Archive for September, 2008

root N

September 25th, 2008 1 comment

Jason Wright recently sent me an advance copy of a preprint from his group that sums up the state of knowledge of the 27 multiple exoplanet systems that are currently known to orbit ordinary stars. It’s really quite remarkable, in scanning through the table of planets, how alien the systems are, how, on the whole, they are so unlike the solar system.

We’re fast approaching the tenth anniversary of the discovery of the three planets orbiting Upsilon Andromedae. I vividly remember setting up integrations of the outer two orbits in that system just after it was announced, and watching the eccentricities of planets “c” and “d” cycle through their huge (compared to solar system) variations. At that time, I had never bothered to give secular theory the slightest consideration (aww, that stuff was all worked out in the 18th century). It was a revelation to watch the orbits shimmer and vibrate as the integrator ticked off the centuries at the rate of a million years an hour.

As the multiple-planet business enters its second decade, emphasis is shifting toward the detection of systems with ever-lower planet masses. Ups And packs at least two thousand Earth masses into the inner several AU surrounding the star. HD 40307, by contrast has planets that start at only four times the mass of Earth.

As the planetary masses go down, so to do the signal strengths. The Upsilon Andromedae periodogram practically wears its planets on its sleeve, whereas nowadays, the surveys are likely combing though forests of tantalizing yet ambiguous peaks. Detectability increases with the square root of the number of observations, which exerts pressure to spend more telescope time on fewer stars.

From the standpoint of someone who’s interested in planet-planet dynamics, systems like Gliese 876, with its incredible signal-to-noise are clearly the most valuable. From the perspective of someone who’s interested in planet formation and the statistics of the galactic census, the systems with low-mass planets are a bigger deal. A single statistic that captures the relative value of a multiple-planet system could be expressed as:

Where the sum inside the root is over the planets in the system, and the quantities are the planetary masses, M, the rms of the residuals to the fit, $\sigma$, and the radial velocity half-amplitudes, K. The statistic seems to do a reasonable job of aggregating signal-to-noise and the potential for dynamical interaction, while simultaneously placing emphasis on lower mass planets. Plugging in the numbers, the known multiple-planet systems stack up with the following ranking:

Interestingly, the ranking seems to capture the vagaries of the press release industry pretty well. The top six multiple planet systems have all seen their names appear in the New York Times, in some cases on the front page:

HD 40307:

Gliese 581:

Gliese 876:

HD 69830:

Mu Arae:

55 Cancri:

Newsworthiness appears to run out, however, when the list reaches the two-planet system orbiting HD 190360:

Amazon, however, has kindly sponsored a link that puts it up for sale:

Now that flipping houses is passé…

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New Horizons

September 6th, 2008 Comments off

Image Source.

Last May, Mark Marley sent me a link to the photograph shown above. It’s a Cassini image of Alpha Centauri A and B hanging just above the limb of Saturn. It provides an interesting bookend to the remarkable pictures that can be taken from Earth when Saturn and the Moon are close together in the sky. Mystery on the scientific horizon of the year 1610 has transformed itself into mystery on the horizons of today.

Image source.

It’s also a nice coincidence that the actual distance between the two components of Alpha Cen is similar to the distance between Earth and Saturn. Right now, Alpha Cen A and B are more than 20 AU apart, but within our lifetimes, they’ll close to nearly the Earth-Saturn distance as they reach the next periastron of their 80-year orbit in May 2035.

We’re fortunate that we’ve arrived on the scene as a technological society right at the moment when a stellar system as interesting as Alpha Cen is in the very near vicinity. During the last interglacial period, Alpha Cen did not rank among the brightest stars in the sky. A hundred thousand years from now, the Alpha Cen stars will no longer be among our very nearest stellar neighbors, and in a million years, they will have long since faded from naked-eye visibility. At the moment, though, Alpha Centauri is drawing nearer at 25 km/sec, a clip similar to the Earth’s orbital velocity around the Sun. It’s as if we’re on the free trial period of an interstellar mission…

And what of the status of the observational search? In the interim since the last update, Debra Fischer obtained one year of NSF funding to begin high-cadence radial velocity observations of the Alpha Cen system with the CTIO 1.5m telescope in Chile. Debra, along with Javiera and a number of CTIO scientists have worked very hard to get the telescope and a spectrograph into condition for high-precision Doppler work. Many nights of Alpha Cen observations have now actually been carried out, and by all indications, the prospects look quite promising from an instrumental standpoint. The project will need long-term funding, though, since it will take of order 3-5 years of dedicated observation to reach any truly habitable worlds that are orbiting our nearest stellar neighbors.

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De revolutionibus

September 1st, 2008 Comments off

In preparing my talk for the Torun meeting, it seemed appropriate to take a careful look at the book that got the whole planetary systems business going — De revolutionibus orbium coelestium (On the Revolutions of Heavenly Spheres) by Copernicus.

Being not in possession of a classical education, that meant settling for an English translation, but it’s interesting to look at the original Latin editions (which are dramatically out of copyright, and hence available from the ether in the departure lounge at O’Hare if one is willing to fork out for a wi-fi connection). Here’s the frontispiece of Harvard’s edition:

The text translates to:

Diligent reader, in this work, which has just been created and published, you have the motions of the fixed stars and planets, as these motions have been reconstituted on the basis of ancient as well as recent observations, and have moreover been embellished by new and marvelous hypotheses. You also have most convenient tables from which you will be able to compute those motions with the utmost care for any time whatever. Therefore, buy, read and enjoy.

To a modern sensibility, the exhortation to buy the book seems to run at cross purposes with the warning just below (written in Greek for heightened effect):

Let no one untrained in geometry enter here.

Certainly, in trying to make sense of the text, it’s clear that the warning is no empty threat. The book, with its arduous descriptions of ephemerides is tough going. Section 17 of Book V presents a typical example:

Now it was made clear above that in the last of Ptolemy’s three observations Mars, by its mean movement as at 244.5 deg, and its anomaly of parallax was at 171 deg, 26′. Accordingly during the year between there was a movement of 5 deg 38′ besides the complete revolutions. Now for the 2nd year of Antoninus on the 12th day of Epiphi the 11 month by the Egyptian calendar 9 hours after mid-day, i.e. 3 equatorial hours before the following midnight, with respect to the Cracow meridian, to the year of Our Lord 1523 on the 8th day before the Kalends of March 7 hours before noon, there were 1384 Egyptian years 251 days 19 minutes [of a day]. During that time there were by the above calculation 5 deg 38′ and 648 complete revolutions of anomaly of parallax. Now the regular movement of the sun was held to be 257 1/2 deg. The subtraction from 257 1/2 deg of the 5 deg 38′ of the movement of parallax leaves 251 deg 52′ as the mean movement of Mars in longitude. And all that agrees approximately with what was set down just now.

By connecting observations from the Ptolemaic era with his own (and other contemporary) observations, Copernicus was able to achieve a great improvement in timing accuracy. Remarkably, his combination of timing data and positional measurements for solar system planets such as Mars give a signal-to-noise quite similar to the modern data that we currently have for transiting hot Jupiters such as HD 149026b. These extrasolar planets have been observed over hundreds of orbits with both ground-based photometry (for timing) and with radial velocities (for elucidating the orbital figure).

Given that the distances to the planet-bearing stars are millions of times larger than the distances to the solar system planets, this is a testament both to how far we’ve come in 500 years, and simultaneously, to the durability of the Copernican accomplishment.

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