systemic

HD 80606 b is one crazy place. With an orbital eccentricity of e=0.932, its orbit resembles a ball tossed almost straight up with a 111.4 day hang time. I’ve heard that in many European countries, periastron passage (when HD 80606 b whips through its closest approach) is known as ’606 day, and is celebrated by a day off work filled with drunken and disorderly parades. I’m trying to bring the tradition over to the United States.

Today (as viewed from Earth) HD 80606 b is just starting to pick up speed on its inward plunge to the next ’606 day, which occurs on August 31, 2006. The planet has spent the June and July cooling off near the far point of its orbit, at a distance of about 0.85 AU from the central star. It’s possible that weather in the upper atmospheric layers of the planet has spawned a street of category 10 hurricanes that will tear unimpeded around the planet until the steadily mounting insolation turns the driving rains into steam. During the month of August, the planet will fall in almost the full distance to the star, eventually swooping within 6 stellar radii as it whips through periastron.

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 are available on both the downloadable systemic console and at the CDS repository (see Naef ef al 2001). The recent catalog paper by Butler et al. (see exoplanets.org) tabulates an additional set of 46 high quality velocities for HD 80606. Using the console to get a joint fit to the two datasets gives an updated set of orbital elements: P=111.4298 days, M=3.76 Jupiter masses, and e=0.9321.

Several years ago, when the California-Carnegie radial velocities for HD 80606 started coming in, Geoff let me have an advance look at them. When I synched the new Keck points up against the Swiss points (which I’d extracted from a published postscript figure) I noticed something interesting. The Keck point obtained on Feb. 2, 2002 was more than 100 m/s above a cluster of Swiss velocities that had been obtained very close to periastron passage.

I got excited. The Keck observation suggested that the magnitude of the periastron swing is larger than had been estimated by the published fit. This in turn suggested that the eccentricity of the planet was even larger than the published value of e~0.93. I did an orbital fit and uncertainty analysis on the combined dataset. The best-fit eccentricity came out at a whopping e=0.971 +/- 0.018. An eccentricity this high implied that the planet was regularly swooping to within 2.5 stellar radii of the star. In order for this to be possible, the so-called tidal Q for the planet would have to be very high — higher than the value of around a million that had been inferred from the orbital circularization radii for the hot Jupiters.

In order to confirm the high eccentricity, it would be necessary to obtain more radial velocity measurements in the vicinity of the periastron swing. In June of 2004, I calculated a list of the upcoming periastron dates, and found that one was scheduled for July 11th, 2004 (UT), just a few weeks away. I looked at the schedule for the Keck I telescope, and saw that the California Carnegie team had been assigned a run covering July 8th, 9th, 10th, 11th and 12th. Then I checked where HD 80606 would be located in the Mauna Kea sky. The star was setting rapidly, and was already fairly far to the west at sunset, with and hour angle of more than five hours, and airmass of about three.

I wrote to Geoff and told him about the combined fit that suggested a high eccentricity. Would the star be high enough above the horizon for Keck to observe? He wrote back right away. He was also computing a high value for the eccentricity, and yes, it would be within the limits of observability if the telescope operator was notified in advance.

In the plot just above, I’ve reproduced the predicted radial velocity curve during the course of the run. The four vertical red lines show 8:00 PM Keck time on July 8th, 9th, 10th, 11th, and 12th, 2004. Amazingly, the fit suggested that during the brief window of observability on July 10th local time (July 11th UT), the star would be smack in the midst of its most rapid acceleration! The radial velocity fit suggested that a standard six-minute exposure started at 07:30 PM on July 10th would span a reflex velocity change of 60 m/s. By contrast, it takes Jupiter 6 years to indude a 12 m/s velocity change in the Sun.

I waited impatiently through the run, eager to learn what the velocities would be. I kept my fingers crossed that the eccentricity would hold up at e=0.97. Money in the bank. Even if the velocities drove the eccentricity down to its 1-sigma low bound, to e=0.953, it would still be an exciting result, with potentially important consequences for the internal structure of the planet.

On July 10th, at 11 pm PDT (8 pm Hawaii time) I sat at my kitchen table, and imagined the scene on Mauna Kea, with the great dome open to the sky, and Keck I leaning practically on its side, straining to catch the rays of a distant star fading into the last moments of twilight. I thought of the planet itself, stellar furnace filling half the sky, literally jerking the star back into space as it screamed through periastron.

On the morning of the 13th, Geoff sent an e-mail with the velocities. The new fit gave e=0.945. I was stunned. What the @#%? I looked at the velocities themselves, On the 10th, on what was supposed to have been big night, the velocity had failed to rise at all from the value on the 9th. On the 11th, the velocity was only somewhat higher. It was clear that the big swing had occurred several hours afterward. On the 12th, the velocity was high, and clearly past the peak. The planet had arrived at periastron slightly more than a full day later than predicted.

The measured eccentricity was 2-sigma low, an occurrence that one expects less than 2.5% of the time. By chance, the high Keck velocity on Feb. 2, 2002 randomly came within one part in 2000 of arriving exactly at the radial velocity maximum. The fitting program interpreted this high point as suggesting a higher eccentricity than the planet actually has.

I was depressed for the next fifteen minutes. As usual, 95 to 97% of the “cool” discoveries that one turns up in the course of scientific life turn out to be spurious. You have to keep throwing your hat into the ring.

For a theorist, the path of least resistance leads to the abstract. I start to think of planets as signal-to-noise, as peaks on a periodogram. As grant proposals come due, as manuscript drafts bounce back and forth between editors, authors and referees, it’s easy to forget that the planets are really out there, falling endlessly through empty space.

On Monday, we drove up to the Lick Observatory. From the hot rush-hour smog of I-680 in downtown San Jose, the summer-yellow folds of the Diablo range rise out of the hazy valley air. The white telescope domes cling to the highest ridgeline. Exit at Alum Rock. Drive several miles east. The city thins out into suburban sprawl. The Mt. Hamilton Road starts just at the point where the mountains begin to slope up steeply. It takes nearly an hour to cover the 19 miles to the summit, where the observatory buildings sleep mirage-like in the quiet sunlight. Hawks circle against the blue sky. The grasses have dried to straw, and the heat draws the smell of sage and pine resin into the still air.

The dome of the Automated Planet Finder is in place now, and the telescope is nearing completion. It’s visible just to the right of the larger three-meter dome in this photo taken from the main observatory building. The Automated Planet Finder will produce long strings of precise radial velocity measurements. Very soon, we’ll be posting synthetic data sets on the systemic back-end that mimic the observational cadences that this telescope will be capable of providing. It will detect some very interesting planets.

The 36-inch refractor, housed in the great dome of the main building, is still in perfect working order, but it has long since ceded it’s relevance to the cutting-edge. In 1892, E. E. Barnard used it to discover Amalthea, the tiny fifth satellite of Jupiter. This was the last moon in the Solar System to be discovered with the naked eye. More than a century later, the telescope waits silent and unused through most nights. The body of James Lick lies interred at its base. Crickets, lodged in unseen corners of the old building, chirp intermittently in the dark.

Support astronomer Bryant Grigsby brought the great refractor to majestic life. To locate an object on the sky, he repeatedly executed a delicately choreographed sequence of maneuvers. The dome must be rotated so that the slit is positioned on the correct part of the sky. The giant polished and inlaid wood floor must be raised or lowered by up to 16 1/2 feet to bring the eyepiece to eye-level. The 25,000 pound, 57-foot long telescope, perfectly balanced on its pivot, is pulled by hand into rough position, followed by a series of fine adjustments to bring the target into view. The great refractor is priceless. If it’s broken or rendered inoperable, it won’t be replaced. Bryant told me that it took many nights to acquire the confidence to maneuver it on his own.

Just before midnight, he swung the telescope low, nearly to its declination limit, and brought Neptune into view. In the high-power eyepiece, it swam, a dim, very pale, bluish-white circle cut out against matte black. Several star-like points were in the field. One of them may have been Triton. Using Illustrator, I’ve tried to capture how it looked.

What I can’t fully capture, though, is what it is like to stare, for long unhurried minutes, at a giant frigid world on the fringe of our Solar System, with the crickets chirping in warm dry quiet of the dome, illuminated faintly by the glow of a low-watt red bulb and a window open to the distant twinkling lights of the city grid.

Potentially the most interesting feature on the downloadable systemic console is the “sonify button”, which integrates the model planetary system specified by the state of the console sliders and produces a .wav format CD-quality audio file of the resulting radial velocity waveform. Not interested in planets? The console is a stand-alone non-linear digital synthesizer. It’s capable of producing strange, remarkable, musically useful sounds. They merely need to be located within the uncountable infinity of solutions to the gravitational N-body problem.

First, use the console to build an interesting multi-planet system (for this purpose, there’s no need to try to fit whatever data is in the window.) Then click the sonify button. This brings up a dialogue window which enables the user to make several specifications for the sound file that is produced.

The most important user-specified parameter is the frequency onto which the orbital period of the shortest-period planet on the console is mapped. If, for example, the innermost planet has a period of 365.25 days, then a 440 Hz map will play 440 years worth of evolution in one second. (440 Hz corresponds to the A below middle C.) Mapping the radial velocity curve onto a high-frequency note extends the total number of orbits that go into the sample, and thus increases the integration time required to produce the sample. You can also specify the length of the sample, and you can exert simple control over the attack and decay rate of the envelope for the overall waveform.

Once you’ve produced the soundfile, it appears in the “soundClips” subdirectory within the systemic parent directory. Both of these directories are automatically created when you download and expand the console — see the instruction set for the downloadable console for more details. With a Macintosh, you get the best results if you play the sample right from the folder. i-Tunes seems to want to convert the samples to .mp3 format in a manner that introduces audible noise, and we’re not yet sure how to resolve this issue.

To the extent that planets orbit independently of one another, the console behaves like a simple additive synthesizer, in which the individual Kepler waveforms add to form a composite sound. Much more interesting, is the situation when planets experience significant gravitational interaction, leading, for example, to resonance and to nonlinear instability (here are examples, 1, 2, from the resources page of both types of waveforms). Close encounters provide discontinuities between individual blocks of sound that resemble the results of granular synthesis.

The strongest 2-planet mean-motion resonances occur when the pair of planets share a common period and engage in a one-to-one resonant motion. There are a variety of different one-to-one resonances, including binary planet orbits (e.g. Earth and Moon), trojan configurations, and generalizations of retrograde satellite orbits. In this last catefgory, one can have two planets with the same semi-major axis, but with different eccentricities. If one starts the planets in the following configuration, then the motion is dynamically stable, and evolves in a complicated way over time.

The motion leads to an interesting audio wave-form, in which you can hear the system cycling between configurations in which both planets are modestly eccentric and configurations in which one orbit is nearly circular while the other one is highly eccentric. As a specific example, set the console to the following configuration: P1=P2=10 days, M1=M2=0.3 Mjup, MA1=180., MA2=190., e1=0.9, e2=0.1, long1=0.0, long2=0.0. If you increase MA2 to about 225 degrees while keeping the other parameters fixed, you’ll hear the system go unstable.

Evolving, high-eccentricity orbits tend to have an insect-like quality, which brings to mind the 1986 album, The Insect Musicians, by Greame Revell (formerly of SPK). From the album jacket:

For the two years 1984-85, Graeme Revell travelled from Australia to Europe, to Africa, Indonesia and North America recording and negotiating copyrights of insect sound recordings. It took another full year sampling and metamorphosing some fourty sounds thus gathered using the Fairlight Computer Musical Instrument, to produce this record. The only sounds used are those of insects, altered digitally and combined into a unique orchestra of instruments, an orchestra of strange and delicate timbres, music of natural rhythm and texture.

Image Source.

Back in March, I wrote about how the systemic console could be used to locate a tentative second planet orbiting 51 Peg. The power in the residuals periodogram, and an extensive Monte-Carlo analysis show strong evidence for a Saturn-mass world in a habitable-zone orbit. I was thus quite excited on Saturday when the California-Carnegie group released a heavy-hitting catalog paper that includes (among many other interesting things) 256 re-analyzed Lick Observatory velocities for 51 Peg. These velocity data points are of high quality, with generally small errors.

After using the console to fit out 51 Peg b, the residuals periodogram for all the data still shows a strong secondary peak. The period has shifted, however, to 345 days, and the relative power has declined somewhat with the addition of the new Lick data:

When the residuals are folded at a 345 day period, there’s a visible hint of periodicity:

Note, however, that there are a huge number of points in the right-hand part of the diagram. These are primarily points taken at Lick during the Fall of 1995, just after the Swiss discovery announcement. There’s a scarcity of points near the middle of the diagram resulting from the near-match between 345 days and one year. The star can’t be observed when it’s near the Sun in the sky.

Using the console to get a 2-planet fit, the preferred mass of “c” is still about a Saturn mass, but the eccentricity has increased to e=0.59. This is a worrisome development. The system is still perfectly stable, and an eccentricity of 0.59 is certainly within the range exhibited by exoplanets. The problem is that the fit has adjusted itself so that the pronounced radial velocity swings of the outer planet tend to occur where there is no data.

The Lick data therefore seem to have taken some of the air out of 51 Peg c. It would be good to see whether there’s any hint at all of planet “c” if we consider just the Lick velocities. This is easy to do. Just delete the line containing “51peg_ELODIE04.vels” from the 51peg_B06L.sys file in the datafiles directory that comes with the downloadable console.

Don’t worry if you screw something up. You can toss out a busted console and download a fresh one because they’re free! The only problem with downloading a lot of consoles is that the Internet is not something you just dump something on. It’s not a truck. It’s a series of tubes. And if you don’t understand those tubes can be filled, and if they are filled, when you try to get your new console out, it gets in line and its going to be delayed by anyone that puts into that tube enormous amounts of Internets, enormous numbers of consoles.

When one looks at the Lick data set by itself, the one-planet fit has a required jitter of only 3.6 m/s. This is pretty well in line with the level of astrophysical non-planet noise that would be expected from a star like 51 Peg. There’s really nothing in the Lick-only data to suggest that the model needs a second planet. The strong 350-day residual periodicity is thus present in the Swiss data, but not in the Lick data. In particular, the residuals periodogram to the one-planet fit shows absolutely nothing of interest near 350 days

In my post from last March, I wrote that:

It could very well be true that the 356. day periodicity is due to a systematic effect in the data that has nothing to do with a planet. I would not be surprised at all if this is the real explanation. That is, the observational results might be subject to a small seasonally dependent effect produced by the telescope — as a straw-man example, the temperature of the instrument might have a slight effect on the measured radial velocity. The variation could also have an astrophysical source that has nothing to do with a second planet.

The latest data release from the Lick group certainly seems to favor this conclusion. A telescope-dependent effect is highly unlikely to be present in two independent data sets. The fact that the periodicity is present in only one set of data points toward and Earth-based, rather than a 51 Peg c-based explanation for the periodicity. In the older post, I also wrote that:

As a working scientist, I’ve found that about 95 to 97% of the seemingly publishable “discoveries” that I stumble across end up being spurious for one reason or another. Hope springs eternal, but it always pays to temper one’s enthusiasm!

Continues to be true.

Image Source.

Saturday was an epic day for the radial velocity consuming public. Paul Butler and the California-Carnegie planet search team published a blockbuster paper in the Astrophysical Journal, and it looks like the first weekend’s gross is gonna be huge. The paper announces the detections of five new planets, and publishes re-analyzed and (in many cases) greatly expanded radial velocity data sets for no less than eighty three planet-bearing stars. The velocities are all available in machine-readable tabular form. No dextering, no unfolding, no typing, no postscript extractions. As an added plus, the paper also provides the latest estimates for jitter, mass, metallicity, and vsin(i) for all of the tabulated stars.

Needless to say, there’s a great deal of interesting data in this compendium. The updated 55 Cancri velocities, for example, should aid the characterization of a fully self-consistent model of that system. The slew of fresh velocities will be of great help in constraining the uncertainties in the transit predictions for planet bearing stars.

I dug right in to see how the 51 Peg system (described in a series of posts detailed here) is holding up. There are now 256 new and updated velocities from Lick Observatory to complement the 153 published Swiss velocities. The time-series shows a well-sampled mixture of long-term cadence and intensive monitoring.

Needless to say, 51 Peg b is still present with a vengeance. The power spectrum of the combined 409-point data set has a certain overwhelming 4.231 day character:

The data set phased at 4.2307 days shows a very nice sinusoid. About a thousand orbits have been folded down to make this plot:

So how does 51 Peg “c” fare in the new dataset? I’ll post an analysis tomorrow. If you’re impatient, though, you can use the downloadable console to investigate what the new data has to say.

Image Source

We’re working hard to keep the systemic project moving forward.

Eugenio, as of July 14th, has compiled and documented all of the published radial velocity data sets, and has been designing and developing the “KeckTAC” code, which will be a workhorse for systemic’s next phase. The published datasets are all available on the systemic systems catalog. Aaron has stripped the console down to its component parts, and he’s rebuilding it with new features, faster algorithms and a sleekly expandable architecture. Stefano has been tweaking the systemic backend [sign up and get fittin', y'all -ed.], and will be arriving at UCSC in the Fall to do his Ph.D. research. We’re hoping that part of his thesis will be a statistical analysis of the final results of the 100,000 star systemic simulation.

When I was in graduate school, I spent a lot of time doing research on brown dwarfs (objects between 13 and 75 Jupiter masses that lie in the mass range between giant planets and red dwarf stars). At that time, circa 1992, no bona-fide brown dwarfs had actually been found, but the prospects for detecting them seemed reasonably good. My friend Todd Henry, who was a graduate student at the University of Arizona, and who was hunting for brown dwarfs using the speckle method, told me something that stuck in my mind.

“Face it, Greg,” he said, “the reason you’re interested in brown dwarfs is not because you’re interested in Brown Dwarfs — the reason you’re interested in brown dwarfs is because you’re really interested in planets, and brown dwarfs are just one stop away on the line.”

He was right.

A similar logic might apply today, “The reason I’m interested in giant planets is not because I’m really interested in Giant Planets — the reason I’m interested in giant planets is because I’m really interested in habitable terrestrial planets, and giant planets are one stop away on the line.”

Image Source.

Several weeks ago, the planet count at the extrasolar planets encyclopedia notched up by one with the announcement by Artie Hatzes and his collaborators that Pollux (Beta Geminorum) is accompanied by a ~2-3 Jupiter mass planet on a 590 day orbit. This world has been under construction for a long time. The first published radial velocity data point for the star dates back to Nov. 15th, 1980, and Hatzes et al. brought 55 new radial velocities to the table to seal the detection. The planet was independently confirmed by Reffert et al., who (in a preprint posted July 7th) deliver an additional 80 high-precision velocities.

All told, there are now seven published datasets, and all are available on both the on-line and downloadable versions of the console. When folded together, at a 593 (1.6 year) period, a full quarter century’s worth of radial velocity data show the planet quite nicely.

After the Sun, Pollux is the 17th brightest star in the sky. It’s prominently visible both because it’s close (34 light years) and also because it’s an intrinsically bright K0III giant star. Pollux is about 1.9 times more massive than the Sun, and is already coming to the end of its life. It has left the main sequence, and is beginning its long trek up the red giant branch of the Hertzsprung Russell diagram.

In last Saturday’s post, I wrote about predictions of the core-accretion hypothesis with respect to planet formation. The ability to quickly build a Jovian-mass planet depends on the surface density of solid material in the protostellar disk. A lot of solids leads to rapid buildup of cores, and hence the ability of planets to achieve rapid gas accretion before the protostellar disk dissipates. (The spiral wave-induced evolution of marginally gravitationally stable disks leads one to expect that disk masses will correlate with the masses of the central stars, see this paper for a lot more discussion.) All other factors being equal, one expects that Jupiter-mass planets will be rarer around stars that have significantly less mass than the Sun, and that conversely, Jupiter-mass planets will be more common around planets of somewhat higher mass than the Sun. (Note that for really massive stars, the luminosity of the star itself will rapidly photo-evaporate the disk, which will cause problems for giant planet formation via core accretion).

Unfortunately, it gets increasingly harder to apply the radial velocity detection method to Main Sequence stars that are considerably more massive than the Sun. The higher temperatures of these stars lead to weaker spectral lines. Weaker spectral lines make it hard to get really accurate radial velocities. Higher mass stars also tend to be fast rotaters, which further smears out the lines, and they are often subject to pulsations which can mimic the radial velocity signature of an orbiting planet. Above about 1.3-1.4 solar masses, it thus becomes hard to survey main sequence stars for planets.

Luckily, however, a trick can be used to assess the planet frequency for high-mass stars. As a star that has ~1.5-3 solar masses ends its main-sequence hydrogen burning life, its core begins to contract and its outer layers swell up and cool down. The atmosphere of the star then regains the wealth of spectral lines that can be used to make accurate radial velocity measurments, and hence detect planetary companions. The core accretion theory predicts that planet hunting around such giant stars should be a highly profitable enterprise.

Image source.

Four out of five astrophysicists surveyed recommend the core-accretion theory to those interested in planet formation theories.

Oklo regulars know that I lean toward core-accretion over gravitational instability as an explanation of the dominant mode of planet formation. I think that core-accretion does a superb job of explaining the planet-metallicity connection, and I don’t think that the initial conditions that underlie hydrodynamical calculations that show disk fragmentation are physically realistic.

The key aspect of core-accretion is that it is a threshold phenomenon. If a planetary core reaches a Neptune-like mass of ~10-20 Earth masses while there is still gas in the protoplanetary disk, then it will rapidly accrete that gas, and (in most cases) increase its mass by a factor of ten or more. On the other hand, if a core reaches a Neptune mass after the gas is gone, then the growth will cut off, and the core will end its days as a modest ice giant.

The amount of time that it takes for a core to reach the phase of rapid gas accretion depends sensitively on the amount of solid material that is available in the disk in the form of planetesimals. A disk with a high surface density of solids is capable of rapidly assembling a core, thereby forming a Jovian-mass gas giant quite quickly. Recent simulations suggest that an average protostellar disk surrounding a star of solar metallicity will lie right at the threshold of being able to manufacture a Jovian planet. This result gives a satisfying mesh with the observations. As stellar metallicity exceeds solar, the fraction of stars with detectable Jovian-mass planets increases very rapidly. Disks that form their Jovian planets early-on are better able to migrate them into the terrestrial region where they can easily be detected. Stars of solar mass and metallicity will tend to have giant planets that remained, like Jupiter, more or less where they formed. Stars with subsolar metallicity will rarely be accompanied by Jupiter-mass planets.

In addition to explaining the planet-metallicity connection, core-accretion provides a number of other testable predictions. Our simulations suggest that a growing planet orbiting a star with 40 percent of the Sun’s mass will require more than 10 million years to “go Jovian.” After 10 million years, however, the gas in most protostellar disks is long gone. The core-accretion theory predicts, therefore, that low-mass red dwarf stars should very often be accompanied by Neptune-mass planets but should almost never have Jupiter-mass companions.

The surface density of solids in a protostellar disk is correlated with metallicity, and some heavy elements are more important than others. Oxygen, for example, in the form of water ice, is of fundamental importance for building cores. At given mass and overall metallicity, therefore, a disk that is naturally rich in oxygen should be better able to form Jupiter-mass planets. Silicon-rich disks too, should have an enhanced capacity for building gas giants.

image source

The data from the Hipparcos satellite indicate that it’s very likely that Proxima Centauri is in orbit around Alpha Centauri. Proxima has not simply been caught in the midst of a stellar drive-by. It’s cool, certainly, that our nearest stellar neighbors are going along to get along, but is there any scientific importance in the fact that Proxima and Alpha are gravitationally bound?

The answer to this question is a definite yes.

If Proxima is in orbit around Alpha, then we can safely assume that the three stars formed together from the same giant molecular cloud. Therefore, all three have the same age and metallicity. Alpha Centauri A and B, furthermore, are among the best-studied stars in the galaxy; a query to Simbad on Alpha Cen returns a cool 311 citations during the 1983-2006 timeframe. The fact that they are so close and so bright means that very detailed and accurate models can be made of their properties. It’s been clear, for example, since the early 1970s, that the stars are more metal-rich than the Sun. The most recent determination (by Jeff Valenti and Debra Fischer) puts the metallicity at 0.19 “dex”, or 150% of the solar value. Other recent studies suggest even higher metallicities. A detailed modeling study by Eggenberger et al. 2004 finds an age for the stars of 6.52 billion years (plus or minus 300 million years). Proxima was 2 billion years old when the Sun and Earth formed, and it will outlast the Sun on the Main Sequence by 5 trillion years.

Metallicities for red dwarf stars are notoriously difficult to determine. Low-mass red dwarfs are cool enough so that molecules such as titanium oxide, water, and carbon monoxide are able to form in the stellar atmospheres. The presence of molecules leads to a huge number of lines in the spectra, which destroys the ability to fix a continuum level, and makes abundance determinations very difficult.

Recent progress on the red dwarf metallicity problem has been made by Bonfils et al. (2005) who employed a clever approach. They use the fact that when a red dwarf is a member of a multiple system (like Proxima) in which the primary star is more massive, then the metallicity of the red dwarf can be induced by measuring the metallicity of the primary star. Bonfils et al. found 20 nearby binary pairs where this trick was possible, thus giving them the metallicities of 20 red dwarf stars. They then developed an empirical metallicity calibration for red dwarfs based on easily measured photometric indices. Using this technique, they were able to estimate that GJ 876 has a metallicity of +0.02 dex, very close to the solar value. (The fact that GJ 876 is not particularly metal-rich makes one wonder how it managed to put together such an off-the-hook planetary system, but that’s a different topic.)

With Proxima bound to Alpha, we know that its metallicity is ~0.2 dex, which will provide a very important new point of improvement for calibrations based on the Bonfils et al. technique. Of the 20 stars in the Bonfils calibration, only five were above solar metallicity, and only one (GL 324) is as metal-rich as Proxima. Looks like Proxima has provided yet another opportunity for a class project for this Fall.

Just about everyone wants Alpha Centauri to harbor habitable planets. The fact that Proxima is gravitationally bound to Alpha will help make this a reality.

Given what we know about planet formation, it’s extremely likely that there are terrestrial planets in orbit around both Alpha Centauri A and Alpha Centauri B. Simulations by Wiegert and Holman (1997) show that the habitable zones of both planets are likely dynamically stable. Elisa Quintana and her collaborators (2002) have carried out accretion calculations that indicate that terrestrial planet formation should proceed very easily around both stars (with 3-5 terrestrial planets expected for each). Because the metallicity of Alpha Centauri is higher than the Sun, the naive expectation is that these planets should contain of order two times as much mass as our own terrestrial planets.

At first glance, one expects that the Alpha Centauri planets will be very dry. The period of the AB binary pair is only 79 years. The orbital eccentricity, e=0.52, indicates that the stars come within 11.2 AU of each other at close approach. Only refractory materials such as silicates and metals would have been able to condense in the protoplanetary disks around Alpha Centauri A and B. To reach the water, you need to go out to the circumbinary disk that would have surrounded both stars. With only A and B present, there’s no clear mechanism for delivering water to the parched systems of terrestrial planets.

Enter Proxima. With its million-year orbit, it has gone around Alpha roughly 6500 times. The periodic perturbations induced by its close approaches will dislodge comets from the outer circumbinary regions, and send them sailing in to smack the terrestrial planets, delivering the much-needed water and mass-extinctions. Detailed simulations need to be done to look into this process (yet another Proxima-inspired class project).

I’m willing to bet a hundred dollars that the Alpha Centauri Ab and Bb exist, and that these planets are reasonably close (or inside) the habitable zones. How can we confirm the existence of these planets?

The spin axis of Alpha Centauri A is aligned with the angular momentum plane of the AB binary, which indicates that the planets will almost certainly orbit relatively close to the binary plane as well. The binary plane is inclined by 11 degrees with respect to our line of sight (79 degrees with respect to the plane of the sky) and so transits are a long-shot.

What about radial velocities? For sake of example, let’s assume that there’s a 2 Earth-mass planet in a habitable orbit around Alpha Centauri B. The habitable zone for B lies at 0.75 AU, which corresponds to an orbital period of 250 days. Assuming a circular orbit, and adopting and i=79 degree orbital inclination, the radial velocity half-amplitude is 10.6 centimeters per second.

In a series of posts in May, I looked in detail at the Swiss discovery of three Neptune-mass planets in orbit around HD 69830. These detections were based on 74 high-precision radial velocity measurements of a K0V star that is essentially identical in age and mass to Alpha Centauri B. HD 69830 “d”, the most distant planet in that system, induces a half amplitude of K=220 cm/s, with an error of 19 cm/s.

Given that HD 69830 d was detected with 74 measurements, Poisson statistics indicate that 484 times more observations will be required to detect our putative 2-Earth mass Alpha Centauri B “b” with a similar level of confidence. That means 35,816 RV data points, which means 35,816 individual spectra, which is a lot.

Surprisingly, however, such a program is not totally outside the realm of possibility. Because of its extreme proximity, Alpha Centauri B is a bit more than 100 times brighter in the sky than is HD 69830. This means that for a given signal-to-noise, a spectrum for Alpha Centauri B can be obtained 100 times faster than a spectrum of HD 69830. The crucial limiting factor to obtaining observations of Alpha Centauri B will be the readout time for the CCD. If I am interpreting the HARPS instrumental web pages correctly, this readout time for a high-resolution spectrum is 197 seconds (if someone is in the know on this, please post a comment). A reasonable observation cadence, then, seems to be about 210 seconds per observation, meaning that Alpha Cen B b can be detected on HARPS using 208 dedicated 10 hour nights.

Image source.

Last week, I wrote about a plan to send a tiny spacecraft on a trip to the vicinity of Alpha and Proxima Centauri. The idea is to employ a multi-stage rocket to boost a tiny payload toward the stellar system at high speed. When the destination is reached, the principle of gravity de-assist (in the form of successive close flybys of the stars) is used to haul the spacecraft into a bound orbit without using any on-board fuel. [This, of course, is an exercise in orbital dynamics, and not mission proposal. There are better ways to get to Alpha Centauri.]

The problem was tackled by UCSC graduate student Jeremy Wertheimer as his term project for my Astrophysical Dynamics class. Our initial plan was to use a multiparameter minimization scheme (such as the genetic algorithm or simulated annealing) to vary the incoming trajectory of the spacecraft until we found the largest arrival speed that allows for a final bound orbit. To do this requires us to have a precise orbital model for the Alpha AB — Proxima trio.

Amazingly, we discovered that the most recent papers in the literature (from the early 1990s) had arrived at the conclusion that Proxima Centauri is not bound to the Alpha Centauri binary, but rather is in the process of merely drifting past them like a ship in the night. The a-priori odds of Proxima being so close, and so nearly bound, are less than one in a million, but nevertheless, the best position and velocity measurements at that time suggested that this was indeed the case.

In the intervening years since the Matthews & Gilmore 1993 and Anosova et al. 1994 Proxima-Alpha papers were published, there has been a tremendous improvement in our knowledge of the positions, distances, and space velocities of the nearby stars. This improvement is largely due to the European Space Agency’s Hipparcos astrometric satellite, which flew between November 1989 and March 1993 (and whose data was published in June 1997). Hipparcos obtained excellent 3D positional and plane-of-the-sky velocity measurements for both Alpha and Proxima Centauri. When combined with mass and radial velocity measurements for the three stars, the Hipparcos data allows a much better determination of the orbit.

When Jeremy computed an orbit for Proxima using the updated Hipparcos data, he discovered that the measurements now suggest that Proxima Centauri is just barely bound to the Alpha AB pair. He found an enormous elliptical orbit with semi-major axis 272212 AU. (This works out to a whopping 4.3 light years, which is coincidently quite close to the current Sun-Proxima distance.) Clearly, this orbit is much too large, but it’s encouraging to see that the centroid kinematic measurements now indicate that Proxima is formally bound to Alpha.

Even the latest measurements for the Proxima-Alpha Centauri positions and velocities contain uncertainties. In particular, it turns out that the absolute radial velocity for Proxima Centauri has a (still surprisingly large) 1-sigma uncertainty of 200 meters per second. Proxima’s radial velocity in turn has an important effect on whether the three stars are gravitationally bound. Jeremy ran a Monte Carlo simulation in which he drew 10,000 models of the Proxima-Alpha system parameters from the Gaussian distributions implied by the uncertainties in the observations. When he plots the binding energy of these models against the value for Proxima’s radial velocity, he finds that 44% of the trial systems are bound (that is have total energy = gravitational energy + kinetic energy less than zero).

Many of the bound trial systems have energies very close to zero, and hence place Proxima in absurdly large orbits around Alpha. In these configurations, Proxima is currently at the periastron (that is, the near-point) of its orbit. An object in a highly eccentric orbit, on the other hand, spends most of its time near apastron (the orbital far-point).

To illustrate how objects tend to spend their time near apastron, here’s a home-made mpeg-4 stop-action animation of a peppercorn orbiting a kumquat in an ellipse with e=0.90. (Try this version if the other one loads a screen of gibberish).

.

If Proxima is indeed bound to Alpha, then we would (a-priori) expect to find it near apastron. In the figure above, the Monte-Carlo generated orbits in which Proxima is close to apastron have been marked with stars. These orbits all fall in the part of the graph where Proxima’s radial velocity is in the vicinity of -22.1 kilometers per second. We thus have a prediction: if Proxima’s radial velocity is measured to high accuracy, then the value will be ~-22.1 kilometers per second, rather than the current value of ~-21.8 kilometers per second.

In the figure below, I’ve plotted two of the Monte-Carlo orbits for Proxima with respect to Alpha. The “two sigma” orbit is an example of a realization in which Proxima is slightly closer to apastron than periastron. The orbits are projected onto the plane of the sky, and superimposed on an actual photograph of Centaurus (with the full Moon digitally superimposed to give a sense of scale). If our analysis is correct, it should take Proxima about a million years to make one orbit of Alpha, and the semi-major axis of the orbit should be about 1/6th of a light year: