systemic

This post continues the oklo.org posts: (1) the black cloud, and (2) disks.

There are two competing, completely distinct theories that describe how a giant planet like Jupiter can be generated from a protostellar disk of gas and dust. The first theory, formation via gravitational instability, lends itself to large-scale hydrodynamical simulations and extraordinary animations that can be downloaded over the Internet. It’s an easy theory to grasp. The second theory, formation via core accretion, presents a more complicated chain of events, but nevertheless contains the story that seems (in my opinionated opinion) to be most nearly correct. Let’s look at what these two theories say, and let’s examine the evidence in favor of and against each.

In the gravitational instability picture, the outer lagging remnants of the molecular cloud core fall in and land on the protostellar disk, causing it to grow in mass. As the disk mass increases, it begins to be influenced by its own gravity. That is, it starts to feel a tendency to fragment in response to its own weight. Simultaneously, the pressure of the gas in each nascent fragment pushes back and partially offsets the fragment’s inclination toward collapse. Pressure thus acts as a small-scale stabilizing influence against collapse. In addition, the differential rotation of the disk (material closer to the star orbits faster) tries to sheer a growing fragment apart. Differential rotation thus acts as a large-scale stabilizing influence against gravitational collapse.

The question boils down to the following: Does gravity win, allowing a Jupiter-mass planet to rapidly form as a condensation in the disk, or do shear and pressure win, keeping the disk free of giant-planet fragments?

The situation lies within the general framework of a linearized hydrodynamical stability analyses, and can be analyzed mathematically. The analysis leads to a so-called stability criterion, the famous Toomre Q:

Where c_s is the sound speed in the disk, kappa is the epicyclic frequency, G is Newton’s gravitational constant, and sigma is the disk surface density. If Q<1 at any radius in the disk, then the disk is unstable with respect to m=0 (ringlike) disturbances. If Q is slightly greater than 1, computer simulations show that the disk is prone to strong non-axisymmetric instabilities, and hence experiences exponential growth of disturbances and eventual fragmentation.

As with any seemingly abstruse physical phenomenon, The disk instability analysis can be illuminated with an analogy. In this case, the appropriate analogy involves a rock band, a house party, kegs of free beer, and uninvited punks and thugs.

Neophyte rock bands need to attract audiences for their shows. Hence, they need to provide inducements. Free beer does the trick. Free beer, or more precisely, flyers posted all over a college campus advertising a party serving free beer, act in analogy to the self-gravity of a disk. As I have discovered (through direct experience, back in my reckless, rock-band fronting youth), such a course of action can lead to instability. If you flyer a campus with news of free kegs, then dozens to hundreds of punks and thugs, whom no-one has ever seen before, and whom no-one wants to see again, will descend upon the hapless band’s house-party show. Amplifiers are destroyed. Holes are kicked in sheetrock. The cops show up, and the band does not play. This outcome can be profitably compared to a disk that undergoes a gravitational collapse into Jovian-mass fragments.

[Above: Our bass player (at a show of ours that was shut down by the cops after several songs). He later graduated with a Ph.D. in Physics, after defending his dissertation on 2D quantum black holes.]

In practice, however, the police do not always show up at house-party shows. Sometimes, the band gets to play. This happier outcome is abetted by two stabilizing effects. Just as in the case of the disk gravitational instability, one of these stabilizing effects operates on large scales, and the other operates on small scales. On the large scale, one can create an analog of “differential rotation” with a lack of specificity on the flyers regarding the precise time of the show. Punks drift in. They see that they don’t particularly like how the band sounds. They see the long lines to the kegs. They drift away. The band plays its entire set to a modest audience, and the cops don’t show up. Support on small scales, the analog of “pressure” is provided by a quite different effect: body odor. The thugs that show up invariably smell poorly, and the unpleasantness associated with a sweaty throng of them will drive some away. If the pressure is high enough, that is, if the thugs smell badly enough, then the show proceeds, and instability is again averted.

For readers familiar with the linearized analysis that leads to the Toomre Q criterion, here’s an illustration of how the analogy can be applied to the standard WKB dispersion relation:

In a future post in this series, we’ll explain why the weight of observational and theoretical evidence seems to be shifting against the gravitational instability hypothesis. The computer simulations, which become ever more impressive with each inexorable tick of Moore’s law, show that in order for fragments to form and then last as planets, the rate of cooling in the disk must be extremely efficient. Rapid cooling robs a nascent fragment of its ability to produce pressure, and hence permits gravitational collapse. Perhaps more importantly, the computer simulations also show that a disk will suffer from a whole panoply of instabilities before its mass grows large enough to trigger the full-blown collapse of Jupiter-like planets.

These instabilities take the form of spiral waves of the same type that occur in spiral disk galaxies such as M51, shown in the HST photo at the top of the post. In a protostellar disk, the spiral wave action pushes pulse after pulse of gas out of the regions of the disk that are in the most danger of fragmenting directly into planets. Some of this gas is forced to large distances from the central star, while the majority flows inward and eventually winds up on the star. In all likelihood, most protoplanetary disks manage to avoid direct fragmentation.

Frequent visitors to oklo.org will have noticed that the new posts have dried up over the past several days. I was out of town to attend the 2nd annual Mitchell Institute Symposium at Texas A&M. This is a conference that brings together speakers from a broad range of sub-disciplines in Astronomy and Physics. Ten gallon hats off to Texas! I had a great time. Warm weather, informative talks, and the Aggies all called me “Sir”. My plan for next week is to get the UCSC Banana Slugs to start up with that tradition.

As part of the conference, I was asked to give a public talk on Extrasolar Planets. It was an all-day scramble on the laptop to get all my slides together into a coherent whole, but the talk ended up being a lot of fun. The audience was highly informed and engaged. The TAMU Physics Department definitely got the word out. I was completely stunned this morning to find that I was on the the front page of the Bryan-College Station Eagle, and I was even recognized at the College Station Airport cafe while I was waiting for my flight out. Unbelievable.

Here’s a link to a quick-time movie, as well as a .pdf file with the slides that I showed during the talk. I’ve also put the sound files (you had to be there to know what I’m talking about) here, here, and here in .wav format. A future oklo post will go into much more detail about what’s being heard in these files, and how they are generated.

If you’re new to the site, here’s a bit of information. Oklo.org is the home base for the systemic collaboration, which is a public participation research project aimed at obtaining a better characterization and understanding of extrasolar planets. Everyone is invited to participate, and details and updates are given regularly in our systemic faq posts.

We have been developing both the oklo.org site, as well as the systemic console using a Mac OS-X platform. We have been testing both the site and the console using Internet Explorer, and we have gotten generally good results, but it is clear that some users are experiencing problems. We are working hard to clear these issues up. We’re astronomers by trade, and, and sadly, at the moment, it’s strictly amateur hour when it comes to website development. As an example, you should see a menu of links directly to your right. I recently saw the oklo.org site on a Windows-IE combination in which the links had been mysteriously pushed all the way down to the bottom of the page. I had to scroll all the way down to even see them.

Also, if you are a Macintosh user, run the console in Safari. There is a still a Java issue with the Firefox on OS X. Firefox should, however, work fine on both Linux and Windows machines if your Java libraries are up to date…

In early June of 2001, I was sitting at my desk at the NASA Ames Research Center trying to debug a computer simulation. Outside my window, the traffic was gridlocked on Highway 101. The distant folds of the Diablo Range shimmered in the California Sun. The phone rang, jarring me out of my abstracted state of mind.

“Dr. Laughlin? Its Robin McKie of the London Observer.”

His voice seemed friendly and reasonable, and I’ll admit that I was pleased to have warranted a call from an overseas reporter. To the best of my recollection, our conversation started something like this:

“Well the reason I’m calling is because I recently saw an abstract of your work concerning this so-called idea of `Astronomical Engineering’, and I was wondering if you could take a few minutes to fill me in on what its all about?’’

Read more…

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

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

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

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

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

Read more…

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

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

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

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

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

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

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

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

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

The orbits of the two planets look like this:

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

Maybe.

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

One evening last August (0. 12. 19. 12. 10. 10.) I was filling my car with gasoline. Venus hung low and bright above the horizon in the deep blue twilight. In the foreground stood the glowing red and yellow symbol of Shell Oil. Swirling coils of aromatic hydrocarbons dissipated in the cool marine air.

The ancient Maya were obsessed with Venus. At the times when it was visible, they covered windows and doorways to protect against its rays of mirrored sunlight.

Venus’ brilliance in our skies arises partly because of its proximity, and partly because it is completely covered with thick white clouds that drift through the upper layers of a CO2 atmosphere roughly 100 times more massive than Earth’s. Venus, however, may not always have been so inhospitable. The high Deuterium to Hydrogen ratio in its atmosphere indicates that it has lost a lot of water. It is possible that during the first billion years of the Solar System’s history, Venus had liquid water, perhaps even an ocean, on its surface. If this was the case, then Venus shone down with less brilliant menace in the Archean skies.

In two, or perhaps three billion years from now, the Earth will have shared Venus’ fate, and will glow with pure-white intensity in the salmon twilight of the Martian evenings.

(Note: the above image of Venus in transit is a screenshot detail from a .jpg image on the website of the Venezuelan Centro de Investigaciones de Astronomia.)

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

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

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

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

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

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

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

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

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

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

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

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

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

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

There’s a new data set on the Systemic Console. To access it, launch the console, and select systemic002 from the system menu (it’s the second from the bottom of the list).

Let’s just say I’ve often wondered whether these particular data can be modeled by a stable planetary system.

Yesterday’s post talked about how Young, Binzel and Crane (2001) used high-cadence photometric observations of Charon transiting the disk of Pluto to construct a two-color image of Pluto’s surface. Transiting extrasolar planets can be employed in a similar way to create an image of the strip of stellar surface that lies beneath the path of an occulting planetary disk. Resolution-wise, this procedure is the effective equivalent of a satellite in low-Earth orbit making a detailed image of a stripe across a sand grain sitting on the Earth’s surface.

In 2001, Tim Brown and his collaborators used the STIS spectrograph on Hubble Space Telescope to obtain what has become an iconic composite light curve of the HD 209458 b transit. It’s probably fair to say that the majority of talks given by astronomers on the general topic of extrasolar planets have a powerpoint slide that shows the Brown et al. data. (The astro-ph version of their article is here).

Here’s a figure (done in Adobe Illustrator, like all of the other www.oklo.org diagrams) that shows their data:

The Brown et al. light curve contains 684 time samples spaced at an average cadence of 80 seconds with a relative precision of one part in 10,000 per photometric data point. (This photometric accuracy is easily good enough to detect the transit of an Earth-sized planet across the face of a Solar-size star if one knew when and where to look.) Because HST can only observe for about half of its 96.5 minute orbit, and because the transit lasts 184.25 minutes, the light curve was obtained by stitching together photometry from groups of observations obtained on four separate transits that took place between April 25 and May 13, 2000.

An interesting feature of the above diagram is that the transit light curve does not have a flat bottom. This results from brightness variations on the surface of the star itself. Stellar disks display a phenomenon known as limb darkening. If you can resolve a star (as one effectively does when one obtains a photometric light curve of a transit) you see that the center of the stellar disk is brighter than the edges. This effect occurs because when one looks at the stellar limb, the line of sight samples higher, cooler layers of the stellar atmosphere. When one looks straight at the middle of the star, one is seeing further in, to deeper, hotter layers. For a star like the Sun or HD 209458, this effect is quite significant. The intensity at the limb is only about 40% as much as that at the center of the stellar disk. The curved bottom of the time-series, then, could be inverted and processed to construct an image of the surface of the star beneath the planet. Additionally, if the transit is observed through different color filters, then one can build a colored image of the stellar strip.

More recently, Brown and Company have made similar HST observations of the TrES-1 transit. Their light curve in this case shows a bizarre uptick, which causes the transit to resemble a one-toothed grin:

The interpretation of this feature is that the planet covered up a starspot as it traversed the face of the star. Starspots — that is, sunspots on other stars — are cooler, and hence dimmer than their surroundings. When a starspot is occulted by the planet, the fraction of blocked starlight decreases. Photometric light curves really do give us an image of a strip of the stellar surface.

For those who prefer not to shave with Ockham’s razor, there’s a second, rather more exotic interpretation of the TrES-1 transit light curve. It’s possible (although highly unlikely!) that a second, longer-period, planet was also transiting TrES-1 at the time when the uptick in the light curve was recorded, and that the inner (known) planet happened to pass underneath the outer planet, as seen from Earth. According to Tim Brown (during a talk I heard him give in Japan) this model, while crazy, does just as good a job of fitting the photometric data!

TrES-1 is an 11.8 magnitude star, and the transits are thus highly suitable for measurement by amateur astronomers using the technique of differential aperture photometry. On the transitsearch.org website, there’s an extensive discussion of amateur observations that were made in the months following the discovery of the transit by Alonso et al. Many of these amateur light curves show strange asymmetric features. It’s likely that they were also observing the planet crossing over starspots. If this was indeed the case, then the 2-planet interpretation of the “tooth” can be safely ruled out.

I should emphasize that transit observations using HST are of blockbuster-level scientific value. The exquisite HST photometry allows a very accurate measurement of the planetary radius, which in turn puts strong constraints on our theoretical models of the planetary interior (see this post for more information). The transit also strongly constrains the elements of the planetary orbit, and the color-dependence of the light curves permits the measurement of atmospheric constituents such as sodium and carbon monoxide.

The above diagram for the TrES-1 transits is adapted from a review article entitled, When Extrasolar Planets Transit their Parent Stars that I co-authored with Dave Charbonneau (Harvard University), Tim Brown (The High Altitude Observatory), and Adam Burrows (The University of Arizona). It will be published in the forthcoming Protostars and Planets V Conference Proceedings.

Here at www.oklo.org we strive to keep things on the positive tip, but I do have one disappointing piece of news to report. I was a Co-I on Tim Brown’s recent HST Cycle 15 proposal to obtain a high-precision photometric time series of the HD 149026 b transit. The resulting light curve would have had higher photometric precision than both the TrES-1 and HD 209458 b time series shown above. The light curve would have had a higher cadence, the individual points would have been good to about one part in 20,000. (At magnitude 8.16, HD 149026 is about thirty times brighter than TrES-1, and the new ACS camera on HSTT is better-suited to the photometric transit-measurements that the defunct STIS spectrograph that was used by Brown et al. for HD 209458). Unfortunately, we learned yesterday that the proposal was not accepted. This is a bummer. An HST transit light curve would have dramatically improved our characterization of the planet that has already provided the first incontrovertible evidence for the core-accretion mechanism of giant planet formation. I think that the HD 149026 light curve would likely have been as informative as the Brown et al. HD 209458 light curve, which was recently shown as #4 in the list of Hubble’s top ten scientific achievements.