systemic

Higher resolution version.

The opportunity to travel is a splendid benefit of being an astronomer. During this week and last, I’ve been to a whirlwind of European destinations.

Stockholm was the first port of call. For someone whose life is lived at 36.974 degrees North, it is surreal to arrive in the late evening to find the Sun still well above the horizon. Night never really falls. As the hours slip through midnight, the sky merely drifts through gradations of twilight. We don’t yet have addresses for terrestrial planets beyond our solar system, but it’s certain that the galaxy is full of them. We have as yet no clues to the alien geologies, landscapes, biospheres, but the spin axes of planets tend to be tilted. The quality of midsummer twilight in the high latitudes is a phenomena shared by worlds throughout the galaxy.

I gave two talks at the Alba Nova University Center, which hosts a collaboration between astronomers, physicists and biologists, and which is mostly located in a vast award-winning building by architect Henning Larsen. The astronomy offices are arrayed along a hallway that curves for nearly a hundred meters along the top floor. Running above the doorways is a continuous printout of the solar spectrum.

All told, it contains millions of resolution elements, and an absolutely bewildering forest of absorption lines.

Even on closest inspection, each angstrom of the spectrum is smooth and full of detail.

The juxtaposition of the micro and the macro readings is dramatic. The printout also drove home the utterly tiny scale of the Doppler shifts that must be measured in order to detect planets via the radial velocity technique. A large planet such as Tau Boo b generates a radial velocity half-amplitude of 500 m/s, which corresponds to moving (and slightly stretching or compressing) the entire hundred-meter-long diagram up or down the hallway by a few dots of printer resolution. The shift caused by Gliese 581 e, on the other hand, would require a microscope to detect.

A little over a year ago, I wrote two posts (one, two) that described (then) undergraduate student Konstantin Batygin’s work on the classical problem of the dynamical stability of the solar system. Konstantin and I were amazed to discover that the inner planets can be destabilized within the next 5 billion years by a linear secular resonance that brings Mercury’s orbital precession into sync with Jupiter’s — a state of affairs that’s akin to firing the starting gun at a Figure 8 race:

And it wasn’t only Mercury that ran into problems. At t=822 million years, shortly after Mercury’s entrance into a zone of severe chaos, Mars — rovers and all — was summarily ejected from the Solar System.

Just after we submitted our paper to the Astrophysical Journal, we learned that we’d been scooped by LeVerrier’s heir in Paris, Jacques Laskar, who had independently submitted a paper drawing essentially the same conclusions to Icarus.

The papers from last year did not include the effect of general relativistic precession. It seemed prudent to first tackle the classical N-body problem. Ironically, the fact that Mercury’s precession is sped up by General Relativity provides a very significant improvement in the stability of the solar system — “Einstein saves the day.”

A paper in this week’s issue of Nature by Laskar and computer engineer Mickael Gastineu brings effective finality. Laskar and Gastineu used the JADE supercomputer at the French National Computing Center to integrate a staggering 2,501 orbital solutions of the full solar system, each of 5 billion year duration. The integrations include general relativity, the gravitational effect of the Earth-Moon binary, and use an ultra-precise ephemeris. They make millimetric changes to Mercury’s orbit and take advantage of the butterfly effect to gain a statistical assessment of the solar system’s prospects.

And the final answer?

There’s a 1% chance that Mercury’s orbit will be destabilized within the next 5 Billion years. It’s possible (although considerably less likely) that Earth can take a direct hit from Mars as a result of Mercury’s transgressions. The paper makes dramatic reading.

Dramatic enough, in fact, that for the past day and a half, I’ve taken a ride on Laskar and Gastineau’s disaster movie-ready coat tails. I wrote the accompanying News and Views article, which has been nosing into the media alongside their results, and I’ll be talking about orbital dynamics, the history of the few-body problem and planetary collisions later today on NPR’s Science Friday. Listen in if you’d like, or check out the podcast when it comes out.

Earth occulting the Sun, seen from Apollo 12 (source).

The year 1995 fades into increasingly ancient history, but I vividly remember the excitement surrounding Mayor and Queloz’s Nature article describing the discovery of 51 Peg b. Back in the day, the idea of a Jovian planet roasting in a 4.2-day orbit was outlandish to the edge of credibility.

In the five years following the Mayor-Queloz paper, four additional Doppler-wobble planets with periods less than a week (Ups And b, Tau Boo b, HD 187123b, and HD 75289b) were announced. Each one orbited close enough to its parent star to have a significant a-priori probability of transiting, and by mid-1999, the summed expectation for the number of transiting planets grew to N=0.68. Each new planet-bearing star was monitored for transits, and each star came up flat. Non-planet explanations for the radial velocity variations gained credence. The “planets” were due to stellar oscillations. The “planets” were actually mostly brown dwarfs or low-mass stars on orbits lying almost in the plane of the sky.

The discovery of HD 209458b, the first transiting extrasolar planets was therefore a huge deal. Instantly, the hot Jupiters gained true planetary status. There’s a huge leap from a mass-times-a-sine-of-an-inclination to density, temperature, composition, weather. 209458 was the moment when the study of alien solar systems kicked into high gear.

At the moment, we’re within a year of getting news of the first Earth-mass planet orbiting a solar-type star. It’s effectively a coin flip whether the announcement will come from Kepler or from the radial velocity surveys. In either case, the first Earth will likely be too hot for habitability, but within a few years we’ll be seeing genuinely habitable, multi-million dollar worlds. Kepler, for one, will deliver them in bulk.

Enter the TESS mission.

Here’s the scoop: The TESS satellite consists of six wide-field cameras placed on a satellite in low-Earth orbit. If it’s selected, then during its two-year mission, it will monitor the 2.5 million brightest stars with a per-point accuracy of 0.1 millimagnitude (one part in ten thousand) for the brightest, most interesting stars. It will find all of the transiting Jovian and Neptune-mass planets with orbital periods of less than 36 days, and it can make fully characterized detections of transiting planets with periods up to 72 days. Where transits are concerned, brighter stars are better stars. TESS will locate all the bright star transits for Neptune-mass planets and up, and equally important, it will find the best examples of large transiting terrestrial planets that exist.

TESS also provides an eminently workable path to the actual characterization of a potentially habitable planet. Included in the 2.5 million brightest stars are a substantial number of M dwarfs. Detailed Monte-Carlo simulations indicate that there’s a 98% probability that TESS will locate a potentially habitable transiting terrestrial planet orbiting a red dwarf lying closer than 50 parsecs. When this planet is found, JWST (which will launch near the end of TESS’s two year mission) can take its spectrum and obtain resolved measurements of molecular absorption in the atmosphere.

If TESS is selected for flight, we’re literally just five years away from probing the atmospheres of transiting planets in the habitable zone.

There have been a number of recent developments on the Alpha Centauri front.

Several weeks ago, Lee Billings wrote an article for Seed Magazine that delves at length into the hunt for terrestrial planets orbiting Alpha Cen. It hits a really inspiring tone. (I suggest pairing it with Nick Paumgarten’s equally well-written The Death of Kings to get a sense of how we’re living in what is effectively a bizarre superposition of worlds of varying habitability.) In keeping with the zeitgeist, the Alpha Cen story was also picked up last Monday with an article by Joel Achenbach in the Washington Post.

Billings’ article is entitled “The Long Shot”, with the reference being to Project Longshot, the far-out 1988 mission design for an unmanned 100-year nuclear pulse propelled mission to the Proxima/Alpha Centauri system. I, for one, definitely hope to be counted present when such a mission begins phase E.

Interestingly, the Seed article divulges an important clue to the extent of the Geneva Team’s current data set for Alpha Cen B, with the source apparently being a telephone interview with Michel Mayor:

Since 2003, Mayor and his team have used HARPS to search for planets around Alpha Centauri B. Last August, they began observing the star every available night in a strategy similar to Fischer’s.

The italics are mine, and for Alpha Cen fans, this is great news. Recent developments have made it abundantly clear that when HARPS is working full bore on a bright quiet star, it can drill right down into the habitable zone. If we assume that the statement in the above excerpt is accurate, we can put very interesting current limits on habitable planets in the Alpha Cen B system.

The star HD69830 (which harbors three-Neptune mass planets, see e.g. here and here) is a good proxy for Alpha Cen. The data set published in conjunction with the Lovis et al. article in Nature on HD 69830 contains 74 velocities taken over an 826 day period from Oct. 26 2003 through Jan 30 2006. That works out to 0.09 velocities per day, with each velocity having a reported instrumental error of ~0.8 m/s. This means that if Alpha Cen B received similar attention to that paid to HD 69830, then the Alpha Cen B data set as of last August would have contained ~160 velocities, each with ~0.8 m/s instrumental error.

If we look at the time series for HD 69830, however, we see that 160 Alpha Cen B velocities as of a year ago is likely an overestimate. It’s clear that the HD 69830 planets were starting to show after the first six months of observations, and as a result, the cadence on the star was increased by more than a factor of two. Based on the initial cadence on the star, it’s reasonable to expect that Alpha Cen B has been accumulating ~15 velocities per year, which works out to ~75 velocities in August 08 when the cadence was increased.

It seems reasonable to expect that when firing on all cylinders, HARPS can pull in 100 velocities per year for Alpha Cen B. This means that by the end of this summer, the Geneva team could quite reasonable be in possession of an N=175 point time series. Alpha Cen has near year-round observability from La Silla, so we can create a synthetic data sets which spread 75 velocities randomly across five years, followed by a year with 100 randomly spaced velocities. The data that the Geneva team currently have in hand probably look something like this:

The habitable zone for Alpha Cen B is at P~250d. Let’s assume that a planet with this period has an orbit of eccentricity e~0.05, and look at representative Lomb-Scargle periodograms of Monte-Carlo data sets created for different values of the planet mass. In keeping with the results for Gliese 581 and HD 69830, let’s also assume a 1 m/s normally distributed radial velocity jitter produced by the star.

An Msin(i)=4.6 Earth-mass planet in an optimally habitable orbit around Alpha Cen B is worth USD 100K (which seems like a remarkably good deal). Three periodograms for different Monte-Carlo realizations indicate that such a planet would be right on the verge of current “announceability”:

If the mass is reduced to Msin(i)=2.3 Earth masses (which jacks the value to a cool USD 227 million) the data sets (three of which are shown just below) are not quite seeing the planet yet. Another year and a half or so will be required.

During the coming 18 months or so, we’ll therefore be in an interesting situation in which no news on Alpha Cen is very good news. Perhaps any Wall Street types who read this blog might try their hand at pricing an option on Alpha Cen Bb.

And finally, the theoretical objections to the formation of terrestrial planets orbiting Alpha Cen B are dissipating rapidly. I’ll pick up that story in an upcoming post…

An interesting discovery announcement came across the wire on Friday. In an article to be published in the Astrophysical Journal, Steven Prado and Stuart Shaklan of JPL write up their detection of a ~6 Jupiter mass companion orbiting the nearby ultra-low-mass red dwarf VB 10. Their discovery was made astrometrically, using a modern CCD camera attached to the venerable Palomar 200-inch telescope. JPL put out a press release to go along with the article.

VB 10 contains about 78 Jupiter masses, just barely lifting it above the minimum mass required to qualify as a bona-fide hydrogen-burning main sequence star. It’s got roughly ten times the mass and ten times the density of its companion. In the center-of-mass frame, the system configuration looks like this, where I’m taking a guess at the unknown eccentricity:

I wouldn’t call VB 10b a planet in the usual sense. With a mass of order one-tenth that of its parent star, it’s almost certainly straggling in at the very bottom of the stellar initial mass function. It’s a low-mass brown dwarf impinging into the “planet desert” from above. Gravitational instabilities tend to crop up if a protostellar disk exceeds 10% the mass of its central star, so the VB 10 system probably formed via the fragmentation process that leads to binary stars rather than via the core accretion mechanism that seems to be responsible for the majority of Jovian planets. Presumably, a similar fragmentation-based process had a hand in the formation of 2M1207, in which a ~4 Jupiter-mass secondary orbits a ~25 Jupiter-mass primary:

Photo credit: ESO (VLT/NACO)

At a distance of only 19 light years, VB 10 is (relatively speaking) just right next door. In tandem with its wide binary companion Wolf 1055, it currently ranks as the 68th-nearest known stellar system. That one need not travel far afield to find VB 10b means that objects like VB 10b are probably common in orbit around the most dimunitive red dwarfs.

As instrumentation improves, it’ll eventually become possible to survey the satellite systems of objects like VB 10b. In our solar system, Jupiter, Saturn and Uranus all have roughly 2×10-4 of their primary mass locked up in satellites. I’m guessing that this rule of thumb will continue to hold when exomoons start getting detected, but I bet that it won’t hold true for objects that formed via fragmentation.

The VB 10 system is built to last. The primary will enjoy a main-sequence lifetime of close to ten trillion years, during which time the Milky Way-M31 merger remnant will become increasingly isolated from all the other mass that makes up the currently observable universe. Tidal evolution will gradually tighten up the orbit of VB 10b, meaning that the binary will quite possibly survive and harden further during quadrillions of years of encounters with passing degenerates. Barring other catastrophes, gravitational radiation will eventually bring VB 10 and VB 10b together into merger. That shot of good pure H will revive the dead helium remnant of VB 10, causing it to shine for a further hundred billion years or so.