Monthly Archives: March 2007

Systemic Jr. Fit Drive

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

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

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

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

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

HD 118206…

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Most hot Jupiters have orbital eccentricities near zero because the tidal forces exerted on them by their parent stars are strong enough to rapidly circularize their orbits. Any planet whose orbit has been circularized should also be spin-synchronous, and so like our Moon with respect to the Earth, it should turn on its axis once every trip around the star. Synchronicity lends each hot Jupiter a permanent day and night side. This likely imparts a profound effect on both the planetary weather, and on the brightness of the planet when viewed in the infrared at different orbital phases.

All of the planets observed so far with the Spitzer Space telescope have nearly circular orbits, and hence are in (or are very near) the spin-synchronous state. We’re waiting to hear the results of our Spitzer GO-4 application to observe the highly eccentric planet HD 80606b, during an upcoming ‘606 day. If our observing proposal gets a thumbs-up, it’ll dramatically broaden the range of conditions under which planets have been observed. Very shortly, I’ll be posting the results of calculations that Jonathan Langton and I have been doing which predict what the light curve of HD 80606 should look like during the periastron passage in the various Spitzer bands. Here’s a sneak preview of how the temperature distribution on the planet might evolve over a 36-hour period as seen from a direction consistent with our line of sight from the Earth:

In looking over the latest officially published additions to the catalog of extrasolar planets, I noticed that there’s a very interesting object — HD 118203b — that straddles the extremes of the circular hot Jupiters and the ultra-eccentric HD 80606b. This planet was discovered in 2005 by the Swiss Team, has an orbital period of 6.13 days, a mass at least twice that of Jupiter, and a well-determined eccentricity, e=0.3. HD 118203b therefore won’t be spin-synchronous. Rather, as is also the case with HD 80606b (see the diagram here), it’ll have been forced into a state of pseudo-synchronous rotation, in which it does its best to keep one face toward the star during the periastron passage. Its day should be 64.8% as long as its year:

Higher resolution .eps version here.

Which raises a rather interesting question: Why is HD 118203’s eccentricity so high?

Assuming that the planet has a similar structure to Jupiter, the equations of tidal dissipation (see here for a discussion) indicate that the planet’s orbit should circularize in a mere 10-20 million years. This time scale is surprisingly short because the parent star is a subgiant with a radius ~1.5 times larger than the Sun. Something must be exerting a very strong perturbation to keep this planet’s e up.

In their discovery paper, Da Silva et al remark that the residuals around the best 1-planet Keplerian fit to the data are very large. It’s quite straightforward to verify this with the downloadable Systemic console (try it!) Da Silva and company were able to improve their fit by including a linear drift of 49.7 meters per second with their one-planet model. This corresponds to adding the effect of an outer planet that has been observed for only a small part of a single orbit. (The 43 published velocities span a period of 1.1 years.) They speculate that an outer as-yet-uncharacterized planet provides the gravitational perturbation that maintains the high eccentricity for the inner planet.

Last year, Fred Adams and I wrote a computer code (see these papers 1, 2) that includes the effect of general relativistic corrections on long-term planet-planet gravitational interactions. It’s easy to use this program to calculate what the long-term influences of various companion planets would have on HD 118203 b’s eccentricity. I ran a few trial cases, and quickly found that the interactions produced by companions that also provide the observed linear drift in the radial velocities don’t seem to be strong enough to explain HD 118203b’s high eccentricity. Could there be another explanation?

This is the sort of situation where the collaborative systemic back-end is extremely useful. I had a look at the stable fits that have been submitted so far for HD 118203. The best stable, self-consistent fit was uploaded back in October by the user Flanker, and has a reduced chi-square statistic of 1.96:

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This fit might point in an interesting direction for some further inquiry. Instead of using a linear trend to soak up the residuals to the one-planet fit, Flanker added two additional planets. One of the planets has a mass of 0.3 Jupiter masses and is orbiting with a period of 15 days. Its periapse is nearly aligned with the periapse of the inner planet. The resulting short-period secular interaction may well be strong enough to keep the eccentricity of the innermost planet high in the face of tidal dissipation. Flanker’s model also contains an outer planet with an orbital period of 244 days and a minimum mass 0.6 times that of Jupiter.

I think it’s worthwhile to explore additional models for this system that contain planets with short enough periods to intereact strongly with the 6.13 day planet. If the perturbing body has a relatively short-period orbit, then its presence will not be hard to verify with additional radial velocity observations of the star. And also, if Spitzer’s cryogen holds out, HD 118203b might be a very interesting target for a full-phase campaign.

Bootstrap

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

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

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

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

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

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

the uncertainty on the parameters is much larger:

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

Impact!

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The news out of the Planetary Defense Conference is that NASA has the ability to locate all the potentially dangerous asteroids in our solar system by the year 2020, but that the cash to carry out the project is not currently forthcoming.

CNN and many other news outlets carried the story, along with a dramatic artist’s rendition of an asteroid striking the Earth.

That’s a rather large asteroid.

Measuring the circumscribed circles, it appears that the impacting body is 1/10th the Earth’s diameter, or approximately 600 km in radius. A bolide of this magnitude would currently rank as the ~25th largest object in the solar system, larger than Uranus’s moon Umbriel (584 km radius), smaller than Saturn’s moon Iapetus (736 km in radius), and nearly exactly the same size as Pluto’s moon Charon (606 km in radius). Ceres, the largest object in the main asteroid belt, by contrast, has a radius of ~475 km.

Based on the location of the late-afternoon catastrophe relative to the day-night terminator, the impactor seems to have had an orbit that was highly inclined relative to the solar system’s angular momentum plane. Perhaps it was undergoing Jupiter-driven Kozai oscillations prior to striking the Earth.

The last impact of the magnitude shown in the illustration was probably the Moon-forming impact ~4.4 Billion years ago, in which a Mars-sized body struck the Earth. Kevin Zahnle of the NASA Ames Research Center has estimated the distribution of giant impacts after the Moon-forming event. It’s likely that the largest strikes were by bodies with roughly half the radius of the object shown in the above picture.

The consequences of even a 300 km object hitting the Earth are severe. Such an impact is energetic enough to entirely vaporize the Earth’s oceans and create a temporary rock-vapor atmosphere with a surface pressure of ~100 bars. For a period of several months to a few years, the Earth would radiate with a temperature of ~2000 Kelvin — hot enough to glow brightly in the visible region of the spectrum. And depressingly, our planet would be fully sterilized by the event.

This week’s crop

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The year 2007 is off to a reasonably good start. Three more planets were announced by the Geneva Planet Search team at a conference in Chile, bringing the total planet crop for ’07 up to seven.

The rate of planet discovery, however, has definitely leveled off. For the past four years, the detection rate has remained fixed at 26 new planets per year. The low-hanging fruit — the 51 Pegs, the 47 Ursae Majorii, the Upsilon Andromedaes — have all been harvested from the bright nearby stars, and increasingly extractive methods are being brought to bear. Transits are starting to contribute significantly to the overall detection rate. Radial velocity is pushing to planets with progressively lower masses. Surveys such as N2K are rapidly screening metal-rich stars that have high a-priori probabilities for harboring readily detectable planets. The neccessity of finding more planets is driving up the average metallicity of the known planet-bearing stars:

The three new planets, HD 100777b, HD 190647b, and HD 221287b are quite ordinary as far as extrasolar planets go. They all have masses somewhat greater than Jupiter, and they all take more than a year to orbit their parent stars. Their discovery seems not to have registered with the news media:

HD 100777 b, however, is actually deserving of some attention. Its orbital period of 383.7 days places it squarely in the habitable zone of its parent star. The eccentricity, e=0.36, is fairly high, and likely leads to interesting seasonal effects in the atmosphere of the planet.

HD 100777 b lies a regime where we expect to see white water clouds forming in the visible atmosphere. The planet is probably very reflective in the optical region of the spectrum (quite unlike the hot Jupiters, which are likely cloud-free, and which are known to absorb almost all of the starlight that strikes them). Convection of interior heat to the surface of HD 100777b is almost certainly driving collossal thunderstorms, and the atmospheric disturbances created by the thunderstorms likely feed giant vortical storms similar to Jupiter’s great red spot.

It’s also possible that the atmosphere is much clearer in regions where air wrung dry by rainfall is downwelling. This phenomenon occurs on Jupiter, where highly transparent patches occur over several percent of the Jovian surface:

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The Galileo entry probe went right into one of these regions, and sampled very dry air. On HD 100777, the regions of high atmospheric transparency will probably preferentially absorb red and green light (as a result of Rayleigh scattering of incoming photons). The surface, then, in the vicinity of a downwelling region may look something like this:

flyby

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Image: NASA New Horizons Spacecraft (false color by oklo).

One day, one hour, and nine minutes ago, the New Horizons spacecraft sailed flawlessly through its closest approach to Jupiter. A day later, Jupiter still looms large in New Horizon’s field of view, with an angular size more than five times greater than the size of the full moon in our sky.

Jupiter, during its 4.5 billion year history, has been visited by at least seven other probes. Pioneer 10, Pioneer 11, Voyager 1, Voyager 2, Ulysses, Galileo, and Cassini have all successfully made the journey. This latest encounter was buried beneath the news of a 500-point drop in the Dow Jones Industrial Average. The flyby, in fact, hasn’t even made it onto the Astronomy Picture of the Day!

A decade ago, many of the metal atoms in the New Horizons spacecraft were still buried in the Earth’s crust. A bit more than a year ago, the assembled spacecraft was flown, in a sealed pressurized container, to Cape Canaveral for launch. All through the past several weeks, it’s been taking pictures of the Jovian system. Most of the data will be radioed back to Earth over the coming months. The image above was taken on Monday, and shows a Von Karman vortex sheet trailing away from the Little Red Spot, currently the second-largest storm in the Solar System.

In a sense, the Jupiter encounter was mostly utilitarian. It boosted the spacecraft’s heliocentric velocity (at the expense of Jupiter’s orbital energy) and cut down the travel time to Pluto.

The next scheduled mission to Jupiter is Juno, the Jupiter Polar Orbiter, which is scheduled to arrive at the Jovian system in 2016.