systemic

Photo credit: Bill Lowenburg — From the Crash Burn Love Project

I sure enjoyed that article on Figure-Eight racing in last Sunday’s New York Times. The piece is a shameless sop, of course, to the smug ironic-hipster segment of the NYT readership — not unlike twelve-packs of Pabst Blue Ribbon stacked up in front of the checkout counter at Whole Foods — but it’s also a great story. The racers adhere to a pure recession-era hellenic ideal, risking life and limb for glory, complete with six-time world champion Bob Dossey channeling a latter-day wrath of Achilles.

And the exoplanet connection? Orbital mean-motion resonances with large libration widths bring to mind a smoothly-running Figure-Eight race. The planets roar around the parent star, continually missing each other at the intersections of their crossing orbits. Here’s an animation of the HD 128311 2:1 resonant pair, strobed over several hundred orbits.

(Animation was causing the site to slow down, so I took it down.)

To date, several such systems are known. In addition to HD 128311 b and c, a similar state of affairs also seems to hold in the HD 82943 and HD 73526 systems, both of which appear to harbor planets in 2:1 mean motion resonance with large libration widths. For all three of these systems, however, the degree of confidence that the correct dynamical configuration has been identified is somewhat less-than-satisfying. Rather than directly observing the resonant dynamics, one notes in each case that a whole bundle of model systems can be constructed which fit the radial velocity data. Within these large sets of allowed configurations, the ones that are dynamically stable over time scales of order the stellar lifetime tend to have large libration widths.

By contrast, Gliese 876 — the one system for which the radial velocity solution provides direct and unambiguous access to the resonant configuration — has its two largest planets lying very deeply in 2:1 resonance, and the libration width is just a few degrees. It bothers me that Gliese 876 seems to be so qualitatively different. It’s easy to wonder whether there might be an error of interpretation for the indirectly characterized systems.

Resonance libration widths are more than just a curiosity. They provide a record of the conditions that likely existed in the protostellar disks from which the planets formed. A turbulent disk produces transient density fluctuations that cause the libration width of a resonant pair of planets to undergo a random walk, much as a stochastically driven pendulum will, on average, tend to gradually increase the height of its swing. The plot below (which comes from a 2008 ApJ paper written with Fred Adams and Anthony Bloch) shows the results of five individual simulations in which gravitational perturbations mimicking those arising from disk turbulence are applied to integrations of the Gliese 876 A-b-c system. In each case, the libration width of the resonant argument tends to increase with time. Perhaps the Gliese 876 system was very lucky, and despite being buffeted managed to end up with a tiny swing. More likely, the gas flow in Gliese 876’s disk was relatively calm and laminar.

Until now, almost everything we know about extrasolar planets in resonance has come from the radial velocity surveys. This year, Kepler is also starting to contribute, with the announcement of  a new system — Kepler 9 — which exhibits detectable transit timing variations. The planets orbiting Kepler 9 were announced with media fanfare during the recent Haute Provence meeting, and a detailed article (Holman et al. 2010) will soon be published in Science. The Kepler 9 set-up is oddly reminiscent of Gliese 876. Two Saturn-sized (and somewhat less than Saturn-mass) planets orbit with periods currently in the vicinity of 19 and 39 days. Further in, an unfortunate super-Earth is stuck is a blistering 1.6-day orbit. Here are the orbits drawn to scale.

The planetary and stellar radii are not to scale, but rather, are sized to conform to the NASA press release artist’s impression of the system…

Kepler 9’s orbital geometry represents quite an extraordinary draw! All three planets can be observed in transit, and the strong gravitational interactions between the two outer planets lead to large deviations from strict periodicity. Indeed, the system is simultaneously tantalizing and maddening. The parent star is many times fainter than Gliese 876, meaning that it will be difficult to get a large collection of high-quality radial velocity measurements. In order to really characterize the dynamics of the system, it will be necessary to lean hard on transit timing measurements. The observations published in the Science article have a low per-point timing cadence; skilled amateur observers can obtain timing measurements that have higher precision and which significantly extend the time baseline, and so the system presents an excellent opportunity for small telescopes to obtain cutting-edge results. The parent star (in Lyra) is still up in the Northern Hemisphere’s evening sky, and there are transits coming up!

During the time that Kepler monitored the system last year, the orbit of the outer planet, “c” (P~38.9 d) was observed to be steadily decreasing by 39 minutes per orbit, and the orbital period of the inner planet, “b”  (P~19.2 d) was increasing by 4 minutes per orbit. Clearly, this state of affairs can’t continue indefinitely. If the system is in a 2:1 mean motion resonance, then over the long term, the periods of the two planets will oscillate around well-defined average values. The Kepler measurements strobed the system over a relatively small fraction of its overall cycle. An analysis of the planetary disturbing function (in which all but the most significant terms get thrown out) indicates that the libration time should be of order the orbital timescale (40 days) multiplied by the square root of the planets-to-star mass ratio (~100), or about ten years.

We don’t know exactly which part of the cycle Kepler dropped in on, and so the second derivative (rate of change of the rate of change) of the period could be either positive or negative. This means that there is a significant uncertainty on when the next transits will occur, but it also means that accurate measurements will immediately give a much better idea of what is going on.

The next opportunities will occur on October 5th (for 9c) and October 8th (for 9b). As always, observers should use the TRESCA website to double-check observing details and to submit light curves after the observations have been made. As the dates approach, I’ll post specific details for small-telescope observers — it will take a global effort to ensure that definitive observations are made. We’ll also soon be releasing an updated version of the systemic console that will allow for the modeling of TTVs in double-transit systems.

…are often risky, but can be illuminating nonetheless.

The astronomy decadal report, which was issued a few weeks ago, set forth three big-picture goals for the next decade: (1) searching for the first stars, galaxies, and black holes; (2) seeking nearby habitable planets; and (3) advancing understanding of the fundamental physics of the universe.

It’s looking quite likely that goal number two will be the first to get substantially met. For quite a while now, a plot of year of discovery vs. the known planetary Msin(i)’s has provided grist for speculation that the first announcement of an Earthlike Msin(i) will occur this year…

In all likelihood, the surface of the first Earth-mass object detected in orbit around a sun-like star will be better suited to oven-cleaning than life as we know it. An interesting question, then, is: when will the first potentially habitable planet be detected? As readers know, such a world will very likely be detected via either transit (MEarth, Warm Spitzer or Kepler) or by the radial velocity technique (HD 40307, Alpha Cen B, etc. etc.).

Earlier this year, I struck up an e-mail conversation with Sam Arbesman, a Research Fellow at Harvard who studies computational approaches to the social sciences. Sam has a rather eclectic spectrum of interests, and writes pieces for the Boston Globe and the New York Times on topics ranging from mesofacts to baseball statistics. He’s also in charge of collecting fares for the Milky Way Transit Authority.

We carried out a scientometric analysis to arrive at what we believe is likely to be a reasonably accurate prediction of the discovery date of the first potentially habitable extrasolar planet with a mass similar to Earth.

Our paper has been accepted by the journal PLoS One, and Sam just posted to arXiv, apparently with little time to spare. The best-guess date that emerged from the analysis is May 2011.

Audaciously, alarmingly close! Certainly soon enough, in any case, for us to look rather sheepish if we’re off by a significant amount…

Exciting times for the exoplanet field. The announcement of the first million-plus dollar world is only days to weeks to months or at most a year or two away, and in the interim, the planet census keeps expanding.

At the same time, however, all the new planets are accompanied by a certain creeping degree of frustration. I have a feeling that these worlds, and especially the super-Earths, will prove to be even more alien than is generally supposed. Artist impressions do a good job when it comes to gray and airless cratered surfaces, but are necessarily inaccurate or impoverished or both in the presence of masses more than a few tenths that of Earth. And because of the distances involved, we won’t be getting the really satisfying images any time soon.

With my provincial day-to-day focus on Gl 876, Gl 581, HD 80606 et al., I tend to forget that we’ve got a full-blown planetary system right here in our back yard. It caught me by surprise, months after the fact, and via a thoroughly tangential channel, that a sober-minded case can be made for the presence of methane-based life on Titan. In fact, a detailed case has been made, complete with specific predictions, and, startlingly, those predictions now seem to have been confirmed.

In 2005, Chris McKay (whose office was just down the hall when I worked at NASA Ames’ Planetary System Branch) wrote an Icarus paper with Heather Smith proposing that methanogenic life might be widespread on Titan. McKay and Smith argue that one macroscopic consequence of such life would be a depletion of ethane, acetylene, and molecular hydrogen in Titan’s near-surface environment. Recent work seems to indicate that all three compounds are indeed depleted, which is very interesting indeed.

The details, and an assessment of the odds are a topic for another post. The simple fact that Titan is in the running at all is absolutely remarkable. Toto, I’ve a feeling we’re not on Mars anymore. Methane-based life in the Saturnian system would seemingly stand a far higher chance of stemming from a completely independent genesis. If Titan has managed to put together a biosphere, then there could very well be more life-bearing planets in the Galaxy than there are people.

The prospect of widespread life on Titan brings to mind the descent of the Huygens probe on January 14, 2005. I remember wondering, in the days running up to the landing, what the probe was going to see, and thinking that it was a once-in-a-lifetime moment of anticipation. Titan is the only world in our Solar System in which there was seemingly a chance, albeit very slim, of having a genuinely world-altering scene unfold upon touchdown. I knew that in all likelihood, the scene was likely going to look something like a cross between the Viking  and Venera panoramas, but I couldn’t quite squelch that lotto-player’s like expectation that pictures of a frigid silurian jungle would be radioed back across light hours of space…

As everyone knows, there was no golden ticket in the chocolate bar, but might we still have a chance to see something really exotic when the next probe touches down?

It’s always seemed to me that the relatively mundane ground-level view at the Huygen’s landing site was somewhat at odds with the electrifyling promise implicit in the probe’s descent sequence. From 150 kilometers up, the haze is just starting to part — the view is not unlike the one that Percival Lowell had through his telescope of Mars. Faint dusky markings that one can connect in the mind’s eye to just about anything:

From 20 kilometers up, a wealth of detail is visible. Alien rivers, shorelines, islands?

The Huygen’s signal was extremely weak. The images arrived in a jumble, with Earth’s largest radio telescopes straining to hear them. It’s interesting to imagine what the level of anticipation might have reached had we known of the atmospheric depletions, and had the images arrived in real time as the probe drifted down toward the surface. Here’s the view from six kilometers up. Think of the looking out the window of a Jetliner several minutes after the start of descent from cruising altitude:

From 2 kilometers up:

From .6 kilometers up:

From a mere 200 meters altitude:

What if we carry out the same exercise and land a probe at a random spot on Earth? To roughly 1-sigma confidence, we’d come in for a splashdown somewhere in the ocean. Out of sight of land, no macroscopic life visible, just water, clouds and blue sky, and just like Huygen’s landing on Titan, a disappointment with respect to what might have been…

So I decided to wrap up the post by forcing the hand of chance. Using true random numbers (generated, appropriately enough by random.org through the use of Earth’s own atmospheric noise) I drew a single random location on the surface of a sphere, and calculated the corresponding longitude and latitude. The result?

-26.478972 S, 132.022361 E.

Google Maps makes it possible to drift in like Huygens for a landing sequence at any spot on Earth. The big picture, of course, is completely familiar, so the suspense is heightened in this case by successively zooming out.

The next scene, which is roughly a mile on a side, is quite readily set into the mental context. The random spot is in the Australian outback. Red dust, scattered rocks, scrub brush, spindly trees, and most evocatively, a building, a cul-de-sac, and a lonely stretch of dirt road bisecting the lower right corner of the view. Of course, had the probe come in a few decades ago, the scene would be no less tantalizing than what we had from Huygens at similar altitude. Those could easily be boulders, not treetops.

Aside from the roads, at a scale similar to where Titan was first revealed, Titan holds out, if anything, more promise than -26.478972 S, 132.022361 E:

To set context, one can zoom all the way out. By coincidence, -26.478972 S, 132.022361 E is not far from the zone peppered by the reentry of Skylab on 11 July 1979, which ranged from 31° to 34°S and 122° to 126°E.

With a simulated Earth landing, we’re allowed to cheat, and get the full scoop on our landing spot. This is as simple as enabling geo-tagged photos and Wikipedia entries:

The wikipedia links are here and here. -26.478972 S, 132.022361 E is just over a rise from a solar power station on the Anangu Pitjantjatjara Yankunytjatjara local government area.

And imagine a probe touching down just in time to record this scene:

Image source.