Seeing in the Dark

This evening (Sept. 19th) the US Public Broadcasting Service is running a documentary on amateur astronomy which will include a section on extrasolar planets. The production is called Seeing in the Dark and it looks like it should be a very interesting and well done program.

Featured in the film are my friends and collaborators Ron Bissinger and Debra Fischer. Ron (whose day job is CEO of Alpha Innotech) has been a core member of Transitsearch.org from the beginning, and has consistently obtained great observations of transiting planets. Debra (an astronomy professor at SFSU) has, among her many accomplishments, discovered literally scores of extrasolar planets using the radial velocity technique. Both Ron and Debra’s work has been the focus of many past posts on this website.

So tonight, set your telescopes to acquire HD 185269, enable the robotic photometric observing mode, and sit down in front of the tube with a bowl of popcorn!

follow-up still in order…

potomac river

In the last post, I pretty much wrote off HD 17156 b, which was the subject of last week’s transitsearch.org photometric follow-up campaign. Ron Bissinger observed the star during the latter part of the transit window, and saw no evidence of a transit. Tonny Vanmunster wrote with the news that Belgium was clouded out.

Soon after the post went up, however, Jose Manuel Almenara Villa of the Instituto de Astrofisica de Canarias posted a comment:

Hi Greg,

I observed HD17156 in the transit window. Unfortunately the night was windy, affecting the small telescope so the photometry is not so clear as we would wish. Anybody else observe?

It’s possible that I have a central transit. I can show you some plots if you want. I will try to observe again on December 3 (I think that is my next opportunity).

Regards,
Jose

On Saturday, Jose sent me his photometric plots, I should point out that he emphasized once again that the night was windy. In his plots (I’ve rewritten the labels in illustrator so that they show up better on the narrow blog-page format) the black dots are individual observations (R filter, 7 s exposures), the red dots bin 6 observations, and the blue dots bin 12 observations.

On the night before the night of the transit window, he got baseline photometry which shows considerably less scatter, and which does a nice job of showing his excellent photometric technique:

He fit a simple trapezoidal transit template to his data. The resulting fit has a duration of 169 minutes, a depth of 0.007 magnitudes, and a mid-transit time (HJD) ~ 2454353.614. These values are all quite close to what one would expect if HD 17156 b really is transiting. The possible event ends just prior to the start of Ron Bissinger’s time series.

So what to think? It’s most important to reiterate Jose’s point that the weather was not particularly good, and that a block of critical data is missing during the event itself. I myself have contracted transit fever several times in the past, and have built up sufficient immunity to refrain from getting too excited. I think a conservatively realistic assessment would say that there’s still an 11% chance that HD 17156 b transits are occurring, and that the uncertainty in the window has been narrowed down significantly. Over the long run, if transitsearch.org is going to succeed, then its important to stay cautiously optimistic. The good thing about a transit is that it repeats with clockwork regularity (barring the unlikely, but tough-luck situation where dynamically induced precession of the node induces transit seasons.) The next chance to observe HD 17156 during the transit window falls to North America on Oct. 1, where hopefully there’ll be multiple observers on the sky. We’re bad – We’re Nationwide…

To end on a heartfelt note, I think that the global collaborative efforts that go into these transitsearch campaigns have been both fun and inspiring, even when the result is the high-probability flat-line light curve. It would be exciting, though, if Jose ends up leading a discovery paper with the other participating observers as co-authors.

Results

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It’s not looking good for transits by HD 17156 b. Ron Bissinger of Pleasanton, California obtained a block of photometric data that covered a significant chunk of the transit window. His time series lasts from JD 2454353.68 through 2452353.88, and shows no hint of an event:

His observations were taken just after the peak of the transit midpoint histogram:

No word yet on whether anyone in Europe or the eastern US were able to observe during the first half of the window. If you got data, let me know.

Also, the Gliese 176 window has opened up. If you’ve got a telescope, a CCD, and a free evening, you know what to do!

Discover a planet

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My tight 30-minute layover in Denver turned into an eight-hour delay yesterday when a solenoid somewhere in our Boeing 777 malfunctioned just prior to pushback, giving me an unexpected opportunity to attempt to catch up on all the work that’s been piling up.

After 6 hours of tapping on the laptop, I’d exhausted my effectiveness, so I bought glossy magazines from the airport newstand. In the latest issue of Portfolio from Conde Nast, you can read an in-depth Vanity Fair style puff piece on ex-Tyco CFO Mark Swartz’s life in the Big House, and, in one of the advertisements, you’re encouraged to use a Visa “Signature” card to charge up some of the finer experiences in life. Quite to my surprise, #17 on a list that includes “See the Tony Awards live”, and “Test-drive a supercar”, is “Discover a planet”.

Now regular visitors to oklo.org all know that you can get your planet-discovery experience right here on the systemic backend without ever having to reach for your wallet. In fact, just yesterday, we learned from Gregory’s latest preprint on astro-ph that Eric Diaz (and a number of other systemic users) appear to have made the first characterizations of the most statistically probable planetary system fits to the HD 11964 radial velocity data set.

The HD 11964 data set was published by Butler et al. (2006). Two planets are already known to orbit this star. HD11964 b has roughly 1/3rd of a Saturn mass and a ~38-day orbit, whereas HD 11964 c is a sub-Jovian mass planet on a ~2110-day orbit. There’s a wide dynamically stable gap between the two planets, making this system a fertile hunting ground for additional companions.

Gregory does an extensive statistical analysis and argues that there’s strong evidence for a sub-Saturn mass planet on a year-long orbit. Eric Diaz’s version of this planet shows up in the fit that he submitted to systemic back in July 2007:

Eric also suggests the presence of a 12.4-day planet in the system. The Gregory analysis suggests that this planet is not statistically significant, but I’m going to add it to the transitsearch.org unpublished candidates list. There’s certainly no reason not to have a look-see if anyone has unused photometric capability.

HD 17156 at inferior conjunction (right now!)

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It’s 01:58 UT Sep. 10, and HD 17156 has moved into its transit window. Hopefully photometric transit observers across Europe have clear skies. If you’re collecting data, drop us a note on the comments page!


Sep 09, 2007 Europe Satellite Map Source.

Most of California looks pretty good for catching the latter part of the transit window once it gets dark tonight. I was up on Mt. Hamilton last night, and even though it was clear, there was a strong smell of smoke in the air. Bits of gray ash from the nearby forest fires were floating down like snow, and so they couldn’t open the dome of the 36-inch.


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The odds of a HD 17156 transit are 10.9%, so its best not to get hopes up too high. Its always good to have the next candidate ready to go, and as luck has it, there’s another good one in the hopper.

Endl et al. have published a preprint describing the discovery of a Neptune-mass planet orbiting the nearby red dwarf star Gliese 176 (aka HD 285968). This discovery is further evidence in favor of the core-accretion prediction that Neptune planets should be common around low-mass stars whereas Jovian-mass planets should be relatively rare. Endl et al.’s new planet has an orbital period of 10.24 days, an a-priori transit probability of 3%, and an expected transit depth of 0.4%. This is a low-amplitude signal, but it is nevertheless accessible to many experienced amateur astronomers. The discovery paper makes no mention of a photometric transit search, making this planet a very attractive Transitsearch.org candidate. The star is located at RA 04:43, Dec +18:57, and the next transit window is centered on Sep. 15, 2007.

fit to be timed

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

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

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

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

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

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

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

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

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

Try it for yourself!

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

HD 17156 b

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Last week, I wrote a post introducing HD 17156 b, a Jovian planet on a highly eccentric 21.2-day orbit around a V=8.17 solar-type star lying 250 light-years away in Cassiopeia (RA=2h 50m, Dec=72 deg).

A photometric check for transits by HD 17156 b was reported in the discovery paper, but due to the nearly three-week orbital period, it was only possible to rule out about 25% of the transit window. Given the highly favorable geometry of the planetary orbit, this means that there’s an impressive ~11% chance (8.25% if you take the discount) that the planet can be observed in transit. The expected transit depth is a very respectable 1%, and given the bright parent star, it’s a straightforward detection for small-telescope observers everywhere in the Northern Hemisphere.

What’s it worth to catch HD 17156 b in transit? From a crass cash-money standpoint, one can estimate a dollar value. Because the planet has a long period and an eccentric orbit, it would be the first transiting example of its kind, and would thus be expected to generate a fairly large number of citations. From a career standpoint, an ADS citation is worth at least $100 (see, e.g. here). Based on the citation count for the TrES-1 discovery paper (144 citations in three years) it’s reasonable to expect that at one decade out, a HD 17156 b transit would garner of order 200 citations, for a conservative total value of 20K. Given the 10% probability of the transit coming through, the resulting expectation value is equivalent to having twenty Benjamins floating down from the black velvet of the night sky.

I used the systemic console’s bootstrap utility to generate a set of orbital fits to the published radial velocities for HD 17156. Each orbital fit describes a unique sequence of central transit times. For a particular transit opportunity, the aggregate of predicted central transit times from the different fits can be plotted as a histogram. Here’s the resulting plot for the transit opportunity that’ll occur next Monday (HJD 2454353.68):

The uncertainty in the time of central transit is ~0.3 days. A window this narrow is rare for a planet that hasn’t yet been thoroughly checked. In fact, as far as Transitsearch.org opportunities are concerned, it doesn’t get much better than this. Extending our opportunity cost analysis, the expected monetary return for observations within the 1-sigma transit window is an impressive $114 per hour. (Only rarely does the expected return per hour exceed minimum wage for existing transit opportunities.)

Scientifically, a transit by HD 17156 b would certainly be very exciting. The planet should be heating up very rapidly during its periastron passage, which should spur the generation of hemispheric-scale vortices and an 8-micron light curve that’s detectable with the Spitzer telescope. Observation of the secondary eclipse (assuming it occurs) would allow for a measurement of the global planetary temperature near the orbital apastron.

The frame above is from a hydrodynamical study of HD 17156 b that Jonathan Langton has just finished computing. If all the talk of dollars, ephemerides, opportunity cost, and expectation value is leaving you stressed out, then just kick back with this fat 1.0 MB .mov of the simulation and get your groove on.

eclipse (a transit by any other name)

Image Source: APOD.

Last night, the alarm went off at 2:45 AM, just prior to the start of the full lunar eclipse. Remarkably, the fog had stayed away. The air was slightly warm, and the town was absolutely quiet. The shadow of the Earth was covering nearly the entire lunar surface, with just a small oblique portion of the lower right hemisphere still in sunlight. A few minutes later, the whole moon was glowing a dull orange-red against the easily visible stars of the ecliptic. It was creepy, weird. Definitely worth getting out of bed for.

The Sun and the Moon occupy nearly the same angular size in Earth’s sky. This means that to good approximation, the patch of sky covered by the moon during a central lunar eclipse contains stars that can see the Earth in transit across the face of the Sun.

And during a lunar eclipse, they see a double transit.

The famous “tooth” in the HST light curve for TrES-1 is generally attributed to the planet passing over starspots, but for those who prefer not to shave with Occam’s razor, it can be equally well modeled by a double transit.

transit of TrES-1 obtained with HST

Last night, during the eclipse, the Moon (at RA 22h 26 min, Dec= -09 deg 57 min) was only a few degrees away from the planet bearing stars GJ 876, GJ 849, HD 21707, and HD 219449.

ƒr3$h R4Ð14£ V3£0(1713$

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

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

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

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

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

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

Countdown

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August 1st marked the most recent ‘606 day, which came and went without wide remark. Perhaps this was because in late Summer, HD 80606 rises and sets in near-synch the Sun, and is thus lost from the Earth’s night skies.

At the moment, HD 80606b is headed back out toward apastron.

The global storms and shockwaves that were unleashed at the beginning of August are dissipating rapidly, and the flux of heat from the planet is likely fading back down to the sullen baseline glow that arises from tidal heating.

HD 80606’s next periastron passage occurs on November 20th, and the Spitzer Space Telescope is scheduled to observe the whole event (details here). It’s going to be a big deal. Spitzer can only observe HD 80606 during two three-week windows each year, and fortunately, the Nov. 20th Periastron passage occurs during one of these windows. It’s literally the only opportunity to catch HD 80606 b’s big swing before Spitzer’s cryogen runs out in 2009.

The orbital geometry of the periastron passage looks like this:

Each marker of the orbit is separated by one hour. The prediction for the pseudo-synchronous rotation of the planet is also indicated. The planet should be spinning with a period of 36.8 hours. Jonathan Langton’s hydrodynamics code predicts what the temperature distribution on the planet should look like at each moment from Spitzer’s viewpoint in our solar system:

Transitsearch.org observers have covered a number of the HD 80606 b transit opportunities, and it seems pretty certain that the planet doesn’t transit. This isn’t surprising. The geometry of the orbit is such that when the planet crosses the plane containing the line of sight to the Earth, it’s quite a distance away from the star. Not so, however, for the secondary transit. There’s a very respectable 15% chance that Spitzer will detect a secondary transit centered two hours prior to the periastron passage.

Even if the planet doesn’t transit, we should be able to get a good sense of the orbital inclination from the shape of the light curve. If the orbit is nearly in the plane of the sky, then we should see a steady rise followed by a plateau in the 8-micron flux coming from the planet. For more nearly edge-on configurations, the flux peak should be clearly discernable. The observations are scheduled to start 20 hours prior to periastron and end 10 hours after.

Vorticity

Vorticity can be thought of as the tendency of a paddlewheel to spin if placed in the flow. High vorticity is a large counter-clockwise spin, zero vorticity is no spin, and a large negative vorticity is a tendency to spin clockwise. The climate models of short-period extrasolar planets that Jonathan Langton and I have developed show a remarkable variety of vorticity patterns on their surfaces, in keeping with the incredibly stormy and complex nature of their atmospheres. Here’s a gallery of Mercator-projection vorticity maps for the known strongly irradiated Jovian planets that have significant eccentricities. The red arrows indicate the wind speeds and directions across the planetary surfaces. These figures are all from a paper that’s currently under review at the Astrophysical Journal (see here for an overview of the numerical method that we’re using). Also, a shout-out is due to Edward Tufte for advocating the strong graphic-design effect of small spots of saturated color on a gray-scaled backdrop.


HAT-P-2b
:

Here are 1.1 MB North Pole, South Pole and Mercator Projection animations of the HAT-P2b vorticity evolution.

HD 80606 b
:

1.1 MB Mercator animation here.

HD 185269 b:

1.1 MB Mercator animation here.

HD 108147 b

1.1 MB Mercator animation here.

HD 118203 b
:

1.1 MB Mercator animation here. The animations above are hosted on the Oklo Corporation’s servers.

It’s interesting to compare the vorticity maps with the temperature distributions on the planetary surfaces (shown in the same order as above):

Gigantic

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The TrES survey announced the discovery of a new transiting planet today, raising the number of known transits to twenty (including Mercury and Venus). The new planet, “TrES-4”, has a mass of order 84% that of Jupiter, and with a radius of 1.67 Rjup, it’s pumped to nearly five times Jupiter’s volume:

The false color image of Jupiter was produced from near-infrared data obtained with the Gemini telescope. The even more luridly false-color representation of TrES-4 is based on a vorticity map from one of Jonathan Langton’s recent simulations.

In order for TrES-4 to be swollen to its current size, it needs to be experiencing heating of order 6×10^27 ergs per second. One way to do this is to have a significant perturbing companion which drives large time-averaged variations in TrES-4’s orbital eccentricity. So far, there are only four published radial velocities for TrES-4, so the orbit could easily be non-circular. More provocatively, if strong orbital forcing is indeed occurring, then there’s a reasonable chance that the perturber might also be observable in transit. I recommend that Transitsearch.org observers keep this bad boy under constant supervision.

Whorls

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HAT-P-2b. The name doesn’t exactly ring of grandeur, but this planet — a product of Gáspár Bakos’ HAT Net transit survey — is poised to give the Spitzer Space Telescope its most dramatic glimpse to date of a hot Jupiter.

HAT-P-2b’s orbit is remarkably eccentric for a planet with an orbital period of only 5.6 days, and by a stroke of luck, periastron is located almost exactly midway between the primary and the secondary transits (as viewed from Earth). The strength of the stellar insolation at periastron is nine times as strong as at apastron, which more than guarantees that the planet will have disaster-movie-ready weather.

On June 6th, Josh Winn and his collaborators used the Keck telescope to obtain 97 radial velocities for HAT-P-2. The observations were timed to occur before, during, and after primary transit, and the Rossiter-McLaughlin effect is clearly visible in their data (preprint here):

The symmetry of the Rossitered points indicates that the angular momentum vector of the planetary orbit is aligned with the spin pole of the star:

schematic diagram showing rossiter effect

This state of affairs also holds true for the other transiting planets — HD 209458b, HD 149026b, HD 189733b — for which the effect has been measured. The observed alignments are evidence in favor of disk migration as the mechanism for producing hot Jupiters.

With its apparent magnitude of V=8.7, the HAT-P-2b parent star is roughly ten times brighter than the average planet-bearing star discovered in a wide-field transit survey. The star is bright enough, in fact, to have earned an entry in both the Henry Draper Catalog (HD 147506) and the Hipparcos Database (HIP 80076), but with its surface temperature of 6300K (F8 spectral type) it was too hot to have been a sure-fire “add” to the ongoing radial velocity surveys. Prior to this May, it had been entirely ignored in the astronomical literature (save a brief mention in this paper from 1969).

HAT-P-2’s intrisic brightness and its planet’s orbital geometry mean that in a relatively compact 34-hour observation, Spitzer can collect on the most interesting features of the orbit with high signal-to-noise. In particular, there is an excellent opportunity to measure the rate at which the day-side atmosphere heats up during the close approach to the star. The planet, in fact, presents such a remarkable situation that a block of Director’s Discretionary time was awarded so that the observations can be made during the current GO-4 cycle. They’ll be occurring soon.

Both HAT-P-2b and HD 80606 b will provide a crucial ground truth for extrasolar planetary climate simulations. Jonathan Langton’s current model, for example, predicts that that the temperatures on HAT-P-2b will range over more than 1000K. At the four times shown in the above orbital diagram, the hemisphere facing Earth is predicted to show the following appearances:

Spitzer, of course, can’t resolve the planetary disk. It measures the total amount of light coming from the planet in chosen passband. At 8-microns, the planet’s light curve should look like this:

The temperature maps only hint at the complex dynamics of the surface flow. A better indication is given by the distribution of vorticity,

which we’ll pick up in the next post…

Showing Mercury the Door (Part 1).

The long-term stability of the planetary orbits has been a marquee-level question in astronomy for more than three centuries. Newton saw the ordered structure of the solar system as proof positive of a benign deity. In the late 1700s, the apparent clockwork regularity of interaction between Jupiter and Saturn helped to establish the long-standing concept of Laplacian determinism. In the late Nineteenth Century, Poincaré’s work on orbital dynamics provided the first major results in the study of chaotic systems and nonlinear dynamics, and began the tilt of the scientific worldview away from determinism and toward a probabalistic interpretation.

In the past ten years, it has become fairly clear that the Solar System is dynamically unstable, in the sense that if one waits long enough (and ignores drastic overall changes such as those wrought by the Sun’s evolution or by close encounters with passing stars) the planets will eventually find themselves on crossing orbits, leading to close encounters, ejections and collisions. The question has shifted more to the following: What (if any) chance is there that the planets will experience orbit crossings within the next 5 billion years?

It’s clear that the probability of the planets going haywire prior to the Sun’s red giant phase is pretty small. Computers are now fast enough to integrate the eight planets forward for time scales of ten billion years or more. Konstantin Batygin, a UCSC physics undergrad who has been collaborating with me, has been running a suite of very long term solar system integrations, and he’s been getting some nice results.

It’s well known that over the long term, the planetary orbits are chaotic. The Lyapunov timescales for the planetary orbits in both the inner and the outer solar system are of order a few million years, which means that for durations longer than ~50 Myr into the future, it becomes impossible to make a deterministic prediction for exactly where the planets will be. . We have no idea whether January 1, 100,000,000 AD will occur in the winter or in the summer. We can’t even say with complete certainty that Earth will be orbiting the Sun at all on that date.

We can, however, carry out numerical integrations of the planetary motions. If the integration is carried out to sufficient numerical accuracy, and starts with the current orbital configuration of the planets, then we have a possible future trajectory for the solar system. An ensemble of integrations, in which each instance is carried out with an unobservably tiny perturbation to the initial conditions, can give a statistical distribution of possible long-term outcomes.

Here’s a time series showing the variation in Earth’s eccentricity during a 20 billion year integration. In this simulation, the Earth experiences a seemingly endless series of secular variations between e=0 and e=0.07 (with a very slight change in behavior at a time about 10 billion years from now). The boring, mildly chaotic variations in Earth’s orbit are mostly dictated by interactions with Venus.

Mercury, on the other hand, is a little more high-strung.

These two plots suggest that the Solar System is “good to go” for the foreseeable future. Indeed, work by Norm Murray and Matt Holman suggests that the four outer planets have a dynamical lifetime of order one hundred quadrillion years. Work by Jaques Laskar, however, suggests that the inner solar system might be on far less stable footing. Konstantin has obtained some very interesting new results on this particular point, which we’ll be sharing in an upcoming post…

HAT-P-3b

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The HATNet survey’s latest single, “3b” landed on the charts last week at #12. This hot (Teff~1053K) new disk shows a definite metal influence, which makes sense, given that [Fe/H] for the parent star is an Ozzy-esque +0.27. You can get a free download of the paper from the Extrasolar Planets Encyclopaedia.

The past twelve months has seen the inventory of known transiting planets more than double, as wide-field surveys such as TrES, Exo, and HATnet start to reach the full production end of their observational pipelines. As the number of planets reaches the threshold for statistical comparisons, interesting trends (or possible trends) have started to emerge.

By far the most remarkable correlation, however, has been with respect to sky location. Among the fourteen fully announced transiting planets orbiting stars with V<14, every single one is located north of the celestial equator.

Planet

Mass

Mjup

Period

days

Dec V
Gl 436b 0.07 2.64385 +26 42 10.68
HAT-P-1 b 0.53 4.46529 +38 40 10.4
HAT-P-3 b 0.61 2.8999 +48 02 11.86
HAT-P-2 b 8.64 5.63341 +41 03 8.71
HD 149026 b 0.36 2.8766 +38 21 8.15
HD 189733 b 1.15 2.21857 +22 43 7.67
HD 209458 b 0.69 3.52475 +18 53 7.65
TrES-1 0.61 3.03007 +36 38 11.79
TrES-2 1.98 2.4703 +49 19 11.41
TrES-3 1.92 1.30619 +37 33 12.4
WASP-1 b 0.89 2.51997 +31 59 11.79
WASP-2 b 0.88 2.152226 +06 26 11.98
XO-1 b 0.9 3.941534 +28 10 11.3
XO-2 b 0.57 2.615838 +50 13 11.18

Looks like there’s some opportunity down under…