systemic

CoRoT-exo-2 c?14
greg posted in systemic faq, exoplanet detection on December 21st, 2007

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The CoRoT mission announced their second transiting planet today, and it’s a weird one. The new planet has a mass of 3.53 Jupiter masses, a fleeting 1.7429964 day orbit, and a colossal radius. It’s fully 1.43 times larger than Jupiter.

The surface temperature on this planet is likely well above 1500K. Our baseline theoretical models predict that the radius of the planet should be ~1.13 Jupiter radii, which is much smaller than observed. Interestingly, however, if one assumes that a bit more than 1% of the stellar flux is deposited deep in the atmosphere, then the models suggest that the planet could easily be swollen to its observed size.

The surest way to heat up a planet is via forcing from tidal interactions with other, as-yet unknown planets in the system. If that’s what’s going on with CoRoT-exo-2 b, then it’s possible that the perturber can be detected via transit timing. The downloadable systemic console is capable of fitting to transit timing variations in conjunction with the radial velocity data. All that’s needed is a long string of accurate central transit times.

The parent star for CoRoT-exo-2-b is relatively small (0.94 solar radii) which means that the transit is very deep, of order 2.3%. That means good signal to noise. At V=12.6, the star should be optimally suited for differential photometry by observers with small telescopes. With a fresh transit occurring every 41 and a half hours, data will build up quickly. As soon as the coordinates are announced, observers should start bagging transits of this star and submitting their results to Bruce Gary’s Amateur Exoplanet Archive. (See here for a tutorial on using the console to do transit timing analyses.)

The latest on 55 Cancri7
greg posted in systemic faq, exoplanet detection on November 6th, 2007

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Here’s a development that systemic regulars will find interesting! In a press release today, came announcement of the detection of a fifth planet in the 55 Cancri system (paper here). The new planet has an Msin(i) of 0.144 Jupiter masses, a 260-day orbital period and a low eccentricity. The detection is based on a really amazing set of additions to the Lick and Keck radial velocities:

For background on the 55 Cancri system, check out this oklo.org post from December 2005.

The outer four planets in the 55 Cancri system all have fairly low eccentricities in the new five-planet model. This leads to a diminished importance for planet-planet interactions, but nevertheless, the system does require a fully integrated fit. Deviations between the Keplerian and integrated models arise primarily from the orbital precessions of planets b, c, and e that occur during the long time frame spanned by the radial velocity observations.

Eugenio has added the velocities onto a fully updated version of the downloadable systemic console. The new version of the console adds a wide variety of new features (including dynamical transit timing) that were formerly available only on the unstable distribution. Check it out, and see the latest news on the console change log and the backend discussion forum. Over the next month, we’ll be talking in detail about the new features on the updated console.

Very shortly, a new entries corresponding to the updated 55 Cancri data sets will be added to the “Real Stars” catalog on the systemic backend. I’ll then upload my baseline integrated 5-planet fit to the joint Keck-Lick data set. I’m almost certain that with some computational work, this baseline model can be improved. Such a task is not for the squeamish, however. Obtaining self-consistent 6-body models to the 55 Cancri data set is a formidable computational task for the console. There are 29 parameters to vary (if the Lick, Keck, ELODIE and HET radial velocity data sets are all included). The inner planet orbits every 2.79 days, and the data spans nearly two decades. Fortunately, Hermite integration is now available on the console. Hermite integration speeds things up by roughly a factor of ten in comparison to Runge Kutta integration.

There have been hints of the 260-day planet for a number of years now because it presents a clear peak in the residuals periodogram. After the 2004 announcement of planet “e” in its short-period 2.8 day orbit, Jack Wisdom of MIT circulated a paper that argued against the existence of planet “e”, and simultaneously argued that there was evidence for a 260-day planet in the data available at that time. More recently, a number of very nice fully self consistent fits to the available data have been submitted to the backend (by, e.g., users thiessen, EricFDiaz, and flanker). Their fits all contain both the 2.8 day and the 260-day planets, and happily, are fully consistent with the new system configuration based on the updated velocities. Congratulations, guys!

Interestingly, the best available self-consistent fits to the system indicate that planets b and c do not have any of the 3:1 resonant arguments in libration. It will be interesting to see whether this continues to be the case as the new fits roll into the systemic backend.

Systemic in the Classroom1
greg posted in systemic faq on September 24th, 2007

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In our development of the systemic console and the systemic backend, we’ve strived to build a professional-quality tool that can be used by the general public. There’s no better way to get a sense of them planetary discovery process than to participate yourself, and so we’d like to encourage astronomy instructors to fold the systemic console into their curricula.

This link points to a Word format document of a sample homework assignment that makes use of both the console and the systemic backend. We’ve had good success with this particular problem set at UCSC, and it’s currently being implemented at MIT as well. The level has been found to be appropriate to an astrobiology class for science majors. There’s no math prerequisite, so it can also be fully useful for a non-major survey course.

If you’re an astronomy instructor and you’d like to incorporate hands-on planet finding into your course, let me know, and we can set up a fit submission aggregator for your students on the systemic backend.

fit to be timed2
greg posted in systemic faq on September 8th, 2007

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One reason why extrasolar planets are so exciting is because they are accessible. You don’t need a Ph.D. or a large laboratory or a space-borne telescope to make an important discovery. There are very few areas in science where such a wide pool of workers can contribute in a fully meaningful way.

On the systemic backend, the focus is largely on planet characterization through the analysis of radial velocity data. At Transitsearch.org, the goal is to provide the information that will allow small telescope observers to discover transiting planets. Transitsearch, however, is mainly a repository for transit predictions. We maintain information about when and where to look, but we fall short when it comes to explaining how to obtain high-precision photometry. There has long been a need for a good end-to-end manual on the art and science of photometric transit detection.

Bruce Gary is an experienced observer of transiting extrasolar planets, and is a member of the XO network, which has had made several discoveries over the past year and a half (see e.g. here). Bruce has written a book, Exoplanet Observing for Amateurs which he’s made available for free in .pdf form.

Bruce has also launched the Amateur Exoplanet Archive (AXA), which is a repository for light curves obtained for known transiting planets. If you get a photometric transit time series of one of the planets, then make sure that you submit it to Bruce’s archive. With all the data in one place, everyone will have easy access for analysis projects.

Transit midpoint times can be measured from individual light curves, and a sequence of midpoint times can be used to improve the characterization of a particular planetary system. To this end, Stefano has extend the .sys file format used by the systemic console to include “transits” data files (which take a .tds suffix, and which are separate from the .vels files that the console has used all along). If you have transit data, it’s simple to implement one of these files for yourself.

To see how it works, consider the recently discovered transiting planet XO-2. The published radial velocity data for this planet is already bundled with the console. On the AXA site, a total of five transits have already been archived for XO-2. Each of these transits has a measured Heliocentric Julian Date (HJD) for the time of transit midpoint, along with an associated uncertainty. I copied these data into a newly created “X0-2.tds” file in my console’s datafiles folder:

I then added the following lines to the .sys file for the XO-2 system:

Having done that, I launched the latest (“unstable” Aug. 21, 2007 version) of the systemic console. Stefano has been steadily improving the console’s algorithms, user interface, and performance. If you’ve been working with the standard stable downloadable console, you’ll immediately notice that there’s a lot of new functionality. We’ll be getting a manual out as soon as the much-anticipated Systemic Jr write-up is completed, but in the meantime, there’s a wide variety of resources on the backend that can help you navigate the latest console features.

With the .tds file linked in, the observed transit midpoint times appear as vertical red lines in the radial velocity timeline window. If the “fit transits” option is unchecked, then the console considers only the radial velocity data. If the “fit transits” option is checked, however, then the observed transit times are included as data to be fit. The uncertainties in the transit midpoints can be very small, and so this provides a very strong constraint on the period of the orbit and the time at which the planet crosses the plane containing the line of sight to the Earth. Note that the transit fitting can be done in a fully self-consistent N-body fashion if integration is enabled.

Try it for yourself!

As more transit data is accumulated, it will become possible to do some increasingly sophisticated analyses. Transit timing is potentially a very powerful method for detecting additional, as-yet unseen perturbing bodies in a given system. Objects like Gl 436 b are especially good candidates for this type of approach, and quite a bit of photometric data is being accumulated during the Gl 436 transits.

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greg posted in systemic faq, worlds on August 27th, 2007

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Eugenio has finished combing through this summer’s literature, and has added twenty newly published radial velocity data sets to both the systemic backend and to the current version of the downloadable systemic console. As a result of his efforts, new or augmented data is now available for the following stars: Cha Ha 8, GJ 317, HD3651, HD5319, HD11506, HD17156, HD37605, HD43691, HD75898, HD80606, HD89744, HD125612, HD132406, HD170469, HD171028, HD231701, NGC2423, NGC4349, HAT-P-3, and TrES-4. As always, the published literature citations for the velocities are contained in the “vels_list.txt” file that comes bundled with the systemic console download. The vels_list.txt file can be indispensible if you want to publish results that use the systemic package as a research tool — indeed, we’re quite excited that researchers are starting to adopt the console in the course of carrying out state-of-the-art research (see, e.g. here.)

There’s quite a bit to explore with these new data sets. Eugenio has had a first look, and included in his recommendations are:

GJ 317: This system (discovered by John Johnson and the California-Carnegie planet search team, preprint here) is only the third red dwarf that’s been found to harbor a Jovian-mass companion. The data shows clear evidence for one planet “b”, with at least 1.2 Jupiter masses and a 693-day orbit, and there’s a strong hint of a second planet in the radial velocity variations. Check it out with the console!

HD 17156: This data comes from a recent paper by the California-Carnegie team. There are radial velocities from both the Keck and the Subaru telescopes, and the signal-to-noise of the orbit is very high.

The data show a ~3 Jupiter-mass planet on a 21.2 day orbit. The orbit is remarkably eccentric for a planet on such a short period, leading to a 25-fold variation in the amount of light received during each trip around the star.

It’ll be interesting to get a weather forecast for this world, and it’s also important to point out that the orientation of the orbit is very well suited for the possibility of observing transits. Periastron is reasonably close to being aligned with the line of sight to Earth, leading to an a-priori transit probability of more than 10%. In the discovery paper, a preliminary transit search is reported, but only about 1/4th of the transit window was ruled out. With a Dec of +71 degrees and a nice situation in the winter sky, this is definitely one for Transitesearch.org’s Finland contingent.

transitsearch dot org0
greg posted in systemic faq, exoplanet detection on June 4th, 2007

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Gl 436 b was the first planet to be detected in transit after the radial velocity detection of the planet itself was publicly announced. Gillon et al.’s discovery shows that the basic strategy of checking known Doppler wobble stars for transits can pay off dramatically, and indeed it’s recharged my interest in keeping transitsearch.org up and running.

Successful transit predictions depend on having accurate ephemerides, which in turn depend on fits to the most recent radial velocities available. The period error in an old fit builds up to the point where the predicted transit window is longer than the orbital period itself. Indeed, relying on a published fit that’s five, six, or even eight years old, is akin to showing up at the 2007 Grammy Awards in a 2001 Escalade.

We’ve thus started the job of making sure that the transitsearch.org candidate tables are as up to date as possible. I’ve committed to spending a bit of time each day checking and updating the master orbit.data and star.data files that are used as input to the cron job that runs every night to update the prediction tables. In each case, we’ll use the most recent published orbital data for a given planet.

In addition, the eighteen known transiting planets have all had their ephemeris tables updated using the latest literature values for the orbital parameters. I got the most of these data from Frederic Pont’s useful summary table, and took the radial velocity half-amplitudes from exoplanet.eu and exoplanets.org. At the moment, the occultations are all treated as central transits by my code, which means that the predicted transit durations will in general be longer than the actual observed events. This discrepancy will be patched shortly, but in the meantime, the predicted transit midpoint times in the ephemeris tables should be extremely accurate for all 18 planets. (See the candidates faq for more information).

We’ve made the decision to base the main transitsearch.org candidates table only on published orbital fits that have appeared in the refereed literature. In many cases, however, one finds a need to go beyond predictions based on published fits. There are two main circumstances under which this can occur. (1) The systemic console provides the ability to obtain fits to all existing radial velocity data for any given system. For many systems, one thus has the opportunity to obtain orbital parameters for the planet that are more accurate than published values that are based on fewer data sets. (2) You may have used the console to locate a candidate planet that is not yet published. If this planet can be observed in transit, then you’ve got dramatic confirmation of your discovery.

Eugenio has written an extension to the bootstrap window of the most recent version of the console that allows anyone to make transit predictions for any planet produced by the console. In an upcoming post, we’ll look in detail at how this new feature works.

Systemic Jr. Fit Drive0
greg posted in systemic faq on March 24th, 2007

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A big thank-you to everyone who’s been participating in the drive to characterize and study the catalog of synthetic “Systemic Jr.” planetary systems on the Systemic Backend. There’s now enough data to indicate that the analysis is going to be very informative. We’re looking forward to revealing the properties of the underlying planetary systems that were used to generate the data. In the meantime, we need your help to adequately characterize all 520 systems. Data in need of better characterization are marked by flags:

Our backend server is now swarming with various hard-working software robots that Stefano has assembled. The 100-year stability bot is rousted out of bed and set to work whenever a new fit is submitted. It reports a quick initial assessment of orbital stability. Planetary systems that pass through the 100-year stability screen are then put in a queue to wait for the attentions of the 1000-year stability bots. Systems that make it through 1000 years with less than a 1% change in semi-major axis of their planets are awarded a snazzy green flag:

Occasionally, systems that are in mean-motion resonance can show periodic semi-major axis variations of more than 1% while still remaining indefinitely stable. A resonance bot that will go through the fits and check for these special cases is currently being readied.

Systems that pass the minimum stability requirement are handed to a bootstrap bot which uses the bootstrap method to estimate uncertainties on the planetary orbital parameters for each stable fit. We’re currently running the bootstrap bot under the assumption that the orbits are pure Keplerian ellipses, and so the calculations are usually quite rapid. Very shortly, the error estimates for the parameters in submitted fits to the real systems and the Systemic Jr. systems will be showing up on the back-end data pages.

Finally, an “F-bot” has been activated which performs successive F-tests on submitted multiple-planet systems. Using its results, we’ll have a better idea of when the addition of a planet to a system is warranted.

Bootstrap1
greg posted in systemic faq on March 10th, 2007

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Stefano and Eugenio have been making quite a bit of development progress on the downloadable systemic console. A new version of the console (available for beta testing on the systemic backend) is now capable of providing an estimate of the uncertainties on the orbital elements associated with a fit to a particular data set.

Radial velocity data don’t provide an exact determination of planetary orbits. The most obvious shortcoming is that Keplerian orbital fits can’t determine the inclination of the planetary orbits, and so for a given system, we’re only able to measure then mass of the planet multiplied by the sine of the unknown inclination angle. Furthermore, the stellar radial velocity signal created by a planetary system is corrupted by astrophysical noise introduced by the parent star, as well as by noise introduced during the measurement process here on Earth.

Determination of the true uncertainties in a planetary orbital model is a subtle problem (for more detail, see Eric Ford’s recent work in this area). As a first straightforward step, we’ve implemented the so-called “bootstrap” method of error estimation into the console. The bootstrap works by taking the original data set, and then successively redrawing time + velocity + uncertainties triples from the data with replacement. This procedure creates alternate realizations of the original data set in which some of the original measurements appear more than once, and in which some don’t appear at all. The best-fit parameters obtained by the console are then used as a starting guess to fit the bootstraped data sets. The standard deviations measured from the distributions of orbital elements thus obtained give error estimates for the parameters of the original fit.

The bootstrap routine is menu-accessed, and is simple to use. First, create a fit to a dataset. In the example just below, I’ve fitted to the data for HD 80606:

Once the fit has been polished, the bootstrap can be run. In the default configuration it uses Keplerian fitting and does 100 trials.

HD 80606 has been observed for nearly 20 orbital periods, and velocities have been obtained at a wide variety of orbital phases. As a result, the orbit is very well constrained. The bootstrap indicates that the uncertainty on the e=0.932 eccentricity is only 0.003. For other systems, such as hd 20782, which also seems to have a high eccentricity:

the uncertainty on the parameters is much larger:

Give the routine a try! In upcoming posts, we’ll talk more about how uncertainty estimates will be incorporated into the planetary catalogs on the backend.

The exoplanet prediction market1
greg posted in systemic faq, exoplanet detection, worlds, non-technical posts on February 20th, 2007

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At first glance, the market capitalization of the Chicago Board Options Exchange, and the list of astronomers active in the field of extrasolar planets would appear to have nothing to do with one another. These two disparate entities are connected, however, by the fact that they’ve both undergone explosive growth over the past decade, and both are continuing to grow. They signify highly significant societal trends.

I think it’s safe to predict that in 25 years, the market for financial derivatives, and the level of economic activity associated with exoplanets will both be far larger than they are now. It’s interesting to ask, will there be an unanticipated co-mingling between the two? And if so, how will it occur?

One very realistic possibility is the development of an exoplanet prediction market, in which securities are issued based on particular fundamental questions involving the distribution of planets in the galaxy. Imagine, for example, that you’re an astronomer planning to devote a large chunk of your career to an all-or-nothing attempt to characterize the terrestrial planet system orbiting Alpha Centauri B. In the presence of a liquid, well-regulated exoplanet prediction market, you could literally (and figuratively) hedge your investment of effort by taking out a short position on a security that pays out on demonstration of an Earth-mass planet orbiting any of the three stars in Alpha Centauri.

Prediction markets have been adopted in a very wide range of contexts, ranging from opening weekend grosses for big-budget movies, to forecasts of printer sales, to the results of presidential elections. A highly readable overview of these markets by Justin Wolfers (who was featured last week in the New York Times) and Eric Zitzewitz of the University of Pennsylvania is available here as a .pdf file. The ideosphere site contains a wide variety of markets (trading in synthetic currency) and includes securities directly relevant big-picture questions in physics, astronomy and space exploration. Here’s the price chart for the Xlif claim,

which pays out a lump-sum of 100 currency units if the following claim is found to be true:

Evidence of Extraterrestrial Life, fossils, or remains will be found by 12/31/2050. Dead or extinct extraterrestrial Life counts, but contamination by human spacecraft doesn’t count. (Life engineered or created by humans doesn’t count.) The Life must have been at least 10,000 miles from the surface of the Earth. If Earth bacteria have somehow got to another planet and thrived, it counts, as long as the transportation wasn’t by human space activities.

It’s very interesting to compare the bullish current Xlif price quote of 72 with the far more bearish sentiment on Xlif2, which is currently trading at an all-time low of 17,

and which pays out if “extraterrestrial intelligent life is found prior to 2050″, and more specifically,

Terrestrial-origin entities (e.g. colonists, biological constructs, computational constructs) whose predecessors left earth after 1900 do not satisfy this claim. If the intelligence of the ET is not obvious, the primary judging criteria will be either a significant level of technological sophistication (e.g. radio transmitting capability) or conceptual abstraction (e.g. basic mathematical ability). Radio signals received or similar tell-tale signs of intelligence (e.g. archeological discoveries) detected and accepted by scientific consensus as originating from intelligent extraterrestrials would satisfy the claim even if not completely understood by the claim judging date.

Recently, open-source software has been released that makes it straightforward to set up a prediction market. We’ll soon have the world’s first exoplanet stock market up and running right here at oklo.org. In the meantime, feel free to submit specific claims (in the comments section for this post) that might lend themselves to securitization…

Lonely Planet Guide to the Hyades13
greg posted in systemic faq, exoplanet detection on February 9th, 2007

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It’s been a hectic week, and now that it’s February, my New Year’s resolution to write 2-3 posts per week managed to lose its shaky option on my priorities.

Eugenio stopped by my office this afternoon to outline his latest code developments for the console. He’s mostly finished implementing a Bulirsch-Stoer integrator. Once this algorithm is tested and operational, it will produce very significant speed-ups for the fitting and the stability analysis of tough multiple-planet systems such as 55 Cancri and GJ 876. Then it’ll be on to a rollout of the bootstrap method for computing uncertainties for the orbital elements in the planetary fits.

“So did you see the new planet?” he asked.

“Huh?” I hadn’t heard anything about it.

Turns out that Bunei Sato and his collaborators have detected a periodic radial velocity variation for the star Epsilon Tauri. Their preprint is on the Astrophysical Journal’s website, but it doesn’t seem to have hit the preprint server yet. This star is a prominent member of the nearby Hyades cluster, and is easily visible to the naked eye as part of the well-known “V”-shaped asterism near Aldeberan in the sky.

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Eps Tau is bright enough to have garnered 40 different names in the Simbad catalog, and it’s now listed in the console menu and on the systemic backend as HD 28305. This is one of the most straightforward radial velocity datasets that you’ll come across, and thus makes a good system for first-time users to fit. A few debonair moves with the downloadable console conjure up a model planet with a period of 594 days, an orbital eccentricity e=0.15, and a minimum mass 7.6 times that of Jupiter:

Epsilon Tauri is one of the four stars in the Hyades that are currently nearing the end of their lives and are evolving through the red giant phase. It’s 14 times larger than the Sun, and it’s luminosity is 97 times the solar value. It weighs in at 2.7 solar masses, making it the most massive star known to harbor a planet.

So what’s the story? The Hyades are a metal-rich cluster. One would naively expect that the supersolar composition of the precursor star-forming giant molecular cloud would have lead to a large fraction of the cluster members harboring readily detectable planets. It’s also true that stars somewhat more massive than the Sun should harbor a higher-than-average fraction of giant planets. Eps Tauri scores on both counts.

[Note: John Johnson’s thesis work at UC Berkeley and Bunei Sato’s RV survey are both capable of providing observational support for the hypothesis of a positive correlation between the detectable presence of a planet and the mass of the parent star. See talk #1 on the Systemic Resources page for more details.]

Young Cluster NGC 3603, Source: NASA

It’s important to keep in mind, however, that a cluster environment will have a strong effect on giant planet formation. Currently, the Hyades are 600 million years old, and the cluster has lost a large fraction of its O.G.s to the general galactic field through the process of dynamical escape. If we extrapolate back to the cluster’s early days, we find that the Hyades would have resembled the Pleiades 500 million years ago, and would have looked like the Orion Nebular Cluster during the first few million years of its existence.

The UV radiation environment in the original Hyades cluster was fierce. The protostellar disks of the individual Hyads were likely photoevaporated before the growing planetary cores were able to reach the runaway gas accretion phase that gives rise to Jupiter-mass planets (see our paper on this topic). When we get the full inventory of planets in the Hyades, I think we’ll find plenty of Neptunes and terrestrial planets, but almost nothing in the Jovian range. Indeed, work by Bill Cochran and the Texas RV group has demonstrated that the Hyades are generally deficient in massive planets.

My guess is that Epsilon Tauri b is an example of a planet that formed through the gravitational instability mechanism. Gravitational instability should generally produce more massive planets (e.g. HIP 75458 b, and HD 168443 b and c) and its efficacy will be little-affected by UV radiation from neighboring stars. It likely occurs once per every several hundred stars that are formed, and so it’s perfectly reasonable that there’s one star in the Hyades that has a planet formed via the GI mechanism.

For more information, this series: 1, 2, 3, 4, 5, 6, and 7
of oklo posts compares and contrasts the gravitational instability and core accretion theories for giant planet formation.

a bunch of cool new stuff0
greg posted in systemic faq on February 2nd, 2007

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Stefano and Eugenio have both been working hard on the systemic console and backend, and as a result of their efforts, we’re now able to roll out a number of new features.

The backend now features a systemic wiki in which users can collaborate on a wide variety of writing projects related to systemic in particular and extrasolar planets in general. Features include discussion pages for individual systems, the framework for a comprehensive console and backend manual, and an exoplanetary news wire. Our first news service is being provided by Mike Valdez, who combs astro-ph every day and extracts any new preprints that are germane to the those interested in exoplanets. Stefano wrote the code from scratch, so there are endless possibilites for customization. Give it a try.

On the console front, Eugenio has aggregated a uniform listing of the literature sources of all of the radial velocity data sets provided by the console. This information is in a file vels_list.txt, which is now included in the systemic.zip package. If you are using the console for scientific research that you intend to publish, it’s now a snap to get the correct citations for any of the individual systems included on the console.

Many users have expressed interest in what our own solar system would look like to a dedicated radial velocity observer on another star. Eugenio has put together an expansion pack that contains 17 manufactured data sets based on the Solar System. A second expansion pack contains an analogous set of manufactured data sets for various plausible configurations of planets orbiting Alpha Centauri A and B. Both are available on the downloads page for the downloadable systemic console.

Check it out!

mp3s of the spheres0
greg posted in systemic faq, non-technical posts on January 18th, 2007

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New users are still streaming into oklo.org. If you’re a first-time visitor, welcome aboard. You’ll find information that you need to get started in this post from several days ago.

The EZ-2-install downloadable systemic console is the primary software tool that we provide for analyzing data from extrasolar planetary systems. The tutorials 1,2, and 3 are the best way to learn how to use the console. Over the past few months, we’ve been adding a range of new capabilities that go beyond the features described in the tutorials and which improve the overall utility of the software. We’ll be explaining how these new features work in upcoming posts, and for our black-belt users, we’re also putting the finishing touches on a comprehensive technical manual.

When we designed the console, our main goals were to produce a scientifically valuable tool, while at the same time make something that’s fun and easy to use. Early on, we settled on the analogy with a sound mixing board, in which different input signals (planets) are combined to make a composite signal.

We’ve pushed the audio analogy further by adding a “sonify” button to the console. When sonification is activated, you can turn the stellar radial velocity curve into an actual audible waveform. If you create a system with several or more planets, these waveforms can develop some very bizarre sounds. From a practical standpoint, one can often tell whether a planetary system is stable by listening to the corresponding audio signal. Alternately, the console can be used as a nonlinear digital synthesizer to create a very wide variety of tones.

Here are links (one, and two) to past posts that discuss the sonification button in more detail. If you come up with some useful sounds, then by all means upload the corresponding planetary configurations to the systemic back-end.

Armchair Planet Hunting4
greg posted in systemic faq, non-technical posts on January 15th, 2007

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The Associated Press just published an article on how the Internet has facilitated an increasing number of collaborations between amateur and professional astronomers. The systemic project is one focus of the AP piece, and we’re seeing a jump in traffic as a result. If you are a first-time visitor to the site, welcome aboard!

There are several ways that you can use and participate in systemic. Our project home page is a weblog (updated fairly frequently) that gives an insider’s perspective on the latest developments and discoveries in the fast-moving fields of extrasolar planets and solar-system exploration. We write for a target audience of non-astronomers who are interested in astronomy. To get a flavor for the blog, keep reading the posts below, or have a look at a few of our past articles, such as our take on last Summer’s big “is Pluto a planet debate”, our exploration of what planets and galaxies really look like, or our series [1, 2, 3, 4] on the feasibility of detecting habitable terrestrial planets in the Alpha Centauri System.

You should see a set of links just to your right:

These links give you information that you can use to start participating in the actual discovery and characterization of extrasolar planets. (Despite the fact that we’re rocket scientists, we’ve been unable to consistently sweet-talk Microsoft IE into correctly displaying our site. On some versions of IE, you may have to scroll all the way down to the bottom of this page to see the links). The Downloadable Systemic Console is our Java-based software package that allows you to work with extrasolar planet data. The Systemic Backend is a collaborative environment that has the look and functionality of a social networking site. Registration and participation are free. The nearest well-characterized extrasolar planets (GJ 876 b, c and d) are 14.65 light years away, and so the news of useful modern innovations such as pop-ups and spyware hasn’t had time to propagate to those far-distant worlds. Hence the systemic backend is completely free of annoying ads!

One final note: there are two separate channels for registration on systemic. The first, accessed through the “login” tab on the site header above, is part of the Wordpress package that runs the blog. Registration on the blog allows you to comment on our frontend posts. The second, accessed through the “backend” tab on the site header or the link to the right, gives you access to the collaborative php-based environment that constitutes the systemic backend. You can register for either or both, and you don’t need to give your real name or any real-world identifying information other than an e-mail address.

Tune in regularly for more news and updates.

year 2.01
greg posted in systemic faq on November 15th, 2006

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As of tomorrow, oklo.org will have been on the air for one year. We’re pleased with the response that we’ve gotten thus far, and we’re looking forward to rapid progress during year two. A big thank-you is definitely in order to everyone who’s either worked on the site or made regular visits or participated in the ongoing collaborative research!

In recent weeks, the user base on the systemic back-end has grown substantially, and we’ve been pushing the limits of what our ISP is geared to provide. Bluehost provides a very cost-effective package for hosting weblogs and running small-scale sites, but it’s become abundantly clear that one can’t expect to run a web 2.0 startup for $6.95 per month. At that level of expenditure, we’ve been limited to the use of 20% of one processor with a maximum job length of 60 seconds. Stefano has stretched our ration with clever use of cron command, but nevertheless,

has become a refrain tiresomely familiar to backend users, and our attempts over the past week to shift the backend to alternate stop-gap servers have been thwarted by various software incompatabilities.

I’m thus very happy to report that an order has been placed for a dedicated server that will obliterate the current problems. It will be located in downtown Santa Cruz on a high-speed T3 line. We should have everything up and running on it within 2 weeks. It’s spec’d to run the full systemic simulation, the new connection is ready to handle a hoped-for shout-out from boing-boing or slashdot, and the joint package should deliver a much more satisfying end-user experience.

In the meantime, however, keep sending in those fits. Neither sleet, nor snow, nor server overloads shall… We’re very eager to build up a solid distribution of fits for Systemic Junior.

Viewed from afar (Challenge 004)3
greg posted in systemic faq, exoplanet detection on November 13th, 2006

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The fourth systemic challenge turned out to be somewhat less challenging than the first three. Quite a few entrants figured out that the data-set corresponds to our own solar system. Among a large number of excellent models, Mark Kilner turned in the fit with the lowest chi-square: 1.0401. In addition to Jupiter, Saturn, Earth, and Venus, he topped off his system with a spurious Mercury-mass planet in a 5.62 day orbit, which allowed him to take the prize. Nice one, Mark!

Eugenio created the challenge 004 synthetic data set after a conversation in which we decided that it’ll soon be feasible to push the precision of the radial velocity method down to an instrumental error of 0.1 m/s. Even more optimistically, we assumed that the Sun, viewed from afar, exhibits negligible radial velocity noise (more on that soon).

Our Solar System, expressed in the Jacobi orbital elements used by the console, is given by:

The true three-dimensional model that Eugenio actually integrated to produce the synthetic data set also includes the correct values for the planetary inclinations and nodes. Because of the sin(i) degeneracy for Keplerian orbits, the current version of the downloadable systemic console does not include the inclinations and nodes as fitting parameters.

The synthetic data set was created with the KeckTAC program, which mimics realistic observing strategies. In an all-out effort on a particular star, one would combine repeated individual observations to get a composite observation that averages over the effect of short-period oscillations (p-modes) of the star itself. This is the strategy that is being currently used by the Swiss team in their campaigns on stars such as HD 69830 and HD 160691. In the challenge004 dataset, there are 1171 radial velocity measurements spread out over 24 years.

Eugenio describes the procedure he used to fit the data:

The periodogram (and the data) shows Jupiter clearly. Saturn appears as a trend, but the periodogram of the residuals after fitting Jupiter gives a good guess for Saturn’s period. After removing Saturn, Earth pops out in the residuals periodogram. I did not find it easy to fit Jupiter, Saturn, and Earth, but after succeeding, Venus very clearly appears in the residuals. I kept on fooling around with the 4-planet fit to see if there was any chance of finding Mars even though the RMS was telling me that 4 planets was the best that I would likely do. I was hoping that N would be large enough to let me get Mars, but I was not able to see a (significant) signal in the residuals periodogram. If anything, Mercury seemed to be more easily detectable. However, after fooling around with the eccentricities of Saturn, Earth, and Venus, the (weak) signal for Mercury disappeared.

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With the contests wrapped up, we’re now in the business of getting the fits completed for the Systemic Jr. data set. Eugenio recently incorporated an F-test module into the console, which can be used to determine whether the addition of a planet is warranted. We’ll have a post up shortly that explains in detail how this works. In the meantime, see the discussion on the backend, or download a new console and give its new modules a whirl.

Apsidal2
greg posted in systemic faq, worlds on November 7th, 2006

In 1999, Upsilon Andromedae burst onto the international scene with the first known multiple-planet system orbiting a sunlike star. Eight years later, we know of twenty-odd additional multiple-planet systems, but Ups And remains a marquee draw. No other system evokes quite its exotic panache. No other extrasolar planets have garnered names that have stuck.

High in the cold and toxic atmosphere of Fourpiter, Upsilon Andromedae shines with a brilliance more dazzling than the Sun. Twopiter is occasionally visible as a small disk which, near conjunction, subtends about one-tenth the size of the full Moon in Earth’s sky. Dinky, which lies about four times closer to the star than Mercury’s distance to our Sun is lost in the glare.

To date, Upsilon Andromedae has accumulated a total of 432 published radial velocities from four different telescopes. The full aggregate of data is available on the downloadable systemic console as upsand_4datasets_B06L. The velocities span nearly two decades, during which the inner planet, “Dinky”, has executed well over 1000 orbits.

In earlier versions of the console, use of the zoom slider on an extensive data set would reveal a badly undersampled radial velocity curve at high magnification. Eugenio’s latest console release has addressed this problem, however, and the radial velocity model curve now plots smoothly even with the zoom slider pulled all the way to the right.

It’s interesting to look at the best radial velocity fit to all four data sets. The planets are very well separated in frequency space, and so it’s a straightforward exercise to converge on the standard 3-planet fit. Upsilon Andromedae itself is a little too hot (6200K) to be an ideal radial velocity target star, and so the chi-square for the best fit to the system is above three, with a likely stellar jitter of a bit more than 14 meters per second. If Ups And were a slightly cooler, slightly older star, we’d potentially be able to get a much more precise snapshot of the planet-planet interactions. (In that Department, however, there’s always 55 Cancri.)

The best fit shows that the apsidal lines of the two outer planets are currently separated by 30 degrees, and are executing very wide librations about alignment. This configuration continues to support the formation theory advanced two years ago by Eric Ford and his collaborators. They hypothesize that Ups And originally had four giant planets instead of the three that we detect now. The outer two (Fourpiter and, uh, “Outtathere”) suffered a close encounter followed by an ejection of Outtathere. Fourpiter, being the heavier body, was left with an eccentric orbit. Now, 2.5 billion years later, the memory of this disaster is retained as the system returns every ~8,000 years to the eccentricity configuration that existed just after the disaster.

Systemic Jr.0
greg posted in systemic faq on November 5th, 2006

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The activity this week has all been under the hood, and as a result, the systemic front-end has languished without news. Apologies for that! A slew of updates are on the spike.

Stefano is now officially on the roster at Oklo HQ, and we’re very happy to have him here. The atmosphere is caffeine-fueled startup. He’s already implemented numerous updates and improvements to the systemic backend which, when coupled with Eugenio’s progress on the console, put our web 2.0 story into high gear.

There were a number of times last week when the oklo.org site was temporarily unavailable. Our ISP restricts us to no more than 20% of a full processor load, and exceeding this causes the site to shut down for 5 minutes. We’re now in the process of temporarily mirroring the backend on a machine at Lick Observatory, and quite soon we’ll have a dedicated server up and running.

The systemic Junior datasets have now been added to the downloadable systemic console. Eugenio writes (see the backend discussion forum for the full description):

Systemic Jr. is now included in systemic.zip. You will see two drop down boxes in the upper right region of the main console. One is used to choose a real star system, while the other one is used to pick a Systemic Jr. system. Note that while both boxes are enabled, only one data set is actually selected. In the systemic directory, you will see two new items: “sysjrSystems.txt'’ and the directory “sysjrdatafiles.'’ These hold the information needed for Systemic Jr.

As soon as the Lick Observatory server is online, the backend will be able to accept fits to the Systemic Jr. data sets. In the meantime, please save your fits on your local machine. Some of the Systemic Jr. systems may seem familiar. It’s best however, if all of the datasets are approached without a pre-conceived notion of what might be generating them. Once the Systemic Jr. data sets have been fitted, we’ll be able to do a very interesting analysis which will give us some much-wanted information about the nature of the galactic planetary census.

Threaded console available!1
greg posted in systemic faq on October 30th, 2006

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This weekend, Eugenio posted an updated version of the downloadable systemic console. The Java code in this version is fully multithreaded, which means that we’re finally able to provide the much-needed and much-requested “stop” button.

For previous console releases, clicking multi-parameter minimization — “polish” — with integration enabled would often cause the console to effectively freeze as the computer worked it’s way through an exceedingly long bout of computation. With the new version, progress is indicated both by a graphical redrawing of the fit, and by a running tally of the number of Levenberg-Marquardt iterations that have been completed. If things appear to be progressing too slowly, it’s now possible to abort to the latest model state by pressing the stop button.

A “back” button will be activated shortly, which will allow you to step backward through your work to revisit earlier model configurations in the session. These features should significantly improve the overall usability of the console.

Another area where progress has been rapid is in the stability checker. Eugenio has put a lot of detailed information on this new functionality on the general discussion section of the backend. In short, the stability checker can now be used as a full fledged integrator which can write time series data to user-specified files. In a post that will go up shortly, we’ll look at how the stability checker can be used to answer some interesting dynamical questions.

Systemic Jr. is also just about ready to go. Assuming that there’s no unforseen snags, we’re looking to launch it on Nov. 1 (next week). In the meantime, download a fresh console, and give the new features a spin.

challenge 41
greg posted in systemic faq on October 25th, 2006

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Eugenio has put the fourth (and final) systemic challenge system on the downloadable systemic console. This dataset is somewhat easier to decipher than the first and second challenges, which were rather esoteric in their planetary configurations. We hope that you’ll find that this one’s a little more down to Earth. I’d like to have your entries in by Oct 31, 23:59 UT. As with our previous three contests, Sky and Telescope is awarding a Star Atlas to the person who achieves the best model of the system.

For this system, it’s likely possible to drive the chi-square arbitrarily close to unity by successively adding spurious, very low-mass planets that act to soak up random noise in the data. We’re currently working on incorporating some standard statistical test utilities into the console which will make it easier to determine whether adding an extra planet is truly necessary. (This will be the topic of an upcoming post, and see the comment thread on Sunday’s post.) For this contest, however, if there are multiple submissions with reduced chi-square near unity, then the prize will be awarded to the fit that also gets the total number of planets in the underlying model correct.

If you haven’t downloaded the console recently, we’re encouraging you to grab a fresh copy. A number of improvements have been added, and there are also a number of additional radial velocity data sets that have been added in recent weeks. Eugenio has been posting a running commentary on the backend describing the console improvements. We’re also putting the final touches on the Systemic Jr. datasets, which we’re hoping to release at the end of next week.

As a result of some articles in the press and on the Internet, we’ve been continuing to see a large increase in the oklo user base. If you’re visiting the site for the first time, you’ll find information about the project and about our goals on the links to the right. Welcome aboard!

1:2:45
greg posted in systemic faq, exoplanet detection on October 22nd, 2006

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The third Systemic Challenge closed to entries on Friday, and I’ve gone through and evaluated the submitted fits. The results were very encouraging. Eight out of twenty-five submissions corresponded to both the correct orbital configuration and the correct number of planets in the underlying dynamical model.

For challenge 003, we looked to our own solar system for inspiration, and tapped the four Gallilean satellites of Jupiter. Eugenio writes:

The system is a scaled-up version of Jupiter and the four Galilean satellites. To generate the model, I first set the central mass to 1 solar mass. The (astrocentric) period of Callisto was set to 365.25 days, and I required that the mass and (astrocentric) period ratios in the system would remain the same. Here’s the resulting model (using Jacobi elements, with i~88 deg):

Among the eight entries that got both the total number of planets and their periods correct, there was a fair amount of variation among fits that had nearly equivalent values for the chi-square statistic. Chuck Smith (among others) turned in a configuration that bears a very strong resemblance to the actual input system. The four planets in his fit all have nearly circular orbits:

and the resulting radial velocity curve does a very good job of running through the data, with a chi-square value for the integrated fit equal to 1.1005:

A number of other users turned in very similar configurations.

Because of random measurement errors in the data, the true underlying planetary configuration will not necessarily provide the best fit to a given set of radial velocity observations. Often, a better fit can be found for a configuration that is different from the system that generated the data. Steve Undy, for example, achieved a slightly lower chi-square value for his fit by giving a very significant eccentricity to his “Europa”:

The winner of the contest, however, was Eric Diaz, who submitted a 6-planet fit that achieves an integrated chi-square value of 1.04. In addition to the four planets that are actually present in the model, Eric added small planets with periods of 1.06 days and 18.11 days. These objects soaked up some of the residual noise in the fit, allowing for a lower chi-square value, and a copy of the Sky and Telescope star atlas. Nice job Eric!

The contest raises some interesting issues. First, at what point should one stop adding planets to a fit? The chi-square statistic penalizes the inclusion of additional free parameters in a fit, but it’s clear that chi-square can nearly always be lowered by adding additional small bodies to the fit. Second, its very encouraging to see that subtle, but substantially non-interacting systems can be pulled out of radial velocity data sets. In this system, the masses of the planets are small enough so that their dynamical interactions with eachother are not significant over the time-frame that the system is observed. This is in stark contrast to systems such as GJ 876 and 55 Cancri where it is vital to take interactions into account (by fitting with the integrate button clicked on). Finally, I think that we’ll soon see examples of the 1:2:4 Laplace resonance as competitive fits within the existing catalog of radial velocity data sets on the systemic backend.

Gamma Cephei0
greg posted in systemic faq, exoplanet detection on October 19th, 2006

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Guillermo Torres of the CfA recently posted an interesting article on astro-ph in which he takes a detailed look at the planet-bearing binary star system Gamma Cephei.

Gamma Cephei has a long history in the planet-hunting community. In 1988, Campbell, Walker and Yang published radial velocity measurements which show that Gamma Cephei harbors a dim stellar-mass companion with a period of decades. More provocatively, they also noted that the star’s radial velocity curve shows a periodicity consistent with the presence of a Jupiter-mass object in a ~2.5 year orbit around the primary star. In a 1992 paper, however, they adopted a cautious interpretation of their dataset, and argued that the observed variations were likely due to line-profile distortions caused by spots on the stellar surface. From their abstract:

In 1988 Gamma Cep was reported as a single-line, long-period spectroscopic binary with short-term periodic (P = 2.7 yr) residuals which might be caused by a Jupiter-mass companion. Eleven years of data now give a 2.52 yr (K = 27 m/s) period and an indeterminate spectroscopic binary period of not less than 30 yr. While binary motion induced by a Jupiter-mass companion could still explain the periodic residuals, Gamma Cep is almost certainly a velocity variable yellow giant because both the spetrum and (R - I) color indices are typical of luminosity class III. T eff and the trigonometric parallax give 5.8 solar radii independently.

In October 1995, 51 Peg b was announced, and exoplanet research was off to the races. The Walker team, with their futuristic RV surveys had seemingly come close to success, but had not managed to snag the cigar.

In the Fall of 2002, however, the planetary interpretation for the Gamma Cephei radial velocity variations was revived by Hatzes et al., who used McDonald Observatory to extend the data set. They showed that the 2.5 year signal has stayed coherent over two decades, thus effectively ruling out starspots or other stellar activity as the culprit. The planet clearly exists.

Aside from providing a pyrrhic victory for the Walker team, the Gamma Cephei planet is a remarkable discovery in its own right. Its presence showed that gas giants can form in relatively long-period orbits around binary stars of moderate period. In their discovery paper, Hatzes et al. assumed that the binary companion orbits with a period of 57 years, but other estimates varied widely. Walker et al. (1992), for example, adopted 29.9 years, whereas Griffin (2002) use 66 years. The mystery is strengthened by the fact that to date, the companion star has never been seen directly.

The details of the orbit of the binary star are of considerable interest. For configurations where the periastron approach is relatively close, simulations show that the star-planet-star configuration can easily be dynamically unstable.

In his new article, Torres methodically collects all of the available information on the star, and shows that the binary companion to Gamma Cephei has a 66.8 +/- 1.4 year period, an eccentricity of e=0.4085 +/- 0.0065, and a mass of 0.362 +/- 0.022 solar masses. The orbital separation thus lies at the high end of the previous estimates, and renders the stability situation for the system considerably less problematic.

We’re stoked about the Torres paper because it provides references to some truly ancient radial velocities, dating all the way back to a compendium published by Frost and Adams in 1903:

who report 3 measurements made at the University of Chicago’s Yerkes Observatory:

Eugenio has tracked down the various references in the Torres paper, and has recently added all of the available old-school RV’s for Gamma Cephei to the downloadable console. You can access the full dataset by clicking on “GammaCephei_old”:

It’s straightforward to manually adjust the offset sliders to put the radial velocities on a rough baseline. You can then build a rough binary star fit with the sliders, followed by repeated clicking on the Levenberg-Marquardt polish button, with the five orbital elements and the five velocity offsets as free parameters. This gives an Msin(i)=386 Jupiter masses, a period of 24,420 days, and an eccentricity, e=0.4112. Try it! The values that you’ll derive are in excellent agreement with the Torres solution:

With the binary fitted out, try zooming in on the more recent data from the past 10-20 years. You’ll see that the modulation of the radial velocity curve arising from the planet is faintly visible even to the eye. It’s interesting to go in and find the best-fit planetary model…

Follow Ups And other items…2
greg posted in systemic faq, exoplanet detection on October 17th, 2006

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It’s very gratifying to see an increasing number of people logging in to the Systemic Backend, and downloading the console. We’ve also been getting a lot of good feedback from users, which we’ll be incorporating into updated versions of the software.

Several people have noted that the backend is currently assigning chi-square values of zero to uploaded fits! We’re highly aware of this problem, and it likely stems from the fact that we may be exceeding our CPU allocation at our ISP. The back-end code integrates all submitted fits to verify the chi-square statistic for purposes of ranking. For submitted systems with long time baselines and short-period planets, these calculations can wind up being fairly expensive. We’ll let you know as soon as this issue gets resolved. In the meantime, it’s fine to submit fits, but if you get a good one, please save a copy in your own fits directory for the time being.

We’ve been getting a lot of entries for the Challenge 003 system. At the end of this week, I’ll tally up the results, so if you’ve got a fit to submit, go ahead and send ‘er in (using the e-mail address listed on the web-page given in the print version of the October Sky and Telescope). It’s fine to submit multiple fits — I’ll use your best one to determine the final ranking. The challenge 003 system represents an interesting dynamical configuration of a type not yet observed for planets in the wild, and so it’ll be very interesting to see what people pull out. Look for Challenge 004 to appear this weekend on the downloadable console, and shortly thereafter, warm up those processors for the advent of the 100 star Systemic Jr. release.

Yesterday’s post is generating an interesting and vigorous discussion thread. Jonathan Langton and I were hopeful yesterday that his benchmark Cassini-State 1 simulation might show an appropriately asymmetric light curve when viewed from lines of sight inclined to the planetary equator (as is the case for the Ups And observations). Frustratingly, however, when the model light curves are actually computed, they wind up drearily sinusoidal, and the phase offset is independant of viewing inclination:

We’re holding out hope, though, for Cassini-State 2. In that case, there are two angles to vary (the orientation of the pole in the orbital plane, and the viewing inclination) and so it may well be possible to dredge up a good fit to the data. After-the-fact parameter tweaking, however, is highly unsatisfactory! I’m looking very much forward to seeing more data sets like Ups And’s. In particular, HD 189733, should give a very nice full-phase curve, and further down the line HD 80606 should be even more interesting.

stability analysis0
greg posted in systemic faq on October 11th, 2006

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If you’re spending time on the collaborative systemic backend, you’ll know from the discussion threads that Eugenio has been making rapid progress on the downloadable console. He’s in the process of converting the code from a single-thread version to a fully multi-threaded package. Threading is important. It will allow the console to be gracefully reset in the event that a Levenberg-Marquardt polish takes more time than you bargained for, and it will allow for a variety of on-the-fly diagnostics regarding what’s going on under the hood.

The latest version of the downloadable console now contains a multi-threaded orbital stability checker. To see it in action, download a fresh console (making sure to save your old systemic directory if you have built up a library of fits that you want to keep). I pulled up the HD 69830 dataset and quickly worked up a three-Neptune fit that is very similar to the fit reported by the Geneva team in their discovery paper.

The two outer planets are roughly similar in mass to Neptune, while the inner planet, with a period of 8.66 days is somewhat less massive. It’s not immediately clear from looking at the orbital configuration:

that this planetary troika is gonna get along to go along. A stability check is definitely in order. Clicking on the button for the long-term stability module:

brings up a dialog window that you can use to control the stability integration. You specify the maximum timestep duration, the output frequency, and the integration duration and press go. At present, the console implements only a 4th/5th order Runge-Kutta integrator, but we’ll soon supply faster algorithms, including a Wisdom-Holman symplectic map:

For this example, I specified a short 100-year integration (4200 inner planet orbits). This is enough to see whether the system is wildly unstable, but for a more diagnostic check, one would generally like to look at a longer duration (100,000 inner planet orbits, say).

In this first implementation, a system is deemed “stable” if the semi-major axes of all the planets remain constant to within 1% of their initial values during the course of the integration. There are, of course, stable systems (such as a librating, equal-mass 1:1 resonance configuration) where larger semi-axis variations occur, but if semi-major axes vary by more than 1%, it means that considerable orbital energy is being traded back and forth, and the long-term prognosis is not good.

This HD 69830 3-planet fit easily lasts for 100 years. Nevertheless, as noted in the discovery paper, longer-term integrations show that the system is very close to the edge of stability.

I’m still working on the promised post about trojan planets. Look for it tomorrow!

And inside the second envelope…3
greg posted in systemic faq, exoplanet detection on October 9th, 2006

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First, a thank-you to everyone who submitted a fit to the second systemic challenge. I just loaded all the fits into the console and evaluated the chi-squares (with integration turned on). Jose Fernandes, of Lisbon, Portugal, submitted the winner, and will be receiving the $149.99 sky atlas from Sky and Telescope.

Jose’s fit has a reduced chi-square statistic of 3.94, and is comprised of three planets:

The outer two bodies have masses 1.58 and 0.5 times that of Jupiter, with eccentricities of 0.58 and 0.14. They share a common period of 362 days. The fit also has a tiny inner planet with a mass just under 3% that of Jupiter and a period of 50 days. This little guy improves the fit by wriggling the radial velocity curve up and down to statistically grab more points.

The system that actually generated the data was quite similar:

There are two equal-mass planets with masses 1.04 times that of Jupiter, with eccentricities of 0.7 and 0.2. They share a common period of 365 days. The 50-day planet in the winning fit was spurious, as is often the case when a model planet has a mass that is far smaller than its companions.

This system is an example of a one-to-one eccentric resonance. It is based on a system that was discovered by UCSC physics student Albert Briseno in one of the simulations that he ran for his undergraduate thesis, and it was formed as the result of an instability in a system that originally contained more planets. The system experienced a severe dynamical interaction, which led to a series of ejections. After the last ejection, two planets remained. They share a common orbital period, and gradually trade their eccentricity back and forth. Their interaction gives a strong non-Keplerian component to the resulting radial velocity curve for the star, which makes this a tricky system to fit. While the system might seem absurdly exotic, it’s recently been suggested by Gozdziewski and Konacki that HD 82943 and HD 128311 might have their planets in this configuration (you can of course try investigating this hypothesis for yourself with the console). Their paper is here.

The challenge 002 system is an example of a general class of co-orbital configurations in which the two bodies constitute a retrograde double planet. If you stand on the surface of either world, the other planet appears to be making a slow retrograde orbit around your moving vantage as the libration cycle unfolds over several hundred orbits.

In tomorrow’s post, we’ll stay on the topic of co-orbital planets, and look at some interesting new work by Eric Ford on the possibility that we might soon be able to observe planets in Trojan configurations. Two planets in a Trojan orbit librate around the points of an equilateral triangle in the rotating frame. Indeed, when such an arrangement occurs, it’s possible that a particularly interesting dataset might have the capacity to launch a thousand fits.

[For more about 1:1 resonances, see this post and this post. For a discussion about the audio wave forms that they produce, see this post.]

CfA0
greg posted in systemic faq on October 8th, 2006

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Back from a great visit to the Harvard CfA. The exoplanet research effort out there is amazingly comprehensive, and I soaked up a whole range of interesting news items to report. A slew of posts are in the works.

I’ve uploaded my colloquium talk in (1) Apple Keynote format (harvard.key.tar.gz) , (2) Powerpoint format (harvard.ppt.tar.gz), and (3) as a set of .pdfs. The talk was built in Keynote, and thus will look best in that format. Note that the Keynote and Powerpoint files are both quite large (~58MB compressed, ~90MB uncompressed) because they contain a variety of animations. The .pdfs amount to about 7 MB, and show only the splash frames from the animations. Feel free to use any of these slides in presentations or classes (with a shout-out to oklo.org).

Eugenio has been working hard on the console during the past few days. The downloadable version now contains a stability checker which integrates a fit for a user-specified period. Relative changes in the semi-major axes of more than 1% are then used to flag instability. Give it a whirl! We’ll discuss it in more detail in an upcoming post.

Tomorrow, I’ll announce the results of the second systemic challenge. The third challenge system is already available on the downloadable console.