systemic

As anyone who’s used the systemic console knows, the numerical integration of planetary orbits is aggravatingly slow. For modern-day dynamicists, endless pages of algebra are often a thing of the past. Now it’s “hurry up and wait” while the computers grind through the integrations.

If you’re charting the courses of planets that have negligible planet-planet gravitational interactions, then life runs at interactive pace. Instead of integrating 6N coupled ordinary differential equations, you need only solve Kepler’s equation, M = E – e sin E, which parameterizes the position of the planet on its ellipse as a function of time.

In an era of environmental and economic collapse, solving M = E – e sin E for E doesn’t seem like a big problem. Simple iteration, for example, works quite well. Remarkably, however, as pointed out by Peter Colwell in his 1993 book Solving Kepler’s Equation Over Three Centuries, there have been scientific papers written about Kepler’s Equation and its solution in every decade since 1650. From the synopsis of Colwell’s book:

The sole subject of our work is Kepler’s Equation (KE) M = E – e sin E . In its narrowest form, the Kepler problem is to solve KE for E , given M in the interval and e in the interval [0,1]. In virtually every decade from 1650 to the present there have appeared papers devoted to the Kepler problem and its solution. We can see from a list of them that the problem has enticed a wide variety of scientists to comment on or involve themselves in its solution.

It is surely not unique in science for a specific problem to be given so much attention over so long a period–particularly if it resists solution, if its partial solutions are inadequate or unsatisfactory, or if it is recharged with new interpretations and new applications. Still, it is curious that the Kepler problem should have continued to be this interesting to so many for so long. Admittedly it is a problem central to celestial mechanics, but it is a technical little problem for which a number of satisfactory solutions are long known. With the advent of calculators and computers, there is no impediment to achieving quick solutions of great accuracy. The problem has neither the broad appeal of an Olbers Paradox, nor the depth and intractability of a many-body problem.

In common with almost any scientific problem which achieves a certain longevity and whose literature exceeds a certain critical mass, the Kepler problem has acquired an undeniable luster and allure for the modern practitioner. Any new technique for the treatment of transcendental equations should be applied to this illustrious test case; any new insight, however slight, lets its conceiver join an eminent list of contributors.

Perhaps the most influential article of the 1990s that touches directly Kepler’s equation is Wisdom and Holman’s 1991 paper that describes the N-body map. The basic idea is that the trajectories of interacting planets can be divided neatly into a part consisting of Keplerian motion, and a part consisting of the derangements brought on by the interplanetary gravitational tugs. A Wisdom-Holman integration avoids forcing the computer to continually rediscover Kepler’s ellipse, reducing much of the integration to repeated numerical evaluations of Kepler’s equation. For orbital integrations that don’t involve close encounters, this trick leads to an order-of-magnitude speed up. N-body maps have made it possible to (for example) readily integrate the motion of the solar system planets for the lifetime of the solar system.

As the first decade of the new millennium starts to draw to a close, I was pleased to see that the 350+ year tradition is continuing. In a recent astro-ph posting, Eric Ford shows how graphics cards can be commandeered to implement highly parallelized numerical evaluations of Kepler’s equation. Using mixed-precision arithmetic, he shows that graphics cards can offer a speed-up of a factor of ~600 over console-style evaluations of M = E – e sin E that use the regular ‘ol CPU. Having the clock hands move 600 times faster really brings Markov Chains to stochastically vibrant life.

And the 2010s? I think quantum computation might turn the order N^2 N-body problem into an order-N computation (see this post). That’ll free up the GPUs so that everyone can get back to playing Grand Theft Auto.

Image copyright 1951, 20th-Century Fox.

A search on “Alpha Centauri” in the news archives of the New York Times turns up an average of one or two hits per year, including a scattering of genuine astronomical news clippings about the stellar system itself.

For example, on August 31st, 1904, a bulletin datelined Lick Observatory reported that the distance to Alpha Centauri has been determined “spectroscopically”, although it’s fully uncommunicative of any further details. On December 27th 1925, there was an item (unfortunately tagged pay-to-play) that seems very much in the oklo.org vein:

NEAREST STAR FLIES TO US FROM SPACE; Its speed is Fourteen Miles a second. TWENTY-FIVE thousand years hence New York will be able to see Alpha Centauri our nearest stellar neighbor. Alpha Centauri travels toward the earth at the rate…

In many of the citations, Alpha Cen hits the stands in its role as a cultural touchpoint. For example, in the Dec. 28th, 1969 edition, one finds a post-Apollo, pre-Watergate prediction (presumably a joke):

Reading the Tea Leaves — What will happen in 1970… Vice President Agnew, cut in on a split screen, suggests that the U.S. launch a crash program to go to Alpha Centauri, the nearest star.

Similarly, upon reading Friday’s NYT edition, 20th Century Fox executives must have been elated to find that their publicity stunt for The Day the Earth Stood Still has been given a promotional write-up in the science section. Last Friday at Noon, it seems that the big-budget remake of the Cold-War classic was beamed in its entirety to Alpha Centauri. To one-sigma precision, the transmission will be illuminating Alpha Cen Bb sometime between Monday April 22nd, 2013 and Saturday April 29th, 2013, just a few months into Obama’s second term.

So what are the smart-money odds that the movie will actually get watched in the Alpha Cen system? Oklo.org recommends the following conditional probabilities:

fp = Chance of a habitable planet orbiting Alpha Cen B = 0.6

fl = Chance that live evolved on that planet = 0.01

fi = Chance that life developed intelligence = 0.1

fr = Chance that intelligence understood Maxwell’s Equations = 0.01

fn = Chance that Maxwell’s Equations are currently understood on Alpha Cen Bb = 64,000 / 3×10^9 = 0.0000213.

This gives (fp)x(fl)x(fi)x(fr)x(fn) = one in eight billion, with Alpha Cen Ab kicking in an additional one in a trillion chance.

The numerator in fn is a decision-market estimate corresponding to the long-term running mean (not median!) result of polling students in my classes as to how long they think we’ll remain capable of building radios. The denominator is an estimate of the span of past time during which Alpha Cen Bb could have conceivably harbored intelligence.

Signals beamed to other worlds are readily subject to misinterpretation. I’ve always enjoyed Michael Arbib’s take on the 1961 version of the Drake signal turned up side down:

Friday’s transmission does make one thing clear, though. If a genuine ETI signal is ever beamed to Earth, it’ll almost certainly be a commercial advertisement. The primary problem of interpretation will simply be to figure out how to wire back our cash.

UPDATE:

In the comments section, bruce01 makes the following astute observation:

Alpha Centauri, at declination -60 degrees, is barely above the horizon even from Florida. The web site:
http://www.deepspacecom.net/
says they are located near the Kennedy Space Center which is north of latitude 28 degrees. This makes the zenith angle of Alpha Centauri greater than 88 degrees as seen from the Space Center. You need to add to your equation the probability that the “beamed” signal made it through the Earth’s atmosphere without being totally scattered.

Indeed. Furthermore, for the entire duration of the broadcast, Alpha Cen (RA 14h:39m, DEC -60deg:50min) was below the horizon as viewed from 28 35 06N, 80 39 04W. One can’t help but wonder whether bruce01 may have made a vital contribution to the solution of the long-running Fermi Paradox.

I’m absolutely confident, though, that any organization with the reach and technical expertise advertised by the Deep Space Communications Network would maintain a fully staffed southern hemisphere station for their broadcasts to the southern skies.

I like it when remarkable exoplanet results are disguised within more-or-less innocuously titled papers. A nice example occurred this summer, with “The HARPS search for southern extra-solar planets. XIII. A planetary system with 3 Super-Earths (4.2, 6.9, & 9.2 Earth masses)”. While it’s true that the three planets orbiting HD 40307 are indeed cool, the Geneva team announced much bigger news in the discussion section of the article. They reported, almost offhandedly, that 1/3 of solar-type stars have sub-Neptune mass planets with periods of 50 days or less. That’s the most important planet news since the discovery of hot Jupiters.

Another instance can be found in last weekend’s astro-ph mailing under the file-to-read-later title, “A Smaller Radius for the Transiting Exoplanet WASP-10b“. In this article, John Johnson and collaborators demonstrate 0.47 millimagnitude per-sample photometry with a cadence of 1.3 minutes from the ground. At first glance, their light curve of a WASP-10b transit looks like it came from outer space:

For comparison, here’s the classic 2001 HST composite light curve of the HD 209458b transit that really did come from outer space:

The HST light curve has an 80 second (1.33 min) cadence, and a per-point precision of 0.11 millimagnitudes. Because of HST’s low-Earth orbit, however, it took four separate transits to assemble the composite light curve:

On a per-transit basis, then, Johnson et al.’s ground-based photometry is 22% the value of the HST photometry. That is extraordinary value for the dollar.

The WASP-10 curve was obtained with a type of CCD called an orthogonal transfer array, which controls how the starlight is spilled onto the individual pixels. By distributing the incoming photons in a highly disciplined manner over a larger area of the detector, saturation is staved off, and the duty cycle is improved.

WASP-10-b is a 12.7 magnitude star, and so its transit light curve certainly benefits from having control stars of similar magnitude in the field of view of the 2.2m telescope. The most interesting transiting planets occur around brighter stars (accessible to Spitzer). Nevertheless, it seems quite probable that an observational set-up using a neutral density spot filter for the primary star would allow similar precision on brighter stars. (Back in the day, Tim Castellano used the spot filter technique to check HD 187123 for transits by its hot Jupiter.)

It’s interesting to look at a few of the possibilities that open up if one can do 80sec–0.47mmag photometry from a facility that’s not dauntingly oversubscribed.

Transit timing is high on the list. TTV precision scales in direct proportion to photometric precision, and it scales with cadence to the -1/2 power. For the Wasp-10b transit, the moment of the central transit was measured to a precision of 7 seconds. At this level, it’s possible to sense the presence of very small perturbing planets, especially if one also has precise radial velocities. Stefano has been burning the midnight oil to improve the systemic console for research-grade use. One of the primary capabilities of the new console is an enhanced transit timing analysis suite that is capable of fully exploiting timing measurements at the 5-10 second level. We’ll be officially rolling out the new console quite soon. (In the interim, you can get the current build here.)

Should transit timing indicate the presence of an Earth-mass perturbing companion, then there’s a reasonable chance that the perturber also transits the parent star. If the timing model can give good predictions for when the transit might occur, then 80sec–0.47mmag is fully sufficient to detect Earths from the ground.

In the figure just below, I’ve zoomed in on an out-of-transit portion of Johnson et al’s Wasp-10b light curve. At this scale the 10^-4 depth of a transiting Earth is just resolved at weblog resolution. By binning the photometry into half-hour chunks, one reaches this resolution. A transit by an Earth-sized planet could thus be a multi-sigma detection in a single night. Hot Damn!

And then there’s the Transitsearch angle. There are a number of Neptune-mass planets that (to my knowledge) have not been adequately checked for transits because their predicted photometric depths were just too small. At the 80sec-0.47mmag level, these planets come right into play. A short list would include (1) 55 Cancri e (11 Earth masses, 10.1% transit probability, 0.065% transit depth), (2) HD 219828b (19 Earth masses, 15.6% transit probability, 0.027% transit depth), 3) HD 40307b (4.3 Earth masses, 6.8% transit probability, 0.052% transit depth), (4) HD 69830b (10.2 Earth masses, 4.9% probability, 0.072% transit depth), and (5) HD 160691d (14.38 Earth masses, 5.6% probability, 0.056% transit depth). Assuming that your RV fits are up to date and that you’re first on the sky with one of these bad boys, your expectation value can run into hundreds of thousands of Swiss Francs per hour.

Academics across the United States know the feeling at the end of the long Thanksgiving weekend. Four days were to be given over (at least partially) to catching up with a long list of slipped deadlines and overdue tasks. Like the last line of a haiku, Sunday afternoon arrives.

The red dwarf stars, on the other hand, have mastered the art of having enough time. A trillion years from now, the science of extragalactic astronomy will have long since ended, but Proxima Centauri, our nearest stellar neighbor, will be shining more or less unaltered from its current recessionista persona.

Proxima will never turn into a red giant. Like the other low-mass red dwarfs, it will grow steadily brighter and bluer as it ages, eventually turning itself into a helium white dwarf that gradually cools and fades to black.

The galaxy is filled with red dwarfs, and so as a result, the total luminosity of the Milky Way will stay surprisingly constant for a long time to come. A few years ago, Fred Adams, Genevieve Graves and I wrote a conference proceedings that looks in detail at the future luminosity evolution of the galaxy.

As the Milky Way’s stellar population ages, the more massive stars (The Sun, Sirius, Alpha Cen A and B, Tau Ceti et al.) die off. For hundreds of billions of years, their flagging contributions to the galactic luminosity are very nearly compensated by the increase in luminosity of smaller stars. This state of affairs will persist until about 800 billion years from now, at which time the remaining main sequence stars will all have less than ~30% of the solar mass. These stars never experience the large luminosity increase associated with the red giant phase, and the galactic light curve declines gently for about 7 trillion years as the lowest mass stars slowly die. During this long autumn, the galaxy as a whole should look quite blue, because the light is dominated by stars that have aborted their journey up the red giant branch and grown bluer. Eventually, after about 8 trillion years, even the smallest stars have run out of hydrogen and the night sky finally goes black for the duration.

Just trying to put the arrival of Monday morning in perspective.

When I got home last Saturday, Sirius had just risen above the neighbors’ roof. The air was dramatically clear. In spite of the Santa Cruz city lights, I could make out stars down to fourth magnitude. The seeing, however, must have been incredibly bad, with a large amount of turbulence at high altitude. Sirius was twittering stochastically from white and blue to brief moments of intense, unmistakable fire-engine orange. Scintillation has got to be at the root of the red Sirius anomaly.

The back of every introductory astronomy textbook contains separate one-page lists of the nearest stars to the Sun and the brightest stars in the sky. I’ve never paid much attention to the lists of brightest stars. Rigel, Deneb, and Hadar are hundreds of parsecs away, hot-tempered, short-lived and ultimately rather tiresome. It’s more interesting to pore over the lists of nearest stars. Alpha Centauri, Eta Cassiopeiae, Tau Ceti, 61 Cygni, Barnard’s star…

It’s always seemed odd to me that Sirius and Alpha Cen are at or near the top of both lists. Sirius, the brightest star in the sky, is in the fifth-nearest system, and Alpha Cen A, the fourth-brightest star is in the nearest system. It’s as if Henry Winkler lived three houses down your street in one direction and Barry Manilow lived five houses up the street in the other direction.

Over a lifetime, the constellations seem fixed, but on geologic timescales, the Sun rapidly drifts through completely new lists of nearest stellar neighbors. A kilometer per second is a parsec in a million years, and stars in the solar neighborhood have a velocity dispersion of ~30 km/sec. This means that the list of nearest 100 stellar systems undergoes a complete turnover roughly every 300,000 years, and over Earth’s 4.5 billion year lifetime, the tables in the back of the Astronomy 101 textbooks have gone through thousands of completely different editions.

The Hipparcos catalog multi-parameter search tool lists 1549 stars with distances less than 25 parsecs. For stars like Alpha Cen B and Sirius, this list is complete. That is, if we go out to 25 parsecs, we know about all the K0V stars, whereas the census of the lowest-mass (and hence extremely dim) red dwarfs is significantly incomplete beyond five parsecs or so. The 1549 nearest stars in the Hipparcos catalog all have their apparent V magnitudes listed and these are easily converted to absolute magnitudes since the distances are known to high accuracy. With the absolute magnitudes in hand, I wrote a short program that repeatedly draws new random 3D distributions of the 1549 stars within our 25-parsec sphere. By doing this, it’s possible to get a sense of how unusual it is to have stars like Sirius and Alpha Cen B essentially right next door. Given that this is just a blog post, I ignored any modifying effects arising from individual stars adhering into binary and multiple systems.

First, Sirius. I ran 1,000 trials, and filtered for instances in which a star that is instrinsically as bright or brighter than Sirius lies as close or closer than Sirius’ current 2.64-parsec distance. This condition was satisfied in 31 of the trials, and in one trial, two stars fit the bill. In a rough sense, then, the presence of Sirius is “unusual” at the 3% level.

As Oklo readers are no doubt aware, I’m rooting for a high-cadence Doppler velocity campaign on Alpha Cen B. The relevant question in this case is: What are the odds that we have a stellar neighbor that is as visibly bright or brighter than Alpha Cen B (V<1.34) with an absolute magnitude equal to or fainter than B (Mv>5.71)? We want a bright star so that a smaller telescope can be used, and so that a maximum number of observations can be made. We want an intrinsically dimmer cooler star because the radial velocity method works at the peak of its ability with K-type dwarfs, and because the radial velocity half-amplitude at given mass is larger and because the habitable zone is closer to the star.

Interestingly, adopting this criterion, Alpha Cen B is also unusual at the 3% level. In 1000 trials, a star that’s intrinsically dimmer than Alpha Cen B that (as a result of proximity) is visibly brighter on the sky occurred 28 times, and in one instance, two such stars made the grade.

Alpha Cen B is special for a number of other reasons: (1) metallicity, (2) binary plane orientation, (3) presence of Alpha Cen A as a control star, (4) sky position, (5) age. It’s sort of like having it turn out that Bono lives right next door.

I was reading a newspaper article last weekend, and ran across one of the more satisfying aphorisms. Chance favors the prepared mind. I just like the ring of that.

Along roughly similar lines, it’s curiously inspiring when someone gets a great, lucky opportunity, and then really steps up to the plate and knocks the ball out of the park. I’ve been trying to identify the best examples of this phenomenon. Consider, for example, when Brian Johnson was offered the lead vocal for AC DC. It’s hard to argue with worldwide sales of 42 million for Back in Black.

What about instances drawn from Astronomy? Johannes Kepler jumps to mind, but everyone already knows the the raft of Copernicus-Brahe-Galileo-Kepler anecdotes. I like the story of Joseph Fraunhofer (lifted from Wikipedia):

Fraunhofer was born in Straubing, Bavaria. He became an orphan at the age of 11, and he started working as an apprentice to a harsh glassmaker named Philipp Anton Weichelsberger. In 1801 the workshop in which he was working collapsed and he was buried in the rubble. The rescue operation was led by Maximilian IV Joseph, Prince Elector of Bavaria (the future Maximilian I Joseph). The prince entered Fraunhofer’s life, providing him with books and forcing his employer to allow the young Joseph Fraunhofer time to study.

After eight months of study, Fraunhofer went to work at the Optical Institute at Benediktbeuern, a secularised Benedictine monastery devoted to glass making. There he discovered how to make the world’s finest optical glass and invented incredibly precise methods for measuring dispersion. In 1818 he became the director of the Optical Institute. Due to the fine optical instruments he had developed, Bavaria overtook England as the centre of the optics industry. Even the likes of Michael Faraday were unable to produce glass that could rival Fraunhofer’s.

The quality of Fraunhofer’s optics played a large role in providing Bessel with the precision that he needed to measure the parallax of 61 Cygni. In explicitly demonstrating the staggering distances to the stars, Bessel was able to bring to a 200+ year scientific quest to a dramatic finish. Hard to argue with that.

Anybody who knows anything about candy knows that “fun size” isn’t any fun at all. The same is true for terrestrial planets. Fun size objects like Mercury, the Moon, Ceres, Vesta and Pallas are airless cratered and dead.

For the past several years, I’ve been agitating for a dedicated radial velocity search for potentially habitable King-size terrestrial planets in the Alpha Centauri system. A number of factors (brightness, age, spectral type, metallicity, orientation, and sky position) make Alpha Cen B overwhelmingly best star in the sky for detecting habitable planets from the ground and on the cheap.

Planets are dynamically stable in the habitable zone of Alpha Cen B. It’s also true that if one starts with hundreds of lunar-sized embryos in the Alpha Cen system, then the formation of King-size terrestrial planets is effectively a given.

But there’s a snag. Those embryos may never have formed. Recent work by Philippe Thebault and his collaborators makes a case that the Alpha Centauri system provided an unfavorable environment for the accretion of planetary embryos, and as a result, the prospects for finding a habitable planet right next door may be depressingly slim. Thebault et al’s first paper (here) clears out the planets around A, and their second paper, which came out at the beginning of this month (here), deals effectively with B.

The basic idea works like this. During the epoch when kilometer-sized bodies are trying to accrete and grow, the presence of a binary stellar perturber forces planetesimal orbits in the circumprimary disks to be eccentric. This eccentricity forcing occurs in the presence of gas drag on the planetesimals. For a population of equal-mass bodies, gas drag and gravitational forcing cause the periastra of the planetesimal orbits to line up. When such phasing occurs, neighboring particles have small relative velocities, collisions are gentle, and the planetesimals are able to grow via collisional agglomeration.

Unfortunately, both the forced eccentricity and the phase angle relative to the binary periastron depend on planetesimal mass. If the disk contains bodies of different sizes, then one gets crossing orbits and larger collision velocities. Planetesimals don’t stick together when they’re bashed together.

Thebault and his collaborators sum up their bottom line results in the following table (which I’ve clipped directly out of their Alpha Cen B paper):

The column on the left lists the initial conditions. The column on the right gives the radius beyond which construction of embryos is thwarted. Conditions that are consistent with the disk that gave rise to our Solar System are encapsulated in the “minimum-mass solar nebula” (MMSN) nominal case. When the MMSN is used as an initial condition for Alpha Cen B, the region exterior to 0.5 AU is unfriendly to accretion. In order for embryos to form in the habitable zone, one’s best bet is to crank up the disk gas density by a factor of at least several. (The table indicates that a 10xMMSN initial conditions allows embryos to form all the way out to 0.8 AU).

Even when confronted with these results, I’m still cautiously long Alpha Cen Bb. It’s not that I think the simulations are wrong or that there is any problem with the outcomes that they produce. Rather, I don’t think a high gas density in the inner AU of the Alpha Cen B disk is cause for alarm. In a nutshell, I don’t see evidence that the MMSN is of any particular utility for explaining the extrasolar planetary systems that we’ve found so far, and hence I’m not depressed that high gas densities were required for Alpha Cen B to have fostered an accretion-friendly environment. Reconstitute, for example, the HD 69830 protoplanetary disk or the 55 Cnc protoplanetary disk. I’m plain skeptical of the validity of a fiducial MMSN scaling for the disks that orbited the Alpha Cen stars. The Alpha Cen binary has twice the total mass of the Solar System, and more than two thousand times the total angular momentum.

We need to do the experiment and find out what’s really there.

As more and more extrasolar planets are characterized, the correlation diagrams steadily increase in their intrinsic appeal. Each planet is attached to a number of interesting quantities (planetary Msin(i), period, and eccentricity, and parent star metallicity, apparent brightness and mass, to name just a few).

The two most important correlation diagrams are probably the mass-period diagram and the eccentricity-period diagram. Ideally, one would like to plot logM, logP, and e in three dimensions, but I’ve always felt that static 3D diagrams don’t work very well. I think one is best off scaling the size of the symbol to Msin(i) and going with a 2D diagram of eccentricity vs log Period. I fooled around with various scalings, and decided that a point radius proportional to Msin(i)**0.4 looks the best.

That leaves color to impart additional information. As the number of planets increases, one is increasingly better off allowing the points in correlation diagrams to be partially transparent. An opacity of 0.7 give an immediate depth of field for overlapping points, and will continue to work well on Keynote slides until there are more than a thousand planets.

The planet-metallicity correlation can be made evident by mapping the metallicity of the parent star onto the hue of the point. With a rainbow scale where red is Fe/H=-0.5 (low metallicity) and violet is Fe/H=0.5 (high metallicity) it’s immediately clear that the planets found to date are skewed toward metal rich stars.

Looks cool.

The Mathematica Hue command allows control of hue, saturation, brightness and opacity. The HSB color scheme potentially allows for quantities to be displayed simultaneously, meaning that 6D correlation diagrams are possible. Can the saturation and brightness indices be put meaningfully to work?

I think the answer is probably yes, but my sense is that it will be tough to get a full return from all three color dimensions. In the diagram below, metallicity maps to hue (as before) and the V magnitude of the parent star maps to brightness. Only hues from 0.00 to 0.70 are used, to avoid the wrap-around. Saturation is left at 1.00 for all points:

Barfy colors are now in the lead, and some extra information is imparted. The hot Jupiters (in the lower left hand corner of the diagram) are noticeably darker than the eccentric giants. This is because increasingly, the hot Jupiters are being located by transit surveys, which look at much dimmer stars than does the RV method which surveys stars that are typically in the V=5-8 range. The extra color dimension is thus giving a sense of one of the biases in the diagram — Hot Jupiters are overrepresented because they’re easier to find.

What happens when one uses all three color dimensions? In the following diagram, the degree of color saturation is mapped to the mass of the parent star. With the first scaling that I tried, there’s not a whole lot of change from the previous plot. I think, though, that with more experimentation, the color saturation can be put to use. Note, too, that the dynamic range is reduced by the up-front demand for 70% transparency.

The diagrams really benefit from higher resolution. For example, looking at the hot Jupiters, there’s an interesting zone of avoidance at the lower left hand corner. The lower-mass planets are not populating the region that contains the hottest and most circular hot Jupiters. This might stem from a fundamental composition difference, although it’s also true that Neptune-mass planets don’t turn up yet in transit surveys.

Last night, I noticed Venus and Jupiter hanging low and bright about ten degrees apart in the deep blue twilight. Noctilucent cirrus clouds hinted that the full Moon had just risen on the other side of the sky. No matter how intricate the detail in a radial velocity curve, no matter how fine-grained the transit ingress, there’s something undeniably tantalizing and mysterious about the direct image. There’s a certain solidity to seeing with your own eyes.

The embargo just lifted, and by now, the news of the images of the planets orbiting HR 8799 and Fomalhaut are all over the media. NYTimes, check. Washington Post, check. Fox News, check.

I was very happy to see that the media coverage of these two amazing, largely independent discoveries ended up quite fair and balanced. I had been wondering whether perhaps HR8799 would get shouldered out of the limelight. There’s definitely something to be said for steppin’ into the ring with the HST Press Machine at your back, and a cool-looking picture of a planet orbiting (of all stars!) Fomalhaut. A star with a name like a rocket.

Fomalhaut, furthermore is Magnitude 1. HR8799 checks in with B=6.198 and V=5.964. “It’s up now, in the Great Square of Pegasus, slightly too dim to see with the naked eye. But your cat’s eyes are actually sensitive enough to see it! If you’re so inclined, you can make your cat go outside tonight and share in this historic discovery.”

I think it’s quite significant that these planets have been detected around stars that are more massive than the Sun. We already know from the radial velocity surveys (and specifically the targeted surveys of John Johnson and Bunei Sato) that higher-mass Jovian planet formation was more efficient around higher-mass stars than around stars of solar mass and below. Johnson and Sato surveyed “retired” A-type stars that are now turning into red giants, and which are cool enough to have the deep lines in their spectra that the RV-detection method requires. Johnson and Sato both independently found that these stars are frequently producing planets that are more massive than Jupiter in orbital periods of several hundred days.

Sato’s detection in early 2007 of a 7.6 Jupiter-mass planet orbiting Epsilon Tauri (2.7 solar masses) in the Hyades is probably a good example of the type of planet that’s showing up in these new images, and Eps Tau b provides good support for the case that this category of objects arose from gravitational instability. The Hyades were a tough environment for planet formation via core accretion, due to the intense UV radiation that caused the disks to lose gas quickly (see this oklo post).

Remnant debris disks would be expected around young stars that had massive enough disks to trigger gravitational instability. Also, in general, the more massive the star, the more massive the disk. And finally, if the planets formed via gravitational instability, one wouldn’t expect a bias toward high metallicity. If this idea is correct, as more of these planets are imaged, there shouldn’t be a metallicity correlation with the parent star.

Bruce Macintosh was kind enough to point me to some links that his team has set up. The images and movies are well worth a visit:

Travis and Christian put together a temporary holding pen at
http://www.photospheres.us/barman/HR8799/

My personal favorites are the “real” orbital motion one
http://www.photospheres.us/barman/HR8799/Movie00-HR8799-real-orbitalmotion.mov

and the movie showing the rotational imaging technique:
http://www.photospheres.us/barman/HR8799/Movie04-HR8799-adi.mov
(left panel is raw Keck images with the image derotator off, so artifacts
are fixed while stuff on the sky rotates; middle panel is image with a
weighted-moving-average PSF subtracted; rightmost is the cumulative derotated
image.)

Also a finding chart showing HR8799 and 51 Peg.

The HR8799 family portrait, with three planets zipping around on Keplerian orbits immediately brings to mind our own outer solar system. Ironically, however, if the GI formation hypothesis is correct, we’re actually observing planetary systems that have even less kinship to our own than do systems like HD 209458b and 51 Peg that harbor hot Jupiters (which oddball as they seem, probably formed via core accretion, just like Jupiter).

The HST photo of the photoevaporating molecular clouds of M16 is the iconic go-to image, but it’s always struck me as veering toward flash over substance. The “pillars of creation” name combines with the visual cues to create the illusion that you’re looking at something in an up-down gravitational field.

I think my favorite astronomical image is the not-quite-so-famous photo of Barnard 68. Here, one gets a far more immediate and accurate sense of what one is actually seeing. A cold, black self-gravitating cloud, looming in the foreground, blotting out the stars. It’s easy to imagine a sped-up film which depicts the cloud boiling and writhing with its internal turbulence.

There’s a certain undeniable menace to the dark cloud, and not without reason. If we rewind the tape by 4.54 billion years, all the material in our own solar system would have looked not unlike Barnard 68. If viewed in time-lapse, the pre-solar dark cloud would have collapsed from inside out upon itself, leading to the formation of the Sun, the planets, and eventually, a vanguard of five delicately engineered probes heading tentatively out into the galaxy. There would have indeed been cause for long-term concern…

Creepy undertones aside, Barnard 68 is a great slide to show during talks about star and planet formation. If the Sun is a 0.2mm grain of sand in San Francisco, Barnard 68 is half a mile across and located roughly at the distance of Los Angeles. The dark cloud itself is the equivalent of grinding up one percent of three small grains of sand, and dispersing the resulting powder through a half-mile wide volume.

The last time I gave a talk, it occurred to me that I’d never had enough faith in common sense to actually question whether that last analogy is appropriate, and indeed nobody in an audience has ever called me on it. Is it really possible to grind up 3% of a sand grain so that it creates an opaque half-mile wide cloud? That sounds totally nuts!

Asteroid 99942 Apophis (Image Source).

The absolute finest that one could envision grinding up a sand grain, while still retaining it in some sense as powdered “sand”, would be to the level of individual silica (SiO2) molecules. A 0.2 mm grain contains roughly 6×10^17 silica molecules. There’d thus be ~2×10^16 molecules available to disperse through the half-mile-wide volume of our model for Barnard 68. Scaling up to the solar mass, this would imply a Barnard 68 chock full of kilometer-wide asteroids, whereas in reality, the dust in Barnard 68 is micron-sized, roughly the consistency of cigarette smoke.

If the metals in Barnard 68 were in the form of km-wide asteroids, the cloud would indeed be transparent — fewer than one in a billion of the photons from the background stars would be absorbed on their way through the cloud.

Image Source.

The month of October slipped by. No new oklo posts. Like seemingly everyone else, I’ve been in a state of continual distraction regarding the election. Instead of writing posts about planets, spare moments are spent scanning the news.

Sometimes, if you’re waking up in the middle of the night, there’s perspective in the knowledge that one can build a fully to-scale model of the Earth-Sun system by taking a grain of sand and holding it two arms lengths away from a dime. A real time simulation can then be put into effect by moving the sand grain through 6.92 degrees per week.

I do have a post nearly done in draft form, but my colleague, Prof. Jonathan Fortney, eliminated any chance that I’ll get it finished and posted before Nov. 5th, by introducing me to fivethirtyeight.com. Over there, you can get the latest polling data with a 10,000-trial Monte-Carlo sheen:

Jason Wright recently sent me an advance copy of a preprint from his group that sums up the state of knowledge of the 27 multiple exoplanet systems that are currently known to orbit ordinary stars. It’s really quite remarkable, in scanning through the table of planets, how alien the systems are, how, on the whole, they are so unlike the solar system.

We’re fast approaching the tenth anniversary of the discovery of the three planets orbiting Upsilon Andromedae. I vividly remember setting up integrations of the outer two orbits in that system just after it was announced, and watching the eccentricities of planets “c” and “d” cycle through their huge (compared to solar system) variations. At that time, I had never bothered to give secular theory the slightest consideration (aww, that stuff was all worked out in the 18th century). It was a revelation to watch the orbits shimmer and vibrate as the integrator ticked off the centuries at the rate of a million years an hour.

As the multiple-planet business enters its second decade, emphasis is shifting toward the detection of systems with ever-lower planet masses. Ups And packs at least two thousand Earth masses into the inner several AU surrounding the star. HD 40307, by contrast has planets that start at only four times the mass of Earth.

As the planetary masses go down, so to do the signal strengths. The Upsilon Andromedae periodogram practically wears its planets on its sleeve, whereas nowadays, the surveys are likely combing though forests of tantalizing yet ambiguous peaks. Detectability increases with the square root of the number of observations, which exerts pressure to spend more telescope time on fewer stars.

From the standpoint of someone who’s interested in planet-planet dynamics, systems like Gliese 876, with its incredible signal-to-noise are clearly the most valuable. From the perspective of someone who’s interested in planet formation and the statistics of the galactic census, the systems with low-mass planets are a bigger deal. A single statistic that captures the relative value of a multiple-planet system could be expressed as:

Where the sum inside the root is over the planets in the system, and the quantities are the planetary masses, M, the rms of the residuals to the fit, $\sigma$, and the radial velocity half-amplitudes, K. The statistic seems to do a reasonable job of aggregating signal-to-noise and the potential for dynamical interaction, while simultaneously placing emphasis on lower mass planets. Plugging in the numbers, the known multiple-planet systems stack up with the following ranking:

Interestingly, the ranking seems to capture the vagaries of the press release industry pretty well. The top six multiple planet systems have all seen their names appear in the New York Times, in some cases on the front page:

HD 40307:

Gliese 581:

Gliese 876:

HD 69830:

Mu Arae:

55 Cancri:

Newsworthiness appears to run out, however, when the list reaches the two-planet system orbiting HD 190360:

Amazon, however, has kindly sponsored a link that puts it up for sale:

Now that flipping houses is passé…

Image Source.

Last May, Mark Marley sent me a link to the photograph shown above. It’s a Cassini image of Alpha Centauri A and B hanging just above the limb of Saturn. It provides an interesting bookend to the remarkable pictures that can be taken from Earth when Saturn and the Moon are close together in the sky. Mystery on the scientific horizon of the year 1610 has transformed itself into mystery on the horizons of today.

Image source.

It’s also a nice coincidence that the actual distance between the two components of Alpha Cen is similar to the distance between Earth and Saturn. Right now, Alpha Cen A and B are more than 20 AU apart, but within our lifetimes, they’ll close to nearly the Earth-Saturn distance as they reach the next periastron of their 80-year orbit in May 2035.

We’re fortunate that we’ve arrived on the scene as a technological society right at the moment when a stellar system as interesting as Alpha Cen is in the very near vicinity. During the last interglacial period, Alpha Cen did not rank among the brightest stars in the sky. A hundred thousand years from now, the Alpha Cen stars will no longer be among our very nearest stellar neighbors, and in a million years, they will have long since faded from naked-eye visibility. At the moment, though, Alpha Centauri is drawing nearer at 25 km/sec, a clip similar to the Earth’s orbital velocity around the Sun. It’s as if we’re on the free trial period of an interstellar mission…

And what of the status of the observational search? In the interim since the last oklo.org update, Debra Fischer obtained one year of NSF funding to begin high-cadence radial velocity observations of the Alpha Cen system with the CTIO 1.5m telescope in Chile. Debra, along with Javiera and a number of CTIO scientists have worked very hard to get the telescope and a spectrograph into condition for high-precision Doppler work. Many nights of Alpha Cen observations have now actually been carried out, and by all indications, the prospects look quite promising from an instrumental standpoint. The project will need long-term funding, though, since it will take of order 3-5 years of dedicated observation to reach any truly habitable worlds that are orbiting our nearest stellar neighbors.

In preparing my talk for the Torun meeting, it seemed appropriate to take a careful look at the book that got the whole planetary systems business going — De revolutionibus orbium coelestium (On the Revolutions of Heavenly Spheres) by Copernicus.

Being not in possession of a classical education, that meant settling for an English translation, but it’s interesting to look at the original Latin editions (which are dramatically out of copyright, and hence available from the ether in the departure lounge at O’Hare if one is willing to fork out for a wi-fi connection). Here’s the frontispiece of Harvard’s edition:

The text translates to:

Diligent reader, in this work, which has just been created and published, you have the motions of the fixed stars and planets, as these motions have been reconstituted on the basis of ancient as well as recent observations, and have moreover been embellished by new and marvelous hypotheses. You also have most convenient tables from which you will be able to compute those motions with the utmost care for any time whatever. Therefore, buy, read and enjoy.

To a modern sensibility, the exhortation to buy the book seems to run at cross purposes with the warning just below (written in Greek for heightened effect):

Let no one untrained in geometry enter here.

Certainly, in trying to make sense of the text, it’s clear that the warning is no empty threat. The book, with its arduous descriptions of ephemerides is tough going. Section 17 of Book V presents a typical example:

Now it was made clear above that in the last of Ptolemy’s three observations Mars, by its mean movement as at 244.5 deg, and its anomaly of parallax was at 171 deg, 26′. Accordingly during the year between there was a movement of 5 deg 38′ besides the complete revolutions. Now for the 2nd year of Antoninus on the 12th day of Epiphi the 11 month by the Egyptian calendar 9 hours after mid-day, i.e. 3 equatorial hours before the following midnight, with respect to the Cracow meridian, to the year of Our Lord 1523 on the 8th day before the Kalends of March 7 hours before noon, there were 1384 Egyptian years 251 days 19 minutes [of a day]. During that time there were by the above calculation 5 deg 38′ and 648 complete revolutions of anomaly of parallax. Now the regular movement of the sun was held to be 257 1/2 deg. The subtraction from 257 1/2 deg of the 5 deg 38′ of the movement of parallax leaves 251 deg 52′ as the mean movement of Mars in longitude. And all that agrees approximately with what was set down just now.

By connecting observations from the Ptolemaic era with his own (and other contemporary) observations, Copernicus was able to achieve a great improvement in timing accuracy. Remarkably, his combination of timing data and positional measurements for solar system planets such as Mars give a signal-to-noise quite similar to the modern data that we currently have for transiting hot Jupiters such as HD 149026b. These extrasolar planets have been observed over hundreds of orbits with both ground-based photometry (for timing) and with radial velocities (for elucidating the orbital figure).

Given that the distances to the planet-bearing stars are millions of times larger than the distances to the solar system planets, this is a testament both to how far we’ve come in 500 years, and simultaneously, to the durability of the Copernican accomplishment.

Sometimes, when I give a talk, I’m asked why the extrasolar planets don’t have evocative names.

Names and labels carry a heavy freight and they get people worked up. The agonized IAU deliberations vis-à-vis Pluto’s status as a plutoid or a planet or a dwarf planet constituted by far the biggest planet news of 2006, dwarfing, for example, the discovery of the triple Neptune system orbiting HD 69830. It’s unlikely that New Horizons would have gotten its congressional travel papers in order had Pluto been a plutoid right from the start.

When new comets and asteroids are discovered, their names generally follow on fairly quickly. Comets are bestowed with the name of the discoverer(s), and as a result, Dr. Hale and Mr. Bopp are entwined together in immortality. With asteroids, the discoverer gets the naming rights (subject to certain IAU rules), resulting in both some cool choices, (99942) Apophis, (3040) Kozai, as well as a Kilroy-was-here sloop of John B’s: (6830) Johnbackus, (20307) Johnbarnes, (4525) Johnbauer, (15461) Johnbird, (12140) Johnbolton, (16901) Johnbrooks, (11652) Johnbrownlee, (26891) Johnbutler, etc. etc.

Galileo, in sighting the moons of Jupiter, made the first telescopic discovery of solar system objects. Ever on the eye for an angle, he tried to increase his odds of patronage by naming his new moons “The Medicean Stars” in reference to Cosimo II de’ Medici, fourth Grand Duke of Tuscany. It’s now generally agreed that Mr. Medici, whatever his merits, was rather dramatically undeserving of the following accolades:

Serenissimo Grand Duke, “scarcely have the immortal graces of your soul begun to shine forth on earth than bright stars offer themselves in the heavens, which, like tongues [longer lived than poets] will speak of and celebrate your most excellent virtues for all time.”

Later in the seventeenth century, when Giovanni Cassini discovered Saturn VIII, V, III, and IV, he tried the same tactic. Three hundred and twenty two years later, his prose reads like a purple toad:

In the Conclusion, the Discoverer considers that the Antient Astronomers, having translated the Names of their Heroes among the Starrs, those Names have continued down to us unchanged, notwithstanding the endeavour of following Ages to alter them; and that Galileo, after their Example, had honoured the House of the Medici with the discovery of the Satellites of Jupiter, made by him under the Protection of Cosmus II; which Starrs will be always known by the Name of Sidera Medicea. Wherefore he concludes that the Satellites of Saturn, being much more exalted and more difficult to discover, are not unworthy to bear the Name of Louis le Grand, under whose Reign and in whose Observatory the same have been detected, which therefore he calls Sidera Lodoicea, not doubting but to have perpetuated the Name of that King, by a Monument much more lasting than those of Brass and Marble, which shall be erected to his Memory. [1]

In order to forestall just these sorts of embarrassments, the current IAU naming convention specifies that, the names of individuals or events principally known for political or military activities are unsuitable until 100 years after the death of the individual or the occurrence of the event.

The Medicean Stars are neither medicean nor stars, and so it’s not surprising that the name failed to stick. In 1847, the names of the Sidera Lodoicea were finally standardized to Iapetus, Rhea, Tethys, and Dione, all of which just sound right. It’s remarkable that nearly two hundred years elapsed before the final names were assigned.

At present, there’s no IAU sanction for naming extrasolar planets. Sometimes astronomers give it a go anyway, as seen here in the abstract for astro-ph/0312382:

Three transits of the planet orbiting the solar type star HD209458 were observed in the far UV at the wavelength of the HI Ly-alpha line. The planet size at this wavelength is equal to 4.3 R_Jup, i.e. larger than the planet Roche radius (3.6 R_Jup). Absorbing hydrogen atoms were found to be blueshifted by up to -130 km/s, exceeding the planet escape velocity. This implies that hydrogen atoms are escaping this “hot Jupiter” planet. An escape flux of >~ 10^10g/s is needed to explain the observations. Taking into account the tidal forces and the temperature rise expected in the upper atmosphere, theoretical evaluations are in good agreement with the observed rate. Lifetime of planets closer to their star could be shorter than stellar lifetimes suggesting that this evaporating phenomenon may explain the lack of planets with very short orbital distance.

This evaporating planet could be represented by the Egyptian God “Osiris” cut into pieces and having lost one of them. This would give us a much easier way to name that planet and replace the unpleasant “HD209458b” name used so far.

The name Osiris doesn’t seem to have caught on, perhaps because (5×10^9)(3.17×10^7)(1×10^10) is a good deal less than (1.4×10^30). Also, I’d tend to disagree that HD 209458b is “unpleasant”. A sequence of letters and numbers carries no preconception, underscoring the fact that these worlds are distant, alien, and almost wholly unknown — K2 is colder and more inaccessible than Mt. McKinley, Vinson Massif or Everest.

Ray Bradbury, in several of his stories, tapped into the profound significance of names. In the 2035-2036 section of The Martian Chronicles, he wrote:

The old Martian names were names of water and air and hills. They were the names of snows that emptied south in the stone canals to fill the empty seas. And the names of sealed and buried sorcerers and towers and obelisks. And the rockets struck at the names like hammers, breaking away the marble into shale, shattering the crockery milestones that named the old towns, in the rubble of which great pylons were plunged with new names: Iron Town, Steel Town, Aluminum City, Electric Village, Corn Town, Grain Villa, Detroit II, all the mechanical names and the metal names from Earth.

I think we’ll eventually reach the extrasolar planets, and in so doing, we’ll find out what their true names are.

Yikes! It was brought to my attention this morning that the transitsearch.org domain name expired last week. The robots at Network Solutions were apparently posting their anxious renewal demands off into the great unknown. Visitors to transitsearch.org are now presented with a blandly science and astronomy themed page with links to topics such as “Save the planet” and “NASA Jobs”. Vaguely curious, I clicked on “NASA Jobs” and discovered that astronauts can earn online degrees in as fast as one year.

Renewal of the Transitsearch domain is now in progress using a sepulchural fax-based procedure. An inevitable credit card payment and a few days lag time, and everything should be back in working order. In the meantime, you can always access the candidates page at the oklo server, where the transit tables continue to be brewed anew every ten minutes:

http://207.111.201.70/transitsearch/dynamiccontent/candidates.html

And oklo.org? A chronic lack of posts, yes, but no, we’re not on vacation. The referee’s report on our HD 80606 results. A better transitsearch algorithm and table design. The rejuvenation of the console and the systemic backend. Doppler Survey schedule optimization. Etc. Etc., all soaking up much more time than expected.

I’m very hopeful, though, that the solution to the anagram can be revealed sooner rather than later…

It’s a struggle to stay afloat in the non-stop flow of results. As a case in point, the Mayor et al. discovery preprint for HD 40307 b, c, and d has already been up on astro-ph for several weeks, and I only just a chance to read it carefully. The paper spells out the details of the announcement made at the Nantes conference last month, and ends with some bromides that seem to telegraph that the photometric transit search for planets b, c, and d is not yet definitive:

One of the most exciting possibilities offered by this large emerging population of low-mass planets with short orbital periods is the related high probability to have transiting super Earths among the candidates. If detected and targeted for complementary observations, these transiting super-Earths would bring a tremendous contribution to the study of the expected diversity of the structure of low-mass planets.

No controversy in that paragraph. It’ll be undeniably dope when the super-Earths start materializing in transit. Given that population of hot sub Neptunes in our Galaxy is apparently more than five times larger than the human population, it’s also likely that a significant number of these planets transit bright stars, and that’s good news for JWST.

In the interim, it’s not hard to see why the jury is still out on transits for HD 40307 b,c, and d. With its period of 4.61 days, the ~4 Earth-mass HD 40307b has a healthy a-priori transit probability of ~7%. Its expected transit depth, however, is a meager 0.05%. So far, the shallowest known transit for an extrasolar planet is that of HD 149026 b, which, at 0.3%, is fully six times deeper.

A ground-based detection of transits by HD 40307b would be quite a coup indeed. Is it feasible?The parent star HD 40307 is a K dwarf that’s quite similar in both spectral type and apparent magnitude to HD 189733. We can thus draw on the HD 189733 transits to get a ball park idea of the quality of the photometric data that one might expect from HD 40307. The best published ground-based light curve for HD 189733 that I could find comes from Bakos et al. (2008), who used the FLWO 1.2m telescope in Arizona to get the time series that I’ve reproduced just below. The skimpy expected depth of a central transit by HD 40307b is shown for comparison. The situation looks daunting.

The out-of-transit data in this light curve has a reported RMS scatter of 2.6 mmag for photometric points taken every 17 seconds (binned data is shown in the figure). Naive statistics thus imply that a 0.5 mmag central transit by HD 40307b could be detected by the FLWO 1.2m with at least several sigma confidence. Life, however, is more than root N. Systematic errors are probably large enough to scotch a discovery on a single night of observation, but nevertheless, by repeatedly observing, either with multiple nights or with multiple telescopes, a detection seems within reach. And it’s worth in excess of USD 5M. (At the moment, it seems there’s little need for European or Asian observers to hedge their currency risk.)

In the event that photometric campaigns aren’t up to the task, it’s in the realm of possibility that a transit by HD 40307b could be extracted via a spectroscopic detection of the Rossiter-McLaughlin effect. Assuming a 1 km/sec rotational velocity for the star, the expected half-amplitude of the Rossiter distortion is similar to the error bars on the published radial velocities. In the following figure, I’ve dished up a simulated Rossitered data set from HARPS, superimposed (with an offset for clarity) on a blown-up version of the radial velocity plot in the paper. During a single occultation, the radial velocities can produce a ~0.85 sigma detection.

In this case, the economics are a bit steeper, but still viable. At the current dollar-euro exchange rate, I’d estimate that USD 15K is a fair price for a HARPS night. (Forgive all this yak yak about currency — as an American traveling in Europe at the moment, I’m rather shocked to be seeing $6.24 0.7l bottles of water at the airport newstand!). One would need 4 hours, or half a night to observe the transit and get adequate baseline. To be at least four-sigma sure, you’d want to rack up ~20 full transits (which would take quite a while). Factoring in the expectation value of 0.07 arising from the transit probability, this works out to a USD ~2M detection.

Visitors to oklo.org over the past several weeks have frequently been greeted with page loading from the 2400 baud era, or worse yet, with the dreaded grey and yellow “highload.html” page.

I’ve been fully distracted with other projects, and so I didn’t really give it much attention. In what’s best described as a case of wishful thinking, I chalked the slowdown to the traffic spike that came in when the anagram post got written up at the NY Times site.

Over the weekend, things suddenly got much worse. It was clear that something was wrong. A little digging revealed that the wordpress installation was out of date, and was being exploited to the hilt by link spammers. The normally lightfooted footer.php script in the themes directory was staggering under a 427 kB load of grungy links. Oklo dot org was under full scale assault by dreary robots with single minded enthusiasms for cia1is and satellite TV.

A complete reinstall seems to have fixed the problem. It’d be tragic if those evil robots win.

On a related note, it might be worthwhile to sift through all those CoRoT lightcurves for photometric banner ads. As Luc Arnold writes in the abstract for “Transit Lightcurve Signatures of Artifical Objects” (astro-ph/0503580):

The forthcoming space missions, able to detect Earth-like planets by the transit method, will a fortiori also be able to detect the transit of artificial planet-size objects. Multiple artificial objects would produce lightcurves easily distinguishable from natural transits. If only one artificial object transits, detecting its artificial nature becomes more difficult. We discuss the case of three different objects (triangle, 2-screen, louver-like 6-screen) and show that they have a transit lightcurve distinguishable from the transit of natural planets, either spherical or oblate, although an ambiguity with the transit of a ringed planet exists in some cases. We show that transits, especially in the case of multiple artificial objects, could be used for the emission of attention-getting signals, with a sky coverage comparable to the laser pulse method. The large number of expected planets (several hundreds) to be discovered by the transit method by next space missions will allow to test these ideas.

Download 1017 x 761 px version here.

This dry range is near Gabbs, Nevada.

I remember stopping at a bar in Gabbs on a Saturday night in October 1993. We were low on gas, having foolishly skipped a possibility to fill up at Walker Lake. We’d been driving all day. In the deserted gravel lot, the sky was freezing black and spangled with stars.

I drank a beer and talked to the only other patron — a grizzled Vietnam veteran who worked at the molybdenum mine. The word molybdenum sounded strange, exotic. In 1993, the price of molybdenum was in free fall, and in 1994, it would reach a low of $3,510 per metric ton ($1.59 per pound). The mine was laying off workers and was in danger of closing.

The gas station in Gabbs was closed. The bartender called the nearest possibility, the old Pony Express station Middlegate, 50 miles north. “You’re in luck, they’ve got gas.”

The current spot price for Molybdenum oxide is 33.50 dollars per pound, a less-noticed example from the many changes that make 1993 seem increasingly a part of a bygone millennium. Hundreds of extrasolar planets, e-mail inboxes that routinely receive hundreds of messages (mostly spam) per day, and this uneasily growing realization that the raw materials may be the deciding factor after all.

I wonder whether the extrasolar planets will ever have a flatly practical economic value. The scramble to detect new planets often feels like a land rush, but is there a real possibility that we’ll eventually pack up and go to these systems that are showing up in the correlation diagrams? Do the economics of interstellar travel ever work out?

In this context, it’s slightly disconcerting to remember that the molybdenum has already made the interstellar journey (see e.g. here). The most abundant Mo isotope is molybdenum-98, which constitutes 24.14% of Earth’s molybdenum. These atoms were produced both via the s-process, which takes place in red giant stars, and where a chain of slow neutron captures is interspersed with beta decays, and by the r-process, which occurs in supernovae.

The fact that the resources made the trip for free makes it seem a little more likely that we may well be able to get more, but only if we pay…

Man! Like everyone else over the past 24 hours, I’ve been thinking about that new crop of Superearths.

The conventional wisdom (over which I was waxing enthusiastic a mere 36 hours ago) holds that Mayor’s new population of planets are essentially failed giant planet cores which began forming at considerably larger radii in the protostellar disk and then experienced significant inward migration as they built themselves up. In this scenario, the Superearths arise from more or less the same sort of process (but with a different outcome) that formed the giant planets in our own solar system.

What’s struck me, however, is the odd resemblance between a multiple-planet system like HD 40307 and the regular satellite systems of the Jovian planets. In both cases, the characteristic orbital period is of order a week, and the system mass ratio (satellites-to-central-body) is of order 2 parts in 10,000.

In the Ward-Canup theory, the regular satellites of the Jovian planets are thought to have formed more or less in situ in gas-starved disks (see here for more discussion). If the new population of planets is somehow the result of an analogous formation process, then they really will be superEarths, as opposed to subNeptunes, and as a consequence, their transit depths will be small.

This morning, I awoke to an inbox full of indications that there was indeed plenty of drama in the club.

From one of our correspondents:

He threw out dozens of new systems, very graphically, on slips of paper, like playing cards, floating down on a pile on the screen. Very dramatic. But no HD numbers on those slips!

He predicts 1 to 1.5 Earth sensitivity by around 2010 (extrapolating a trend).

He has been monitoring about 400 FGK slow rotators since 2004, with HARPS.

Can do 0.5 m/s today, 0.1 m/s in near future.

Noise sources are astroseismology, which settles to about 0.1 m/s after 15 minutes of integration, and a worse one, star spots, which settle to about 0.5 m/s after 15 minutes but do not drop lower, even though theory says level should drop to about 0.1 m/s.

He says he has 40 new candidates in the 30-50 day period range, and mass less than 30 Earths.

Nevertheless, after the drama, he did report 3 Neptune-type systems, all focused on the Super Earth theme of the meeting.

The centerpiece was definitely HD 40307, a deep southern K2.5 V star only 40 light years distant, with a metallicity roughly half that of the Sun. It has three detected planets, with Msin(i)’s of 4.2, 6.9, and 9.2 Earth masses, and corresponding periods of 4.31, 9.62, and 20.45 days. It’s fascinating that these planets are close to, but aren’t actually in a 4:2:1 resonance. This is really a remarkable detection.

With 40 candidates in the pocket, the Geneva team does, however, seem to be keeping some of their powder dry, perhaps in anticipation of a low-mass transit. Here’s a link to the ESO press release, which has triggered 93 news articles and counting.

In the press release image, HD 40307d is definitely all that and a bag of chips. Puffy white clouds, azure seas, continents, soft off-stage lighting…

On December 29th 1959 at the annual meeting of the American Physical Society at Caltech, Richard Feynman gave a remarkable talk entitled “There’s plenty of room at the bottom” in which he foresaw the impact that nanotechnology could have on materials science. At the beginning of the lecture he remarked (in a vernacular that dates him to the Eisenhower era):

I imagine experimental physicists must often look with envy at men like Kamerlingh Onnes, who discovered a field like low temperature, which seems to be bottomless and in which one can go down and down. Such a man is then a leader and has some temporary monopoly in a scientific adventure.

Over the past several years, the oklo.org party line has been that the radial velocity method for exoplanet detection is similarly equipped with the potential to go down and down in planet mass, and to continue with at least a respectable share of the lead in the ongoing scientific adventure.

That said, the Doppler returns so far this year have been underwhelming. If we look at the latest planet-mass vs year of discovery diagram on exoplanet.eu (no pulsar planets, no microlenses), the detection rate seems to be holding up, but the crop of announced low-mass planets is nonexistent. Of the 22 new planets so far in ‘08 that have been detected via radial velocity, 16 were initially detected by the transit surveys.

What’s up with that?

We’re seeing core accretion in action. The baseline prediction of the core accretion theory for giant planet formation is that once a planet reaches a crossover threshold, where the mass of gas and solids is equal, then rapid gas accretion ensues, and the planet grows very rapidly to Jovian size or even larger. When the galactic planetary census is complete, one thus expects a relative dearth of planets with masses in the range between ~20 and ~100 Earth masses. In the freewheelingly unrefereed forum of a blog post, I can go ahead and dispense with an analysis that takes all the thorny completion issues and selection biases into account and state unequivocally that:

(Courtesy as usual of the exoplanet.eu statistics plot generators)

Planets that do make the grade and blow up to truly Jovian size are the beneficiaries of protostellar disks that had solid surface densities that were well above the average. At a given disk mass, a disk with a higher metallicity has a higher surface density of solids, which is the reason for the planet-metallicity correlation. Disks with higher oxygen and silicon fractions relative to iron will also have high solid surface densities, which is the reason for the planet-silicon correlation. And M stars have trouble putting their Jovian cores together fast enough to get the gas while it’s still there, which is the source of the planet-stellar mass correlation.

As one pushes below Neptune-mass, these correlations should all get much weaker, and the fraction of producing stars should go way up. It’s hard, at the ~10% success rate level for a protostellar disk, to make a Jupiter, and it should be straightforward, at (I’ll guess) the 50% success level for a protostellar disk to make a Neptune.

The gap between Neptune and Saturn is the source of the current RV planet drought. At given velocity precision (in the absence of stellar jitter), it takes ~25x more velocities to detect a Neptune than to detect a Saturn. To make progress, it’s necessary to stop down the number of stars in the survey and focus on as many old, quiet K-type stars as possible. We’re talking HD 69830.

The indications at Harvard were that the Geneva group has been doing just that. In a few hours, Michel Mayor is scheduled to give the lead-off talk at the Nantes meeting on extrasolar super Earths. I’ll post a rundown of what he has to say just as soon as the Oklo foreign correspondents file their reports…

On Friday, I flew back from the Boston IAU meeting, still buzzing with excitement. On Saturday, I woke up with what might best be described as a transit-induced hangover (an entirely distinct condition from transit fever). I’d basically allowed all my professorial responsibilities to slide for a week. On my desk is a mountain of work, a preliminary exam to assemble, and a horrifying backlog of e-mail.

Ahh, but like an exotic sports car bought on credit, it was worth it. The meeting was amazing, certainly the most exciting conference that I’ve ever attended. Big ups to the organizers! Planetary transits are no longer the big deal of the future. They’re the big deal of the right here right now. Spitzer, Epoxi, MOST, HST and CoRoT are firing on all cylinders. The ground-based surveys are delivering bizarre worlds by the dozen. And we’re clearly in the midst of very rapid improvement of our understanding of the atmospheres and interiors of the planets that are being discovered.

From a long-term perspective, the conference’s biggest news was probably provided by the Geneva group, in the form of Christophe Lovis’ presentation on Tuesday afternoon. In his 15-minute talk to a packed auditorium, Lovis covered a lot of ground. I scrambled to take notes. My reconstructed summary (hopefully without major errors) runs like this:

The HARPS planet survey of solar-type stars contains ~400 non-active, slowly rotating FGK dwarfs. Observations with the 3.6-meter telescope have been ongoing since 2004, and over time, their emphasis has been progressively narrowed to focus on stars that harbor low-amplitude radial velocity variations with RMS residuals in the 0.5-2.0 m/s range. The current observing strategy is to obtain a nightly multiple-shot composite velocity of an in-play candidate during block campaigns that run for 7-10 nights.

During the first few minutes, Lovis reviewed the current status of the published results. The Mu Arae planets (including the hot Neptune on the 9.6-day orbit, see here and here) are all present and accounted for. The HD 69830 triple-Neptune data set (see here, here and here) now contains twice as many velocities, with virtually no changes to the masses and orbits of the three known planets. Long-term scatter in the HD 69830 data set is at the ~90 cm/sec level, indicating either the effect of residual stellar jitter, or perhaps the presence of additional as-yet uncharacterized bodies.

He then announced that there are currently forty-five additional candidate planets with Msin(i)<30 Earth masses, P<50 days and acceptable orbital solutions. And that’s not counting candidates orbiting red dwarfs.

He then began to highlight specific systems. To say that planets were flying thick and fast is an understatement. Here’s the verbatim text that I managed to type out while simultaneously attempting to focus on the talk:

Rumor has it that some of these systems will be officially unveiled at the upcoming Nantes meeting on Super Earths. Odds-on, with 45 candidates in play, we’ll soon be hearing about a transiting planet with a mass of order ten times Earth’s. I won’t be at the Nantes meeting, but the stands will be harboring agents of the Oklo Corporation.

The talk finished with an overview of the statistics of the warm Neptune population. Most strikingly, a full 80% of the candidates appear to belong to multiple planet systems, but cases of low-order mean motion resonance seem to be rare [as predicted --Ed.] . There is a concentration of these planets near the 10-day orbital period, and the mass function is growing toward lower masses. Significant eccentricities seem to be the rule. And finally, I think it was mentioned that the planet-metallicity correlation is weaker for the warm Neptunes than for the population of higher-mass planets.

Seems like core accretion is standing the test of time.

Note on the images: Gaspar Bakos (of HAT fame) had the cool idea of machining metal models for the planets of known radius which are correct in terms of relative size, and which have the actual density of their namesakes. HAT-P-6, for example, is constructed from a hollow aluminum shell, and with a density of ~0.6 gm/cc it would float like a boat. HAT-P-2b, on the other hand, which packs 8.6 Jupiter masses into less than a Jovian radius, has the density of lead and (not coincidently) is made out of lead. It’s startling to pick it up. CoRoT-Exo-3b, which was announced at the meeting, has a mass of twenty Jovian masses, and a radius just less than Jupiter. I guess that one will have to be made from Osmium.

Earth, at ~5.5 gm/cc, on the other hand, can be readily manufactured from a variety of different alloys.

Jonathan Fortney has the office next to mine at UCSC, and so we’re always talking about the Spitzer observations of extrasolar planets. The Spitzer Space Telescope has proved to be an extraordinary platform for observing planets in the near infrared, and during the past year, the number of published and planned observations has really been growing rapidly.

Increasingly, with the flood of data, I’ve been finding that I have trouble keeping mental track of all the photometric observations of all the planets that Spitzer has produced. Let’s see, was Tres-1 observed in primary eclipse? Did someone get a 24-micron time series for HD 149026? And so on.

So Jonathan and I decided to put together a poster that aggregates the observations (that we know of) that have either been completed, or which have been scheduled. The relevant information for each campaign includes the star-planet system, the bandpass, and the duration and phase of the observation. We wanted the information for each system to be presented in a consistent manner, in which the orbits, the stars, and the planets are all shown to scale (and at a uniform scale from system to system). As an example, here’s the diagram for HD 189733:

In putting the poster together, we were struck by the variety of different observational programs that have been carried out. Some of the diagrams, furthermore, with text removed, have a delicate insect-like quality.

(The figure just above shows Bryce Croll’s planned 8-micron observations of Transitsearch.org fave HD 17156b. Croll’s campaign will attempt to measure the pseudo-synchronous rotation period of the planet.)

I’m going to Boston next week to attend the IAU transit meeting, and so I printed out a copy of the poster to put up at the meeting:

Here’s a link to the Illustrator file and the .pdf version. Full size, it’s two feet wide and three feet tall. Going forward, I’ll update the files as new observations come in.

“Getting scooped” is an ongoing occupational hazard for astronomers. An interesting idea pops into your head, or a significant peak starts to emerge in a periodogram, and you drop everything to do an analysis and write up your idea or discovery for submission. If your idea seems to work, and as your story takes shape on paper, it occurs to you that there are plenty of other colleagues who could easily have latched on to what you’ve just done. After all, there are only so many nearby red dwarfs in the sky!

The invention of the telescope at the beginning of the seventeenth century led to very rapid progress in astronomy, and because telescopes are relatively straightforward to make once the principle is understood, astronomers suddenly faced heightened competition, and with it, the ever-unnerving possibility of getting scooped.

Anagrams were brought into use as a method of protecting one’s priority of discovery while simultaneously keeping a discovery under wraps in order to obtain further verification. Galileo was an early adopter of anagrams. After observing Saturn, he circulated the following jumble of letters:

s m a i s m r m i l m e p o e t a l e u m i b u n e n u g t t a u i r a s

When he was ready to announce that Saturn has a very unusual shape when seen through his small telescope, he revealed that the letters in the anagram can be rearranged to read, Altissimum planetam tergeminum observavi, or “I have observed the highest planet tri-form.”

Galileo’s telescope wasn’t powerful enough to allow him to decode what he was actually seeing when he observed Saturn. The true configuration as a ringed planet was first understood by Christiaan Huygens, who, in 1656, with the publication of the discovery of Titan in De Saturni luna observatio nova, also circulated an anagram to protect his claim to discovery:

a a a a a a a c c c c c d e e e e e h i i i i i i i l l l l m m n n n n n n n n n o o o o p p q r r s t t t t t u u u u u.

In 1659, Huygens revealed that the anagram can be decoded to read, Annulo cingitur, tenui, plano, nusquam cohaerente, ad eclipticam inclinato, or “It is surrounded by a thin flat ring, nowhere touching, and inclined to the ecliptic.”

The most appealing anagrams rearrange the true sentence into a satisfyingly oblique haiku-like clue. In connection with his discovery of the phases of Venus, Galileo issued an anagram that read, Haec immatura a me iam frustra leguntur, or “These immature ones have already been read in vain by me.” When properly reconstructed, the letters reveal that, Cynthiae figuras aemulatur Mater Amorum, or “The Mother of Loves [i.e. Venus] imitates the figures of Cynthia [i.e. the moon]“.

So, in service to this venerable tradition, but without adhering to the hoary custom of couching everything in Latin, let me just say that,

Huge Applet, Unsearchable Terrestrials!

Note that according to the wikipedia,

The disadvantage of computer anagram solvers, especially when applied to multi-word anagrams, is that they usually have no understanding of the meaning of the words they are manipulating. They are therefore usually poor at filtering out meaningful or appropriate anagrams from large numbers of nonsensical word combinations.