systemic

A core prediction of the core accretion model for giant planet formation is that the frequency of readily detectable giant planets should increase with both increasing stellar metallicity and with increasing stellar mass:

It’s now well established that the above diagram is zeroth-order correct, but until fairly recently, the conventional wisdom held that there is little evidence for a strong planet-metallicity correlation among the handful M-dwarf stars (for example, Gliese 876) that are known to harbor giant planets. One is then naturally led to speculate that the odd giant planets in a systems like Gliese 876 might be the outcome of gravitational instability rather than core accretion.

The profusion of molecular lines in the atmospheres of M dwarfs make it hard to determine their metallicities using the techniques of spectral synthesis that work well for hotter stars like the Sun. Fortunately, though, the red dwarfs’ legendary stinginess provides another opportunity for assessing metallicity. Red dwarfs are so thrifty, and they evolve so slowly, that every single one that’s ever formed has barely touched its store of hydrogen. With all the fuel gauges pegged to full, a critical parameter’s worth of confusion is removed. Red dwarfs of a particular mass should form a well-defined one-parameter sequence in the Hertzsprung Russell diagram, and that parameter should be metallicity. If one can accurately plot a particular low-mass star on a color-magnitude diagram, then there should exist a unique and high-quality mapping to both the star’s mass and its metallicity. Physically, an increase in metallicity leads to a higher photospheric opacity, which provides an effective layer of insulation for a star. Add metals to a red dwarf and it will move down and to the right in the Hertzsprung Russell diagram.

Because of the nightmarish complexity of red dwarf atmospheres, it’s not easy to find the calibration that allows one to make the transformation between an observed absolute magnitude and color index (e.g. M_K and V-K) to the stellar mass and metallicity. In 2005, however, Xavier Bonfils and his collaborators made a breakthrough by employing a simple should’ve-thought-of-that-myself technique: Binary stars generally stem from a common molecular cloud core, and so the members of a binary pair should thus generally have very similar metallicities. In particular, if you measure the metallicity of an F, G, or K binary companion to an M-dwarf, then you can assume that the M-dwarf has the same metallicity. Do this often enough, and you can infer the lines of constant M-dwarf metallicity on a color-magnitude diagram. With the calibration in place, metallicity determinations for field red dwarfs are simply a matter of reading off the nearest iso-metallicity locus. Here’s the key diagram from the Bonfils et al. paper:

The puzzling outcome of the Bonfils et al metallicity calibration was that the rare giant-planet bearing M-dwarfs such as Gliese 876 and Gliese 849 didn’t appear to be particularly metal rich, and that worked to undermine confidence in the core accretion picture. One would naively expect that a low-mass disk will need all the help it can get in order to build giant planet cores before the gas is gone. If anything, the planet-metallicity correlation should be strongest among the M-dwarfs.

Important recent progress was made last year by John Johnson and Kevin Apps, who published a reevaluation of Bonfil et al’s. isometallicity loci in the color-magnitude diagram. Johnson and Apps point out that application of the Bonfils et al. calibration produces an aggregate of local M-dwarf stars that have a significantly lower average metallicity than that for the local FGK stars. There’s little reason to expect such a dichotomy, which implies that the Bonfils et al. correlation may be systematically underestimating metallicity by roughly a factor of two. No small potatoes!

Johnson and Apps adjusted the calibration to bring the metallicities of the local M dwarfs into line with the metallicities of the local FGK dwarfs. Here’s a slightly adapted version of their key diagram:

With the revised calibration, Gliese 876 turns up with a metallicity twice that of the Sun, and there is excellent evidence that the planet-metallicity correlation holds strongly for the M dwarfs that harbor relatively massive planets. Furthermore, it’s hard to argue with the two recent papers (one, two) from the California Planet Survey which report the detection of relatively massive planets orbiting two nearby M dwarfs, both of which have extremely high metallicities with the revised calibration.

The statistics are still small-number, but there’s a strong hint that the planet-metallicity correlation for Neptune and sub-Neptune mass planets orbiting M-dwarfs is stronger than it appears to be at FGK (where it’s effectively non-existent). Gliese 176, and Gliese 436, for example, are both quite metal-rich. I bet that a survey like Mearth could jack up its yield by shading its telescope visits to favor the high-metallicity stars on the observing list…

Indeed, if we plot Gliese 1214 (V=15.1±0.6, K=8.78±0.02, parallax=0.0772±0.0054”, distance modulus=0.562±0.16) in comparison to the stars in the local volume, it looks like Gliese 1214 has of order twice solar metallicity if we adopt the nominal values for V,K and the distance. That’s very intriguing…

As the decade draws to a close, it’s hard not to be amazed at the progress that’s been made on every research front related to extrasolar planets.

An area that I think is now ripe for progress comprises coordinated multi-observer checks for transits by super-Earth/sub-Neptune planets. There are now over thirty known extrasolar planets with Msin(i)’s less than that of Gliese 436b (which tips the scales at 23 Earth masses). Of these, only CoRoT-7b has so far been observed to transit, and it’s very probable that the current catalog of low-mass RV-detected planets contains one or more transiting members. Needless to say, it’d be very interesting to locate them.

To my knowledge, the lowest-amplitude transits that have been observed by amateur astronomers have been those by HD 149026b. This anomalously dense Saturn-mass planet induces a photometric transit depth of roughly 0.4%.  State-of-the-art amateur detections show the transit very clearly. Here’s an example (the observer was Luboš Brát of the Czech Republic) taken from the TRESCA database:

The identification of transits by small planets certainly won’t be a picnic. Super-Earths and  sub-Neptunes orbiting G and K stars present targets that are intrinsically much tougher than HD 149026. Unless the parent star is a red dwarf, the expected transit depths will generally be less than 0.1%, and it’ll be extremely difficult for a single small-telescope observer to obtain a definitive result.

On the other hand, if a platoon of experienced observers mount a coordinated campaign on a single star, then there’s a possibility that a startlingly good composite light curve might be obtained. In theory, if one were to combine the results from sixteen independent observers, one could obtain a light curve of the equal signal-to-noise as the HD 149026b curve shown above, but for a planet with a transit depth of only 0.1%.

I spent time this weekend making sure that the transitsearch.org transit predictions for the known RV-detected low-mass planets are as up-to-date and accurate as possible. I found that HD 7924 is a good candidate star with which to test a coordinated observing strategy. The star harbors a low-mass RV-detected planet was announced earlier this year (discovery paper here):

HD 7924b has Msin(i)~10 Earth Masses, a P=5.3978d orbital period, and a 6.7% a-priori chance of being observable in transit. The (folded) photometry in the discovery paper is of quite high quality, and shows that the star is not photometrically variable. The photometry also indicates that transits with depth greater than 0.05% are probably not occurring. The parent star, HD 7924 is a K-dwarf, with a radius of something like 78% that of the Sun, which means that if the planet is a sub-Neptune it’ll have a central transit depth of order 0.075%, whereas if it is a rocky object, the depth will likely be less than 0.05%. The 1-sigma uncertainty on the time of the transit midpoint is about 0.35 days. The parent star has V=7.2, and with Dec=+76 deg, it’s circumpolar for high-latitude observers (RA=01h 21m).

Here are the next predicted transit midpoints (dates and times are UT):

HJD        Y    M  D  H  M
2455182.04 2009 12 16 12 51
2455187.01 2009 12 21 12 14
2455192.41 2009 12 26 21 48
2455197.81 2010  1  1  7 21
2455203.20 2010  1  6 16 54
2455208.60 2010  1 12  2 28

Because HD 7924b’s period is known to an accuracy of 0.0013 days (2 minutes), participating Northern-hemisphere observers can obtain data during any of the upcoming opportunities. Their light curves, once standardized, can in theory be stacked to obtain increased precision. It would be very interesting to get a sense of the practical limits inherent in such an approach. I think the best way to test the limits is to give the observations a try!

A recent e-mail from Bruce Gary prompted me to pay a return visit the Exoplanet Transit Database (ETD) which is maintained by the variable star and exoplanet section of the Czech Astronomical Society. I came away both impressed and inspired. The ETD is really leveraging the large, fully global community of skilled small-telescope photometric observers.

There are hundreds of citizen scientists worldwide who have demonstrated the ability to obtain high-quality light curves of transiting extrasolar planets. I’ve developed many contacts with this cohort over the past decade through the Transitsearch.org project, and small-telescope observers played a large role in the discovery of the two longest-period transits, HD 17156b, and HD 80606b.

Once a particular planet has been found to transit, there is considerable scientific value in continued monitoring of the transits. Additional perturbing planets can cause the transit times to deviate slightly from strict periodicity, and a bona-fide case of such transit timing variations (TTVs)  has become something of a holy grail in the exoplanet community. A perturbing body will also produce changes in the depth and duration of transits as a consequence of changes in the orbital inclination relative to the line of sight. Moreover, for favorable cases, a large moon orbiting a transiting planet can produce TTVs detectable with a small telescope from the ground.

New transiting planets are being announced at a rate of roughly one per month. The flow of fresh transits continuously improves the odds that systems with detectable TTVs are in the catalog, but also makes it harder for any single observing group (e.g. the TLC project) to stay on top of all the opportunities.

The Exoplanet Transit Database maintains a catalog of all publicly available transit light curves. At present, there are 1113 data sets distributed over 58 transiting planets. The ETD site provides a facility for photometric observers to upload their data, and also provides online tools for observation scheduling and automated model fitting. Simply put, this is a groundbreaking resource for the community.

The ETD also provides concise summaries of the state of the data sets. Light curves are divided into five quality bins, depending on the noise level, the cadence, and the coverage of the photometry:

It’s interesting to go through the summary reports for each of the transiting planets. Here’s the current plot of predicted and observed transit times for Gliese 436b, the famously transiting hot Neptune:

The data show no hint of transit timing variations. (So what’s up with that e?)

In other cases, however, there are hints that either the best-fit orbital period needs adjustment, or that, more provocatively, the TTVs are already being observed. TrES-2 provides an intriguing example:

In sifting through the database, it looks like XO-1, CoRoT-1, Hat-P-2, OGLE-TR-10, OGLE-TR-132, OGLE-TR-182, TrES-1, TrES-3, and WASP-1 are all worthy of further scrutiny.

Over the past year, as a result of Stefano Meschiari’s efforts, the Systemic Console (latest version downloadable here) has been evolving quite quickly behind the scenes. Stefano and I are working on a paper which illustrates how the console can be used to solve the TTV inverse problem through the joint analysis of radial velocity and transit timing data. In the meantime, it’s worth pointing out that the ETD database lists transit midpoints in HJD for all of the cataloged light curves. These midpoints can easily be added to the .tds files that come packaged with the console.

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.

and at 880K it’s close to ten times hotter (but likely the same color) as the original edition.

In the twenty months following Gillon et al.’s startling discovery that Gliese 436b is observable in transit, literally dozens of additional transiting planets have been found. New transiting hot Jupiters are now routine enough that they’re generally trotted out in batches. Reported cases of transit fever have also been on the decline, with symptoms often amounting to little more than a passing distraction.

That said, it’s been been a very long dry spell waiting for a second example of a transiting Neptune-mass planet, which makes HAT-P-11b both exciting and newsworthy. In a preprint that muscled its way to the top of today’s astro-ph mailing, Gaspar Bakos and collaborators have produced a admirably solid analysis of what’s definitely the toughest ground-based detection to date.

HAT-P-11b’s transit depth is 4.2 millimag, which is the smallest planet-produced dip yet detected by a photometric survey. (HD 149026b has a smaller transit depth, but it was discovered via the Doppler velocity method and then followed up photometrically for the transits during the time windows predicted by the orbital solution.) The HAT-P-11b analysis was further confounded by a photometrically variable parent star and ~5m/s stellar jitter on the radial velocity observations. The paper is definitely worth reading carefully.

HAT-P-11b is quite similar in mass and radius to Gliese 436b, and it’s actually somewhat larger than Neptune on both counts. When the mass and radius are compared to theoretical models, it’s clear that, like Gliese 436, it’s mostly made of heavy elements (that is, some combination of metal, rock and “ice”) with an envelope of roughly 3 Earth masses of hydrogen and helium). It’s completely dwarfed when placed next to an inflated hot Jupiter, HAT-P-9b, for instance:

Interestingly, HAT-P-11b seems to have a significant eccentricity, on the order of e=0.2. Drawn to scale with the parent star, the orbit looks like this:

The dots demarcating the orbit are not to scale. With 500 pixels of resolution, you can just barely see the planet. (I put one in front of the star, and tacked a copy onto the orbit for good measure.)

The e=0.15 eccentricity of Gliese 436b has caused a lot of consternation. For any reasonable value of the so-called tidal quality factor, Q, the circularization timescale for Gliese 436b’s orbit is considerably shorter than the age of the system. This has led to attempts (to date unfulfilled) to locate Gliese 436c. HAT-P-11b doesn’t have this problem. For a given Q, it’s circularization timescale is a full thirty times longer than that of 436b. The orbit will still be measurably eccentric even when the 0.8 solar mass primary starts to turn into a red giant.