Archive for December, 2005

systemic 001

December 27th, 2005 1 comment

saturn as seen by the approaching cassini probe (nasa/jpl)

The goal of the systemic research collaboration is to improve our statistical understanding of the galactic planetary census. This will be accomplished through a large-scale simulation in which the public is invited to participate.

At the core of the systemic simulation, we have generated a realistic catalog that contains 100,000 stars, and we have created planetary systems in orbit around some of these stars. As the collaboration unfolds, the systemic catalog of stars will be “observed” using a realistic model of the radial velocity technique, and a radial velocity data set for each star will be made available. Participants will use the systemic console (or their own software if they choose) to discover and characterize planets within the data sets.

The measured orbital properties and distributions of the planets that are uncovered in the systemic data sets will eventually be compared with the known properties of the planets that were placed into orbit around the systemic catalog stars.

Why the name systemic?

We have four answers: (1) The collaboration utilizes a planetary system integrator console. (2) We are seeking to better understand the statistical distribution of planetary system initial conditions in the galaxy. (3) We hope that the collaboration will make the analysis of extrasolar planetary systems more evident, “Ahh, now I see!” (4) Finally, and most importantly, the planetary systems that we have designed are fully internally consistent. (More on this later.)

The project will officially start in early 2006. In the meantime, we have released a beta version of the systemic console, along with three tutorials (1, 2, and 3). The site is also a weblog where we’ve been posting a variety of articles on the topic of extrasolar planets and their detection and characterization.

Currently, the systemic console has access to a number of published radial velocity data sets for real stars containing known planetary systems. We have also added the first star of the systemic catalog (which coincidently shows definite indications of harboring a planetary system). Launch the console, choose systemic001 from the system menu, and use the comment space for this post to let us know what you find!

— The Systemic Team,

Greg Laughlin — UC Santa Cruz

Stefano Meschiari — University of Bologna

Eugenio Rivera — UC Santa Cruz

Paul Shankland — US Naval Observatory

Aaron Wolf — UC Santa Cruz

Categories: systemic faq Tags:

i wish i had an evil twin

December 21st, 2005 Comments off


A hundred, or even fifty-five years ago, it was thought that Mars and Venus might both harbor complex life, and the aspirations of science fiction writers and adventurers were pinned squarely on those two worlds. With the advent of space probes, however, we visited these planets, and the dream of lush sister worlds orbiting our own Sun was shattered. Mariner 2 reported the hot sulfurous truth about Venus; the crushingly poisonous atmosphere has no water and is hot enough to melt lead. Mars, when brought into focus by the Mariner and Viking probes, was only somewhat less disappointing. Aside from flood channels that have been bone-dry for billions of years, and the faint possibility that microbial life clings to the fringes of hypothesized hot springs, Mars has little to offer in the way of luxurious alien romance. For this, we must turn to other planets around other stars.

But we can still speculate. What would have happened if our solar system harbored a second, truly Earthlike, truly habitable world? What if there had been a genuine marquee destination for the cold war rockets?

Is such a planetary configuration dynamically feasible? We know that the continuously habitable zone around a star like the Sun may be relatively narrow. Is it possible to fit two Earth-mass planets within? More specifically, what would happen if we placed an exact copy of the Earth in the Earth’s orbit, with Earth’s orbital elements, and with the only difference being a 180 degree advance in the mean anomaly. In other words, what would the dynamical consequences be if Earth had a twin on the other side of the Sun?

In 1906, the German astronomer Maximillian Franz Joseph Cornelius Wolf discovered an asteroid at roughly Jupiter’s distance from the Sun which was orbiting roughly 60 degrees ahead of Jupiter, and thus forming a point of an Equilateral triangle with Jupiter and the Sun. It was soon realized that the orbit of this asteroid was very stable, since it is positioned at the so-called Jovian L4 point, one of the five stable Lagrangian points associated with the Sun and Jupiter. These points represent special solutions to the notorious three-body problem, and were discovered in 1772 by the Italian-French mathematician Joseph Louis Lagrange. The following diagram was lifted from the wikipedia:

Lagrange points (from Wikipedia)

Wolf named his Jupiter-L4 asteroid 588 Achilles, after the sulky Greek hero of Homer’s Illiad. A year later, August Kopff discovered a similar asteroid, this one orbiting at the so-called L5 point, 60 degrees behind Jupiter. In keeping with the Homeric tradition launched by Wolf, Kopff named his asteroid 617 Patroclus, after Achilles’ gentleman friend and fellow greek warrior. Thus, with fitting cosmic symmetry, the two heroes were immortalized in the heavens to either side of mighty Jupiter.

Later in 1907, Kopff discovered a third co-orbital asteroid of Jupiter, this one near L4, which he named 624 Hektor, in honor of Achilles’ Trojan nemesis. Hubble Space Telescope observations indicate that Hektor is actually a contact binary, HST image of asteroid 624 Hektor
in which two asteroids are effectively glued together by their weak gravity. In 1908, Wolf discovered yet another object (659 Nestor) near Jupiter’s L4 point. It was clear that a whole class of Trojan asteroids existed, and in order to keep things straight, it was decided that asteroids found near L4 would be named after Greeks (the Greek camp), whereas asteroids near L5 would be named after Trojans (the Trojan camp). Hektor and Patrocles, who were thus orbiting in the camps of their respective enemies, were given the unique status of spies.
Nearly two thousand trojan asteroids are now known. Even minor figures such as Hektor’s infant son (1871 Astyanax) are now attached to asteroids, and the Illiad’s roster is nearly completely exhausted. Trojan asteroids of recent province, such as 84709 2002 VW120 are relegated to the status of neutral observers.

The US Navy maintains a website that charts the orbital motion of a number of trojan asteroids. (The Navy’s involvement seems rather appropriate, as it was Helen, whose beauty was sufficient to launch a thousand ships, who touched off the Trojan War.) As a Trojan asteroid orbits the Sun, it also orbits about its Lagrange point by executing two essentially independent librations. The combination of the two librational motions leads to an intricate motion when viewed in a frame that rotates along with Jupiter.

orbit of 1437 Diomedes in a frame that rotates with Jupiter

Back to our hypothetical Doppelganger of the Earth.

In the language of Lagrange, when we place a new world on the opposite side of the Sun from the Earth, we have populated the L3 point. A linear perturbation analysis shows that if an object at L3 is perturbed, then the orbit will drift steadily away from the initial L3 location. That is, the orbit is linearly unstable, in contrast to the the orbits at L4 and L5, which are linearly stable, and hence stick around in the vicinity of trojan points, even when they are subjected to orbital perturbations.

A computer is required to find out what would happen to the orbits of the Earth and our hypothetical twin planet. It turns out that the motion is nonlinearly stable. The Earth and its twin would be perfectly content, and, in a frame rotating with a 365 day period, the motion of the two planets over a period of years would look like this:

horseshoe orbit for equal mass planets

As one planet tries to pass the other one up, it receives a forward gravitational pull. This forward pull gives the planet energy, which causes it to move to a larger-radius orbit, which causes its orbital period to increase, which causes it to begin to lag behind. Likewise, the planet which is about to be passed up receives a backward gravitational pull. This backward pull drains energy from the orbit, causes the semi-major axis to decrease, and causes the period to get shorter. The two planets are thus able to toss a bit of their joint orbital energy back and forth like a hot potato, and orbit in a perfectly stable variety of a 1:1 orbital resonance, known as a horseshoe configuration. The horseshoe orbit is an example of the negative heat capacity of self-gravitating systems, which is one of the most important concepts in astrophysics: If you try to drain heat away from a self gravitating object, it gets hotter.

Here’s a thought. It is dynamically possible that 51 Peg b (or any of the other extrasolar planets that do not transit within the predicted window) is actually two planets participating in a stable 1:1 orbital resonance…

While we’re on the topic of far-out planetary configurations, another type of allowed 1:1 configuration is the 1:1 eccentric resonance, an example of which is shown below. In this situation, two Jupiter-mass planets share the same period, but have very different eccentricities.

1:1 eccentric resonance

Over time, the planets pass their eccentricity back and forth in an endless resonant cycle. If one of these configurations is found orbiting a sun-like star, it will induce a very distinctive radial velocity curve which will allow an unambiguous determination of the planetary masses and inclinations. And you can rest assured that the code that generates the systemic database is fully aware of the different flavors of one-to-one resonance.

This post isn’t yet complete, so check back later if it has caught your interest…

Categories: worlds Tags:

The black cloud

December 11th, 2005 Comments off

We came from a black cloud.

barnard 68

Stated with such conviction and simplicity, the theory of planet formation is as remote and dogmatic as, say, the creation myth of the ancient Greeks: “In the beginning, there was chaos”

Going about everyday life, with the flip-top cell phone, the busy schedule, the cars with soft leather seats, traffic reports on the radio, blogs dissecting politics, the idea of planet formation, the fact that the Earth hasn’t always existed has no chance for a foothold. You must shut everything off and stare at a dark night sky.

Easier said than done. Almost certainly, your night sky does not induce much wonder. Part of my own view, for example, is blocked by the neighbor’s garage. The nearer streetlights are brighter than the full moon, and they suffuse the air in prismatic halos of light. Some stars are visible, even the best-known constellations. Orion in the winter. The Big Dipper. But on the whole, the stars hardly concern us because we can hardly see them.

To see the stars as they are really meant to be seen, you probably need to plan a trip. Look at a satellite image of the country taken at night, or better yet, use a dark sky finder java applet, and drive to the spot on a clear, warm, windless and moonless night. It is a strange condition of our state of affairs that an applet can help us obtain what was once obvious to anyone who simply looked up. A price paid for a modern world of ease and comfort. A perfectly dark clear night is now, quite literally, a commodity.

earth at night

Let your eyes dark-adapt, and then look up. The effect is overwhelming. Stars. So many of them that the bright ones hardly matter. On a truly dark night, the Milky Way is unmistakable. It spills a swath of patchy luminosity across the dome of the sky. A barred spiral galaxy, seen edge-on, and from within. One hundred billion intensely glowing stars, like sand grain jewels, each separated by miles. Faced with this firmament, the idea that we came from a black cloud seems somehow more within the realm of the possible.

Black clouds, giant billowing masses of molecular hydrogen and helium laced with dust of the consistency of cigarette smoke congregate in the spiral arms of the Milky Way. Their centers are frigid, ten degrees Kelvin, and if you could watch a time-lapse movie of a million years compressed into a minute, you would see them billow and boil.

Within a cloud, the cold dense gas is always poised to collapse in on itself under its own weight. Disaster is staved off by the roiling currents in the gas, and the magnetic field lines that thread the cloud. The cloud contains a tiny fraction of charged particles, ions and free electrons that are outnumbered by neutral atoms and molecules by a factor of a billion or more.

Charged particles are tied to magnetic field lines. Motion of charges drags the magnetic field lines along, and vice versa. Magnetic field lines, however, don’t like being compressed or twisted. They have a tendency — verging on insistence — to spring back into shape. This prevents the ions and electrons from joining the gravitational collapse of the cloud. The ions and the electrons, in turn, bounce continuously against the neutral particles in the cloud, and in so doing, delay the great inward crush.

Most of the time, the frantic collisions of the ions are decisive. The great unwieldy black cloud is torn apart by the tidal forces of the galaxy before it can collapse under its own weight. The cloud dissipates like Arizona thunderheads in the face of approaching night. Occasionally, however, the ions and electrons are overwhelmed. Neutral gas slips past their efforts and pools in the centers of the clouds. This process gains momentum, the ions lose their effectiveness, and vast gulfs of the cloud begin to collapse.

HST image of IC 2944

Picture the scene 4.56 billion years ago when the solar system began to form. The atoms that now constitute the Earth have already been forged. Every atom of hydrogen in the molecules of the pre-solar cloud has already seen 9 billion years of history.

For some of that hydrogen, the past was uneventful. Atoms born in regions of the big bang that, by dint of the role of quantum dice, were a few parts in a million less dense than their surroundings were left cool and marooned in the stretches of space between the Milky Way and nearby galaxies. For billions of years, they fell through intergalactic space, to land, by chance, on the disk of the Milky Way just prior to the assembly of the giant molecular pre-solar cloud.

Other hydrogen atoms, some of them now vibrating in molecules massed in aqueous solution in your blood, or indentured to the long-chain monomers that form the polycarbonate shells of laptop computers, have experienced more colorful histories, having flowed, in some cases, in the oceans of now-dead terrestrial planets that orbited ancient generations of stars. Heavy atoms have less ancient pedigrees. The Earth’s carbon comes mostly from soot blown off of red giant stars. The gold was created in supernovae.

As the scene of the formation of the solar system unfolds, a gigantic volume of gas settles gradually into the core of the giant molecular cloud. where increasingly, the magnetic fields are losing their grip. At the center of the cloud, the view of the stars has long since been blotted out. It is utterly black and frigidly cold, but for ears pitched 24 octaves below middle C, it is not silent. The cloud rumbles and groans. The sound is like the ocean, like an earthquake, but it is also beyond simple description, and it permeates the vast stygian gulf.

Eventually, the cloud begins to collapse in earnest. Not all together, but from the center. As the gas in the center begins to form a protostar, the layer just above the center loses its support against gravity and begins to career inward as well. A wave of rarefaction radiates upward, triggering a downward avalanche of gas.

As the collapse picks up speed, a new effect becomes apparent. Gas that has fallen from large distances does not land on the central protostar. Rather, it falls onto a differentially spinning disk, a platter of gas and dust that orbits the actual center. The original protosolar molecular cloud harbored an ever-so-slight random component of rotation, and this rotation is eventually expressed in the form of the spinning protostellar disk. The basic principle — conservation of angular momentum — is what causes the skater to spin so fast when the arms are pulled in. For the protostellar disk, the originally outstretched arms of the cloud extended for a fraction of a light year from from the core.

The idea that the Sun and planets arose from a spinning disk of gas and dust dates to the eighteenth century. Isaac Newton, whose theory of universal gravitation explains the motion of the planets (and is thus the basis of the systemic console), was dismissive of a natural origin for the Sun and Planets. He issued a firm rejoinder against the whole idea of a natural cosmogony.

Where natural causes are at hand, God uses them as instruments in his works, but I do not think them alone sufficient for the creation.

The idea of creation as the product of natural law stems from the free-thinking spirit of the enlightenment. Georges Louis Leclerc, Comte de Buffon, formulated one of the first natural cosmogonies. His idea is that a comet struck the sun, throwing out the material that later condensed into the planets. This theory accounted for the fact that the planets all orbit the sun in the same direction. Immanuel Kant postulated that the planets arose via condensation from a spinning cloud of gas. Kant’s idea was developed later, independently, by Laplace, who imagined that the disk contracted as it cooled, leaving behind a succession of rings that fragmented to form the planets.

The idea that the Earth originally arose from a disk of gas and dust is tough to accept now (other than simply believing it because one has been told) and it was even harder to accept in the 1700s, when evidence was scarce. Laplace, in 1802, explained his theory to Napoleon, who didn’t like it. Napolean angrily exclaimed,

And who is the author of all this?

Thomas Jefferson, furthermore, celebrated as one of our more erudite presidents, had this to say:

Dreams about the modes of creation, inquiries whether our globe has been formed by the agency of fire or water, how many millions of years it has cost Vulcan or Neptune to produce what the fiat of the creator could affect by a single act of will are too idle to be worth even a single hour of any man’s time.

The eighteenth century cosmogonies are couched in quaint language and are not fully correct, but they are nevertheless surprisingly close to the mark. They stand up particularly well when compared to other theories of genesis that were motivated by new technologies of observation. (see for example Regnier de Graaf’s observations and theory of the homunculus). William Herschel and others mistakenly believed that the galaxies and nebulae that they saw through their telescopes were actually solar systems in the process of formation. Saturn’s rings provided another observable manifestation of a disk orbiting a central object. And although the scales are vastly different (a galactic disk is 100 million times larger than a protostellar disk, which is in turn 30,000 times larger than Saturn’s rings) the disks themselves are a ubiquitous phenomenon. They arise whenever material (gas, rocks, dust) crowds into orbit around a central object. By observing how galaxies and planetary rings behaved, but without an understanding of the length scales that were being observed, it was still possible to make reasonable inferences about the behavior of protosteller disks.

Astronomy is inherently simpler than biology.

Categories: worlds Tags:

55’s the limit

December 9th, 2005 1 comment

55 Cancri is an ordinary nearby star, barely visible to the naked eye. Through a modest telescope (or, more practically, with the use of the Goddard Skyview) one sees that it is actually a binary pair.

Goddard Skyview Image of 55 Cancri

55 Cancri “A” (the bright star in the middle of the above photo) harbors an extraordinary planetary system. Indeed, it was the subtlety and the depth of the 55 Cancri radial velocity data set that motivated us to develop the systemic console. The fact that the 55 Cancri system continues to defy easy categorization gives us confidence that the systemic collaboration will be a worthwhile project.

Where to begin?

Click on the system menu on the console, scroll down, and select 55 Cancri. (If you’re unfamiliar with the console, and if you’re the methodical type, there are three tutorials available on the menu bar to the right. Otherwise, just follow along!) The published radial data for 55 Cancri now appears in the main console window. The sweeping spray of points, with its curiously non-uniform distribution, contains a fascinating narrative in its own right.

The very first point in the data set has a timestamp of JD 2447578.73 A Julian Date Converter tells us that this was 9:31 PM on Monday Feb. 20, 1989 (Pacific Standard Time). The observation was obtained by Geoff Marcy at the Shane 3-meter telescope at Lick Observatory on Mt. Hamilton, and the velocity error is 9.7 m/s. Back in 1989, Geoff and his colleague Paul Butler were laboring to improve their iodine cell technique, and were struggling to get enough telescope time to adequately track the motion of about 70 nearby solar type stars with the eventual hope of detecting giant planets.

The first 10 radial velocity points were obtained at a rate of 1 to 3 per year. With hindsight, it is easy to see that these 10 points are ample cause for a planet-hunter to be optimistic. The radial velocity variation in the first 10 points spans more than 100 meters per second, suggesting a signal with a signal-to-noise of at least five. The periodogram of these ten points shows a strong peak at 14.65 days, indicating that the data could be explained by a planet with 80% of Jupiter’s mass, circling on an orbit lasting just over two weeks.

Today, if such a planet were discovered, the announcement would not make the news, and the major excitement would be among amateur transit hunters, who would likely have a new high-priority follow-up candidate with a ~5% transit probability. (A two-week period is right at the borderline where transits can be reliably confirmed or ruled out by the photometric collaborators working with the RV-discovery teams prior to announcement of the planet).

In 1993, however, nobody was expecting to find Jovian planets in 14-day orbits. Conventional wisdom at the time was informed by the architecture of our own solar system, and held that gas giant planets should be found beyond the so-called snowline (located at r=4-5 AU) of the protostellar disk. Although the theory of orbital migration had been studied in considerable detail, nobody had proposed that giant planets might regularly spiral in and then be marooned on very short-period orbits. I don’t know whether Geoff and Paul even considered the possibility that the 14.65 day peak in their data was real. If they saw the peak, it is more likely that they would have ascribed it to an alias, an artifact of their uneven hard-won sampling.

During 1994, the velocities suddenly started to trend upward. This would have seemed rather disconcerting, and may even have raised alarm. Was some unaccounted-for instrumental or astrophysical process affecting the newer radial velocity data? Certainly, at the end of 1994, the case for a planet orbiting 55 Cancri would have been weaker than it had been a year earlier.

Nevertheless, the 55 Cancri campaign was at an important turning point. The last measurement of 1994 (JD 2449793.80) has a remarkably lower error (3.3 m/s) than any of the earlier radial velocities. In November of 1994, the Schmidt camera optics on the “Hamilton” spectograph at Lick Observatory had been upgraded, and the resulting improvement effectively tripled the intrinsic resolution to which the spectral lines could be discerned. With the ability to measure radial velocities to a precision of 3 m/s, the planet search had suddenly entered an entirely new realm. When one is in the business of detecting Jupiters, a velocity measurement with 3 m/s precision is literally 10 times as valuable as a velocity with 10 m/s precision.

In October 1995, Mayor and Queloz announced their discovery of a Jupiter-like planet in a 4.5 day orbit around the nearby star 51 Peg. Due to a catalog error that misclassified 51 Peg as a subgiant, it had not been included in Geoff and Paul’s survey, but they were able to rapidly confirm the Swiss discovery.

All at once, the idea of a gas giant with a 2-week orbit was no longer outlandish at all. The telescopes on Mt. Hamilton, which had been slipping inexorably in worldwide prestige as larger telescopes were built on higher mountains, were suddenly at the forefront of relevance. The Lick 3-meter telescope-iodine-cell-spectrograph combination was the best instrument in the world for obtaining precision doppler velocities of bright stars such as 55 Cancri. Extrasolar planets were front page news. Alotments of telescope time increased dramatically. In the six months running from December 1995 through May 1996, 55 Cancri was observed 41 times at Lick. This drastic increase in the cadence of observations is easily visible in the radial data:

1996 RVs

With the 41 high-quality observations, the presence of the 14.65 day planet was obvious in the power spectrum.

RV powerspectrum

In October 1996, Paul, Geoff, and several other collaborators announced the discovery of the 14.65 day planet, and in January 1997, they published the discovery in a now classic paper that also introduced the world to the inner planetary companions of Tau Bootes and Upsilon Andromedae.

With eight years of data, it was clear that other bodies were present in the system. In the discovery paper, Butler et al. wrote:

The residuals exhibit a long-term trend, starting at -80 m/s in 1989 and climbing to +10 m s-1 by 1994 (the velocity zero point is arbitrary). The velocities appeared to decline toward 0 m s/1 during the past year, although at least another year of data will be required for confirmation. This trend and the possible curvature in the velocity residuals are consistent with a second companion orbiting HR 3522 [aka 55 Cancri] with a period P > 8 yr and M sin i > 5MJUP.

This speculation proved to be correct. Use the console to get a best-fit for the 14.65 day planet, and compute the periodogram of the residuals to the fit:

RV residuals powerspectrum

The strongest remaining peak is at 4260 days, corresponding to an 11.7 year orbit (very similar to Jupiter’s 11.8 year orbital period). Keeping the orbits circular, use the “polish” button to produce a Levenberg-Marquardt optimized fit. Zoom in and scroll to show the time interval between 1996 and 2002. The gaps each year when the star is behind the Sun as seen from Earth are easily visible:

Lick RVs 1996-2002

The two planet system does quite a reasonable (but by no means perfect) job of reproducing the observed radial velocities. After the announcement of the first planet at the end of 1996, interest in the star died down to some degree. The number of target stars being observed at Lick was being increased as Debra Fischer stepped in to manage the Lick Survey, and other systems, especially Upsilon Andromedae, were clamoring for telescope time. During the 1998 season, 55 Cancri was observed only twice. By 1999, however, the Upsilon Andromedae system had been sorted out, and renewed attention was focused on 55 Cancri. During 2000 and 2001, it became clear that the system likely contained at least three planets. With the 14.65 and (in my fit) 5812 day planets removed from the radial velocity curve, the residuals periodogram shows a peak at 44.3 days:

residuals of the residuals

The signal from the 44.3 day planet is not as strong as for the other two planets, but a large number of velocities from 2002 seemed to clinch the case for this third planet:

residuals of the residuals

Use the console to optimize the three planet fit using circular Keplerian orbits. When I do this, the chi-square statistic is reduced to 6.4, and the rms scatter is 12.5 m/s. The fit is still not perfect. Either the planets are eccentric, or there are additional planets in the system.

Categories: detection, systemic faq Tags:

Why does HD 209458 b wear an XXL?

December 8th, 2005 Comments off

extrasolar planetary transit

In 1999, the sun-like star HD 209458 was discovered to harbor a transiting planet on a 3.52 day orbit. This was a big deal. The recurring occultations permitted, for the first time, an accurate measurement of both the radius and the mass of an extrasolar planet, and there have been a huge number of follow-up observations of the transits using a variety of telescopes and techniques. The most impressive result came from Brown et al. (2001), who used the (now defunct) STIS instrument on the Hubble Space Telescope to obtain a photometric light curve that has precision of about one part in ten thousand per 80-second sample:

extrasolar planetary transit

The plot above can be found in the Astrophysical Journal , or, alternately, the paper containing the plot is available for free at the arXiv preprint server. A careful analysis of the photometric curve and the radial velocity data (which can be explored using the systemic console), combined with estimates for the size, mass and other properties of the parent star, indicates that the planet, HD 209458 “b”, has a radius about 1.35 times larger than the radius of Jupiter, and a mass of 0.69 times Jupiter’s mass. The temperature on the surface of the planet should be a toasty ~1200 K.

Various teams of scientists, including a group led by Peter Bodenheimer here at Santa Cruz, and independent groups led by Tristan Guillot and Gilles Chabrier in France, and Adam Burrows’ group in Arizona have all developed detailed computer programs that can predict how planets respond when placed in different physical environments. Everybody agrees that a gas giant planet with a standard hydrogen-helium composition and the mass and surface temperature of HD 209458 b should have a radius (corresponding to the 1-Atm pressure level) that is about 5-10% larger than Jupiter. The observed size of the planet is thus far out of agreement with the theoretical models. The planet is too large!

As soon the size problem became clear, a number of explanations for HD 209458 b’s large radius were put forward. The Burrows group (2003) pointed out that the planet may appear large during the transit because we are looking obliquely through long path lengths in the planetary atmosphere. Tristan Guillot and Adam Showman (2002) suggested that the ferocious winds on the planetary surface are transferring energy into the deeper layers of the planet, and that this extra source of energy is enough to bloat the planet to its observed size. These two phenomena don’t require anything special about HD 209458 b, and so both hypotheses predict that other planets with similar masses and temperatures should have similarly inflated radii. This doesn’t seem to be the case, however. In August 2004, a transiting planet of very similar mass and temperature was found in transit around an 11.8 magnitude star known as Tres-1 (Alonso et al. 2004). This planet has exactly the size (~1.05 Jupiter radii) predicted by the baseline theories. It thus appears that there is something unusual about HD 209458 b.

One intriguing possibility, suggested by Peter Bodenheimer, Doug Lin and Rosemary Mardling in 2001, is that another planet exists further out in the HD 209458 system. This planet would be exerting gravitational perturbations on HD 209458 b, which would cause its orbit to maintain a small eccentricity. If a planet like HD 209458 is in an eccentric (non-circular) orbit, then it experiences significant tidal stretching and squeezing which generate heat in the planetary interior. In a follow-up paper published in 2003, Bodenheimer et al. calculated that an orbital eccentricity, e=0.03 would likely be sufficient to generate enough tidal heating to inflate HD 209458 b to the observed size.

At that time, there were only 30 high-precision radial velocity measurements of HD 209458, and it was easily possible to find 2-planet fits to the radial velocity data which had (1) a small non-zero eccentricity for HD 209458 b, as well as (2) a second planet with a period of order 80 days, and a mass of ~0.12 Jupiter Masses. In the following diagram, the orbits are to scale, but the star and especially the planets are grossly too big.

a perturbing body

Over the past two years, the California-Carnegie Planet Search Team used the Keck telescope to obtain a number of additional radial velocity measurements of HD 209458, and these have been published in a new paper. The full set of (out-of-transit) measurements have been loaded into the system menu of the systemic console. In our paper, our conclusion was that HD 209458 b is likely the only RV-detectable planet in the system, and that its orbit is most likely circular (more on this in a future post). See, however, if you can use the console to find viable 2-planet fits that have the correct period for the inner planet P=3.52474541 d, and which have a required RMS jitter for the star of less than 5 m/s. (Technically, you should also apply a simultaneous constraint on Mean Anomaly and eccentricity that arises because the time of central transit is known very accurately, but the console doesn’t yet have this capability. If you find a good fit, and post it here, we can likely fold in the additional timing constraint without greatly changing the basic orbital parameters).

The number of known transiting planets has been increasing steadily, and the total now stands at nine. Using the results of Peter Bodenheimer’s planetary structure code, we can compare the planets predicted sizes with their observed sizes:

the properties of the known transiting planets

(Here’s a larger-size .pdf of the above table, which will appear in an upcoming PPV review article). Three of the planets in the table, HD 209458b, HD 149026b, and HD 189733b, have radii that do not agree at all with the predictions. HD 209458b (and to a slightly lesser extent) HD 189733b are both larger than predicted, whereas HD 149026b is too small, likely because it has a huge rocky core:

a size comparison

These discrepancies indicate that the bulk properties of the transiting planets must depend significantly on factors other than their mass and estimated effective temperatures. Like the planets of our solar system, the extrasolar planets are imbued with interesting individual personalities.

Categories: detection Tags:

fresh extrasolar planets

December 8th, 2005 Comments off

fresh extrasolar planets

In a recent article appearing in the Astrophysical Journal, Vogt et al. (2005) published radial velocity data for six stars that appear to harbor multiple low-mass companions. The data for all six stars (HD 37124, HD 50499, HD 108874, HD 128311, HD 190360, and HD 217107) have been added to the system menu of the Systemic Console:

new systems in the console

If you’ve worked through the console tutorials 1, 2, and 3, take a crack at using the console to fit these systems. HD 37124, in particular, is open to several different stable 3-planet configurations. In my current personal favorite fit, three very nearly equal-mass planets are caught up in an endless (or at least multi-billion year) cycle of rub-a-dub-dub. An .mpg animation of the long-term dynamical evolution of the orbits is here. Because the planets in this particular fit are fairly widely spaced, the motion is quite well described by second-order secular theory.

Categories: detection, systemic faq Tags:

i wear my sunglasses at night

December 5th, 2005 Comments off

Of all the photographs that our robot emissaries have radioed back to Earth, my vote for the most stunning is the Hubble ACS image of the “Sombrero Galaxy”, M104. The glow of its halo makes the the idea of 100 billion stars seem comprehensible.

HST ACS mosaic of M104

It’s important to remember, however, that the Hubble image is actually a long CCD time-exposure to light gathered by a 240 cm mirror. If you could be somehow transported to a location in space where M104 looms large in the sky, you would see that HST imparts a severely inflated expectation. From a distance, say, of 300,000 light years, M104 would be so dim that you would see only a faintly ominous, faintly glowing flying saucer.

Approximate naked-eye view of M104 from ~300,000 light years distance

Indeed, the great Andromeda Galaxy, M31, subtends an angle larger than the full Moon in the sky, and it is literally almost directly overhead right now (9:36 PM, Dec 3, latitude 36.97 deg N). The storms from earlier this week have blown through. The sky sparkles with brilliant clarity. Yet when I step outside and look up, I can’t see the Andromeda Galaxy at all. It’s too faint. In a 1:10,000,000,000,000 scale model of M31, the stars are like fine grains of sand separated by miles. Our Galaxy, the Andromeda Galaxy, and the Sombrero Galaxy are all essentially just empty space. To zeroth, to first, to second approximation, a galaxy is nothing at all.

A Hot Jupiter, on the other hand, seen at similar angular size, is undeniably impressive.

HD 149026 b in the crescent phase

The dayside, blindingly illuminated by the scorching proximity of the star, is roughly 500 times brighter than desert sand dunes on a midsummer day. In order to look at the illuminated side of the planet at all, you need extremely dark wraparound sunglasses, or better yet, an eyeshield made from #10 welders glass (where #14 welder’s glass is recommended for those who stare at the sun).

With the brilliance of the dayside cut to a manageable level, what would you see? The majority of the light coming from the planet is simply reflected starlight. If the planet uniformly reflects the light that strikes it, then you simply see a blank white surface if the parent star is similar to the Sun, and a yellow-orange to orange-red expanse if the parent star is a cooler K-type or M-type dwarf star.

The gases that make up the outer layers of the planet do not reflect all frequencies of light equally, however. The air of the outer layers of a hot Jupiter is a scaldingly toxic witches brew of hydrogen, helium, steam, methane, ammonia, cyanide, acetylene, hydrogen sulfide, soot, and a whole host of other hardy, reactive, and generally unpleasant compounds.

In our solar system, for example, Uranus and Neptune have distinctive blue-green casts because at the level in their atmospheres where light is primarily reflected, the ambient methane gas is highly effective at absorbing red frequencies. The originally white sunlight is reflected with a blue-green hue by the selective removal of red.

Uranus and Neptune (from Voyager II)

The photo (mosaic) below was obtained by the Cassini spacecraft as it was flung past Jupiter on its way to Saturn. The images were processed to give the same view that the naked eye would see. Jupiter reflects an enormous amount of detail from its cloudy face.

True-color Cassini mosaic of Jupiter

Across the swathes of Jupiter where the visible clouds tower to great heights, the eye sees regions that are frigid, eighty degrees colder than the depths of an Antarctic winter (-200 F). In such a cold environment, icy compounds of Ammonia are stable, and their presence lends the clouds a reddish hue. Jupiter’s Great Red Spot is an example of just such a topographic high.

On other regions of Jupiter’s visible surface, the atmosphere is transparent to greater depths. As on Earth, where clear skies are associated with dry air, so too on Jupiter. When we look down into the drier Jovian regions, we see to lower lying decks of cloud where the temperature is about the same as a chilly Arctic night. Here, the chemistry in the clouds causes their color to tend toward lighter shades, whites, beiges, ochers.

Like any non-transparent object, Jupiter glows with its own radiation. Because the outer layers of Jupiter are so cold, this intrinsic light lies in the infrared. Seen with an infrared detector (such as this view made at 5 microns with the NASA IRTF) Jupiter is a dramatic sight.

IRTF 5 micron image of Jupiter

In the rattlesnakes-eye view, the Red Spot forms an oval of relative darkness. The high clouds act like a blanket that blocks the warmer underlying layers from view. In the infrared, the dry areas, where we see the deepest, glow the brightest. In an ironic twist of fate, the Galileo atmospheric probe parachuted into one of the driest regions of the Jovian atmosphere, a so-called 5 micron hot spot (circled in the image above).

On a hot Jupiter, the surface gas is heated to temperatures in the 1000-1500 K range on the dayside. Computer simulations show that winds of hellacious strength tear continually around the planet, carrying heat from the dayside and disgorging it into the night. The atmosphere on nightside glows brilliantly. Turbulent brick-red whorls merge into fiery tendrils of orange braided with dazzling white.

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A most eccentric character

December 1st, 2005 Comments off

Of all the known extrasolar planets, HD 80606b — in both the technical and the colloquial sense — is the most eccentric. This world has at least five times the mass of Jupiter, and it circles its parent star on an extremely elongated 111.4 day orbit:

planetary orbit for HD 80606 b

Today (as seen from Earth!) HD 80606b is still near the far point of its orbit, at a distance of about 0.85 AU from the central star. The temperature in the upper atmospheric layers of the night-side has possibly dipped low enough so that torrential rains and violent thunderstorms are rumbling across its vast billowing horizons. During the rest of December and through most of January, the planet will fall in almost the full distance to the star, eventually swooping within 6 stellar radii as it whips through periastron. On January 26th, at the moment of closest approach, the temperature at the cloud tops will exceed 1000 Kelvin. The auroral displays will be dramatic beyond compare, and indeed, during the days to either side of periastron passage, it might be worth tuning in to the planet on the decameter band.

The discovery of the planet and its orbital solution were announced by the Geneva Observatory Planet Search Team in an April 04, 2001 ESO press release, and the radial velocities have since been made publicly available (right on!) at the CDS repository (see Naef et al 2001). You can therefore use the systemic console to fit this system and examine how radial velocity curves behave for extremely eccentric orbits.

The star HD 80606 is accompanied by a visual binary companion, HD 80607. The projected separation of the two stars is 2000 AU (fifty times the Sun-Pluto distance). When the HD 80606 b travels through the segment of its orbit that lies between the two stars, the night-side cloud tops of the planet are lit by the distant binary companion to ambient brightness that is very similar to a fully moonlit night on Earth. The two stars have similar masses, sizes, and temperatures to the Sun, but, like many of hosts of short-period massive planets, they are enriched in “metals” (gold, chromium, iron, carbon, oxygen, etc. etc.) by a factor of more than two relative to the solar value.

How did the planet get into its weird orbit?

Wu and Murray (2003) have suggested that HD 80606b’s extreme eccentricity is the result of a three-body interaction known as the “Kozai effect” between the planet and the two stars.

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