systemic

Israelian et al’s Nature paper on the planet-stellar lithium correlation (featured in last week’s post) caused quite a stir in the community. The depletion of lithium in the atmosphere of a solar-type star seems to be a prerequisite for the presence of a detectable planetary system. Here’s the paper’s plot again, this time, with Alpha Cen A added for effect.

Had Israelian et al.’s paper come out a decade ago, much of the ensuing hubub would have focused on the fact that low lithium abundance is an effective signpost to planetary systems. Nowadays, though, mere detection of new planets is passé. Everyone knows there are tons of planets out there. Focus is shifting to finding the lowest-mass (and preferably transiting) planets around the brightest M, K, and G main sequence stars in the Sun’s neighborhood. There is a short, highly select, list of worlds that have been, and will eventually be, followed up to great advantage with HST, Warm Spitzer, and JWST.  All of the Sun’s most alluring stellar neighbors are under heavy and ongoing scrutiny, and in fact,  it’s these particular stars (in the form of the HARPS GTO list) that enabled discovery of the planet-lithium correlation.

So planet-finding utility aside, the intense interest in the planet-lithium effect stems from the fact that it’s guaranteed to be imparting an important clue to the planet-formation process.

With over 400 planets known, clear populations are starting to emerge. It’s remarkable that the strength of the lithium-planet correlation seems to be largely independent of the masses and periods of the planets themselves. The mass-period diagram for planets, on the other hand, shows that there are at least three distinct concentrations of planet formation outcomes:

It’s important to keep in mind that Israelian et al.’s correlation holds over only a very narrow range of stellar temperature. The M-dwarfs (Gliese 581, Gliese 876), the K-dwarfs (HD 69830, Alpha Cen B), and the F-dwarfs (Upsilon Andromedae) all fall outside the band of utility. This dovetails nicely with standard models of stellar evolution that suggest the amount of Lithium depletion in stars with masses very close the the Sun (that is, stars falling in the narrow effective temperature range of the above plot) depends sensitively on both the efficiency of convection and also on rotational mixing. That is, the stars that show the lithium-planet effect, are exactly the stars where subtle differences in properties seem to generate a big effect on lithium abundance.

After writing last week’s post, I got an e-mail from Jonathan Irwin (of MEarth fame) who makes several interesting points:

The low lithium could be more of a coincidence resulting from the long-lived circumstellar disks that are presumably needed to form planets.

Mediation of the stellar rotation rates by long-lived disks is thought to be responsible for generating the wide dispersion in rotation rates observed in open clusters around 100Myr age, and there have been suggestions (e.g. Denissenkov et al.’s paper that appeared on astro-ph 2 weeks ago) that the slowly-rotating stars evolve developing some degree of decoupling of the rotation rates of their radiative core and convective envelope, whereas the rapidly-rotating stars evolve more like solid bodies.

Bouvier (2008) has suggested that the shear at the radiative convective boundary resulting from this could mix lithium into the interior more efficiently, and thus could result in lower lithium for stars that were slow rotators, preserving evidence of their rotational history even though the final rotation rates all converge by the solar age.  Some evidence for this last part exists in the form of a correlation between rotation and lithium in young open clusters such as the Pleiades.

A hypothesis along these lines seems quite appealing to me. As long as a protoplanetary disk is present, and as long as its inner regions are sufficiently ionized, then there’ll be a connection between the stellar magnetic field and the magnetic field of the disk. To a (zeroth) degree of approximation, the equations of ideal MHD allow us to envision the situation as consisting of a rapidly rotating star connected to a slower-rotating disk by lot of weak rubber bands. The net effect will be to slow down the stellar rotation to bring it into synch with the rotation at the inner edge of the disk.

Trying to sound like a tough-guy, I stressed the importance of predictions in last weeks post. If Irwin’s hypothesis is correct, then the formation of the Mayor et al. 2008 planet population is associated with disks that contain lots of gas, even in regions interior to R~0.1 AU. I’d thus expect that the “super Earths” are actually “sub Neptunes”, and that we can expect considerable H-He envelopes for the majority of these planets.

Another speculative prediction concerns the stars that aren’t depleted in lithium. In Irwin’s picture, these stars had short-lived disks and lost their gas relatively rapidly. This shouldn’t hinder the formation of terrestrial planets, but one would expect that the final configurations of the rocky planets would sport higher eccentricities, as there was little or no gas to damp the orbits down during the final stages of terrestrial planet accretion (see this paper for more on this).

Philippe Thebault sent me a link to an article on the Alpha Centauri planet search published earlier this month in the Frankfurter Allgemeine Zeitung. The text is in German, but the Google translator does a passable job of getting the gist across.

I got my first inkling of the Geneva Planet Search’s Alpha Centauri campaign through Lee Billings’ article in Seed Magazine. (See this post). In the Frankfurter Allgemeine article, Francesco Pepe gives further details — Alpha Cen B is one out of ten stars that are receiving special scrutiny for terrestrial planets at HARPS. They are getting one observation every two weeks, meaning that the star is being hit roughly one out of every two of their planet search nights:

“Allerdings müssen wir uns Harps mit anderen Gruppen teilen”, sagt er. Zudem ist Alpha Centauri B nur einer von zehn Sternen, die sie auf erdähnliche Planeten absuchen wollen. “Aber alle zwei Wochen schauen wir damit auf Alpha Centauri, und das Gerät ist sehr effizient.”

This quote implies that my speculations regarding the Geneva team’s data collection rate on Alpha Cen B were somewhat overheated. Instead of getting 100 ultra-high-precision HARPS velocities per year, it looks like a more realistic estimate of their current rate is 25 velocities per year. Since signal-to-noise increases as the root of the number of observations, this means that the minimum mass threshold for Alpha Cen Bb at any given time is approximately doubled relative to my estimates at the beginning of the Summer. Instead of arriving at 2.5 Earth masses in the habitable zone a bit more than a year from now, they’ll be at roughly 5 Earth masses.

Now nobody likes backseat drivers. As the saying goes, “theorists know the way, but they can’t drive”, and theorists have had a particularly dismal record in predicting nearly everything exoplanetary.

But nevertheless, I’m urging a factor-of-four increase to that data rate on Alpha Cen B. I would advocate two fully p-mode averaged velocities per night, 50 nights per year. I know that because Alpha Cen B is so bright, the duty cycle isn’t great. I know that there are a whole panoply of other interesting systems calling for time. It is indeed a gamble, but from the big-picture point of view, there’s a hugely nonlinear payoff in finding a potentially habitable planet around Alpha Centauri in comparison to any other star.

During the next few months, it’s inevitable that one of the numerous Super-Earths that have been turning up in the radial velocity surveys will be announced to be observable in transit (see, e.g. this post). When that occurs, we’ll effectively have had our last first look at a truly new category of planet — the logarithmic mass interval between Earth an Uranus is currently by far the largest among the 70-odd planets that have accurately determined radii. My own guess is that the emerging population of super-Earths will be better described as a population of sub-Neptunes. That is, the transit depths will indicate compositions that are largely water.

So if 5-Earth mass planets turn out to be primarily water-based rather than rock-based, it’s (in my mind) an argument in favor of cranking up the data rate on Alpha Cen B. There were no structurally substantial quantities of water in the Alpha Cen planet-forming environment. If we’re seeing sub-Neptunes rather than super-Earths in the HD 40307, Gliese 581, et al. systems, then the odds are heightened that any planets orbiting Alpha Cen B are less than 2 Earth masses. There’s no payoff in tuning your Alpha Cen B strategy for sub-Neptunes. Finding truly terrestrial-mass planets will require paying full freight.

In the early nineteenth century, the detection of stellar parallax was a problem fully equivalent in both scientific excitement and prestige to the modern-day detection of the first potentially habitable extrasolar planet. I think it’s worth noting that the prize of discovery of the first stellar parallax went not to the eminently capable (but overly cautious and slow-moving) observer who accumulated data on the best star in the sky, but rather to an observer who focused on a rather obscure star in the constellation Cygnus.

Here’s a link to the article, “Thomas Henderson and Alpha Centauri” by Brian Warner of the University of Cape Town.

At first glance, through a telescope, Venus looks like it just might be habitable. Earth-like mass. Earth-like size. Close to the Sun, yes, but the white clouds reflect most of the incident sunlight.

A lifetime ago, it was perfectly reasonable to imagine that swampy Devonian-era conditions prevail on Venus. In his remarkable book, Venus Revealed, David Grinspoon recounts an expert opinion voiced by the Nobel-prize winning chemist Svante Arrhenius in 1918:

The humidity is probably about six times the average of that on Earth. We must conclude that everything on Venus is dripping wet. The vegetative processes are greatly accelerated by the high temperature, therefore, the lifetime of organisms is probably short.

There’s definite allure to the watery Venus meme. C.S. Lewis does an interesting treatment in Perelandra. I’ve always liked Ray Bradbury’s vision of Venus in The Long Rain:

The rain continued. It was a hard rain, a perpetual rain, a sweating and steaming rain; it was a mizzle, a downpour, a fountain, a whipping at the eyes, an undertow at the ankles; it was a rain to drown all rains and the memory of rains. It came by the pound and the ton, it hacked at the jungle and cut the trees like scissors and shaved the grass and tunneled the soil and molted the bushes. It shrank men’s hands into the hands of wrinkled apes; it rained a solid glassy rain, and it never stopped.

Frustratingly, just as the prospect of interplanetary travel was evolving into a concrete engineering problem, Venus’ spoilsport nature was revealed. In the late 1950s, Venus was observed to be glowing brightly in the microwave region of the spectrum (see, e.g. this article). The immediate — and ultimately correct — interpretation is that the microwaves are the long-wavelength tail of blackbody emission from a lead-melting surface, but at that time, the situation was not entirely clear. Even as the first astronauts were orbiting the Earth, one could optimistically chalk up the Venusian microwaves to phenomena in its ionosphere. (See, for example, this 1963 review). The space race, the cold war, the whole twentieth century would have unfolded very differently had Venus been Earth-like beneath its inscrutable clouds.

August 27, 1962 — Launch of an Atlas Agena B with Mariner 2: Destination Venus.

The microwave radiometer on Mariner 2 brought a quick end to fading hopes of a habitable Venus. Here’s the link to the baleful 1964 summary of the mission results. With the equally bleak assessment of Mars courtesy of Mariner 4, genuinely habitable extraterrestrial worlds in the solar system were a no-go. The space race fizzled out. Now we’re looking at retro-futuristic voyages to the Moon in the 2020s and dreaming of Alpha Centauri.

Speaking of which, two recent theoretical papers have come down on the pro-planet side of the ongoing terrestrial-planets-orbiting-Alpha-Centauri debate. In an article that’ll be on astro-ph within the next day or so, Payne, Wyatt and Thebault suggest that outward migration of planetary embryos in the Alpha Cen B protoplanetary disk can provide a mechanism for circumventing the problems associated with habitable planet formation in the binary environment. In the second paper (posted to astro-ph earlier this year) Xie and Zhou argue that a modest inclination between Alpha Cen A’s proptoplanetary disk and Alpha Cen B’s orbit can also tip the balance quite significantly in favor of terrestrial planet accretion around A (and with similar logic applying to planet formation around B).

Last November, in the comments section to the Alpha Cen Bb post, I was asked:

What do you think the odds now are of there being a planet somewhere in the Alpha Centauri system?

I answered:

Hazarding a guess, I’d say 60%. A better answer might be, “High enough to warrant mounting an inexpensive (in comparison to most other planet-search efforts in operation or contemplation) ground-based search.”

I’d like to raise those odds to 68.3%.

There have been a number of recent developments on the Alpha Centauri front.

Several weeks ago, Lee Billings wrote an article for Seed Magazine that delves at length into the hunt for terrestrial planets orbiting Alpha Cen. It hits a really inspiring tone. (I suggest pairing it with Nick Paumgarten’s equally well-written The Death of Kings to get a sense of how we’re living in what is effectively a bizarre superposition of worlds of varying habitability.) In keeping with the zeitgeist, the Alpha Cen story was also picked up last Monday with an article by Joel Achenbach in the Washington Post.

Billings’ article is entitled “The Long Shot”, with the reference being to Project Longshot, the far-out 1988 mission design for an unmanned 100-year nuclear pulse propelled mission to the Proxima/Alpha Centauri system. I, for one, definitely hope to be counted present when such a mission begins phase E.

Interestingly, the Seed article divulges an important clue to the extent of the Geneva Team’s current data set for Alpha Cen B, with the source apparently being a telephone interview with Michel Mayor:

Since 2003, Mayor and his team have used HARPS to search for planets around Alpha Centauri B. Last August, they began observing the star every available night in a strategy similar to Fischer’s.

The italics are mine, and for Alpha Cen fans, this is great news. Recent developments have made it abundantly clear that when HARPS is working full bore on a bright quiet star, it can drill right down into the habitable zone. If we assume that the statement in the above excerpt is accurate, we can put very interesting current limits on habitable planets in the Alpha Cen B system.

The star HD69830 (which harbors three-Neptune mass planets, see e.g. here and here) is a good proxy for Alpha Cen. The data set published in conjunction with the Lovis et al. article in Nature on HD 69830 contains 74 velocities taken over an 826 day period from Oct. 26 2003 through Jan 30 2006. That works out to 0.09 velocities per day, with each velocity having a reported instrumental error of ~0.8 m/s. This means that if Alpha Cen B received similar attention to that paid to HD 69830, then the Alpha Cen B data set as of last August would have contained ~160 velocities, each with ~0.8 m/s instrumental error.

If we look at the time series for HD 69830, however, we see that 160 Alpha Cen B velocities as of a year ago is likely an overestimate. It’s clear that the HD 69830 planets were starting to show after the first six months of observations, and as a result, the cadence on the star was increased by more than a factor of two. Based on the initial cadence on the star, it’s reasonable to expect that Alpha Cen B has been accumulating ~15 velocities per year, which works out to ~75 velocities in August 08 when the cadence was increased.

It seems reasonable to expect that when firing on all cylinders, HARPS can pull in 100 velocities per year for Alpha Cen B. This means that by the end of this summer, the Geneva team could quite reasonable be in possession of an N=175 point time series. Alpha Cen has near year-round observability from La Silla, so we can create a synthetic data sets which spread 75 velocities randomly across five years, followed by a year with 100 randomly spaced velocities. The data that the Geneva team currently have in hand probably look something like this:

The habitable zone for Alpha Cen B is at P~250d. Let’s assume that a planet with this period has an orbit of eccentricity e~0.05, and look at representative Lomb-Scargle periodograms of Monte-Carlo data sets created for different values of the planet mass. In keeping with the results for Gliese 581 and HD 69830, let’s also assume a 1 m/s normally distributed radial velocity jitter produced by the star.

An Msin(i)=4.6 Earth-mass planet in an optimally habitable orbit around Alpha Cen B is worth USD 100K (which seems like a remarkably good deal). Three periodograms for different Monte-Carlo realizations indicate that such a planet would be right on the verge of current “announceability”:

If the mass is reduced to Msin(i)=2.3 Earth masses (which jacks the value to a cool USD 227 million) the data sets (three of which are shown just below) are not quite seeing the planet yet. Another year and a half or so will be required.

During the coming 18 months or so, we’ll therefore be in an interesting situation in which no news on Alpha Cen is very good news. Perhaps any Wall Street types who read this blog might try their hand at pricing an option on Alpha Cen Bb.

And finally, the theoretical objections to the formation of terrestrial planets orbiting Alpha Cen B are dissipating rapidly. I’ll pick up that story in an upcoming post…

In 1803, the fledgling United States purchased the Louisiana Territory from France, and thereby entered into what has wound up being one of history’s better real estate deals. Napoleon, as the principle on the sell side, remarked at the time, “This accession of territory affirms forever the power of the United States, and I have given England a maritime rival who sooner or later will humble her pride.” In somewhat typical fashion, the US House of Representatives was slower to grasp the stupendous advantage of the bargain, with Majority Leader John Randolph standing firmly against the purchase. Fortunately, a measure to axe the deal wound up failing by two votes, 59-57.

The Louisiana Purchase price was a (suspiciously spam-like) USD 15 million. For a payment of gold bullion and bonds, the United States obtained the entire western drainage of the Mississippi River. This constitutes ~2 million square miles, or roughly 1% of Earth’s ~200 million square mile total surface. Using the price of gold as a measure of inflation (Gold was USD 19.39 per oz. in 1803) the purchase in today’s currency was thus a mere USD 750 million.

Fast-forwarding two hundred years to the present, similarly good land deals are still to be had — not on Earth, but on potentially habitable terrestrial planets orbiting nearby stars! I think it’s fair to say that the successful launch of the Kepler Mission last weekend can be viewed as the first large-scale extraterrestrial land rush.

Oklo readers are doubtless familiar with the Kepler mission specs. The spacecraft will reside in an Earth-trailing orbit, and, during the 3.5-year mission will monitor ~100,000 main sequence stars with a photometric precision of 20ppm at 6.5h cadence. In all likelihood, it’ll detect of order 100 terrestrial planets. The total mission cost will be of order USD 600 million, remarkably close to the cost of the Louisiana purchase in 2009 dollars.

The advent of Kepler allows us to put meaningful prices on terrestrial extrasolar planets. I think the following valuation formula provides a reasonable start:

where $\tau_{\star}$ is the age of the planet-bearing star, and V is the apparent visual magnitude. Kepler’s best planets are likely going to come in with valuations of order 30 million dollars.

Applying the formula to an exact Earth-analog orbiting Alpha Cen B, the value is boosted to 6.4 billion dollars, which seems to be the right order of magnitude.

And applying the formula to Earth (using the Sun’s apparent visual magnitude) one arrives at a figure close to 5 quadrillion dollars, which is roughly the economic value of Earth (~100x the Earth’s current yearly GDP)…