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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.)

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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.

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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.

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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.

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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.

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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.

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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…

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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.

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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.]

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I’ll be gone on a trip to the Harvard CfA for the next several days. While I’m there, I’ll be giving a colloquium talk, and in addition, I’ll be trying to extract all the latest research news items from the CfA’s large group of exoplanet researchers. That’ll likely give me some stuff to write about in upcoming posts.

We’ve now closed the Systemic Challenge 002 contest, and I’ll tally up the results on the plane ride home. Look for a post this weekend that will explain what’s going on in the Challenge 002 data set. Eugenio has cooked up a great batch of RVs for the Challenge 003 system, and we’ll be releasing them this coming weekend.

Note that the dates of the challenges are slipping from what was announced in the S&T article. There’ll still be a total of four systems, but the contests will run over two months rather than one as originally planned. As soon as the contests are finished up, we’ll release the “Systemic Jr.” set of 100 trial systems. Based on our experience with these systems, we’ll make any necessary modifications to the simulation profile, and then we’ll be set to start the long-promised full Systemic simulation. In the meantime, keep submitting fits! I’d really like to see the chi-square come down on a dynamically stable configuration for 55 Cancri.

In other news, we’ve now got confirmations for both WASP-1b and WASP-2b.

On Monday, Mike Fleenor, of Volunteer Observatory in Knoxville Tennessee wrote:

I observed a complete transit of WASP-1b last night under very good conditions. My LC shows mid-transit very close to your predicted center. Details are available here.

Last weekend, Joe Garlitz from Elgin Oregon wrote:

Last night (Fri/Sat) I tried for WASP2 and got some data that looks promising. The data is very noisy and I would not feel comfortable about presenting it without some other confirming (hopefully someone else got data) observations.

I have attached a .jpg image of the data chart. The data is really forced to get any kind of “curve”. The solid line represents a running average over 16.25 minutes, 13 data points.

The individual images are 65sec at an interval of 75 sec. The scope is 200mm @ f/8 with a Cookbook 245 CCD, no filters.

Here’s his lightcurve:

Today, Geir Klingenberg from Norway checked in with a confirmation of Garlitz’s result (which he obtained remotely from a telescope in New Mexico:

Hi Joe,

I observed the ingress of this WASP-2 transit, see here.

Seems to fit your data nicely.

I used a robotic telescope at GRAS: 0.3m SCT @ f/11.9 and a FLI IMG1024.

Way to go, guys!

It was gratifying to watch the first systemic challenge unfold.

After a week of accepting fits, we tallied the entries and determined that Chris Thiessen had obtained to the lowest submitted chi-square. Way to go Chris! Eugenio then added the “challenge001” data set to the systemic backend, so that users can continue to improve and submit fits.

So what was the underlying synthetic planetary configuration that generated the data set?

Both Eugenio and I have had a long-running interest in the GJ 876, a 15-light year distant red dwarf star that is now known to harbor at least three planets. The two outer worlds in the system, which were discovered in 1998 and 2001, are in 2:1 resonance, and form the classic example of a configuration that demands a self-consistent (as opposed to Keplerian) model. Last year, Eugenio led the discovery and characterization of a third planet in the system, which has a mass only 7.5 times that of Earth, and orbits the star every 1.94 days. (Here’s a link to the NSF press release for Rivera et al. 2005.)

We’ve been looking into the possibility of detecting another planet in the system, and in order to do so, we’ve been studying synthetic data sets that contain the three known planets, as well as a fourth, potentially habitable planet in a potentially habitable orbit. The following table gives the parameters of our hoped-for system (which, like the real system, has its invariable plane inclined by 40 degrees with respect to the line of sight.)

The first 155 points in the challenge data set used the actual observing times given in Rivera et al 2005. The remaining 32 points were generated using the version of Eugenio’s Keck_TAC program that we use to produce the systemic synthetic data sets. We then subtracted off the the first epoch time from all 187 observing times and multiplied each of the resulting times by the golden section, 1.618033989. This gives a system that has the dynamical characteritics of the real GJ 876 system, but with orbital periods that are all 1.618 times longer.

After setting up the uploads page on the backend, Eugenio uploaded the best fit that he was able to obtain, which had a chi-square of 3.13. A lot of computation went in to getting this fit, which took several days on a fast desktop machine.

Amazingly, the next day, user Roseundy submitted an even better fit,

which brought the chi-square down to 2.82, with the following comment:

Arrrggghh!!!!!!!! I had this fit on Sep 13, but I thought the ChiSq was too high to bother to submit. Lesson learned.

Eugenio and I were quite excited. Systemic users have clearly gotten at least as good at fitting with the console as we are, and we have been thinking carefully about the problem for quite a while. In the comments section on Roseundy’s fit, Eugenio wrote:

Hi Roseundy, That is awesome work!! All the challenge systems will be based on some known model, possibly a random draw, some noise, and possibly other effects. The random draw and the noise complicate the situation for the modeler (me), so that knowledge of the model will not always result in the best fit. Actually, your result is a major success for the idea behind the systemic collaboration — distributing the process of fitting radial velocity data sets. Because I really don’t know precisely how the random draw and the noise affected the model, it may still be possible to get even lower chisq values. I encourage everyone to continue fitting this system (as well as others). It does require patience and perserverence.

Chris Thiessen wrote:

Roseundy, I’m very impressed. The two major planets have such different Keplerian and integrated fits that I was never able to get them to work well together. How did you get the two planet solution? I’m not sure I would have let the 48 day planet develop that much eccentricity if I’d seen a trend. Maybe I missed out that way. Great work!

Whereupon Roseundy revealed the secrets of his fitting method:

Once I saw how close the planets were, I realized I needed to work with integration turn on. This, of course, slowed things down painfully. To make progress, I cut down the dataset (the middle third of the velocity data) and played with that until I got a good (chi^2 of 7 or so) fit. I backed that out to the full data set (very painful) and then added additional planets based on the residuals. I polished until I got the fit you see. I’m sure it can be improved, but I lost patience with it. I would like to see three improvements to the console to make this easier in the future: 1. be able to subset the data 2. be able to select which planets are to be integrated together, using Keplerian calculations for the rest. this would help with systems where only a few planets substantially interact with each other 3. (my vote for the most important) a natively compiled console. java byte code may be portable, but I don’t it’s very optimized. Having optimized binaries (x86 on Linux preferably) would be a win, I think.

We agree. After the next release of the console, I think it would be a good idea to migrate to a strategy where the systemic community of users can work on the console code open-source style. This is clearly another area where a distributed attack will get important and interesting results.

In any event, thanks to everyone who has been reading the oklo blog and collaborating in the backend. We’ve had over 6,000 unique visitors so far this month, and the project is really starting to show promise.

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An relevant paper showed up on the astro-ph preprint server this morning, “A Bayesian Kepler Periodogram Detects a Second Planet in HD 208487” by P. Ç. Gregory of the University of British Columbia.

Gregory employs a technique known as the parallel tempering Markov Chain Monte Carlo algorithm to argue that the HD 208487 data set contains two planets. The first planet (which was previously announced by Tinney et al. 2005, and confirmed by Butler et al. 2006) has a period of 130 days and a minimum mass 37% that of Jupiter. The second planet in Gregory’s model lies out at a period of 908 days, and has 46% of Jupiter’s mass.

Interestingly, the console does not recover Gregory’s parameters precisely, but it does find a fit that’s extremely similar. (I just uploaded the fit to the systemic back-end.) The radial velocity reflex curve looks like this:

wheras the planetary configuration (at the moment when the first radial velocity data point was obtained on Aug. 8th, 1998) looks like this:

It’s interesting to look at the fits for the latest HD 208487 dataset that have been submitted by participants in the systemic collaboration. At the moment, there are six different fits:

On September 4th, mikevald submitted a 2-planet fit that is a close analog of the one published by Gregory. In the last several days, dstew and andy have also turned in fits that have essentially the same configuration as obtained by Gregory. That’s definitely cool.

In addition to the five fits that look like the Gregory configuration, with the outer planet at a period of P~1000 days, there’s also a completely different take on the system that was submitted this morning by Olweg. In the Olweg fit, the second planet lies interior to the known planet, and has a period of only 29 days. The chi-square is less than one, indicating a slight degree of overfitting. When overfitting occurs, it can easily be remedied by a slight random perturbation of the parameters. It’s very interesting that this fit was completely missed by the Bayesian Kepler Periodogram, so I thought I would have a closer look at Olweg’s model system.

The Olweg radial velocity curve is radically different from the Gregory fit:

The 28.68 day inner planet has a mass of 0.16 Jupiter masses (about 50 Earth masses) and travels on an orbit of modest (e=0.18) eccentricity. There’s a fair amount of planet-planet interaction in this system over the time scale of the radial velocity observations. By the time the fit reaches the end of the data set, there’s a noticeable difference between the keplerian model fit and a self consistent (integrated) model fit:

The system is stable, however, when I did a short test integration of 100,000 years. The secular interaction between the two planets causes the two orbits to execute a complicated dance over a timescale of several thousand years, with the periastron angle of the inner planet orbit mostly librating around an anti-aligned configuration.

As I’ve remarked in an earlier post, we’re currently in the progress of upgrading the downloadable console so that it will be capable of computing estimates of the uncertainties in the orbital elements of a fit. A good way to generate uncertainties in this context is to use the so-called bootstrap method. In the bootstrap, one re-draws the original radial velocity data set with replacement, thus producing alternate realizations of the data in which a fraction of the points appear more than once, and in which a fraction do not appear at all. One then fits to these new datasets, thereby building up distributions for each orbital element. (For more detail, see this paper, which describes in detail how this procedure was applied to the radial velocity data set for HD 209458.) When I run a self-consistent bootstrap analysis based on the Olweg fit, I get the following mean values and standard deviations for the parameters:

This fit is thus quite well constrained, and is a completely viable competing model for describing the hd208487 planetary system. I think the situation here really underscores the value of the systemic collaboration. Many radial velocity data-sets can be fitted by completely different models that offer equally robust fits to the data, while simultaneously maintaining small uncertainties on their bootstrap-estimated parameters.

So how do we know which HD 208487 system (if either) is correct? I’m hoping that the Monte Carlo simulation that will make up phase II of the systemic project will give a great deal of insight into when a particular orbital model can be deemed secure.

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Data data data. Robert Wittenmyer and his colleagues at the University of Texas have just posted a paper on astro-ph that contains a slew of new radial velocities for several famous planet-bearing stars, including 47 UMa, 14 Her, and 16 Cyg B. The velocities are all tabulated in the paper, so we’ll have them up on the systemic backend very shortly. [I’ll post a comment to this post when they’re up on the site. If you’re totally gung ho to get them right away, you can extract them from the posted latex file at astro-ph, and then add them manually to systemic’s datafiles directory.]

We always try to add new radial velocity data sets as soon as they become publicly available, and lately, these updates have been occurring roughly once per week. For the time being, the simplest way to get your fresh V’s is to rename your old systemic directory, and then download a new console. When the new console and catalog data are downloaded and unzipped, you can copy any previous fits and soundfiles that you’ve created into the new fits and soundClips directories.

The data in the Wittenmyer paper come from both the Harlan J. Smith 2.7-meter telescope and the Hobbey-Eberly 9.2-meter telescope. The cadence of the Smith telescope observations typifies the usual pattern of radial velocity survey data. The individual points are spaced essentially randomly in time, with many days separating each point. The Hobbey-Ebery data, on the other hand, are quite different. These data are much more densely sampled, and many nights contain several velocities in succession. In many stretches, the star is observed every few nights. This pattern results from queue-scheduling, which enables very intensive monitoring of systems that are of particular interest. I think queue scheduling is the wave of the future, and in the systemic simulation, we’ll have many synthetic data sets whose cadences correspond to the queue-scheduled approach.

The most prominent planet orbiting 14 Her has been known since the late 1990s. This world, known as 14 Her “b”, has a minimum mass about 4.6 times that of Jupiter, and a period of ~1770 days. If it were in our solar system, it would orbit in the asteroid belt. The parent star 14 Her is about 90% as massive as the Sun, and is more than twice as metal-rich. Given the planet-metallicity connection, it’s absolutely no surprise that 14 Her has a heavy-duty planetary system. I bet that 14 Her “b” has a very interesting system of satellites.

It’s pretty clear from the one planet fit that 14 Her “b” is not the only planet in the system, and over the weekend, several systemic users have submitted interesting fits to the data that reduce the chi-square by adding a second planet. For example, on August 30, user mikevald uploaded a two-planet fit in which the second planet, 14 Her “c”, has a period of 6159 days and an eccentricity e=0.52. This model currently fields the lowest chi-square statistic of any of the submitted 14 Her fits. The orbits in this best-fit system are crossing, however, indicating that the model may not be dynamically stable over the long run. On September 5th, allanfloering submitted a fit with nearly as good a chi-square, in which the outer planet has a 14,669 day period and an eccentricity e=0.09. Allanfloering’s world, if it exists, lies 11.77 AU from 14 Her, out at a Saturn-like distance.

Wittenmyer et al. show that the addition of their new 14 Her data suggests that 14 Her “c” has a period of order 6900 days, albeit with a low eccentricity. In their models, “c” and “b” may be participating in 4:1 resonance. A quick fit on the console with the Wittenmyer et al data included gives a radial velocity curve that looks like this:

corresponding to a planetary configuration that has an outer planet with a modest eccentricity e=0.20.

As soon as the data go up on the site, feel free to try working up improvements. It will be interesting to see how many fits to the full 3-telescope data set are participating in 4:1 resonance.

Hey ya’ll, there’s a whole lotta fittin’ goin on out there in the back 40.

Seriously, though. We’re really seeing a great response from users who are contributing their efforts. Nearly 200 people have registered on the back-end during the past few days, and over 750 different radial velocity fits have been uploaded. Hopefully we’ll see that work continue to flow in, and everyone has been showing admirable patience as we smooth out the inevitable rough spots which began to show up as soon as we had a surge of real users on the site.

If you’re arriving by way of the Sky and Telescope article, you’ll notice that the full universe of 100,000 synthetic stars is not yet listed on the systemic backend. During September, we’re still carrying out the first phase of our planned research effort, which consists of accumulating a wide variety of fits to the full collection of actual, published radial velocity data sets. Very soon, we will have accumulated enough fits to be able to present a dynamic, interactive catalog of candidate planets. A query-based dynamically generated planetary catalog will allow a variety of very interesting questions to be answered. For instance, by how much can one deflate the famous eccentricity-period diagram, while still demanding a prespecified goodness-of-fit for all of the candidate planets?

At the moment, such questions are hard to answer, because (other than here at oklo) there is no consolidated repository of radial velocity data and associated self-consistent fits.

In order to make dynamically generated planet catalogs scientifically useful, we’re going to have to provide several more tools to the users. As I mentioned yesterday, the console will soon be multi-threaded, which will make it easier to use for high-performance work. In the interim, however, you can have the console print a stream of diagnostic messages by launching it from the command line. For example, on linux or OSX architectures, open a terminal (shell), cd to the systemic directory, and type java -jar systemic.jar at the prompt . The diagnostics provide a running update of the progress of the console as it produces fits to the data set.

We’ll also soon be providing a long-term integration window that will allow users to verify that their model systems are dynamically stable. It’s alarmingly easy to find multiple-planet fits to radial velocity data sets that have low values for the reduced chi-square statistic, but in which the planets experience dynamical disasters (collisions, ejections, close encounters, etc.) on a time scale that is short in comparison to the known age of the parent star. Indeed, most of the candidate stars in the back-end catalog are more than 2 billion years old. Young stars tend to be rapidly rotating, which broadens their absorption lines and makes radial velocity measurements less accurate. Rapidly rotating stars also tend to have elevated levels of magnetically driven chromospheric activity, which adds additional noise to the velocity estimates.

And finally, the console needs to provide error estimates on the orbital parameters that it generates. This is best done using the so-called bootstrap method, which we’ll discuss in an upcoming post.

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Wow! The American Scientist and Sky and Telescope articles are clearly getting the word out. We’ve been seeing a significant increase in traffic on the oklo.org site, both in terms of visits (yellow bars) and bandwidth and page views (green and blue bars). The bandwidth increase is especially gratifying. It reflects the fact that many users are registering on the back-end, downloading the console, and submitting fits. As I write this, new and interesting fits for a variety of different radial velocity data sets are rolling in to the star catalog. Our goal of fostering original, public-participation exoplanet research is starting to be realized, and I want to thank everyone who’s lending a hand.

If you’re a first-time visitor to the Systemic Project website, please read the blog entries that were posted prior to this entry. They contain the information you need to start participating, and they give an overview of the current project status. If you are a return visitor, please have a look at the updated back-end. Stefano has made a number of code and design improvements that streamline the workflow and make the site easier to navigate.

On to some planet issues. The Mu Ara (HD 169061) system, which contains four known planets, is shaping up to have significant implications for the systemic project. Intense interest in the system has been spurred by a recent paper from the Swiss group (Pepe et al. 2006) that presents a self-consistent 4-planet model. Pepe et al.’s orbital fit (given in their Table 1) provides an excellent match to the radial velocity data sets, but when they carried out a long-term integration of the system, they found that the gravitational interactions between the planets lead to catastrophe after 76 million years. The parent star Mu Arae has an estimated age of 6.4 billion years, so clearly we don’t yet have a full understanding of what’s going on with this system.

The discord within the Pepe et al. model is provided by the two middle planets, one of which has a 310 day orbit, and the other which orbits in 643 days. The planets are on the edge of the 2:1 mean motion resonance, with the practical consequence that they experience a strongly chaotic orbital evolution. The orbits change eccentricity and orientation on a timescale of only decades:

I’ve made a movie that tracks the evolution of the orbits over 528 years. Here are links to a .mov version (288 kB) and an .mp4 version (1.5 MB). It’s clear from the movie that the interaction is both complicated and unpredictable. The planets display no catastrophic excursions on the 500 year timescale of the movie, but eventually, they experience orbit crossings leading to a likely ejection of the inner 0.5 Jupiter mass planet.

The Mu Ara dataset HD169061_B06P06CH on the console back-end combines both the Pepe et al. data as well as the most recent data from Butler et al. 2006. I’m hoping that someone can get a stable, self-consistent, low chi-square fit to this combined data set. Such a fit would give the best available view of what’s going on with the system, and would underscore the scientific relevance of the systemic project.

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With the verdict in on Pluto, we here at oklo.org will have to revert to sober, scientifically rigorous posts on extrasolar planetary systems to keep our readership and ad rates up. And as soon as I can figure out how to make WordPress launch those “swing for the fences” pop-ups from our site, we’ll be increasing our revenue stream even more.

American Scientist has just published my article on planet formation and extrasolar planets in their September/October issue. The article wraps up with a description of the systemic console, and the systemic collaborative research project. If you’re an American Scientist reader visiting oklo.org for the first time, welcome aboard!

Several posts back, I put up a brief description of the immediate goals of the Systemic collaboration:

The Systemic collaboration is proceeding in three steps. In the first step, which is ongoing, we’ve been gathering all of the radial velocity data that have been published for known planet-bearing stars. These data sets are included in the downloadable systemic console, and the systemic back-end allows participants to upload their own planetary fits to this data. We want to use the data to create a uniform catalog of known planetary systems.

In the second and third phases of the systemic project, we’ll be studying synthetic data sets that have been produced using our own algorithms. “Systemic Jr.” will launch at the beginning of September, and will contain 100 synthetic data sets, four of which will be special challenge systems. The Systemic Challenge, sponsored by Sky and Telescope will be explained in more detail, and will be available at a link on their website. The challenge systems will be released on September 3, 10, 17, and 24, along with a specific set of contest rules. The first person to crack each of these systems will recieve a paperback edition of the Millennium Star Atlas (a $149.95 value). In order to prepare for the contests, go ahead and download a copy of the systemic console, and work through tutorials one, two, and three. A full technical manual for the console is in the works, and will be ready for download quite soon.

Later this Fall, when Systemic Jr. wraps up, we’ll launch the full Systemic simulation. A lot more on this will be posted in the weeks ahead. Our overall goal is to obtain an improved statistical characterization of the galactic planetary census.

The most interesting serious-planet news from the past week has been the paper by the Geneva Extrasolar Planet Search Team that releases an updated radial velocity data set for the nearby solar-type star Mu Arae (also known as HD 160691). As discussed in this post, the console can be used to quickly uncover and characterize the orbits of the four planets that have been announced for the system.

The mu Arae system is remarkable because the two middle planets (with periods P~300 days, planet “d”, and P~640 days, planet “b”) experience strong mutual gravitational interactions during the 5-year time period that the system has been observed. The presence of strong interactions indicates that a model for the system built from independant Keplerian orbits cannot provide a fully realistic fit to the system. In order to build a fully self-consistent fit, one must find an N-body model. The systemic console has this ability, which is enabled whenever the “integrate” box is checked.

N-body integrations are much more time-consuming to compute than simple evaluations of Keplerian fitting functions. The performance of the console thus slows down considerably when integration is enabled. (Note also, that this post now becomes a bit technical. If it sounds like gibberish, you can either skim the next few paragraphs, or, better yet, work through the tutorials on the use of the console.)

Continue reading →

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The October 2006 issue of Sky and Telescope is just hitting the stands. It contains a feature article — Virtual Planet Sleuths — on the usage of the console and the Systemic collaborative project. If you’ve read the Sky and Telescope article, and are a first-time visitor to oklo.org, welcome aboard!

The Systemic collaboration is proceeding in three steps. In the first step, which is ongoing, we’ve been gathering all of the radial velocity data that have been published for known planet-bearing stars. These data sets are included in the downloadable systemic console, and the systemic back-end allows participants to upload their own planetary fits to this data. We want to use the data to create a uniform catalog of known planetary systems.

In the second and third phases of the systemic project, we’ll be studying synthetic data sets that have been produced using our own algorithms. “Systemic Jr.” will launch at the beginning of September, and will contain 100 synthetic data sets, four of which will be special challenge systems. The Systemic Challenge, sponsored by Sky and Telescope will be explained in more detail, and will be available at a link on their website. The challenge systems will be released on September 3, 10, 17, and 24, along with a specific set of contest rules. The first person to crack each of these systems will recieve a paperback edition of the Millennium Star Atlas (a $149.95 value).

Later this Fall, when Systemic Jr. wraps up, we’ll launch the full Systemic simulation. A lot more on this will be posted in the weeks ahead. Our overall goal is to obtain an improved statistical characterization of the galactic planetary census.

In the Sky and Telescope article, I made a rather bold claim that by using the console, it’s possible to find an as-yet unannounced planet around more than a dozen different stars. The 55 Cancri data set, for example, is an excellent place for aspiring planet hunters to try their hand.

The feasibility of detecting planets in the published data sets was illustrated dramatically over the past week. On August 14th, Krzysztof Gozdziewski, Andrzej Maciejewski, and Cezary Migaszewski posted a preprint on astro-ph which describes their detection of a fourth — then unknown and then unconfirmed — planet orbiting HD 160691 (also known as mu Ara). They detected the planet using their own software, which has a similar set of capabilities to the systemic console, and they used the dataset provided by the recent Butler et al. 2006 catalog paper. They found an orbital period of P~307 days for the planet, a nearly circular orbit, and a mass of 0.5 Jupiter Masses.

Today, on astro-ph, the Geneva Radial Velocity Search team published a paper with an updated set of radial velocities of HD 160691 which were obtained with the HARPS instrument at La Silla. In the abstract of their paper, they write: “We present the discovery of mu Ara d, a new planet on an almost circular 310-days period and with a mass of 0.52 Jupiter Masses”.

So there you go, folks! The planets are in the data sets. You just need to download the console, fire it up, get a good fit, and submit it to the Systemic back-end.

[Note: It’s not clear what (if any) “credit” Gozdziewski et al. will get for their discovery. I don’t want to proffer an opinion on who should get credit in a case like this, mainly because I really don’t care. The Systemic backend includes a public-record chronological list of submitted fits for each radial velocity data set. If you turn up a planetary configuration that later gets confirmed by one of the radial velocity teams, you’ll get the personal satisfaction of knowing you knew about the planet first. What you almost certainly won’t get, however, is official credit for the discovery, or the right to name the planet, etc., etc.

For the synthetic planets in phases 2 and 3 of the Systemic collaboration, however, the discoverers will receive official credit, and they will have the right to name the planets if they choose to do so.]

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We’re working hard to keep the systemic project moving forward.

Eugenio, as of July 14th, has compiled and documented all of the published radial velocity data sets, and has been designing and developing the “KeckTAC” code, which will be a workhorse for systemic’s next phase. The published datasets are all available on the systemic systems catalog. Aaron has stripped the console down to its component parts, and he’s rebuilding it with new features, faster algorithms and a sleekly expandable architecture. Stefano has been tweaking the systemic backend [sign up and get fittin’, y’all -ed.], and will be arriving at UCSC in the Fall to do his Ph.D. research. We’re hoping that part of his thesis will be a statistical analysis of the final results of the 100,000 star systemic simulation.

When I was in graduate school, I spent a lot of time doing research on brown dwarfs (objects between 13 and 75 Jupiter masses that lie in the mass range between giant planets and red dwarf stars). At that time, circa 1992, no bona-fide brown dwarfs had actually been found, but the prospects for detecting them seemed reasonably good. My friend Todd Henry, who was a graduate student at the University of Arizona, and who was hunting for brown dwarfs using the speckle method, told me something that stuck in my mind.

“Face it, Greg,” he said, “the reason you’re interested in brown dwarfs is not because you’re interested in Brown Dwarfs — the reason you’re interested in brown dwarfs is because you’re really interested in planets, and brown dwarfs are just one stop away on the line.”

He was right.

A similar logic might apply today, “The reason I’m interested in giant planets is not because I’m really interested in Giant Planets — the reason I’m interested in giant planets is because I’m really interested in habitable terrestrial planets, and giant planets are one stop away on the line.”

Thanks to everyone who has created an account on the systemic backend, downloaded the console, and submitted fits to the HD 69830 data sets. It’s gratifying to see the collaborative effort coming together. We’re starting to get a better understanding of which aspects of the HD 69830 data set seem secure, and which aspects are uncertain.

That outer planet seems to me to be leaning toward the latter category.

For example, I just had a look at data set #17 for HD 69830. Guided first by the console’s periodogram and then by the console’s residuals periodogram, I worked up a two planet fit to the data. I kept the orbits of the resulting 8.66 and 31.7 day planets circular. In the absence of strong planet-planet gravitational interactions or resonant disk migration, I don’t see a clear rationale for assigning non-circular orbits unless the data really demands it.

The residuals periodogram of the 2-planet fit above has peaks near 200 and 400 days. The 200 day peak is a little higher, and indeed, corresponds to the outermost planet announced in the Nature paper published last week.

Use the folding window to look at the case for the 200 day planet. Try updating the period in tiny increments, and watch the data congeal into a relatively sinusoidal pattern. The third planet in the published fit is based on this configuration:

The 400 day data also looks good (although the power is not quite as high). Notice, too, that the phase coverage near 400 days is not as good. This is due both to the limited time baseline of the whole data set, as well as to the fact that the star can be observed only when it is not too near the Sun in the sky.

Apparently, the Las Vegas bookies are giving 3:1 odds in favor of the 200 day planet being correct. That said, however, the 400 day planet rounds out a very nice all-circular fit to the data.

Some of the planets that have been detected via the radial velocity technique have been announced in the refereed literature without the supporting evidence of a published table of radial velocities. For the planets that fall in this category, the end-user gets a star name, a list of orbital elements for the planet, and a graph showing a model velocity curve running through the data points. Occasionally, the data is folded, and only a .gif file of the phased radial velocity fit is published.

In a previous post, I wrote about why I can certainly appreciate the planet detection teams’ reasons for not wanting to divulge their radial velocity data when they announce a new planet. If a star has one detectable planet, then the odds are about 50-50 that another planet will be detected after several additional years of monitoring. For a variety of reasons, multiple-planet systems are scientifically more valuable than single-planet systems. In particular, a multiple-planet system (such as GJ 876) tells a fascinating dynamical story, which in turn yields valuable information about the formation and evolution of the planetary system. Obtaining radial velocities is hard, expensive work.

The unavailability of the radial velocity data sets for some of the planet-bearing stars has led to something of a gray market industry in which the radial velocity plots of the parent stars of interesting multiple-planet systems such as HD 82943 and HD 202206 are digitized, and the radial velocities are reconstructed from the graphs. For an example of this technique, see this preprint on astro-ph.

I bear some of the responsibility for the radial velocity .gif digitization industry. In 2001, a press release was sent out announcing the discovery of eleven new planets. This bumper crop included two particularly amazing systems, HD 80606, and HD 82943. HD 80606 harbors a massive planet on an extremely eccentric orbit, and I was very interested to fit the data myself in order to estimate the uncertainties in the transit windows.

The tabulated radial velocities on which the fits were based were not published, but postscript files showing plots of the radial velocities versus time were posted. I went into the files, and by placing commands to print characters in red, I was able to figure out how the plot was encoded. I was then able to extract the exact measured radial velocities for both HD 80606, and HD 82943 from the press conference postings. I didn’t try to publish the analysis that I did with this data, since the procedure seemed a little under-the-table. I did tell people what I was doing, however, and the radial velocity plots on the websites were soon changed from postscripts to .gif files, which are much harder to reverse-engineer.

One of our initial goals with the systemic collaboration is to provide the ability for anyone who is interested to perform a uniform analysis on all of the radial velocities underlying all of the published planets that make up the current galactic planetary census. In order to do this, we need a mechanism for accurately extracting the data from image files in .gif and .jpg format. Systemic team member Eugenio Rivera has been working on this, and has been getting good results with the Dexter Java Applet (available from ADS). The ADS information page gives the following overview:

Dexter is a tool to extract data from figures on scanned pages from our article service. In order to use it, you need a browser that can execute Java Applets and has that feature enabled. Netscape users can verify this by selecting “Edit” -> “Preferences” -> “Advanced” from the top-bar menu and making sure that the button “Enable Java” is checked.

Dexter can be quite useful in generating data points from published figures containing images, plots, graphs, and histograms, whenever the original datasets used by the authors to produce figures in the papers are not available electronically.

We’ll be posting velocity sets extracted from .gif files shortly, and Eugenio will post a detailed write-up of the technique and pitfalls of “observing” the observations.

This post continues with a thread that we’ve been developing over the past several days (posts 1, 2, and 3). In brief, we’ve found interesting evidence of a second planetary companion to 51 Peg in the published radial velocity data sets.

We first used the Systemic Console to recover 51 Peg’s famous (P=4.231 d) companion from the data, and then looked at the power spectrum of the residuals to the single planet fit:

There is a startlingly large periodicity in the data at a 356.2 day period.

We then used the console to identify this periodicity with an Msin(i)= 0.32 Jupiter-mass planet in an e=0.36, P=357 day orbit.

There’s no question that the addition of this second planet reduces the scatter in the data relative to the model. The question is: can the model be taken seriously? Is 51 Peg “c” really there?

Continue reading →

In the posts for Thursday and Friday, we used the Systemic Console to explore the radial velocity variations of 51 Peg. Aside from harboring the first extrasolar planet discovered in orbit around a Sun-like star, this data set is extraordinary because it contains nearly 270 individual radial velocity measurements taken over a period of over ten years. Very few stars have published data sets that are so extensive.

After extracting the signal of the celebrated 4.231 day planet from the data, we computed a periodogram of the residuals. The calculation shows a strong concentration of power at a 356 day periodicity:

At the end of yesterday’s post, we were left hanging on the suggestion that this strong peak might represent a second planet in the 51 Peg system. Let’s have a look at this hypothesis by making a two planet fit to the data.

If you’ve gone through the systemic tutorials, and are comfortable at the controls of the console, here’s the procedure:

Launch the console and follow the directions given yesterday to obtain the best single-planet fit to the data. Next, activate a second planet, and enter 356. into the data window of the period slider for the second planet. Then, minimize the new planet’s mean anomaly, followed by a minimization on the mass. Next, send all ten orbital parameters for the two planets, along with the velocity offsets off for a polish by the Levenberg-Marquardt algorithm. Note that it’s fine to push the “polish” button several times in succession, to ensure that the algorithm has been given enough iterations to converge to the best fit in the vicinity of your choice of starting conditions.

The console shows that the addition of a second planet improves the fit to the data, dropping the chi-square to 1.7, and reducing the required jitter to 5.4 m/s.

The second planet, which we’ll call 51 Peg “c” (where c stands for “console”, huh, huh) has a period of 356.8 days, a minimum mass of 0.32 jovian masses (slightly larger than Saturn), and an orbital eccentricity, e=0.36. Here’s a link to a screenshot of the console showing all the parameters. This is also an advance look at the next version of the console which Aaron will be releasing in a few weeks.

Using the console’s zooming and scrolling sliders, we can see the modulation of the radial velocity curve. The second planet imparts a visibly non-sinusoidal envelope on the strong carrier signal created by 51 Peg b. The non-sinusoidal shape stems from the significant eccentricity of planet “c”:

Note that we still have to teach the console to draw smooth curves when the zoom level is high! Look for that improvement to show up in about 2 months or so. There’s a lot of other items ahead of it on the to-do list.

The orbits of the two planets look like this:

Does it really exist, this room-temperature Saturn? Is it really out there? Do furious anticyclonic storms spin through its cloud bands? Does it have rings? Does it loom as an enormous white crescent in the deep blue twilight sky of a habitable moon?

Maybe.

Eugenio and I have been working through the weekend to devise statistical tests which can assess the likelihood that this planet exists. We’ll check in shortly with our results

Yesterday, we supplied the Systemic Console with the published radial velocity datasets of the the planetary system that started it all, the original gangsta, 51 Peg.

It’s interesting, after more than a decade of observation, to see what happens as a radial velocity time series acquires a long baseline. Launch the Systemic Console, and select 51 Peg from the system menu. You’ll see a plot that looks like this:

With the “51peg_1.vels” offset slider, it’s easy to separate the two contributing data sets. (One was published by the California-Carnegie Planet Search Team, the other by the Geneva Extrasolar Planet Survey). The Swiss data set gives a long baseline of coverage, whereas the California-Carnegie dataset contains intensive observations taken mostly over the course of a single observing season in 1996. Click on the periodogram, and be patient while the console works through the Lomb-Scargle algorithm. While you’re waiting, you can look eagerly forward to the fact that in Aaron Wolf’s next release of the console (due in a few weeks) the periodogram calculation will be sped up by more than a factor of ten.

The periodogram has an impressive tower of power at 4.231 days. This dataset contains a whopping-strong sinusoidal signal:

To work up 51 Peg “b”, activate the first row of planetary orbital element sliders and type 4.231 into the period box. Then (1) line-minimize the mean anomaly, (2) line-minimize the mass, (3,4) line-minimize both offset sliders, and (5) line-minimize the period. (6) Activate a small eccentricity, (7) move the longitude of periastron slider off the zero point, and then (8) click the Levenberg-Marquardt boxes to the left of each entry box and polish the fit. (If this sounds like gibberish, yet also exciting, we’ve written three tutorials [here, here, and here] that go into detail regarding the use of the console. In addition, all posts marked “systemic faq” contain information about how to use and work with the console.)

When I do this, the console gives me a single planet fit with P=4.2308 days, M=0.4749 Jupiter Masses, and eccentricity e=0.014. These values are in full agreement with the orbital parameters published in the original discovery paper.

Alert readers are likely grumbling that we’ve made no mention of uncertainties in the orbital elements. This is an extremely important and interesting issue for many systems, and we’ll definitely be posting extensively on the topic and theory of computation of errors in orbital elements of extrasolar planets. The entire Systemic research collaboration, in fact, is primarily concerned with resolving the issue of how to establish confidence levels in various types of planetary system configurations.

In the meantime, however, use the console to compute a periodogram of the velocity residuals to the old-school 1-planet fit. A strong peak stands out at a period of 356.196 days. The chi-square statistic of the 1-planet fit is just over 2.00, and the required stellar jitter is about 7 meters per second. This is significantly higher than the 3-5 meters per second of long-term jitter that is expected for a quiet, old G2 IV star like 51 Peg:

Could there be another planet in the system? Could it be, that the console, by virtue of the fact that it readily combines data sets from different published sources, has found a new world (in a habitable orbit no less)? Tune in tomorrow to find out…

Most of the recent scientific papers on the general topic of extrasolar planets start with a sentence very much like this one:

Following the announcement of the planet orbiting 51 Peg (Mayor & Queloz 1995), over 170 planets have been discovered in orbit around solar type stars.

And indeed, Mayor and Queloz’s discovery of the hot Jupiter orbiting 51 Peg was truly a watershed event. Their Nature paper has racked up 764 ADS citations. Of order several billion dollars have been spent (or will shortly be spent) on the worldwide effort to locate and characterize alien solar systems. It’s thus a little weird that the Systemic Console has so far failed to include 51 Peg in its system menu. We’ve just corrected this oversight by adding the two published data sets for 51 Peg.

The closely spaced data near the beginning of the time series is from Marcy et al. (1997), who began intensively monitoring the planet from Lick Observatory as soon as the discovery was announced. The widely spaced data is from the Swiss planet hunting team (Naef et al. 2004), and contains 153 radial velocities obtained over a ~10-year period. The data is catalogued at CDS, and available at this link.

The 51 Peg data sets are interesting for a number of reasons. I’ll check in tomorrow with more details as to why. In the meantime, fire up the console and start finding fits.

55 Cancri is an ordinary nearby star, barely visible to the naked eye. Through a modest telescope (or, more practically, with the use of the Goddard Skyview) one sees that it is actually a binary pair.

55 Cancri “A” (the bright star in the middle of the above photo) harbors an extraordinary planetary system. Indeed, it was the subtlety and the depth of the 55 Cancri radial velocity data set that motivated us to develop the systemic console. The fact that the 55 Cancri system continues to defy easy categorization gives us confidence that the systemic collaboration will be a worthwhile project.

Where to begin?

Click on the system menu on the console, scroll down, and select 55 Cancri. (If you’re unfamiliar with the console, and if you’re the methodical type, there are three tutorials available on the menu bar to the right. Otherwise, just follow along!) The published radial data for 55 Cancri now appears in the main console window. The sweeping spray of points, with its curiously non-uniform distribution, contains a fascinating narrative in its own right.

The very first point in the data set has a timestamp of JD 2447578.73 A Julian Date Converter tells us that this was 9:31 PM on Monday Feb. 20, 1989 (Pacific Standard Time). The observation was obtained by Geoff Marcy at the Shane 3-meter telescope at Lick Observatory on Mt. Hamilton, and the velocity error is 9.7 m/s. Back in 1989, Geoff and his colleague Paul Butler were laboring to improve their iodine cell technique, and were struggling to get enough telescope time to adequately track the motion of about 70 nearby solar type stars with the eventual hope of detecting giant planets.

The first 10 radial velocity points were obtained at a rate of 1 to 3 per year. With hindsight, it is easy to see that these 10 points are ample cause for a planet-hunter to be optimistic. The radial velocity variation in the first 10 points spans more than 100 meters per second, suggesting a signal with a signal-to-noise of at least five. The periodogram of these ten points shows a strong peak at 14.65 days, indicating that the data could be explained by a planet with 80% of Jupiter’s mass, circling on an orbit lasting just over two weeks.

Today, if such a planet were discovered, the announcement would not make the news, and the major excitement would be among amateur transit hunters, who would likely have a new high-priority follow-up candidate with a ~5% transit probability. (A two-week period is right at the borderline where transits can be reliably confirmed or ruled out by the photometric collaborators working with the RV-discovery teams prior to announcement of the planet).

In 1993, however, nobody was expecting to find Jovian planets in 14-day orbits. Conventional wisdom at the time was informed by the architecture of our own solar system, and held that gas giant planets should be found beyond the so-called snowline (located at r=4-5 AU) of the protostellar disk. Although the theory of orbital migration had been studied in considerable detail, nobody had proposed that giant planets might regularly spiral in and then be marooned on very short-period orbits. I don’t know whether Geoff and Paul even considered the possibility that the 14.65 day peak in their data was real. If they saw the peak, it is more likely that they would have ascribed it to an alias, an artifact of their uneven hard-won sampling.

During 1994, the velocities suddenly started to trend upward. This would have seemed rather disconcerting, and may even have raised alarm. Was some unaccounted-for instrumental or astrophysical process affecting the newer radial velocity data? Certainly, at the end of 1994, the case for a planet orbiting 55 Cancri would have been weaker than it had been a year earlier.

Nevertheless, the 55 Cancri campaign was at an important turning point. The last measurement of 1994 (JD 2449793.80) has a remarkably lower error (3.3 m/s) than any of the earlier radial velocities. In November of 1994, the Schmidt camera optics on the “Hamilton” spectograph at Lick Observatory had been upgraded, and the resulting improvement effectively tripled the intrinsic resolution to which the spectral lines could be discerned. With the ability to measure radial velocities to a precision of 3 m/s, the planet search had suddenly entered an entirely new realm. When one is in the business of detecting Jupiters, a velocity measurement with 3 m/s precision is literally 10 times as valuable as a velocity with 10 m/s precision.

In October 1995, Mayor and Queloz announced their discovery of a Jupiter-like planet in a 4.5 day orbit around the nearby star 51 Peg. Due to a catalog error that misclassified 51 Peg as a subgiant, it had not been included in Geoff and Paul’s survey, but they were able to rapidly confirm the Swiss discovery.

All at once, the idea of a gas giant with a 2-week orbit was no longer outlandish at all. The telescopes on Mt. Hamilton, which had been slipping inexorably in worldwide prestige as larger telescopes were built on higher mountains, were suddenly at the forefront of relevance. The Lick 3-meter telescope-iodine-cell-spectrograph combination was the best instrument in the world for obtaining precision doppler velocities of bright stars such as 55 Cancri. Extrasolar planets were front page news. Alotments of telescope time increased dramatically. In the six months running from December 1995 through May 1996, 55 Cancri was observed 41 times at Lick. This drastic increase in the cadence of observations is easily visible in the radial data:

With the 41 high-quality observations, the presence of the 14.65 day planet was obvious in the power spectrum.

In October 1996, Paul, Geoff, and several other collaborators announced the discovery of the 14.65 day planet, and in January 1997, they published the discovery in a now classic paper that also introduced the world to the inner planetary companions of Tau Bootes and Upsilon Andromedae.

With eight years of data, it was clear that other bodies were present in the system. In the discovery paper, Butler et al. wrote:

The residuals exhibit a long-term trend, starting at -80 m/s in 1989 and climbing to +10 m s-1 by 1994 (the velocity zero point is arbitrary). The velocities appeared to decline toward 0 m s/1 during the past year, although at least another year of data will be required for confirmation. This trend and the possible curvature in the velocity residuals are consistent with a second companion orbiting HR 3522 [aka 55 Cancri] with a period P > 8 yr and M sin i > 5MJUP.

This speculation proved to be correct. Use the console to get a best-fit for the 14.65 day planet, and compute the periodogram of the residuals to the fit:

The strongest remaining peak is at 4260 days, corresponding to an 11.7 year orbit (very similar to Jupiter’s 11.8 year orbital period). Keeping the orbits circular, use the “polish” button to produce a Levenberg-Marquardt optimized fit. Zoom in and scroll to show the time interval between 1996 and 2002. The gaps each year when the star is behind the Sun as seen from Earth are easily visible:

The two planet system does quite a reasonable (but by no means perfect) job of reproducing the observed radial velocities. After the announcement of the first planet at the end of 1996, interest in the star died down to some degree. The number of target stars being observed at Lick was being increased as Debra Fischer stepped in to manage the Lick Survey, and other systems, especially Upsilon Andromedae, were clamoring for telescope time. During the 1998 season, 55 Cancri was observed only twice. By 1999, however, the Upsilon Andromedae system had been sorted out, and renewed attention was focused on 55 Cancri. During 2000 and 2001, it became clear that the system likely contained at least three planets. With the 14.65 and (in my fit) 5812 day planets removed from the radial velocity curve, the residuals periodogram shows a peak at 44.3 days:

The signal from the 44.3 day planet is not as strong as for the other two planets, but a large number of velocities from 2002 seemed to clinch the case for this third planet:

Use the console to optimize the three planet fit using circular Keplerian orbits. When I do this, the chi-square statistic is reduced to 6.4, and the rms scatter is 12.5 m/s. The fit is still not perfect. Either the planets are eccentric, or there are additional planets in the system.

In a recent article appearing in the Astrophysical Journal, Vogt et al. (2005) published radial velocity data for six stars that appear to harbor multiple low-mass companions. The data for all six stars (HD 37124, HD 50499, HD 108874, HD 128311, HD 190360, and HD 217107) have been added to the system menu of the Systemic Console:

If you’ve worked through the console tutorials 1, 2, and 3, take a crack at using the console to fit these systems. HD 37124, in particular, is open to several different stable 3-planet configurations. In my current personal favorite fit, three very nearly equal-mass planets are caught up in an endless (or at least multi-billion year) cycle of rub-a-dub-dub. An .mpg animation of the long-term dynamical evolution of the orbits is here. Because the planets in this particular fit are fairly widely spaced, the motion is quite well described by second-order secular theory.