear to be on the shallow side of the paper’s expectations. This could be attributed to our giant planets having greater internal heat flow than the Super-Earths modeled, but that would make the deviation greatest for Jupiter and least for Neptune. The deviation, however, appears to increase in the other direction.

The authors of the paper note that their models did not take into consideration the greenhouse effect of other gasses such as ammonia and methane likely to be found in Hycean planets’ atmospheres, which would add to the greenhouse effect and therefore give a shallower pressure profile for a given temperature. And from looking at our giant planets, this would appear to be the case.

This could mean that an unbound world would maintain a liquid ocean under something like 100+ bars of atmosphere rather than the 1000 bars originally postulated.

iii) Next, I considered the chemistry of Hycean worlds. Using our solar system’s giant planets as a guide, we can expect considerable quantities of methane, ammonia, hydrogen sulfide and phosphine in the atmospheres of Hycean worlds. The methane would stay a gas, but ammonia, being highly hydrophilic, would dissolve into the ocean. If the planet’s nitrogen to water ratio is similar to Earth’s, this would result in an approximately 1% ammonia solution. A ratio like Jupiter’s would give a 13% solution. (Ammonia cleaning fluids are generally 1-3% in concentration.) A 1% solution would have a pH of about 12, but some of this alkalinity may be buffered by the hydrosulfide ion (HS) from the hydrogen sulfide in solution.

It then occurred to me to look at freezing point depression curves of ammonia/water mixtures, and they are really gnarly. An ammonia/water ocean, if cooled below 0°C, will develop an ice cap, but as the water freezes out, this increases the ammonia concentration, causing a considerable depression in the freezing point. If the ocean reaches -60°C, something interesting starts to happen. The ice crystals forming in the ocean and floating up to the base of the ice cap start to sink, as the ocean fluid, now 25% ammonia, is less dense than ice. This will result in an overturn of the ocean and the ice cap. Further cooling will result in the continued precipitation of ice crystals until the ocean reaches a eutectic mixture of approximately 2 parts water to 1 part ammonia, which freezes at -91°C. (For comparison, pure ammonia freezes at -78°C.) Note: all figures are for 1 bar.

When discussing the possibility of liquid water on planets, we have to include the fact that water under sufficient pressure can be liquid up to its critical point of 374°C. The paper takes this into account; but what we see here is that, aside from showing that the range of insolation over which planets can have liquid water is larger than we thought, the range that water can be liquid is also larger than we assumed.

While some passing thought has been given to the possibility of ammonia as a solvent for life forms, nobody appears to have considered water/ammonia mixtures.

iv) Turning from ammonia to methane, I began to wonder if these planets would have a brown haze like Titan. A little bit of research showed that the brown haze of Titan is mainly made of tholins, which are formed by the UV photolysis of methane and nitrogen. Tholins are highly insoluble in hydrocarbons, which is why Titan’s lakes are relatively pure mixtures of hydrocarbons. However, tholins are highly soluble in polar solvents like water. So a Hycean planet with a water cycle would rain out tholins that formed in the upper atmosphere, but if the surface was frozen like Titan’s, they would stay in the atmosphere, forming a brown haze.

This points to the possibility that there are significant differences in the composition of a Hycean planet’s atmosphere depending on whether its surface is frozen or oceanic. and this may be detectable by spectroscopy.

I’m looking forward to finding out more about these planets. In some ways, I feel that in respect to exosolar planets, we are now in a position similar to that of our own solar system in the early 60s – eagerly awaiting the first details to come in.

References

Marit Mol Lous, Ravit Helled and Christoph Mordasini, “Potential long-term habitable conditions on planets with primordial H–He atmospheres,” Nature Astronomy, 6: 819-827 (July 2022). Full text.

Nikku Madhusudhan, Anjali A. A. Piette, and Savvas Constantinou, “Habitability and Biosignatures of Hycean Worlds,” The Astrophysical Journal, (Aug. 2021). Preprint.

Fulton et al, “The California-Kepler Survey. III. A Gap in the Radius Distribution of Small Planets,” The Astronomical Journal, 154 (3) 2017. Abstract.

Christopher P. McKay, ”Elemental composition, solubility, and optical properties of Titan’s organic haze,” Planetary Space Science, 8: 741-747 (1996). Abstract.

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137496 b: A Rare ‘Hot Mercury’

We haven’t had many examples of so-called ‘hot Mercury’ planets to work with, or in this case, what might be termed a ‘hot super-Mercury’ because of its size. For HD 137496 b actually fits the ‘super-Earth’ category, at roughly 30 percent larger in radius than the Earth. What makes it stand out, of course, is the fact that as a ‘Mercury,’ it is primarily made up of iron, with its core carrying over 70 percent of the planet’s mass. It’s also a scorched world, with an orbital radius of 0.027 AU and a period of 1.6 days.

Another planet, non-transiting, turns up at HD 137496 as well. It’s a ‘cold Jupiter’ with a minimum mass calculated at 7.66 Jupiter masses, an eccentric orbit of 480 days, and an orbital distance of 1.21 AU from the host star. HD 137496 c is thus representative of the Jupiter-class worlds we’ll be finding more of as our detection methods are fine-tuned for planets on longer, slower orbits than the ‘hot Jupiters’ that were so useful in the early days of radial velocity exoplanet discovery.

The discoverers of the planetary system at HD 137496, an international group led by Tomas Silva (University of Porto, Portugal), found HD 137496 b, the hot Mercury, in K2 data, its transits apparent in the star’s light curve. The gas giant HD 137496 c was then identified in radial velocity work using the reliable HARPS and CORALIE spectrographs.

The primary is a G-class star a good bit older than the Sun, its age calculated at 8.3 billion years, but with a comparable mass (1.03 solar masses), and a radius of approximately 1.50 solar radii.

Image: HARPS (orange) and CORALIE (blue) radial velocities. In this figure, we present our RV time series. As is clearly seen, the data show a long-term and high-amplitude trend (semiamplitude of ~ 200 m s-1), typical of the signature of a long period giant planet. Credit: Silva et al.

A hot Mercury should turn out to be a useful find in a variety of ways. As the paper notes:

HD 137496 b (K2-364 b) joins the small sample of well characterized dense planets, making it an interesting target for testing planet formation theories, density enhancing mechanisms, and even the possible presence of an extended cometlike mineral rich exosphere. Together with HD 137496 c (K2-364 c), a high-mass (mass ratio…, high-eccentricity planet, this system presents an interesting architecture for planetary evolution studies. Future astrometric observations could also provide significant constraints on the relative inclination of the planetary orbits, unraveling new opportunities to discover the system’s dynamical history.

Keep in mind that most of the planets we now know about have radii somewhere between that of Earth and Neptune. In this range, numerous different system architectures are in play, and a wide variety of possible formation scenarios. As the authors note, high-density planets like HD 137496 b are distinctly under-sampled, which has been a check on theories of planet formation that would accommodate them.

And the theorists are going to have their hands full with this one. HD 137496 b’s parent star shows too little iron to form a planet with this density. I’m going to quote Sasha Warren on this. Working on a PhD at the University of Chicago, Warren focuses on how planetary atmospheres have evolved, particularly those of Mars and Venus. Of HD 137496 b, she has this to say in a recent article on astrobites about how such planets can become more iron-rich:

Firstly, the protoplanetary disks of dust and gas within which planets form around young stars can change in composition as a function of distance from the star. So, it is possible that a combination of high temperatures and magnetic interactions between the host star and the protoplanetary disk concentrated iron-rich materials where HD 137496 b originally formed. This could mean star compositions might not be very useful to help understand what short period rocky planets are made of. Secondly, planets close to their stars like HD 137496 b are so hot that their rocky surfaces can sometimes just evaporate away!

It will be fascinating to see how our theories evolve as we begin to expand the catalog of hot Mercury planets. 137496 b is only the fifth world in this category yet discovered.

The paper is Silva et al., “The HD 137496 system: A dense, hot super-Mercury and a cold Jupiter,” in process at Astronomy & Astrophysics (preprint).

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Exomoons: The Binary Star Factor

Centauri Dreams readers will remember Billy Quarles’ name in connection with a 2019 paper on Alpha Centauri A and B, which examined not just those stars but binary systems in general in terms of obliquity — axial tilt — on potential planets as affected by the gravitational effects of their systems. The news for habitability around Centauri B wasn’t good. Whereas the Moon helps to stabilize Earth’s axial tilt, the opposite occurs on a simulated Centauri B planet. And without a large moon, gravitational forcing from the secondary star still causes extreme obliquity variations.

Orbital precession induced by the companion star is the problem, and it may be that Centauri A and B are simply too close together, whereas more widely separated binaries are less disruptive. I’ll send you to the paper for more (citation below), but you can get an overview with Axial Tilt, Habitability, and Centauri B. It’s exciting to think that our ongoing investigations of Centauri A and B will, one of these days, be able to confirm these results or cause them to be reassessed, assuming we find planets there.

Exomoons in Binary Systems

Quarles (Georgia Institute of Technology) continues to use numerical methods to look at the dynamics in both single and multiple star systems, with his interest in Centauri A and B undiminished. His most recent paper looks at exomoon possibilities at binary star systems, homing in on orbital stability in systems where a companion star forces greater eccentricity. We can look for such moons using transit-timing variations as well as variations in the durations of a transit. All of this gives us no more than hints of a moon, which is too small to be seen, but it opens up new space for such detections.

Co-author Siegfried Eggl (University of Illinois Urbana-Champaign) explains:

“We first had to determine the orbital resonances in the systems we looked at. When moons and planets have slightly elliptical orbits, they don’t always move at the same speed. The more eccentric an orbit, the more frequencies can be excited, and we see these resonances become more and more important. At some point there will be overlapping resonances that can lead to chaos in the system. In our study we have shown, however, that there is enough stable ‘real estate’ to merit a thorough search for moons around planets in double star systems.”

Image: In this map of overlapping orbital resonances, the regions between resonances are colored black and could allow for stable satellite orbits under optimal conditions. The light green curve connects the first point of intersection between adjacent resonances and marks a stability boundary within the three body problem. Credit: Quarles et al.

Transit timing variations (TTV) and variations in the actual duration of the transit (TDV) are the most readily observable effects on the table. TTVs are variations in timing as the planet transits its star. Does the transit show strict periodicity, or is there some variation from one transit to the next? TTVs can be used to demonstrate the presence of other gravitational influences, an unseen planet, or a moon. Transit duration variation measures the time during which any part of the planet obscures the stellar disk. Variations in duration occur as planet and moon orbit a common center of mass.

David Kipping (Columbia University) has been looking at transit timing variations and other factors for a long time in connection with the quest for an exomoon detection, a quest he began as a grad student and continued with his project The Hunt for Exomoons with Kepler. HEK uses dynamics and Kepler photometry in combination, modeling observable effects of a moon on a transit as well as the dynamical perturbations that can be revealed by transit timing and transit duration variations.

Quarles and team have taken the exomoon hunt explicitly into the realm of binary stars, where a stellar companion forces its own perturbations on moons orbiting planets there, affecting their occurrence and orbital evolution. The researchers have applied their findings to hypothetical Earth-Moon analogues at Centauri A and B, and have set up orbital stability limits for exomoons in binary star systems in general.

Gravitational interactions with a companion star can foster greater eccentricity in planetary orbits, with resulting stability issues for moons and implications for detecting them through TTVs. In typical binary systems, “TTV (rms) amplitudes induced by exomoons in binary systems are ?10 minutes and appear more likely for planets orbiting the less massive stellar component.”

In some systems, say the researchers, we would expect the Hill radius — the region around a planetary body where its own gravity, as compared to that of other nearby bodies, is the dominant force in attracting satellites — to shrink, which could cause moons to become unstable. If too close to the host star, the moon could be ejected from its planetary orbit and flung outwards. Zeroing in on Alpha Centauri:

The truncation of the Hill radius through secular eccentricity oscillations and outward tidal migration can influence potential observations of exomoons through TTVs… The TTV (RMS) amplitude is largest when satellites are close to their outer stability boundaries. These mechanisms limit the outer stability limit and can constrain the range of tidal dissipation allowed. The maximum TTV amplitude in a system like ? Cen AB is ?40 min, where we find that an Earth-Moon analog would exhibit ?2 min TTV signature.

The acronym RMS above stands for ‘root mean square,’ a reference to the value of the total waveform of the transit data, but let’s not get too deep into the weeds. The point is that a delicate balance needs to be struck so that the moon can survive. This is what Eggl refers to above as ‘stable real estate.’ But to detect an exomoon, we first have to find planets in the Alpha Centauri system, about which the authors have this to say:

The primary star of ? Cen AB would be a good candidate for searching for TTV inducing exomoons if transiting Earth-analogs were present. However, surveys of ? Cen AB for planets are difficult because of pixel saturation in photometric observations (Demory et al. 2015) and astrophysical noise in radial velocity observations…

And further on:

Observations of ? Cen AB with the Very Large Telescope (VLT) have suggested that any exoplanets there need to be ?20 M? (Kasper et al. 2019), which bodes well for the potential for terrestrial planets. The first results of the New Earths in the ? Centauri Region (NEAR) experiment on VLT uncovered a direct imaging signature of a roughly Neptune-sized planet orbiting ? Centauri A (Wagner et al. 2021), but these early results still await confirmation. Detecting exoplanets in binary star systems is a crucial step in the search for exomoons, where a wide array of methods (including TTVs) can be employed.

A crucial step indeed, but detecting an exomoon is an even tougher task, whether in a binary system or not. In 2020, for example, Chris Fox and Paul Wiegert (University of Western Ontario) theorized that six exoplanets found by Kepler could be hosting exomoons. Studying TTVs in the data, the astronomers noted that these were indirect detections, and that nearby planets could also be responsible for the TTVs.

We’re reminded that this is truly a frontier. Having examined the data, Quarles found that four of these six systems would tidally disrupt their exomoons or lose them to outward migration. He is quoted elsewhere as saying of the six possible moons:

“Could they (exomoons) exist physically? Four (candidate systems) of the six could not, two of the six are possible but the signature they produced aren’t produced by the data. Those two probably aren’t moons.”

Exomoon hunter Kipping found no compelling evidence for any of the six exomoons based on his own work. Moons around gas giants could be interesting venues for habitability, and we know the investigation of such will continue. You’ll recall evidence of a moon forming around the planet PDS 70c, an encouraging sign that a confirmed exomoon is getting closer. So it’s a fascinating part of the process that we now examine forced resonances in binary systems as another way into this daunting problem.

The paper is Quarles et al., “Exomoons in Systems with a Strong Perturber: Applications to ? Cen AB,” Astronomical Journal Vol. 162, No. 2 (14 July 2021) 58 (abstract / preprint). The Quarles paper on orbital obliquity is “Obliquity Evolution of Circumstellar Planets in Sun-like Stellar Binaries,” Astrophysical Journal Vol. 886, No. 1 (19 November 2019). Abstract / Preprint. The Fox & Wiegert paper on exomoon detection cited above is “Exomoon candidates from transit timing variations: eight Kepler systems with TTVs explainable by photometrically unseen exomoons.” Monthly Notices of the Royal Astronomical Society Vol. 501, Issue 2 (February 2021) 2378-2393 (abstract).

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L 98-59 b: A Rocky World with Half the Mass of Venus

ESPRESSO comes through. The spectrograph, mounted on the European Southern Observatory’s Very Large Telescope, has produced data allowing astronomers to calculate the mass of the lightest exoplanet ever measured using radial velocity techniques. The star is L 98-59, an M-dwarf about a third of the mass of the Sun some 35 light years away in the southern constellation Volans. It was already known to host three planets in tight orbits of 2.25 days, 3.7 days and 7.5 days. The innermost world, L 98-59b, has now been determined to have roughly half the mass of Venus.

What extraordinary precision from ESPRESSO (Echelle SPectrograph for Rocky Exoplanets and Stable Spectroscopic Observations). The three previously known L 98-59 planets were discovered in data from TESS, the Transiting Exoplanet Survey Satellite, which spots dips in the lightcurve from a star when a planet crosses its face.

Adding ESPRESSO’s data, and incorporating previous data from HARPS, has allowed Olivier Demangeon (Instituto de Astrofísica e Ciências do Espaço, University of Porto) and team to refine the planets’ mass. Because we already know their radii through transits, we can constrain the density of these rocky worlds. Intriguingly, 30% of L 98-59 d’s mass could be water.

What stands out here, though, is the confirmation of ESPRESSO’s capabilities as we continue to drill down into the centimeters-per-second range that will allow us to probe small rocky worlds around other stars. We’ve seen rapid growth in spectrography through ESPRESSO as well as NEID and, of course, HARPS (High Accuracy Radial Velocity Planet Searcher), which has long been in the forefront of the exoplanet hunt at ESO’s 3.6m telescope at La Silla Observatory in Chile.

ESPRESSO continues to push the boundaries of radial velocity planet detection. There is no hyperbole at all in the conclusion to the paper on this work, which notes that the refinement of mass for the planets in this system, particularly the innermost world:

…represents a new milestone which illustrates the capability of ESPRESSO to yield the mass of planets with RV signatures of the order of 10 cm s-1 in multi-planetary systems even with the presence of stellar activity.

The ESPRESSO data also flag a fourth planet around this star, along with hints of a possible fifth, the latter of which would be in the star’s liquid water habitable zone. The detected planet e has an orbital period of 12.80 days with a minimum mass of 3 Earth masses, while the candidate fifth planet has a period of 23.2 days and a minimum mass of 2.46 Earth masses. It would be in the star’s habitable zone and thus of high interest if confirmed, although there remains the possibility that the signal in the data is the result of stellar activity.

There are no signs of transits from either of these worlds. As this system is likely to become a benchmark for planetary analysis in nearby systems, we’ll keep an eye on the confirmation process for the planet candidate here.

Image: Comparison of the L 98-59 exoplanet system with the inner Solar System.

The three inner worlds at L 98-59 are candidates for atmospheric study through transmission spectrography, where astronomers examine light from the star as filtered through a planetary atmosphere during a transit. The astronomers note that in addition to potential analysis via the James Webb Space Telescope, the Extremely Large Telescope under construction in Chile’s Atacama Desert — scheduled to begin observations in 2027 — may be able to study the atmospheres of these planets from the ground.

In any event, further work with ESPRESSO, the Hubble Space Telescope, and future observatories like NIRPS (Near Infra Red Planet Searcher in Chile) and the Ariel space telescope (Atmospheric Remote-sensing Infrared Exoplanet Large-survey) should be available for atmospheric studies in this interesting system. Adds Demangeon:

“This system announces what is to come. We, as a society, have been chasing terrestrial planets since the birth of astronomy and now we are finally getting closer and closer to the detection of a terrestrial planet in the habitable zone of its star, of which we could study the atmosphere.”

An additional note relates to the tightness of planetary system configurations in multiple planet systems. This is from the paper’s conclusion:

According to exoplanet archive (Akeson et al. 2013), we currently know 739 multi-planetary systems. A large fraction of them (~ 60%) were discovered by the Kepler survey (Borucki et al. 2010; Lissauer et al. 2011). From a detailed characterization and analysis of the properties of the Kepler multiplanetary systems, Weiss et al. (2018, hereafter W18) extracted the “peas in a pod” configuration. They observed that consecutive planets in the same system tend to have similar sizes. They also appear to be preferentially regularly spaced. The authors also noted that the smaller the planets, the tighter their orbital configuration is… [W]e conclude that the L 98-59 system is closely following the “peas in a pod” configuration…

A useful fact, and one that, as the authors add, “further strengthens the universality of this configuration and the constraints that it brings on planet formation theories.”

The paper is Demangeon et al., “Warm terrestrial planet with half the mass of Venus transiting a nearby star,” accepted at Astronomy & Astrophysics (abstract).

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Notes on the Magnetic Ramjet II

Building a Bussard ramjet isn’t easy, but the idea has a life of its own and continues to be discussed in the technical literature, in addition to its long history in science fiction. Peter Schattschneider, who explored the concept in Crafting the Bussard Ramjet last February, has just published an SF novel of his own called The EXODUS Incident (Springer, 2021), where the Bussard concept plays a key role. But given the huge technical problems of such a craft, can one ever be engineered? In this second part of his analysis, Dr. Schattschneider digs into the question of hydrogen harvesting and the magnetic fields the ramjet would demand. The little known work of John Ford Fishback offers a unique approach, one that the author has recently explored with Centauri Dreams regular A. A. Jackson in a paper for Acta Astronautica. The essay below explains Fishback’s ideas and the options they offer in the analysis of this extraordinary propulsion concept. The author is professor emeritus in solid state physics at Technische Universität Wien, but he has also worked for a private engineering company as well as the French CNRS, and has been director of the Vienna University Service Center for Electron Microscopy.

by Peter Schattschneider

As I mentioned in a recent contribution to Centauri Dreams, the BLC1 signal that flooded the press in January motivated me to check the science of a novel that I was finishing at the time – an interstellar expedition to Proxima Centauri on board a Bussard ramjet. Robert W. Bussard’s ingenious interstellar ramjet concept [1], published in 1960, inspired a generation of science fiction authors; the most celebrated is probably Poul Anderson with the novel Tau Zero [2]. The plot is supposedly based on an article by Carl Sagan [3] who references an early publication of Eugen Sänger where it is stated that due to time dilation and constant acceleration at 1 g „[…] the human lifespan would be sufficient to circumnavigate an entire static universe“ [4].

Bussard suggested using magnetic fields to scoop interstellar hydrogen as a fuel for a fusion reactor, but he did not discuss a particular field configuration. He left the supposedly simple problem to others as Newton did with the 3-body problem, or Fermat with his celebrated theorem. Humankind had to wait 225 years for an analytic solution of Newton‘s problem, and 350 years for Fermat’s. It took only 9 years for John Ford Fishback to propose a physically sound solution for the magnetic ramjet [5].

The paper is elusive and demanding. This might explain why adepts of interstellar flight are still discussing ramjets with who-knows-how-working superconducting coils that generate magnetic scoop fields reaching hundreds or thousands of kilometres out into space. Alas, it is much more technically complicated.

Fishback’s solution is amazingly simple. He starts from the well known fact that charged particles spiral along magnetic field lines. So, the task is to design a field the lines of which come together at the entrance of the fusion reactor. A magnetic dipole field as on Earth where all field lines focus on the poles would do the job. Indeed, the fast protons from the solar wind are guided towards the poles along the field lines, creating auroras. But they are trapped, bouncing between north and south, never reaching the magnetic poles. The reason is rather technical: Dipole fields change too rapidly along the path of a proton in order to keep it on track.

Fishback simply assumed a sufficiently slow field variation along the flight direction, Bz=B0/(1+ ? z) with a „very small“ ?. Everything else derives from there, in particular the parabolic shape of the magnetic field lines. Interestingly, throughout the text one looks in vain for field strengths, let alone a blueprint of the apparatus. The only hint to the visual appearance of the device is a drawing of a long, narrow paraboloid that would suck the protons into the fusion chamber. As a shortcut to what the author called the region dominated by the ramjet field I use here the term „Fishback solenoid“.

Fig. 1 is adapted from the original [5]. I added the coils that would create the appropriate field. Their distance along the axis indicates the decreasing current as the funnel widens. Protons come in from the right. Particles outside the scooping area As are rejected by the field. The mechanical support of the coils is indicated in blue. It constitutes a considerable portion of the ship’s mass, as we shall see below.

Fig. 1: Fishback solenoid with parabolic field lines. The current carrying coils are symbolized in red. The mechanical support is in blue. The strong fields exert hoop stress on the support that contributes considerably to the ship’s mass. Adapted from [5].

Searching for scientific publications that build upon Fishback’s proposal, Scopus renders 6 citations up to this date (April 2021). Some of them deal with the mechanical stress of the magnetic field, another aspect of Fishback’s paper that I discuss in the following, but as far as I could see the paraboloidal field was not studied in the 50 years since. This is surprising because normally authors continue research when they have a promising idea, and others jump on the subject, from which follow-up publications arise, but J. F. Fishback published only this one paper in his lifetime. [On Fishback and his tragic destiny, see John Ford Fishback and the Leonora Christine, by A. A. Jackson].

Solving the dynamic equation for protons in the Fishback field proves that the concept works. The particles are guided along the parabolic field lines toward the reactor as shown in the numerical simulation Fig. 2.

Fig.2: Proton paths in an (r,z)-diagram. r is the radial distance from the symmetry axis, z is the distance along this axis. The ship flies at 0.56 c (?=0.56) in positive z-direction. In the ship’s rest frame, protons arrive with a kinetic energy of 194 MeV from the top. Left: Protons entering the field at z=200 km are focussed to the reactor mouth at the coordinate origin, gyrating over the field lines. Particles following the red paths make it to the chamber; protons following the black lines spiral back. The thick grey parabola separates the two regimes. Right: Zoom into the first 100 m in front of the reactor mouth of radius 10 m. Magnetic field lines are drawn in blue.

The reactor intake is centered at (r,z)=(0,0). In the ship’s rest frame the protons arrive from top – here with 56 % of light speed, the maximum speed of the EXODUS in my novel [8]. Some example trajectories are drawn. Protons spiral down the magnetic field lines as is known from earth’s magnetic field and enter the fusion chamber (red lines). The scooping is well visible. The reactor mouth has an assumed radius of 10 m. A closer look into the first 100 m (right figure) reveals an interesting detail: Only the first two trajectories enter the reactor. Protons travelling beyond the bold grey line are reflected before they reach the entrance, just as charged particles are bouncing back in the earth’s field before they reach the poles. From the Figure it is evident that at an axial length of 200 km of the Fishback solenoid the scoop radius is disappointingly low – only 2 km. Nevertheless, the compression factor (focussing ions from this radius to 10 m) of 1:40.000 is quite remarkable.

The adiabatic condition mentioned above allows a simple expression for the area from which protons can be collected. The outer rim of this area is indicated by the thick grey line in Fig. 2. The supraconducting coils of the solenoid should ideally be built following this paraboloid, as sketched in Fig. 1. Tuning the ring current density to

yields a result that approximates Fishback‘s field closely.

What does it mean in technical terms? Let me discuss an idealized example, having in mind Poul Anderson’s novel. The starship Leonora Christina accelerates at 1 g, imposing artificial earth gravity on the crew. Let us assume that the ship‘s mass is a moderate 1100 tons (slightly less than 3 International Space Stations). For 1 g acceleration on board, we need a peak thrust of ~11 million Newton, about 1/3 of the first stage of the Saturn V rocket. The ship must be launched with fuel on stock because the ramjet operates only beyond a given speed, often taken as 42 km/s, the escape velocity from the solar system. In the beginning, the thrust is low. It increases with the ship’s speed because the proton throughput increases, asymptotically approaching the peak thrust.

Assuming complete conversion of fusion energy into thrust, total ionisation of hydrogen atoms, and neglecting drag from deviation of protons in the magnetic field, at an interstellar density of 106 protons/m3, the „fuel“ collected over one square kilometer yields a peak thrust of 1,05 Newton, a good number for order-of-magnitude estimates. That makes a scooping area of ~10 million square km, which corresponds to an entrance radius of about 1800 km of the Fishback solenoid. From Fig. 2, it is straightforward to extrapolate the bold grey parabola to the necessary length of the funnel – one ends up with fantastic 160 million km, more than the distance earth – sun. (At this point it is perhaps worth mentioning that this contribution is a physicist’s treatise and not that of an engineer.)

Plugging the scooping area into the relativistic rocket equation tells us which peak acceleration is possible. The results are summarised in Table 1. For convenience, speed is given in units of the light speed, ß=v/c. Additionally, the specific momentum ß? is given where

is the famous relativistic factor. (Note: The linear momentum of 1 kg of matter would be ß? c.) Acceleration is in units of the earth gravity acceleration, g=9.81 m/s2.

Under continuous acceleration such a starship would pass Proxima Centauri after 2.3 years, arrive at the galactic center after 11 years, and at the Andromeda galaxy after less than 16 years. Obviously, this is not earth time but the time elapsed for the crew who profit from time dilation. There is one problem: the absurdly long Fishback solenoid. Even going down to a scooping radius of 18 km, the supraconducting coils would reach out 16,000 km into flight direction. In this case the flight to our neighbour star would last almost 300 years.

Table 1: Acceleration and travel time to Proxima Centauri, the galactic center, and the Andromeda galaxy M31, as a function of scooping area. ß? is the specific momentum at the given ship time. A ship mass of 1100 tons, reactor entrance radius 10 m, and constant acceleration from the start was assumed. During the starting phase the thrust is low, which increases the flight time by one to several years depending on the acceleration.

Fishback pointed out another problem of Bussard ramjets [5]. The magnetic field exerts strong outward Lorentz forces on the supraconducting coils. They must be balanced by some rigid support, otherwise the coils would break apart. When the ship gains speed, the magnetic field must be increased in order to keep the protons on track. Consequently, for any given mechanical support there is a cut-off speed beyond which the coils would break. For the Leonora Christina a coil support made of a high-strength „patented“ steel must have a mass of 1100 tons in order to sustain the magnetic forces that occur at ?=0,74.

Table 2: Cut-off speeds ?c and cut-off specific momenta (ß?)c (upper bounds) for several support materials. (ß?)F from [5], (ß?)M from [7]. ?y/? is the ratio of the mechanical yield stress to the mass density of the support material. Bmax is the maximum magnetic field at the reactor entrance at cut-off speed. A scooping area of 10 million km2 was assumed, allowing a maximum acceleration of ~1 g for a ship of 1100 tons. Values in italics for Kevlar and graphene, unknown in the 1960s, were calculated based on equations given in [7].

But we assumed above that this is the ship‘s entire mass. That said, the acceleration must drop long before speeding at 0,74 c. The cut-off speed ?c=0,74 is an upper bound (for mathematicians: not necessarily the supremum) for the speed at which 1 g acceleration can be maintained. Lighter materials for the coil support would save mass. Fishback [5] calculated upper bounds for the speed at which an acceleration of 1 g is still possible for several materials such as aluminium or diamond (at that time the strongest lightweight material known). Values are shown in Table 2 together with (ß?)c.

Martin [7] found some numerical errors in [5]. Apart from that, Fishback used an optimistically biased (ß?)c. Closer scrutiny, in particular the use of a more realistic rocket equation [6], results in more realistic upper bounds. Using graphene, the strongest material known, the specific cut-off momentum is 11,41. This value would be achieved after a flight of three years at a distance of 10 light years. After that point, the acceleration would rapidly drop to values making it hopeless to reach the galatic center in a lifetime.

In conclusion, the interstellar magnetic ramjet has severe construction problems. Some future civilization may have the knowhow to construct fantastically long Fishback solenoids and to overcome the minimum mass condition. We should send a query to the guys who flashed the BLC1 signal from Proxima Centauri. The response is expected in 8.5 years at the earliest. In the meantime the educated reader may consult a tongue-in-cheek solution that can be found in my recent scientific novel [8].

Acknowledgements

Many thanks to Al Jackson for useful comments and for pointing out the source from which Poul Anderson got the idea for Tau Zero, and to Paul Gilster for referring me to the seminal paper of John Ford Fishback.

References

[1] Robert W. Bussard: Galactic Matter and Interstellar Flight. Astronautica Acta 6 (1960), 1-14.

[2] Poul Anderson: Tau Zero. Doubleday 1970.

[3] Carl Sagan: Direct contact among galactic civilizations by relativistic inter-stellar space flight, Planetary and Space Science 11 (1963) 485-498.

[4] Eugen Sänger: Zur Mechanik der Photonen-Strahlantriebe. Oldenbourg 1956.

[5] John F. Fishback: Relativistic Interstellar Space Flight. Astronautica Acta 15 (1969), 25-35.

[6] Claude Semay, Bernard Silvestre-Brac: The equation of motion of an interstellar Bussard ramjet. European Journal of Physics 26 (1) (2005) 75-83.

[7] Anthony R. Martin: Structural limitations on interstellar space flight. Astronautica Acta 16 (6) (1971) 353-357.

[8] Peter Schattschneider: The EXODUS Incident. Springer 2021,
ISBN: 978-3-030-70018-8. https://www.springer.com/de/book/9783030700188#aboutBook

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Breakthrough Discuss Ongoing

There is a public YouTube channel for watching the Breakthrough Discuss meetings, which began today and extend through tomorrow. Click here to go to sessions on “The Alpha Centauri System: A Beckoning Neighbor.” I’ll have thoughts on some of these presentations in coming weeks.

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