Incentive Trap 2: Calculating Minimum Time to Arrival

When to launch a starship, given that improvements in technology could lead to a much faster ship passing yours enroute? As we saw yesterday, the problem has been attacked anew by René Heller (Max Planck Institute for Solar System Research), who re-examined a 2006 paper from Andrew Kennedy on the matter. Heller defines what he calls ‘the incentive trap’ this way:

The time to reach interstellar targets is potentially larger than a human lifetime, and so the question arises of whether it is currently reasonable to develop the required technology and to launch the probe. Alternatively, one could effectively save time and wait for technological improvements that enable gains in the interstellar travel speed, which could ultimately result in a later launch with an earlier arrival.

All this reminds me of a conversation I had with Greg Matloff, author of the indispensable The Starflight Handbook (Wiley, 1989) about this matter. We were at Marshall Space Flight Center in 2003 and I was compiling notes for my Centauri Dreams book. I had mentioned A. E. van Vogt’s story “Far Centaurus,” originally published in 1944, in which a crew arrives at Alpha Centauri only to find its system inhabited by humans who launched from Earth centuries later. I alluded to this story yesterday.

Calling it a ‘terrific story,’ Matloff discussed it in terms of Robert Forward’s thinking:

“Bob had a couple of concepts of technological advancement. He had a famous plot of the velocity of human beings versus time. And he said if this is true, and you launch a thousand-year ship today, in a century somebody could fly the same mission in a hundred years. Theyre going to be passed and will probably have to go through customs when they get to Alpha Centauri A-2.”

Customs! Clearly, we’d rather not be on the slow starship that is superseded by new technologies. What Heller and Kennedy before him want to do is to figure out a rational way to decide when to launch. If we make assumptions about the exponential growth in speed over time, we can address the question by adding the time we spend waiting for better technology to the time of the actual journey. We can then calculate a minimum value for this figure based on the growth rates we find in our historical data.

This is how Kennedy came up with a minimum figure of 712 years (from 2006) to reach Barnard’s Star, which is about 6 light years away. The figure would include a long period of waiting for technological improvement as well as the time of the journey itself. Kennedy used a 1.4 percent annual growth in speed in arriving at this figure but, examining 211 years of data on historical speed records, Heller finds a higher annual growth, some 4.72 percent.

From the Penydarren steam locomotive of 1804 to Voyager 1, we see a speed growth of about four orders of magnitude. Growth like this maintained for another 112 years leads to 1 percent of lightspeed.

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Image: A Bussard ramjet in flight, as imagined for ESA’s Innovative Technologies from Science Fiction project. Credit: ESA/Manchu.

But how consistent should we expect the growth in speed over time to be? Heller points out that the introduction of new technologies invariably leads to jumps in speed. We are now in the early stages of conceptualizing the Breakthrough Starshot project, which could create exactly this kind of disruption in the trend. Starshot aims at reaching 20 percent of lightspeed.

Working with the exponential speed doubling law we began with, we would expect that a speed of 20 percent of c would not be achieved until the year 2191. But if Starshot achieves its goal in the anticipated time frame of several decades, its success would see us reaching interstellar speeds much faster than the trends indicate. Starshot, or a project like it, would if successful exert a transformative effect as a driver for interstellar exploration.

We know that speed doubling laws cannot go on forever as we push toward relativistic speeds (we can’t double values higher than 0.5 c). But as we move toward substantial percentages of the speed of light, we see powerful gains in speed as we increase the kinetic energy beamed to a small lightsail like Starshot’s. Thus Heller also presents a model based on the growth of kinetic energy, noting that today the Three Gorges Dam in China can reach power outputs of 22.5 GW. 100 seconds exposure to a beam this powerful would take a small sail probe to speeds of 7.1 percent of c. Further kinetic energy increases could allow relativistic speeds for at least gram-to-kilogram sized probes within a matter of decades.

Usefully, Heller’s calculations also show when we can stop worrying about wait times altogether. The minimum value for the wait plus travel time disappears for targets that we can reach earlier than a critical travel time which he calls the ‘incentive travel time.’ Considered in both relativistic and non-relativistic models, this figure (assuming a doubling of speed every 15 years) works out to be 21.6 years. In Heller’s words, “…targets that we can reach within about 22 yr of travel are not worth waiting for further speed improvements if speed doubles every 15 yr.”

Thus already short travel times mean there is little point in waiting for future speed improvements. And in terms of current thinking about Alpha Centauri missions, Heller notes that there is a critical interstellar speed above which gains in kinetic energy beamed to the probe would not result in smaller wait plus travel times. His equations result in a value of 19.6 percent of c, an interesting number given that Breakthrough Starshot’s baseline is a probe moving at 20 percent of c, for a 20-year travel time. Thus:

In terms of the optimal interstellar velocity for launch, the most nearby interstellar target α Cen will be worthy of sending a space probe as soon as about 20 % c can be achieved because future technological developments will not reduce the travel time by as much as the waiting time increases. This value is in agreement with the 20 % c proposed by Starshot for a journey to α Cen.

We can push this result into an analysis of stars beyond Alpha Centauri. Heller looks at speeds beyond which further speed improvements would not result in reduced wait times for ten of the nearest bright stars. The assumption here would be that Starshot or alternative technologies would be continuously upgraded according to historical trends. Plugging in that assumption, we wind up with speeds as high as 57 percent of lightspeed for 70 Ophiuchi at 16.6 light years.

Thus the conclusion: If something like Breakthrough Starshot’s beaming capabilities become available within 45 years — and assuming that the kinetic energy transferred to the probes it pushes could be increased at the historical rates traced here — then we can reach all ten of the nearest star systems with an interstellar probe within 100 years from today.

Just for fun let me conclude with a snippet from “Far Centaurus.” Here a ship is approaching the ‘slowboat’ that has just discovered that Alpha Centauri has been reached by humans long before. The crew has just puzzled out what happened:

I was sitting in the control chair an hour later when I saw the glint in the darkness. There was a flash of bright silver, that exploded into size. The next instant, an enormous spaceship had matched our velocity less than a mile away.

Blake and I looked at each other. “Did they say,” I said shakily, “that that ship left its hangar ten minutes ago?”

Blake nodded. ‘They can make the trip from Earth to Centauri in three hours,” he said.

I hadn’t heard that before. Something happened inside my brain. “What!” I shouted. “Why, it’s taken us five hund… ” I stopped. I sat there.

“Three hours!” I whispered. “How could we have forgotten human progress?”

The René Heller paper discussed in the last two posts is “Relativistic Generalization of the Incentive Trap of Interstellar Travel with Application to Breakthrough Starshot” (preprint).

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The Incentive Trap: When to Launch a Starship

Richard Trevithick’s name may not be widely known today, but he was an important figure in the history of transportation. A mining engineer from Cornwall, Trevithick (1771-1833) built the first high pressure steam engine, and was able to put it to work on a railway known as the Penydarren because it moved along the tramway of the Penydarren Ironworks, in Merthyr Tydfil, Wales, running 14 kilometers until reaching the canal wharf at Abercynon. The inaugural trip marked the first railway journey hauled by a locomotive, and it proceeded at a blistering 4 kilometers per hour. The year was 1804.

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Image: The replica Trevithick locomotive and attendant bar iron bogies at the Welsh Industrial & Maritime Museum in 1983. Credit: National Museum of Wales.

Consider, as René Heller (Max Planck Institute for Solar System Research) does in a new paper, how Trevithick’s accomplishment serves as a kind of bookend for 211 years of historical data on the growth in speed in human-made vehicles from the Penydarren to Voyager 1. The world’s first production car was the Benz Velocipede (1894), whose top speed of 19 kilometers per hour far surpassed the Trevithick railway, but was put to shame by a Stanley Steamer racing car that reached a then incredible 204 kilometers per hour in 1903.

I mused about the nature of speed in a 2013 post called The Velocity of Thought, and Heller’s new paper has me doing it again, though in entirely different directions. A few more waypoints and I’ll explain what I mean. When the Wright Brothers took to the air in 1903, their Wright Flyer first flew at about 11 kilometers per hour, and we began to see how quickly aviation records could be superseded. A Sopwith Camel of World War I vintage could reach 181 kilometers per hour. By 1944, German test pilot Heini Dittmar was able to take a ME-163 rocket plane to 1130 km/h, a number that wouldn’t be reached again for almost ten years.

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Image: Typical appearance of a Me-163 Komet after landing, waiting for the airfield’s Scheuch-Schlepper tractor and lifting trailer to tow it back for reattachment of its “dolly” maingear. Credit: Wikimedia Commons.

When we get into space, we can note Voyager 1’s 17 kilometers per second as it leaves the Solar System. The Helios solar probes launched in 1974 and 1976 set the current record at 70.22 km/s. And looking forward, the Solar Probe Plus mission is to perform a close flyby of the Sun, reaching a top heliocentric speed of 195 kilometers per second, which works out to 6.5 × 10 ?4 c. If Breakthrough Starshot realizes its goal, an interstellar lightsail may one day head for Proxima Centauri at fully 20 percent of the speed of light.

Part of what occupies René Heller in his new paper is the exponential growth law we can construct between the 1804 Penydarren locomotive and the 17 kilometers per second of Voyager 1 in 2015. From wind- to steam-driven ships and into the realm of automobiles, then aircraft and, finally, rockets, we can extrapolate speeds that may take us into interstellar probe territory some time in this century or the next. Given that an interstellar mission may take longer than the average human lifetime, we thus need to ask a key question. When do we launch?

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Image: Figure 1 from the Heller paper, showing historical speed records. From the paper: “All these values are symbolized with black-rimmed circles in Figure 1, with additional top speed measurements of trains, cars, planes, and rockets shown with different symbols (see legend). The dashed black line illustrates an exponential growth law connecting the 1 m s ?1 speed of the “Penydarren” steam locomotive in 1804 with the 5.7 × 10 ?5 c Solar System escape speed of Voyager 1 in 2015. Credit: René Heller.

For the problem, a classic in science fiction, is to work out the most efficient timing. If we launch a starship at a particular level in our technology, will it not be caught by a faster ship launched at a much later date? Given sufficient technological improvements, a later launch (incorporating the necessary ‘wait time’) could result in an earlier arrival.

Those who have read A. E. van Vogt’s story “Far Centaurus” will recall precisely that scenario, when an Alpha Centauri mission reaches destination only to find it populated by humans who arrived by faster means. It’s a theme that shows up in Heinlein’s Time for the Stars and many other places.

Heller calls this problem ‘the incentive trap.’ And he refers back to Andrew Kennedy’s 2006 paper, which looked at the problem with the assumption of an exponential growth of the interstellar travel speed. Kennedy was assuming a 1.4 % average growth rate, under which a minimum time to reach Barnard’s Star could be calculated: some 712 years from 2006.

What that means is this: There is a total time that includes the waiting time (waiting for improved technology) and the actual travel time, and we can calculate a minimum value for this total time by using our assumption about the exponential growth of the interstellar travel speed. Calculating the minimum value shows us when we can launch without fear of being overtaken by a faster future probe, in hopes of avoiding that “Far Centaurus” outcome.

But was Kennedy right? Heller’s own take on the incentive trap takes into account the possibility that Breakthrough Starshot may achieve a velocity of 20 percent of lightspeed within several decades, an outcome that would, in Heller’s words, “…fundamentally change both the assumptions and the implications of the incentive trap because the speed doubling and the compounded annual speed growth laws would collapse as v approaches c.” And whatever happens with Breakthrough Starshot, the speed growth of human-made vehicles turns out to be much faster than previously believed.

Intriguing results flow out of Heller’s re-examination of what Kennedy had called the ‘wait equation,’ and tomorrow I want to go deeper into the paper to explain how the scientist uses exponential growth law models to show us a velocity which, once we have attained it, will no longer be subject to the incentive trap of faster, later technologies. The results are surprising, particularly if Breakthrough Starshot achieves its goal in the planned 30 years. The implications for our reaching well beyond Alpha Centauri, as we’ll see, are striking.

The Heller paper is “Relativistic Generalization of the Incentive Trap of Interstellar Travel with Application to Breakthrough Starshot” (preprint). The Kennedy paper is “Interstellar Travel: The Wait Calculation and the Incentive Trap of Progress,” Journal of the British Interplanetary Society Vol. 59, No. 7 (July, 2006), pp. 239-247.

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Remembering the Sail Mission to Halley’s Comet

Some years back I had the pleasure of asking Lou Friedman about the solar sail he, Bruce Murray and Carl Sagan championed at the Jet Propulsion Laboratory in the 1970s. NASA had hopes of reaching Halley’s Comet with a rendezvous mission in 1986. Halley’s closest approach that year would be 0.42 AU, but the comet was on the opposite side of the Sun from the Earth, making ground viewing less than impressive. Although the JPL mission did not fly, the Soviet Vega 1 and Vega 2 conducted flybys and the European Space Agency’s Giotto probe, as well as the Japanese Suisei and Sakigake, made up an investigative ‘armada.’

But the abortive NASA concept has always stuck in my mind because it seemed so far ahead of its time. Friedman acknowledged as much in our short conversation, saying that while the ideas were sound, the solar sail technology wasn’t ready for the ambitious uses planned for it. Friedman, of course, would go on to become a founder of The Planetary Society and its long-time executive director, championing sail concepts like Cosmos 1 and the LightSail 1 and LightSail 2 spacecraft. He’s also the author of one of the earliest books on this form of propulsion, Starsailing: Solar Sails and Interstellar Travel (Wiley, 1988).

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Image: This artist’s concept shows an 850-by-850-meter wide solar sail spacecraft approaching Halley’s Comet. Credit: JPL-Caltech.

Starsailing is a slim but compelling book that should be on your shelf if you’re interested in these concepts and their history. Although out of print, it’s readily available through Amazon or eBay sellers. Meanwhile, The Planetary Society’s Jason Davis has made a cache of documents from engineer Carl Berglund available that cover many details of the mission. The self-deprecating Berglund, who refers to himself as a only a ‘cog engineer’ at JPL, joined the project at about the same time that Carl Sagan displayed a model of a solar sail on The Tonight Show, and while he only spent several months working on the sail, his JPL documents remind us just how ambitious the JPL concept had become.

Not one but two designs were under consideration, the first a square sail 850 meters to the side. Bear in mind that JAXA’s IKAROS sail, the largest we’ve yet deployed in space, runs 14 meters to the side. A second design was a heliogyro, a device with long blades aptly described by Davis as looking like “two ceiling fans stacked on top of each other.” There would be 12 sail blades in all, 6 per level, and here the dimensions really are staggering. Each blade was to be 8 meters wide and 6.2 kilometers long, making for 0.6 square kilometers of sail material in a spinning blade configuration that would complete a rotation every 200 seconds.

Let’s take a closer look at that heliogyro, as it’s a design we’ve yet to see in space. In a summary document written in early 1977, Friedman describes the concept this way:

The Heliogyro presents a large reflective area to create the Solar Sail by the use of very long, thin blades, much like helicopter blades, which are used both to reflect the solar pressure and to control the vehicle. The basic concept is to spin the vehicle and to use the centrifugal force to support and stiffen the blade, and to keep it flat relative to the Sun. The spin of the vehicle also aids in the deployment of the Heliogyro blades. In addition, the blades can be pitch controlled, as with a helicopter, in order to provide attitude control and to turn the vehicle so that the reflective plane can have different orientations with respect to the Sun. Thus, the vehicle can either fly in toward the Sun or fly out into the Solar System.

Heliogyro

Image: Halley’s Comet Heliogyro Design. Credit: JPL-Caltech, 1976).

The document depicts a deployment in which the blades unroll from their storage rollers with the help of spin thrusters that are jettisoned after the first 100 meters. After this, solar torque on the blades continues to spin up the vehicle and, over the course of a two-week period, each of the blades unfurls to its full six-kilometer length. Friedman sees the major advantage of the heliogyro as being the support provided by its centrifugal spin, which eliminates the need for a stiffening structure and provides for higher performance than a square sail. The major uncertainty: The dynamics of a 6 kilometer long spinning blade in deep space.

As to sail materials, Friedman describes blades “made out of .1 mil plastic material, with a surface density of less than 4 grams per square meter,” with surface coatings on the back to allow the sail to work at high temperatures close to the Sun. An internal newsletter from Friedman on April 13 of 1977 looks at materials requirements and notes three film candidates: Kapton, Ciba-Geigy polyimid and PBI conformal coated with parylene. These films were specified in the 1.5 to 2.5 µm range in thickness. By way of comparison, the later IKAROS sail was made of a 7.5-micrometer thick sheet of polyimide with thin-film solar cells.

Whichever sail design got the nod, the plan was to launch from the Space Shuttle followed by an inward spiral toward the Sun to about 0.25 AU, after which the sail would leave the ecliptic as it reached speeds in the range of 55 kilometers per second, eventually matching the trajectory of Halley’s Comet in 1986. The sail would be jettisoned at the comet, allowing the craft to use maneuvering thrusters for its operations there, which were to include a landing on the comet itself at the end of the mission.

The heliogyro option ended up winning the competition over the square sail, but sail concepts themselves lost out to solar electrical power, an ion propulsion technology like that used in the Dawn spacecraft. But funding problems and a slower than expected Space Shuttle mission schedule brought all thoughts of a Halley’s Comet mission from NASA to an untimely end.

Friedman writes in Starsailing that in the 1977 to 1978 period, the JPL team produced its design study for the mission with the help of half a dozen industrial contractors and support from the NASA Ames and Langley research centers. It was solid work that showed how viable solar sailing could be as a method of propulsion. He also describes the outcome of the Halley’s mission design:

Despite the confidence of the technical team and the completion of a valid preliminary design, however, the NASA management was conservative. They felt the design and implementation could not be accomplished in time for a 1981 launch to Halley’s Comet. NASA also thought that the technology for solar sailing was not sufficiently ‘mature’ to be implemented on a near-term space project. Indeed, the Halley mission requirements were severe — and even our willingness to incur great risk for great gain was insufficient to overcome management’s skepticism. And as it turned out, the conservatives were right, we could not have done it. It was a self-fulfilling prophecy.

But what splendid work fleshing out solar sail concepts that we continue to explore and find viable. As mentioned above, The Planetary Society’s Lightsail 2 carries the idea forward, and may become the second solar sail to demonstrate controlled flight in space. JAXA, meanwhile, has plans for an IKAROS follow-on mission to study the Jupiter Trojans.

All of that helps us keep the documents Jason Davis has collected online in perspective, a valuable look at work that has contributed to our understanding of a key propulsion concept. Looking through these documents reminds me of days I spent in 2003 going through the Robert Forward notebooks stored at the University of Alabama at Huntsville. That sense of history in the making — or in this case, history that might have been — is palpable as we consider who developed these documents and handled them at the key JPL meetings.

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Image: Dig into documents like this online to see a mission design emerging. Credit: Carl Berglund / The Planetary Society / Louis Friedman.

Friedman includes in one of the newsletters a March 14, 1977 article in Science covering the JPL sail work. It reminds us how exotic sail ideas were at the time. Quoting from it:

[The sail] might also effectively open up the rest of the Solar System to manned spaceflights that cannot be considered now because of tremendous costs. JPL’s Louis Friedman thinks that a flotilla of sunjammers could embark on a manned Mars mission by the end of the century, and foresees a day when fleets of huge kites shuttle through space — as the East Indiamen plied the oceans three centuries ago — making regular stops at Mercury, Venus, Mars or the asteroids.

Exotic ideas indeed, but slowly, surely, beginning to take shape. For more background, see Davis’ Sailing to the World’s Most Famous Comet.

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Starship Congress 2017

I had thought at the end of last year that 2017 would be a year of few conferences held by the various interstellar organizations. In fact, the Tennessee Valley Interstellar Workshop was the only one I was sure would occur, a meeting I knew about because it was being held in partnership with the Tau Zero Foundation as well as Starship Century. Since then, we’ve had news of the Foundations of Interstellar Studies Workshop sponsored by the Initiative for Interstellar Studies. Background on these two, including details on registration and submitting papers, can be found in Interstellar Conference News.

Now the details of a late summer meeting to be held by Icarus Interstellar have emerged. Based on the group’s online description, this is to be the third in the Starship Congress meetings, the first of which I attended in Dallas in 2013. A second was held at Drexel University in Philadelphia in 2015.

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Image: The 2013 Starship Congress in Dallas was a great meeting. In front at the far right, I am easy to spot because I am one of the few in the group shot wearing a light-colored jacket. It’s hard to make out the faces here, but I think that’s Pat Galea to my right, and my son Miles next to Pat. Rachel Armstrong is in front at the left, and although it’s too tricky to identify everyone, I do see Al Jackson, Jim Benford, Eric Davis, Phil Lubin and many other friends. Credit: Icarus Interstellar.

The focus of Starship Congress 2017 is to be the Moon, an unusual choice for a deep space organization, but Icarus asks a good question: “How can we hope to gain experience living, building and working off planet without systematically capitalizing on our nearest, most accessible celestial body?”

It’s a question with both near- and far-term resonances, for we’re also talking about more or less bypassing lunar resources and going straight for Mars, an idea that pulls me up short given our lack of knowledge about human physiology beyond low Earth orbit. We can study human factors in space-based laboratories, and I know that Robert Hampson (Wake Forest School of Medicine) continues to push for a dedicated facility to study biomedical matters outside Earth’s magnetosphere. But dedicated facilities on the Moon should be a part of this.

But let me give you the Icarus Interstellar view, in the form of the call for papers for Starship Congress 2017, reproduced here verbatim.

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Call for Papers

If we want to see interstellar accomplishments in our lifetime we need a staging area in space and we need to be able to get our people and our machines up there.

We dedicate each day of our meeting to addressing actions towards making Space a Place for Everybody and welcome the community to submit papers/presentations for each of the following:

Day 1: The Moon as a Stepping Stone to the Stars (MOON):

  • Living on the Moon: Lunar city planning, lunar resources, construction, power, water, radiation shielding, living and working, economy, sociology.
  • Planetary, Deep Space and Interstellar exploration centered around the Moon: Spacecraft Shipyards, Lunar Space elevators, Planetary and Deep Space remote sensing Telescopes.

Day 2: Massive Space Access Project (MSAP) aka “Children in Space”:

  • Earth to Moon and back: transport vehicles and systems, global logistics, tourism, legal and safety considerations, military presence.
  • Children in Space: Space education, youth space education program, people with disabilities in space, when will we send the first child to space? (when children can go to the moon, everyone will want to go!)

Day 3: Massive Space Based Infrastructure (MSBI):

  • Space and Lunar Industry: Space stations, mining stations, space services, telecommunications, zero gravity and lunar gravity manufacturing technology development.
  • Space arts, sports, community and culture: everything not traditionally considered infrastructure, but which is necessary for humans to live, love and learn on the Moon and in space.

Submit abstracts to starshipcongress@icarusinterstellar.org by Monday, July 3rd, 2017. Papers will be approved on a rolling basis with the final agenda shared on Monday, July 10th, 2017.

Conference Registration

Register for Starship Congress 2017 here.

Hotel Registration

Starship Congress will be held at:

HYATT REGENCY MONTEREY HOTEL & SPA
One Old Golf Course Rd, Monterey, CA 93940, USA
T +1.831.657.6541 Email: megan.whetton@hyatt.com
monterey.hyatt.com

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If you’re interested in presenting at the conference, abstracts can be submitted to starshipcongress@icarusinterstellar.org by Monday, July 3rd, 2017. Papers will be approved on a rolling basis with the final agenda shared on Monday, July 10th, 2017.

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Early System Evolution: The Disks around Epsilon Eridani

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Nine years ago in a piece titled Asteroid Belts, Possible Planets Around Epsilon Eridani, I discussed work that Massimo Marengo was doing on the nearby star, examining rings of material around Epsilon Eridani and considering the possibilities with regard to planets. Marengo (now at Iowa State University) has recently been working with Kate Su (University of Arizona) and other colleagues, using the SOFIA telescope (Stratospheric Observatory for Infrared Astronomy) to help us refine our understanding of the evolving planetary system.

Image: Astronomers (left to right) Massimo Marengo, Andrew Helton and Kate Su study images of epsilon Eridani during their SOFIA mission. Credit: Massimo Marengo.

The researchers used the 2.5-meter telescope aboard the Boeing 747SP jetliner to collect data about the star, working at 45,000 feet in a region above most of the atmospheric water vapor that absorbs the infrared light being studied. Epsilon Eridani is a bit over 10 light years from the Sun, and about a fifth of its age, meaning we have close at hand a stellar system that can help us understand what our own Solar System was like in its youth.

The new paper confirms Marengo’s earlier findings that there are separate inner and outer disk structures, with the possibility that the inner disk is itself made up of more than one debris belt. Says Marengo:

“This star hosts a planetary system currently undergoing the same cataclysmic processes that happened to the solar system in its youth, at the time in which the moon gained most of its craters, Earth acquired the water in its oceans, and the conditions favorable for life on our planet were set.”

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Image: This is an artist’s illustration of the Epsilon Eridani system showing Epsilon Eridani b, right foreground, a Jupiter-mass planet orbiting its parent star at the outside edge of an asteroid belt. In the background can be seen another narrow asteroid or comet belt plus an outermost belt similar in size to our Solar System’s Kuiper Belt. The similarity of the structure of the Epsilon Eridani system to our Solar System is remarkable, although Epsilon Eridani is much younger than our sun. SOFIA observations confirmed the existence of the asteroid belt adjacent to the orbit of the Jovian planet. Credit: NASA/SOFIA/Lynette Cook.

This is fine-grained work, for it requires the astronomers to separate the faint emission of Epsilon Eridani’s circumstellar disk from the bright light of the host star. But when Marengo likens the work with SOFIA to using a time machine, he has an obvious point. Debris disks result when belts of planetesimals are perturbed by newly formed planets, creating collisions that over time break the minor bodies down into dust. We know of more than 400 debris disks around other stars, but we have few systems close enough to study at high resolution. Moreover, what the paper describes as the two benchmark nearby debris disks are around A-class stars, Fomalhaut and Vega. Epsilon Eridani gives us a star much more like the Sun.

Debris disks, which can include rocky and icy bodies as well as gas and dust, can be broad, continuous disks or they can become concentrated into belts of debris. Here the analogy is to our own Solar System’s asteroid belt and Kuiper Belt, two distinct regions with one disk of debris concentrated beyond the orbit of Mars and the other beyond the orbit of Neptune. With an outer cold disk and a warm inner one assumed, the new work focuses on the inner disk. Here there are two different models for how the inner disk is formed, with implications for planets.

One model calls for an inner disk made up of two narrow rings of debris, with one ring roughly at the position of our asteroid belt around the star, and the other at a region corresponding to the orbit of Uranus. The other model sees the inner disk region being populated by dust from the outer, Kuiper Belt-like region, with material inflowing into the inner disk. The latter model assumes a single broad disk in the inner system as opposed to two belt-like rings. The new SOFIA observations favor the narrow belt model rather than a broad continuous disk.

Combining data from SOFIA with earlier Spitzer observations, the researchers found that excess emissions in the inner 25 AU region around the star are the result of a dust-producing planetesimal belt, and perhaps more than one. For it turns out that the resolution achieved by the SOFIA data was insufficient to determine whether the inner disk is itself divided into more than one narrow belts, but it did allow the team to rule out the possibility that the inner region’s warm emissions were the result of dust grains pulled in from an outer, much colder belt.

That favors the first model. The paper makes the case that in the absence of dust grains being dragged in from the cold outer belt, a planet might be necessary to explain what is seen in Epsilon Eridani’s inner disk structure. From the paper:

The observed profiles are not consistent with the case dominated by dragged-in grains (uninterrupted dust flow from the cold Kuiper-belt-analog region) as proposed by Reidemeister et al. (2011). This might suggest the need of a planet interior to the 64-au cold belt to maintain the inner dust-free zone, or a very dense cold belt where the intense collisions destroy the dust grains before they have enough time to be dragged in. In either case, some amount of dragged-in grains from the cold belt can still contribute a fraction of the emission inside 25 au; the exact amount remains to be determined by future high spatial resolution.

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Image: Illustration based on Spitzer observations of the inner and outer parts of the Epsilon Eridani system compared with the corresponding components of our Solar System. Credit: NASA/JPL/Caltech/R. Hurt (SSC).

What we do have, though, is confirmation that we have at least one inner disk, and that it is near the orbit of the Jupiter-class planet that circles the star at a distance comparable to Jupiter’s from the Sun. Kate Su explains:

“The high spatial resolution of SOFIA combined with the unique wavelength coverage and impressive dynamic range of the FORCAST camera allowed us to resolve the warm emission around eps Eri, confirming the model that located the warm material near the Jovian planet’s orbit. Furthermore, a planetary mass object is needed to stop the sheet of dust from the outer zone, similar to Neptune’s role in our solar system. It really is impressive how eps Eri, a much younger version of our solar system, is put together like ours.”

The paper is Su et al., “The Inner 25 AU Debris Distribution in the epsilon Eri System,” Astronomical Journal Vol. 153, No. 5 (25 April 2017). Abstract / preprint.

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