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

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

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

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

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

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

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

Uranus and Neptune have returned to nearly the configuration that they were in at the time of Neptune’s discovery in 1846. Using Solar System Live, it’s easy to see where the planets were located when Galle and d’ Arrest turned the Berlin Observatory’s 9-inch Fraunhofer refractor to the star fields of the ecliptic near right ascension 22 hours:

In 2011, Neptune, with its 165-year period period, will have made one full orbit since its discovery. Uranus, with an 84-year period, will have gone around the Sun almost two times.

Because the planets are fairly close to conjunction, Neptune has recently gone through the phase of its orbit where it exerts its largest perturbation on the motion of Uranus. This was similarly true in the years running up to 1846, and was responsible for LeVerrier’s sky predictions bearing such a stunning proximity to the spot where Neptune was actually discovered by Galle.

LeVerrier (and Adams) were quite fortunate. Without a computer, multi-parameter minimization is hard, and both astronomers cut down on their computational burden by assuming an incorrect distance for Neptune (based on Bode’s “law”). Their solutions were able to compensate for this incorrect assumption by invoking masses for Neptune that were much too large. They carried out remarkable calculations, but nevertheless, luck (in form of the fact that Uranus and Neptune had recently been near conjunction) played a considerable role.

Predictably, as soon as the real orbit of Neptune was determined, the playa haters tried to rush the stage. Benjamin Peirce of Harvard, in the Proceedings of the American Academy of Arts and Sciences 1, 65 (1847) described LeVerrier’s accomplishment as a mere “happy accident”:

I personally think that’s going a bit far. In any case, it’s interesting to compare the two independent predictions with the actual orbit of Neptune. I pulled the LeVerrier and Adams data in the following table from Baum and Sheehan’s book “In Search of Planet Vulcan” :

There’s been no shortage of hard work, and there’s been no shortage of predictions and false alarms, but nevertheless, nobody has managed to discover another solar system planet via analysis of gravitational perturbations. With the extrasolar planets, however, the prospects look a lot better. In particular, the Systemic Backend collaboration can team up with amateur observers to do the trick.

On the Systemic Backend, there are many candidate planets that have had their orbits characterized. As is usually the case with planet predictions, most of the candidates will wind up being spurious, but it’s definitely true that real planets orbiting real stars have been detected by the Backend user base. For example, Gliese 581 c was accurately characterized by the Systemic users several months before it’s announcement by the Swiss (see this post) and the same holds true for 55 Cancri f (see this post).

In the happy circumstance that a candidate planet is part of a system with a known transiting planet, then there’s an increased probability that if the candidate planet exists then it can also be observed in transit. This provides a channel for detection that completely circumvents the need for professional astronomers to carry out confirming radial velocity observations. Amateur observers are currently pushing the envelope down to milli-mag precision. Here’s an out-of-transit observation of the parent star of XO-1b by Bruce Gary:

This photometry is potentially good enough to confirm a Neptune-sized planet in transit across a Solar-type star, which is absolutely amazing.

An initial proof-of-concept observation has recently been carried out. On the systemic backend, the users have been investigating the HD 17156 system, which contains a known transiting planet. User “japf ” (José Fernandes) found that a lower chi-square fit to the published radial velocity data can be obtained if there’s a 6.2 Earth-mass companion on a 1.23 day orbit.

The best-fit eccentricity of the planet would bring it to a hair-raising 2 stellar radii of HD 17156, and if the planet is made of rock or water, it’ll be too small to detect, but nevertheless, it’s at least worth having a look. Jose sent the ephemeris to Bruce Gary, who observed on the opportunity falling on April 20, 04.5 UT.

No transit detected. This in itself was not at all surprising, given the long-shot nature of this particular candidate planet. What’s exciting, though, is that the full pipeline is now in place. There will definitely be strong candidates emerging over the coming months, and I think it’s quite probable that we’ll see a prediction-confirmation that is at least as good a match as was obtained for Neptune in 1846…

Back in 2002, Keith Horne gave a talk at the Frontiers in Research on Extrasolar Planets meeting at the Carnegie Institute in Washington and showed an interesting table:

At that time, there were more than two dozen active searches for transiting extrasolar planets, but only a single transiting planet — HD 209458 b — had been detected. Transits were generating a lot of excitement, but paradoxically, the community was well into its third straight year with no transit detections. The photometric surveys seemed to be just on the verge of really opening the floodgates, with a total theoretical capacity to discover ~200 planets per month.

It’s been six years, and the total transiting planet count is nowhere near 14,000. Most of the surveys on the table have had a tougher-than-expected time with detections because of the large number of false positives, and because of the need to obtain high-precision radial velocities on large telescopes to confirm candidate transiting planets. Indeed, the surveys that were sensitive to dimmer stars have largely faded out. It’s just too expensive to get high-precision velocities for V>15 stars. With the exception of the OGLE survey (which had been set up to look for microlensing during the 1990s, and which had established a robust pipeline early on) none of the surveys that employed telescopes with apertures larger than 12 cm have been successful. The currently productive photometric projects: TrES, XO, HATnet, and SuperWASP all rely on telescopes of 10 to 11 cm aperture to monitor tens of thousands to hundreds of thousands of stars, and all are sensitive to planets transiting stars in the V~10 to V~12 magnitude range. This magnitude range is the sweet spot: there are plenty of stars (and hence plenty of transits) and the stars are bright enough for reasonably efficient radial velocity confirmation.

Yesterday, SuperWASP rolled out 10 new transits at once, dramatic evidence of the trend toward planetary commoditization and of the fact that it’s getting tougher to make a living out on the discovery side. The detection of new planets is growing routine enough that in order to generate a news splash, you need multiple planets, and the more the better. This inflationary situation for new transit news is highly reminiscent of where the Doppler surveys were at seven years ago. For example, on April 4, 2001, the Geneva team put out a press release announcing the discovery of eleven new planets (including current oklo fave HD 80606b).

I’d like to register some annoyance with this latest SuperWASP announcement. There are no coordinates for the new planets, making it impossible to confirm the transits. There is no refereed paper. The data on the website are inconsistent, making it hard to know what’s actually getting announced. I was astonished, for example, that WASP-6 is reported on the website to have a radius 50% that of Jupiter, and a mass of 1.3 Jovian masses:

That’s nuts! If the planet is so small, why is the transit so deep? And a 2200 K surface temperature for a 3.36d planet orbiting a G8 dwarf? Strange. Perhaps the radius and mass have been reversed? In addition, there are weird inconsistencies between the numbers quoted in the media diagram and in the tables. For example, the diagram pegs WASP-7 at 0.67 Jovian masses, whereas the table lists it at 0.86 Jovian masses. WASP-10 has a period of 5.44 days in the table and 3.093 days in the summary diagram. Putting out a press release without the support a refereed paper is never a very good idea, even when there’s a danger that another team will steal your thunder with an even larger batch of planets.

Despite the difficulty in getting accurate quotes from the exchange, it’s interesting to see how the ten new planets stack up in the transit pricing formula. Using the data from the new WASP diagram (except for the 0.66 day period listed for WASP-9) and retaining the assumption that USD 25M has been spent in aggregate on ground-based transit searches, the 46 reported transits come out with the following valuations:

The ten new WASP planets (assuming that the correct parameters have been used) contribute about 1/10th of the total catalog value. There will likely be interesting follow-up opportunities on these worlds from ground and from space, but its unlikely that they’ll rewrite the book on our overall understanding of the field.

It’s interesting to plot the detection rate via transits in comparison to the overall detection rate of extrasolar planets. (The data for the next plot was obtained using the histogram generators at the Extrasolar Planets Encyclopaedia, which are very useful and are always up-to-date.)

It’s a reasonable guess that 2008 will be the first year in which the majority of discoveries arrive via the transit channel, especially if CoRoT comes through with a big crop. Radial velocity, however holds an edge in that it’s surveying the brightest stars, and (so far) has been responsible for progress toward the terrestrial-mass regime. I think that we might be seeing planets of only a few Earth masses coming out of the RV surveys during the coming year. Certainly, everything else being equal, a planet orbiting an 8th magnitude star is far more useful for follow-up characterization than a planet orbiting a 13th magnitude star.

Image Source.

The range of planetary orbits that are observed in the wild is quite a bit more varied than the staid e < 0.20 near-ellipses in our own solar system. For regular oklo readers, the mere mention of Gl 876, 55 Cancri, or HD 80606, is enough to bring to mind exotic worlds on exotic orbits.

Non-conventional configurations involving trojan planets have been getting some attention recently from the cognescenti. Even hipper, however, is a configuration that I’ll call the 1:1 eccentric resonance. Two planets initially have orbits with the same semi-major axis, but with very different eccentricities. Conjunctions initially occur close to the moment of apoastron and periastron for the eccentric member of the pair.

Here’s a movie (624 kB Mpeg) of two Jupiter-mass planets participating in this dynamical configuration.

At first glance, the system doesn’t look like it’ll last very long. Remarkably, however, it’s completely stable. Over the course of a 400-year cycle, the two planets trade their angular momentum deficit back and forth like a hot potato and manage to orbit endlessly without anyone getting hurt.

Here’s an animation (1 MB Mpeg) which shows a full secular cycle. The red and the blue dots show the planet positions during the two orbit crossings per orbit made by one of the planets. It’s utterly bizarre.

These animations were made several years ago by UCSC grad student Greg Novak (who’ll be getting his PhD this coming summer with a thesis on numerical simulations of galaxy formation and evolution). As soon as we can get the time, Greg and I are planning to finish up a long-dormant paper that explores the 1:1 eccentric resonance in detail. In short, these configurations might be more than just a curiosity. When planetary systems having three or more planets go unstable, two of the survivors can sometimes find themselves caught in the 1:1 eccentric resonance. The radial velocity signature of the resulting configuration is eminently detectable if the planets can be observed over a significant number of orbital periods.

Image Source.

Stefano, and Eugenio and I have been completely immersed in several time-critical projects during the past few months, and as a result, the frequency of posts here on oklo.org has not been as high as I would like. We’re starting to see our way clear, however, and very shortly, there’ll be a number of significant developments to report. Also in the cards is a major new release of the console, and a refocus on the research being carried out on the systemic backend. In any case, sincere thanks to all the backend participants for their patience.

Oklo regulars will recall all the excitement last fall surrounding the discovery of transits by HD 17156b. The transit was first observed on September 10th by a cadre of small telescope observers, and was then confirmed 21.21 days later on October 1.

Jonathan Irwin at Harvard CfA has led the effort to analyze and publish the October 1 observations of the transit. The work recently cleared the peer-review process, and was posted on the web a few days ago. (Here’s a link to the paper on astro-ph.)

The night of October 1 was plagued by atrociously aphotometric conditions across the North American continent, and most of the observers who tried to catch the transit were clouded out. Southern California, however, had reasonably clear skies, and three confirming time series came from the Golden State. The Mount Laguna observations were taken from SDSU’s Observatory in the mountains east of San Diego, the Las Cumbres observations were made from the parking lot of the LCOGT headquarters in Santa Barbara, and Transitsearch.org participant Don Davis got his photometry from his backyard in suburban Los Angeles.

The aggregate of data from the October 1 transit allowed us to refine the orbital properties of the planet, and additional confirming observations in a paper by Gillon (of ‘436 fame) et al have given a much better characterization of the orbit.

Because of the high orbital eccentricity, the planet should have very interesting weather dynamics on its surface. Jonathan Langton’s model predicts that the planet’s 8-micron flux should peak strongly during the day or so following periastron passage as the heated hemisphere of the planet turns toward Earth.

By measuring the rise and subsequent decay of the planet’s infrared emission, it’ll be possible to get both a measure of the effective radiative time constant in the atmosphere as well as direct information regarding the planet’s rotation rate. Bryce Croll is leading a team that successfully obtained time on the Spitzer telescope to make the observations.

In another interesting development, a paper by Short et al. appeared on astro-ph last week which proposes the existence of a second planet in the HD 17156 system. The Short et al. planet has an Msin(i) of 0.06 Jupiter masses and an orbital period of 111.3 days. It’s quite similar to the slightly more eccentric (and hence dynamically unstable) version of the HD 17156 system proposed by Andy on the Systemic Backend last December, which was based on the radial velocities and transit timing then available:

The existence of a second planet in the HD 17156 system would be extremely interesting! The immediate question, however, is, how likely is it that the second planet is actually there?

To make an independent investigation, it’s straightforward to use the downloadable systemic console to fit to the available published data on HD 17156. I encourage you to fire up a console and follow along. Now that the Irwin et al. paper is on the web, we have the following transit ephemerides:

These can be added to the HD17156.tds transit timing file in the datafiles directory. The file should be edited to look like this:

When the HD17156v2TD system is opened on the console, it shows both the radial velocity and the transit timing data.

It’s quick work to dial in a one planet fit to the RV and transit timing data. I get a system with the following fit statistics:

The required jitter of 2.12 m/s indicates that a one planet fit to the data should still be perfectly adequate, since the star (which is fairly hot and massive) has an expected stellar jitter of order 3 m/s. Nevertheless, the residuals periodogram does show a distinct peak at ~110 days:

Using the 110 day frequency as a starting point, one finds that ~0.1 Mjup planets do indeed lower the chi-square. I’ve uploaded an example two planet fit to the systemic backend that harbors a second planet in a 113 day orbit and a mass of 0.13 Jupiter masses. Its periastron is aligned with that of planet b, and the RMS has dropped down to 3.08 m/s (for a self-consistent, integrated fit). The implied stellar jitter is a bargain-basement 0.59 m/s, which is almost certainly too good to be true.

When I do an F-test between my one and two planet fits, the false alarm probability for planet ccomes in at 38%. It’s thus fairly likely that the second planet is spurious, but nevertheless, it certainly could be there, and it’ll be very interesting to keep tabs on both the transit timing data and the future radial velocity observations of this very interesting system…

Image Source.

There’s a provocative paper up on the astro-ph today. Ignasi Ribas and two collaborators are reporting the “possible discovery” of a 4.8 Earth mass planet in an exterior 2:1 mean motion resonance with the transiting hot Neptune Gliese 436b. Planet four three six b is the well-known subject of great consternation, great scientific value, and many an oklo.org post. (For the chronological storyline, see: 1 (for background), 2, 3, 4, 5, 6, 7, 8, 9, and 10.)

Here’s the basic idea. Ribas et al. note that a single-planet fit to the Maness et al. (2007) radial velocity data set (which is listed as gj_436_M07K on the systemic console) has a peak in the residuals periodogram at P~5.1866 days:

Using this periodogram peak as a starting point, they get a keplerian 2-planet fit that lowers the reduced chi-square from ~4.7 to ~3.7. They then point out that this detection can potentially be confirmed by measuring variations in transit timing. In their picture, the presently-grazing transit has come into visibility only within the last 2.5 years or so, as a result of orbital precession. The transit light curve should thus be showing significant variations in duration as well as deviations from a strictly periodic sequence of central transit times.

This will be a huge big deal if the claim holds up. For starters, it’ll provide a natural explanation for Gl 436b’s outsize eccentricity. And everyone’s been on the lookout for a strongly resonant transiting system with a short orbital period. For the time being, though, I’m withholding judgment. As a first point of concern, Ribas et al. are presenting a keplerian fit to the radial velocities. Yet for the orbital configuration they are proposing, it’s absolutely vital to take planet-planet interactions into account. One can see this by entering their fit into the console. (Use a mean anomaly at the first RV epoch 2451552.077 for planet b=40.441 deg, corresponding to their reported time of periastron of Tp_b=HJD 2451551.78, and a mean anomaly for planet c=268.14 deg, corresponding to their reported value of Tp_c=HJD 2451553.4.) One can also dial in a long-term trend if one wants, but this isn’t necessary. Once the fit is entered, the reduced chi-square is 3.7. Activate integration. (Hermite 4th-order is the faster method.) When the planets are integrated, their mutual interactions utterly devastate the fit, driving the reduced chi-square up to 85.018. Using the zoomer and the scroller, you’ll see that the integrated radial velocity curve and the keplerian curve start off as a good match, but then rapidly get completely out of phase.

In order to examine the plausibility of a two-planet fit in 2:1 mean motion resonance, one needs to fit the radial velocity data with integration turned on. It is also important to include the existing transit timing data in the fit (and to do this, it’s best to use the most recent, so-called unstable version of the console). Over at Bruce Gary’s amateur exoplanet archive (AXA), there are now three transit timing measurements listed, with the latest obtained by Bruce himself this past New Years Eve. The HJD measurements of central transit should be added to the gj436.tds file, along with the HJD 2454280.78149 +/- 0.00016 central transit time measured by Spitzer.

Ideally, the Spitzer secondary transit timing data should also be included, but at the moment, the distribution version of the console does not have the capability to incorporate secondary transit measurements. One approach would be to get a self-consistent fit, and then see whether the epoch of secondary transit matches that observed by Spitzer.

Have fun…

Image Source

Discoveries relating to transiting extrasolar planets often make the news. This is in keeping both with the wide public interest in extrasolar planets, as well as the effectiveness of the media-relations arms of the agencies, organizations, and universities that facilitate research on planets. I therefore think that funding support for research into extrasolar planets in general, and transiting planets in particular, is likely to be maintained, even in the face of budget cuts in other areas of astronomy and physics. There’s an article in Saturday’s New York Times which talks about impending layoffs at Fermilab, where the yearly budget has just been cut from $342 million to $320 million. It’s often not easy to evaluate how much a particular scientific result is “worth” in terms of a dollar price tag paid by the public, and Sean Carroll over at Cosmic Variance has a good post on this topic.

For the past two years, the comments sections for my oklo.org posts have presented a rather staid, low-traffic forum of discussion. That suddenly changed with Thursday’s post. The discussion suddenly heated up, with some of the readers suggesting that the CoRoT press releases are hyped up in relation to the importance of their underlying scientific announcements.

How much, actually, do transit discoveries cost? Overall, of order a billion dollars has been committed to transit detection, with most of this money going to CoRoT and Kepler. If we ignore the two spacecraft and look at the planets found to date, then this sum drops to something like 25 million dollars. (Feel free to weigh in with your own estimate and your pricing logic if you think this is off base.)

The relative value of a transit depends on a number of factors. After some revisions and typos (see comment section for this post) I’m suggesting the following valuation formula for the cost, C, of a transit:

The terms here are slightly subjective, but I think that the overall multiplicative effect comes pretty close to the truth.

The normalization factor of 580 million out front allows the total value of transits discovered to date to sum to 25 million dollars. The exponential term gives weight to early discoveries. It’s a simple fact that were HD 209458 b discovered today, nobody would party like its 1999 — I’ve accounted for this with an e-folding time of 5 years in the valuation.

Bright transits are better. Each magnitude in V means a factor of 2.5x more photons. My initial inclination was to make transit value proportional to stellar flux (and I still think this is a reasonable metric). The effect on the dimmer stars, though was simply overwhelming. Of order 6 million dollars worth of HST time was spent to find the SWEEPS transits, and with transit value proportional to stellar flux, this assigned a value of two dollars to SWEEPS-11. That seems a little harsh. Also, noise goes as root N.

Longer period transits are much harder to detect, and hence more valuable. Pushing into the habitable zone also seems like the direction that people are interested in going, and so I’ve assigned value in proportion to the square root of the orbital period. (One could alternately drop the square root.)

Eccentricity is a good thing. Planets on eccentric orbits can’t be stuck in synchronous rotation, and so their atmospheric dynamics, and the opportunities they present for interesting follow-up studies make them worth more when they transit.

Less massive planets are certainly better. I’ve assigned value in inverse proportion to mass.

Finally, small stars are better. A small star means a larger transit depth for a planet of given size, which is undeniably valuable. I’ve assigned value in proportion to transit depth, and I’ve also added a term, Np^2, that accounts for the fact that a transiting planet in a multiple-planet system is much sought-after. Np is the number of known planets in the system. Here are the results:

HD 209458 b is the big winner, as well it should be. The discovery papers for this planet are scoring hundreds of citations per year. It essentially launched the whole field. The STIS lightcurve is an absolute classic. Also highly valued are Gliese 436b, and HD 189733b. No arguing with those calls.

Only two planets seem obviously mispriced. Surely, it can’t be true that HAT-P-1 b is 10 times more valuable than HAT-P-2b? I’d gladly pay $85,507 for HAT-P-2b, and I’d happily sell HAT-P-1b for $969,483 and invest the proceeds in the John Deere and Apple Computer corporations.

Jocularity aside, a possible conclusion is that you should detect your transits from the ground and do your follow up from space — at least until you get down to R<2 Earth radii. At that point, I think a different formula applies.