systemic

I’m nostalgic for ’97, when the discovery of a new extrasolar planet was literally front-page news. What’s now cliche was then fully viable poetic sweep. Epicurus and his multitude of worlds. Bruno burning at the stake. In that frame of mind, it’s fascinating to go back and read John Noble Wilford’s extended New York Times piece, written at the moment when the number of known extrasolar planets equaled the number of planets in our own solar system.

Some of the hyperbole still seems fresh, especially with regard to the frequency and diversity of planetary systems:

And the discoveries may be only beginning. One recent study suggested that planets might be lurking around half the Milky Way’s stars. Astronomers have already seen enough to suspect that their definition of planets may have to be broadened considerably to encompass the new reality. As soon as they can detect several planets around a single star, they are almost resigned to finding that the Sun’s family, previously their only example, is anything but typical among planetary systems.

At the recent Porto conference, the Geneva team not only reiterated their claims regarding the frequency of low-mass planets, but actually upped their yield predictions. According to a contact who heard Stephane Udry’s talk, the latest indication from HARPS is that between 38% (at the low end) and 58% (at the high end) of nearby solar-type stars harbor at least one readily detectable M<50 Earth-mass planet. This is quite extraordinary, especially given the fact that were the HARPS GTO survey located 10 parsecs away and observing the Sun, our own solar system (largely in the guise of Jupiter’s decade-long 12-m/s wobble)  would not yet be eliciting any particular cause for remark.

It also looks like planets beyond the snowline are quite common. In yesterday’s astro-ph listing, there’s a nice microlensing detection of a cold Neptune-like planet orbiting a ~0.65 solar mass star with a semi-major axis of at least 3 AU. The microlensing detections to date indicate that Neptune-mass objects are at least three times as common as Jupiter mass objects when orbital periods are greater than five years or so. Microlensing detections are an extremely cost-effective way to build up the statistics of the galactic planetary census during belt-tightening times. Much of the work is done for free by small telescope observers.

Yet another dispatch pointing toward a profusion of planets comes from an article posted last week on astro-ph by Brendan Bowler of the IfA in Hawaii. Work that he’s done with John Johnson and collaborators indicates that the frequency of true gas giant planets orbiting intermediate-mass stars (former A-type stars like Sirius that are now in the process of crossing the Hertzsprung gap) is a hefty 26% within ~3 AU.

An embarrassment of riches? Certainly, the outsize planetary frequency means that the cutting-edge of the planet-detection effort will be shifting toward the Sun’s nearest stellar neighbors, as these are the stars that offer by far the best opportunities for follow-up with space-based assets such as HST, Spitzer, JWST et al.

As competition for ground-based large-telescope RV confirmation of run-of-the-mill planet transit candidates orbiting dim stars heats up, the threshold magnitude (at a given bandpass) at which stars become largely too faint to bother with will grow increasingly bright. We’re talking twelve. Maybe nine. Pont et al., in their discovery paper for OGLE-TR-182b refer to this threshold as the “Twilight Zone” of transit surveys:

The confirmation follow-up process for OGLE-TR-182 necessitated more than ten hours of FLAMES/VLT time for the radial velocity orbit, plus a comparable amount of FORS/VLT time for the transit lightcurve. In addition, several unsuccessful attempts were made to recover the transit timing in 2007 with the OGLE telescope, and 7 hours of UVES/VLT were devoted to measuring the spectroscopic parameters of the primary. This represents a very large amount of observational resources, and can be considered near the upper limit of what can reasonably be invested to identify a transiting planet.

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).

Diamond prospecting proceeds through the identification of indicator minerals such as specific forms of garnet. The garnets can be traced upstream to the Kimberlite pipes. The Kimberlite pipes contain the sparkling gemstones.

Planet prospecting can be done in similar fashion. If you want to jump-start a new planet search, it’s wise to observe metal-rich stars. Stars with more than twice the Sun’s metal abundance are roughly five times more likely than average to harbor one or more planets in the readily detectable hot Jupiter and Eccentric Giant categories. Histogrammed data from Exoplanet.eu shows the metallicity correlation quite nicely:

The metallicity correlation can be readily interpreted in the context of the core-accretion paradigm for giant planet formation. In this picture, nascent planets reach the stage of rapid gas accretion when their rocky-icy cores grow to somewhere in the neighborhood of ten Earth masses. The speed with which a core can be assembled in a protoplanetary disk is a very sensitive function of the density of solid material (e.g. ices and dust) in the disk. The density of solids, in turn, scales with metallicity.

If one explains the planet-metallicity correlation with the core-accretion theory, several predictions follow almost immediately. One expects that low-mass stars will show a paucity of readily detectable giant planets, and that high-mass stars will have a larger fraction of giant planets. Observationally, both of these trends have been shown to hold.

A less-well-known prediction is that one also expects that stars with high oxygen (and by proxy, silicon) abundances relative to iron will also show increased planet fractions at given metallicity. Sarah Dodson-Robinson showed this was true as part of her Ph.D. Thesis. Here’s the the key diagram from her paper on the topic:

A very interesting paper came out in Nature this week which shows an equally compelling, but significantly harder-to-understand abundance correlation. Garik Israelian, and colleagues that include members of the Geneva Team, write (italics are mine):

Here we report Li abundances for an unbiased sample of solar-analogue stars with and without detected planets. We find that the planet-bearing stars have less than one per cent of the primordial Li abundance, while about 50 per cent of the solar analogues without detected planets have on average ten times more Li.

Here’s the graphic from their paper. The filled red circles are planet-bearing stars. Downward arrows indicate that the measurement is an upper limit, and in all likelihood lies at a lower value. Note also, that the y-axis has a logarithmic scale, which de-emphasizes the strength of the effect. To the eye, it’s clear that the lithium abundances of the planet-bearing stars are quite low:

The effect is dramatic, and yet its origin is mysterious and seems to have gone unpredicted. It’s the best sort of scientific puzzle. Lithium is a rather fragile element, and undergoes nuclear fusion in a star when the temperature reaches ~2.5 million degrees. Lithium depletion in the atmosphere of a star can thus be taken as evidence that the gas that’s currently at the surface has, at one point, been mixed far down enough into the star for the lithium to have burned. This implies that the base of the star’s convective envelope has dipped further into the star than the 2.5 million degree isotherm. (The hot F-type stars on the far right of the diagram have very thin convective envelopes nearly right from the start, and so have been unable to burn their lithium.)

So it seems that somehow, the presence of a planetary system (and even one as wimpy as our own solar system) is enough to alter the evolution of the stellar convective envelope. This, in turn, likely has something to do with angular momentum transfer mediated by planets, but quite frankly the story isn’t very clear. Certainly, there will be papers that explain the effect, and certainly, they are being cranked out even as I write, but unless they make specific, testable, and preferably startling predictions, I’d advise taking them with a grain of lithium chloride.

As is usually the case, there’s been little or no shortage of interesting developments in the field of extrasolar planets. The biggest recent news has been the announcement at the Barcelona conference of a definitive mass for the ultra-short period transiting planet CoRoT-7b. It weighs in at a mere 4.8 Earth Masses (copy of the Queloz et al. preprint here).

Recall that CoRoT-7b caused quite a stir earlier this year with its weird properties. The planet’s year is a fleeting twenty hours and twenty nine minutes, and it induces a tiny transit depth of 0.03%. Unfortunately, the parent star presents a less-than-ideal target for high-precision radial velocity work. It has spots that come and go, and its stellar activity produces frustratingly noisy Doppler measurements. As a result, at the time of CoRoT-7b’s initial announcement, there was no definitive measurement of the planet’s mass.

That’s changed, however, with an unprecedentedly all-out deployment of the HARPS spectrograph. From the Queloz et al. preprint:

A total of 106 measurements between 30 and 60 minute exposure time each were obtained over 4 months, and with sometimes 3 measurements being taken on the same night.

Now in my notoriously biased opinion, such observational enthusiasm is perhaps best reserved for stars such as Alpha Cen B, but a fair argument can be made that the massive investment of time did pay off. Remarkably, the radial velocity data set shows that there are two short-period planets in the CoRoT-7 system. The outer companion, which doesn’t transit, has a period of 3.7 days and at least eight Earth masses. Most dramatically, by combining the mass and radius measurements of CoRoT-7b, one arrives at a density of 5.5 grams per cubic centimeter, essentially identical to that of the Earth, suggesting that the planet is largely composed of refractory materials. (I hesitate to apply the term “rocky” to the CoRoT-7c landscape for the same reason that I’d refrain from describing the Amazon Delta as “icy”.)

In a very real sense, the HARPS campaign on CoRoT-7b has given us our last first look at a fundamentally new category of planet — that is, a world lying in the factor-of-fourteen mass gap spanned by Earth and Uranus. And, from exo-political point of view, the stakes surrounding this discovery were very high. The first density measurement of a planet in this category could just as easily have been made by teams combining high-precision Doppler measurements with either (1) Warm Spitzer, (2) ground-based photometry, (3) Kepler, (4) MOST, (5) HST, or (6) CoRoT. So I can imagine that there was a certain impetus underlying the scheduling of that huge block of HARPS time.

The discovery could, however, still be waiting to be made. Despite all the effort with HARPs, there remains a hefty 70% error on the density determination. This means that there’s a ~16% chance that CoRoT-7b is actually less dense than Neptune.

I’ll go out on a limb: CoRoT-7b’s density will turn out to be anomalously high. More than 90% of “super Earths” will turn out to be “sub-Neptunes” as far as their density is concerned.

It’s gratifying to see that Gliese 581 e lands right on a trend line that’s held up for over two decades and a factor of two thousand in planetary mass. It’s amazing that within a year, we’ll be in possession of genuinely Earth-mass planets orbiting nearby stars.

Exoplanetary science has been in high gear now for fifteen years; the first Earth-mass planets are a big-picture milestone, on par with the discoveries of 51 Peg b, Ups And c and d, HD 209458 b and Gliese 876 d. Even more significantly, I think that an Earth-mass planet on the books is going to catalyze a huge shift in emphasis from planetary detection to planetary characterization. The first Mars-mass exoplanet will be met with considerably less acclaim than the first Earth-mass planet. In coming years, the marquee goal of planet hunting will be to locate both representative and particularly unusual planets around the brightest stars possible…

Now I’m certainly not alone in thinking, upon seeing the latest configuration of the Gliese 581 system, Whoa, there’s room for a habitable Earth-mass planet in there…

Using the terrestrial planet valuation formula, an Earth-mass planet with a period of 25 days orbiting Gliese 581 is worth 136 million dollars, and needless to say, its detection would be an exciting development. Gliese 581 f seems like such a made-to-order confection that it’s simply got to be there.

Which is a flimsy argument, I admit, but quite frankly, when it comes to Gliese 581, I have no Alpha. I have no idea how and why the Gliese 581 planets wound up with their presently observed properties and configuration. Furthermore, even if one did have a handle on the sequence of events that led to the formation of b,c,d,e and f, and if one wrote that remarkable result up for publication, hardly anyone would believe it. And for good reason. It’s unlikely that the correct blow-by-blow account of what happened in the Gliese 581 protoplanetary disk would lead to any immediately verifiable predictions for any other planetary systems. We’ve observed enough planets now to know that the aggressive nonlinearity of the formation process leads to a bewildering variety of specific outcomes.

It occurred to me that it I might be able to make creatively disingenuous use of Bode’s Law to “predict” the presence of Gliese 581 f at the desired ~25d planetary period. As it stands, Johann Titius pointed out in 1766 that the orbital spacing of the solar system planets is well represented by d=0.4+0.3*(2^i), with i=-Inf, 0, 1, 2, 4, 5, etc. The law worked for Uranus (i=6) and Ceres (i=3), but then famously overperformed by placing a transuranian planet at 38.8 AU. Given that the Titius-Bode relation contains three parameters (a=0.4, b=0.3, and c=2) it’s possible to choose a,b, and c to exactly reproduce Gliese 581 e, b, and c. Unfortunately, the results for d and and f are then rather less than satisfactory, so I decided to abandon a Bode’s law scheme in favor of a straightforwardly bald assertion of Gliese 581 f’s existence.

It’s perhaps for good reason that the Icarus Editorial Office states:

Icarus does not publish papers that provide “improved” versions of Bode’s law, or other numerical relations, unless they are accompanied by some detailed physical/chemical arguments to explain why the new relation is to be preferred.

In the next post, I’ll look in detail at how and when Gliese 581 f can be detected: scenario four.