systemic

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The California Carnegie planet search team posted a data-rich paper on astro-ph this week. The new article is scheduled to appear in the February 2007 issue of the Astrophysical Journal. Eugenio, exercising his usual diligence, has added the new velocity tables to both the downloadable systemic console and the systemic back-end stellar catalog.

The highlight of the paper is a new two-planet system orbiting HIP 14810, a metal-rich solar-mass star lying 53 parsecs away. The inner planet in the system has a period of 6.66 days, and tips the scales with least 3.84 Jupiter Masses. The outer planet is less massive (Msin(i)=0.76 Mjup), and goes around the star every 95.3 days.

The secular interaction between the two planets compels them to trade angular momentum back and forth. As a result, the inner planet cycles between an eccentricity of 0.02 and 0.15 on a relatively short 5000-year timescale. It’s currently in the high-eccentricity phase of its orbit. The large radial velocity signal-to-noise for the planet means that its eccentricity can be measured quite precisely (have a look at it with the console). The fact that the orbit is clearly non-circular would be strong evidence for the presence of planet c, even if there weren’t enough data to detect c directly. If planet b was the only significant planet in the system, its orbit would have circularized via tidal dissipation on a timescale that is less than the age of the star.

Short-period planets with masses greater than three Jupiter masses are intrinsically rare. Tau Boo b (with a mass of at least 3.9 Jupiter masses and an orbital period of 3.3 days) is the only other object with roughly similar properties. By contrast, 32 planets with periods of less than a week and minimum masses less than Jupiter’s mass are currently known.

In my opinion, the two most robust statistical correlations that have emerged from the first decade of extrasolar planet detection are (1) the planet-metallicity connection and the (2) dearth of high-mass short-period planets. The planet-metallicity correlation makes perfect sense. It’s the natural, expected outcome of the core-accretion process and the fact that Jovian-mass (as opposed to Neptunian-mass) planet formation is a threshold phenomenon. The paucity of high-mass short-period planets, on the other hand, is both weird and completely unexplained. It’s telling us something about the process of planetary formation and migration. We just don’t know what it is.

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Giant planets are interesting. Terrestrial planets are more interesting. Habitable terrestrial planets are the most interesting of all, and it’s nearly guaranteed that we’re living in the age when the first genuinely Earthlike worlds beyond our solar system will be discovered. The only question is which technique will wind up doing it. The big money is on space-based transit photometry, but I think that ground-based RV might take the prize.

The Systemic Challenge 004 system was designed to be a futuristic idealization of what the Sun’s reflex velocity would like if it were observed with high precision from a neighboring star for more than two decades.

The individual radial velocity uncertainties for the 1172 velocities the Challenge 004 datset are each of order 10 centimeters per second. Errors this small are still safely smaller than the sub-meter per second precision that is currently being obtained by the Swiss team (with HARPS) and the California Carnegie team (at Keck). Given the rapid improvement in the radial velocity technique over the past decade, however, it’s not at all unreasonable to expect instrumental precisions of 10 cm/s fairly soon. Many console users were able to extract the four largest-amplitude solar-system planets — Jupiter, Saturn, Earth, and Venus — out of the challenge004 dataset, suggesting that it’s only a matter of time before instrumental precisions and observational baselines arrive at the threshold where truly habitable, Earth-mass planets can be detected from the ground using the radial velocity technique.

A potential show-stopper for this rosy predictive picture is the astrophysical radial velocity noise produced by the stars themselves. If you want to detect a planet with the mass and period of Earth (which induces a radial velocity half-amplitude of only 9 cm/sec) then you need to be assured that the star is quiet enough for the low-amplitude terrestrial planet signal to be detectable. It’s therefore natural to ask the question: what does the Sun’s reflex velocity look like?

The GOLF experiment on the SOHO satellite provides one set of measurements. A massive time-series of radial velocity observations (from 1996 through 2004) has been published, and is now publicly available. The data set contains over seven million radial velocities taken at a 20-second cadence. The main goal in obtaining this data was to study the Sun’s spectrum of p and g-type modes, which show strongest oscillations at periods of a few minutes.

Three alternate calibrations of the GOLF dataset are posted on the project website. Two of these have clearly been processed to filter out low-frequency, long-period radial velocity variations. It’s interesting, however, to look at what the one unfiltered dataset suggests is happening over timescales of a year or more. I sampled the unfiltered data at a cadence of one velocity measurement per several days, and then loaded the resulting time-series into freshly downloaded version of the systemic console:

According to the above time series, the Sun is a pretty noisy star. I scoured the papers on the GOLF site, and could not find any discussion regarding how much of the variation shown above is believed to come from instrumental effects and how much is belieived to be actually intrinsic to the Sun. The fact that both the scatter and the amplitude of the variations seem to be increasing during the run of the data tend to indicate that intrumental effects relating to the aging of the detector play an important role. If anyone has more specific information on this issue (or if anyone is aware of a preferred calibration) please post to the comments section of the post.

What happens to the detectability of planets that are placed in the GOLF time series? To date, the most precise RV detection of an extrasolar planetary system is the Swiss Team’s discovery of the three Neptune-mass planets orbiting HD 69830. As a control experiment, we relabeled the published HD 69830 dataset at systemic003, and placed it on the backend for Systemic users to evaluate. As expected, nearly all of the twelve submitted fits recovered the published configuration, with chi-square reaching down to about 1.20.

For the systemic004 system, we took the published HD 69830 3-planet orbital model and integrated it forward in time to make a synthetic radial velocity curve. We then perturbed this curve with noise values drawn from the unfiltered GOLF dataset (We averaged the velocities into 15-minute blocks to simulate rapid-fire multiple observations that average over high-frequency p-modes). As of Sunday night, there have been 21 fits uploaded for systemic004 [thanks, y'all, -ed.]. None of them manage a chi-square below 2.5, and aside from the innermost planet, none of them make a convincing case for the presence of the planets that were placed in the dataset. Log in to the backend, call up systemic004 from the “real stars” catalog, and you’ll see what I mean.

The conclusion, then, is that if the GOLF data-set gives a realistic determination of the intrinsic radial velocity variation of the Sun, then the Sun is a far noisier star than HD 69830 (and other similarly old, early K-dwarfs). Indeed, you would even be hard-pressed to believe the presence of Jupiter in the GOLF time-series, unless you’ve got the luxury of waiting for at least several Jovian orbital periods.

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Update: The original version of this post tagged systemic003 as the target system and systemic004 as the control system. It’s actually the reverse. In any case, we’re interested in getting multiple fits to both systems. -GL

No post today, just a request:

We’ve been doing an analysis of the detectability of low-mass planets around certain types of stars. In the course of this work, we’ve generated a radial velocity data set, systemic004, which may (or may not) harbor a planetary system. I’d like to ask everyone to (1) download the latest version of the console, and (2) submit your fits to the systemic004 system to the backend. We’ve also included a control system, systemic003, which may look familiar. It would be very useful to have your fits to that system as well.

Thanks in advance! Once we get a batch of fits, I’ll write a post that explains the motivation underlying this request…

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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.

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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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It was a brilliantly clear November afternoon today, and the fact that the Sun’s rays were diminished by 0.0026% mattered not one jot. Mercury was in transit.

I was fortunate to get a glimpse of the event through a telescope. It was about an hour before third contact, and Mercury was clearly visible as a tiny, perfectly round, perfectly black dot set against the pale yellow immensity of the solar disk. There was something about the simplicity of the situation that was quite striking.

Transits, with their odd cadences, link the timescales of human activity to the flow of astronomical time. The June 2004 transit of Venus, for example, took place on the day before the final exam for my introductory Astronomy class. In the weeks leading up to the exam, I would point to Venus shining in the early evening sky, and urge the students to study, “See how it’s getting noticeably lower in the Sky every night at sunset? You can use the angular distance between Venus and the Sun as a countdown clock to the final!” (At which point they’d roll their eyes.)

The next Venus transit is in 2012. The one prior to 2004 took place in 1882, when William Harkness wrote,

We are now on the eve of the second transit of a pair, after which there will be no other till the twenty-first century of our era has dawned upon the Earth, and the June flowers are blooming in 2004. When the last transit season occurred the intellectual world was awakening from the slumber of ages, and that wondrous scientific activity which has led to our present advanced knowledge was just beginning. What will be the state of science when the next transit season arrives, God only knows. Not even our children’s children will live to take part in the astronomy of that day. As for ourselves, we have to make do with the present.

Accurate weather predictions are good for no more than a few days, but transit predictions can be made a long time in advance. For example (according to the Wikipedia) simultaneuous transits of Mercury and Venus will occur in the years 69163 and 224508.

Motions in the inner solar system are nevertheless chaotic, though, with a Lyapunov timescale of order several million years. Our lack of absolutely precise knowledge regarding the positions of the planets at the present moment gradually exponentiates into much larger uncertainties. As a result, we can predict transits millions of years into the future, but we have no ability to predict when the transits of hundreds of millions of years from now will occur.

In fact, there’s even a (thankfully small) chance that the solar system will become dynamically unstable before the Sun swells into a red giant. This afternoon, Mercury seemed utterly insignificant and completely remote when pitched against the solar disk. In the final hours before a collision with the Earth, however, it would present an altogether different sort of impression.

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.

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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.