limit cycle

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The minimum threshold level for amazement will rise quickly once Kepler’s discoveries start to accumulate, and already, it’s getting very hard to remember which transiting planet is unusual for which reason. Let’s see, was it TrES-4 or WASP-17 that had that styrofoam-like density? Or was it both of them?

Even in a crowded field, though, HAT-P-13 is likely to endure as a touchstone. In the next five years, it’s likely that there will emerge only a select handful of systems in which a well-characterized transiting planet orbiting a relatively bright star is being substantially perturbed by a companion on a well-characterized orbit:

After the HAT-13 system was announced, we showed that the planets “b” and “c” should have evolved to an eccentricity fixed point configuration, in which the orbits’ apsidal lines co-rotate, and in which the orbital eccentricity of planet “b” has a very sensitive dependence on its internal structure. Further modeling, using reasonable assumptions, gives strong limits on the tidal Q of planet “b”. In essence, one can potentially accomplish with an exoplanet a big chunk of what the Juno Mission expects to accomplish at Jupiter at of order a thousandth of the cost.

Our analysis assumed that HAT-P-13 b and c are on co-planar orbits. There’s an interesting new paper by Rosemary Mardling that explores the significantly more complex situation that arises if the orbital planes of the planets are significantly misaligned. In this case, tidal dissipation in the inner planet causes the system to settle into a limit cycle, where the eccentricity and the angle between the apsides circulate on a secular timescale, and the easy insight into the structure of planet b is no longer possible.

Interestingly, however, Mardling’s analysis suggests that if the orbits are misaligned, then the mutual inclination is likely to be in the neighborhood of 45 or 50 degrees. A mutual inclination of, say, 30 degrees is inconsistent with the currently observed parameters of planet b. The following two diagrams (figure 8 a and b) from her paper show how this works:

Within the next few months, we should get improved values for the eccentricity and radius of planet b, which will significantly shrink the size of the peach-colored boxes in the two figures above. HAT-P-13c is also currently headed in for periastron, with the next transit opportunity scheduled for April 12, 2010. A transit by planet c would provide strong evidence that the system is reasonably close to co-planar (and would be quite remarkable in its own right!) Furthermore, during the periastron passage of c, there should be readily detectable transit timing variations for b, which should give us a shot at distinguishing between the co-planar case and the case with a mutual eccentricity of 45-50 degrees. In the next post, I’ll look in detail at the numbers…

Red Dwarf Metallicities

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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…

Follow Up

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Astronomers worldwide staggered into work this morning, some of them rudely elbowing their way to the front of the lines at the espresso machines, clear evidence that events surrounding the January 2010 ‘606 holiday season have finally drawn to a close.

Hopefully the data will turn out to be of high quality! As I mentioned in yesterday’s post, ground observers in both Europe and North America were out in force for the event, collecting photometric and spectroscopic data. The action was covered from space as well. We were awarded a generous 84-hour block of time on Warm Spitzer. The telescope started collecting 4.5-micron photometry more than a day prior to the secondary transit, and ended more than two days after the periastron passage.

What do we hope to learn? By observing the run-up to the secondary transit, we should be able to establish an improved baseline temperature for the planet, which should afford a better sense of how much tidal heating is occurring. And during the days following periastron, we expect to see a near-complete drop-off in flux from the planet as the periastron nightside hemisphere rotates fully into view. The 2007 observations came to a frustrating end just as this should have been starting to occur.

In addition to the secondary eclipse and the ground-based observations, Guillaume Hebrard and his collaborators were awarded 19 hours on Warm Spitzer to observe the primary transit at 4.5 microns. Their photometric time series will enable an improved radius measurement for the planet — both because of the highly accurate photometry and because the effects of stellar limb darkening are negligible in the infrared. Their time series will establish a very precise ephemeris for the transit, which will enable future observations to monitor the system for orbital precession.

Looking forward to the results…

in eclipse

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It’s 4pm Wednesday Jan 13th here in Santa Cruz, and the HD 80606b transit has been underway for a few hours. A whole slew of observers worldwide are watching the event, with Northern Europe getting the best view (if the weather is clear).

Last weekend, the Spitzer telescope carried out an 84-hour observation of the system during the window surrounding the secondary eclipse. Our goal was to watch the planet heat up and then cool down rapidly as the unheated night side rotates into view.

Good luck to everyone who’s out there on the sky!

Kepler’s first crop

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The long-awaited initial discoveries from the 600M Kepler mission are in!

At a scientific talk at the AAS Meeting in Washington DC this morning, and in an afternoon press briefing packed with journalists, bright lights and television cameras, the Kepler Team announced the discovery of five new transiting planets. Four are inflated hot Jupiters, and one is a hot Neptune reminiscent of Gliese 436b and HAT-P-11b. Most importantly, the Kepler satellite appears by all accounts to be performing beautifully as it continuously monitors over 150,000 stars for planetary transits.

Here’s a to-scale line-up of the Kepler starting five. Kepler-4b is so small that it’s just barely resolved at a scale where its orbit spans 480 pixels.

The Kepler planets are primarily orbiting high-metallicity, slightly inflated, slightly evolved stars. These particular parent stars were likely selected for high-priority confirmation observations because their abundant, narrow spectral lines should permit maximally efficient, cost-effective Doppler-velocity follow-up.

Among the planets, Kepler-4b, with its composition that’s likely largely water-based, provides further evidence that the majority of short-period planets formed far from their parent stars, beyond the iceline in the protostellar disk, and subsequently migrated inward. Kepler-7b is approximately the density of styrofoam. In a conversation with a reporter, I scrambled for an analogy:

It’s like looking at a football team. You might guess from the team photo that they’re all 250 to 300 pounds. But then you find out that some of them are 25 pounds; that would come as a surprise…

Everyone is looking forward to the big-picture results that will be coming from Kepler a few years hence, as it probes into the habitable zones of Solar-type stars. In the interim, though, the veritable flood of ultra-high precision photometric data arriving via the the Deep Space Network will keep Doppler velocity follow-up observers working the late-night shifts. The parent stars of the new planets are in the V=12.6 to V=13.9 range, roughly 100 times fainter than the prime transit-bearing stars such as HD 209458 and HD 189733.

According to a S&T editor Bob Naeye, who reported on Bill Borucki’s scientific talk this morning, the first 43 days of photometric observations from the satellite generated 175 transit candidates, of which 50 were followed up in detail to extract the 5 announced planets. The Keck I telescope has been the major workhorse for the high-precision RV follow-up efforts that are required to get accurate masses. According to the Keck I Telescope Schedule, 17 nights were allocated to the Kepler team from July through December of last year. Within this time alotment, roughly 50 RV measurements for the 5 new planets were obtained. The velocity precision for Kepler-4b looks to be of order 2-3 m/s, which is excellent. Here are two thumbnails from Borucki’s talk (look carefully to read the y-axis scale):

With a slew of nights and good weather during 2010, it should be possible to get a significant number of additional planets confirmed…

Ringing out the Old Year

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Image by JUNe (source)

At the beginning of the year, I made five exoplanet-related predictions:

1. A 1.75 Earth Mass planet orbiting a Main Sequence star.

2. A confirmed case of transit timing variations.

3. A transiting planet in a well-characterized multiple-planet system.

4. A transiting super-Earth (or more precisely, on the basis of observed composition, a transiting sup-Neptune).

5. 417 planets listed on exoplanet.eu.

So how did I do?

Prediction 1 was just a bit on the optimistic side. At present, the extrasolar planet with the lowest Msin(i) orbiting a Main Sequence star is Gliese 581e, with Msin(i)=1.94±0.22 Earth masses. So the forecast panned out to within the 1-sigma error. (Mayor et al.’s discovery paper is here, oklo.org coverage of the discovery is here, here, and here).

Prediction 2 falls just short of unambiguous fulfillment. HAT-P-13b is clearly going to exhibit transit timing variations, and soon, but as discussed in Bakos et al.’s discovery paper, it’s not clear whether they’ve already been observed.

Prediction 3 is satisfied by HAT-P-13b and c. The characterization is so good, in fact, that we’re able to effectively look inside HAT-P-13b.

Prediction 4 was doubly satisfied. First, by CoRoT-7b (a transiting super-Earth), and second, by GJ 1214b (a transiting sub-Neptune).

Prediction 5: 415 planets are listed (as of 12/31/2009) on exoplanet.eu…

BD 08-2823b (or opportunity comes knocking)

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I was catching up on astro-ph.EP this morning, and came across Paper #20 from the HARPS Search for Southern Extrasolar Planets. The authors report the detection of two new planets orbiting BD 08-2823, a nearby, moderately active K-dwarf. The inner planet in this new system has a mass comparable to Uranus (Msin(i)=14.4 Earth Masses) and an orbital period of 5.60 days — yet another example from the huge population of super-Earths and sub-Neptunes lying in short-period orbits around the Sun’s closest neighbors. As described in the paper, the two new planets emerged serendipitously from a thwarted attempt to identify transiting planets using the Hipparcos database.

What caught my eye about BD 08-2823b, is the fact that the parent star has not yet been monitored for transits. The a-priori probability that BD 08-2823b can be observed in transit is >7%. The star is observable from both hemispheres, at V=9.86 it’s a natural for small-telescope ground-based observers, and it’s up right now!

A successful detection is no walk in the park: The expected transit depth is of order 1.2 millimag, right at the limit of what’s been demonstrated by skilled small-telescope observers. The possible short-term activity of the parent star will demand multiple confirmations in the event that transits are indeed occurring. The current transit ephemeris is uncertain by more than a day to either side of the predicted transit midpoints (just added to the Transitsearch.org candidates table).

The transit valuation metric (described here) assigns a real-world value to the detection of a given transiting planet. It’s a way of cutting through hype, and it keeps a necessary spotlight on the fact that the cost of detecting a given transiting planet is not necessarily proportional to the scientific value of the planet detected.

If BD 08-2823b transits, its value using the metric works out to ~3 Million dollars. In other words, a detection would amount to a major discovery (something that’s getting increasingly harder to pull off, given this past year’s flood of results). In expectation, factoring in the 7% transit probability, the value is 210K. On a per-night basis, this is well over twice the value of Keck time, and yet it can be had by a good observer with a good backyard telescope. The next opportunities are centered on Jan 1st, and Jan 7th.

Dome

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From the short film "Dome" by Tony Misch

Here’s another remarkable YouTube video.

It’s a time-lapse movie that shows the construction of the dome for the Automated Planet Finder Telescope at the Lick Observatory on Mt. Hamilton. The sequence was assembled by Tony Misch (Support Astronomer for Lick Observatory) who created a 3-minute visual narrative by drawing from an archive of 200,000 frames taken at 2-minute intervals between Sept. 15th, 2005, and Aug. 14th, 2006. Be sure to turn up the volume — Paul Alcott’s fine-grained mechanized score is reminiscent of Autechre, and works very well.

The APF telescope will be used by the California Planet Search (CPS) and the Earthbound Planet Search (EPS) projects to carry out high-precision radial velocity monitoring of nearby stars. It’ll start collecting data within the next few months.

A Blue ‘606 Day

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The traditional definition of a “Blue” moon is the third Full Moon in a season containing four Full Moons rather than the usual three. In 1946, Sky and Telescope Magazine inadvertently launched a new, somehow more modern definition of a “Blue” moon as the second Full Moon to occur in a calendar month.

On the scale of urgency, the correct definition of a Blue Moon ranks favorably with such matters of astronomical concern as whether Pluto is a planet. I thus have to admit, that I immediately dropped what I was doing to answer a reporter’s e-mail query:

I read several accounts that the phenomenon will occur on New Year’s Eve based on the recent definition. Do you know if that’s accurate?

I answered:

We here in the United States will indeed be having a Blue Moon on New Year’s Eve according to the currently popular definition of a Blue Moon as “the second Full Moon to occur in a calendar month”.

The times at which the Moon is full (which occurs when the Sun, Earth and Moon form a line as viewed from above) can be calculated with great precision and with zero ambiguity. The current set of Full Moon times are:

02 December 2009 at 07:30 GMT
31 December 2009 at 19:13 GMT
30 January     2010 at 06:17 GMT
28 February   2010 at 16:38 GMT
30 March        2010 at 02:25 GMT

GMT stands for “Greenwich Mean Time”. This is the same as Universal Time, and corresponds to the current time zone for England (where the Greenwich Observatory is located). As you can see, for GMT, there are Full Moons in December 2009.

Here in California, we’re currently on Pacific Standard Time, which is 8 hours behind GMT. That means we had a Full Moon on Dec 1st at 11:30 PM, and we’ll have the next one on New Year’s Eve at 11:13 AM in the morning, giving us a Blue Moon.

In Australia, which lies between 8 and 10.5 hours ahead of GMT, the next Full Moon will occur on New Year’s Day, 2010. Australia, therefore, will not be experiencing a Blue Moon on New Year’s Eve, 2009 (the same is true for Japan, China, etc.).

Revelers in the Far East, however, should not feel left out. If you look at the table above, you’ll see that the Far East will experience a “double Blue Moon” in 2010, in which both the months of January and March will contain two Full Moons.

Blue Moons have no astronomical significance. The “Blue Moon” is just a name in the same sense as a “Hunter’s Moon” or a “Harvest Moon”. The Blue Moons are a purely cultural artifact that arise from the juxtaposition of the celestial clockwork of the lunar and terrestrial orbits with the Gregorian Calendar, which was introduced on 24 February 1582 through a papal bull by Pope Gregory XIII, and which has now been adopted worldwide as the standard civil calendar.

Even though Blue Moons have no astronomical significance, there is something oddly appealing about events that stem from the overlap (or better, the “beating”) between the precise orbital rhythms of planets and moons, and the ebb and flow of human-centered events here on Earth. At my weblog, oklo.org, I’ve been promoting a new holiday, ” ‘606 day”, which occurs every 111.43637 days when the wildly eccentric transiting planet HD 80606b makes its dramatic perihelion passage.

The ‘606 days for 2010 will occur on (adopting Universal Time):

Jan 8, 2010 at 9:49 AM
April 29, 2010 at 8:17 PM
August 19, 2010 at 6:45 AM
Dec 8, 2010 at 5:12 PM

In normal years, there are only three ‘606 days. In 2010, however, we’re lucky to have four. This “extra” ‘606 day is analogous to a blue moon.

Happy Holidays!

-Greg

(For readers unfamiliar with HD 80606b and  ‘606 days, see):

http://oklo.org/2009/01/29/the-big-swing/, http://oklo.org/2009/02/08/whats-your-angle/, http://oklo.org/2009/02/12/ready-set/, http://oklo.org/2009/02/12/go/, and http://oklo.org/2009/02/25/hd-80606b-transit-detected/

Update 1/2/10: Here’s a link to a call-in interview that I did on KPCC (L.A. Public Radio). As you’ll hear, there’s one regrettable gaffe where I say that a year contains “thirty days”… Not quite becoming of an Astronomy Professor!

M for all and all for M

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superEarths and subNeptunes

I’m always impressed by the efficiency with which red dwarfs pack hydrogen, the stuff of flammable zeppelins, into such a small space: Gliese 1214 is more than twice as dense as led. The density of the Sun, on the other hand, is bubblegum by comparison.

Gliese 1214b’s orbital period is a mere 1.58 days. Its 0.014 AU separation from the system barycenter is the smallest yet measured for any planet. Yet because of the high red dwarf density, the star-planet configuration is actually rather spacious. Here’s the system to scale:

Gl1214toScale

It’s interesting to compare this diagram with that of a genuinely close-in planet such as HAT-P-7b, which actually has a somewhat longer 2.2 day orbital period:

At a given period, a red dwarf fills much less of a planetary orbit than does a Sun-like star. If the occurrence rate of planets at a specified period is the same for stars of different masses, then one needs to look at $\sim(M_{\odot}/M_{\rm RD})^{2/3}$ times more red dwarfs than Sun-like stars to find a given number of transits with a particular period.

Gliese 1214b lies at enough stellar radii from Gliese 1214 that its a-priori transit probability was only about 7%. The Mearth survey currently covers only ~2000 stars, and so the fact that the discovery was made so quickly was probably not luck, but rather points to the existence of a very large number of low-mass planets orbiting small stars.

Let’s face it. The big dough goes to chase potentially habitable transiting planets. With this metric, the red dwarfs come out way ahead. If red dwarfs and Sun-like stars have equal occurrence fractions for planets with Earth’s mass and insolation, then a low-mass red dwarf has roughly four times the probability of a Sun-like star of harboring a transiting potentially habitable planet. Twice the temperature means one-sixteenth the area and the square root of sixteen is four. The red dwarfs also present a number of other advantages, see e.g. here, here, and here.

Ryan Montgomery and I have a recent paper out which foreshadows what I think is the inevitability of transit surveys that use the Mearth strategy to target true-Earth analogs the habitable zones of the lowest-mass red dwarf stars. Mearth  is itself very well-positioned to expand in this direction. I also think that a lot of effort will continue to shift toward improved Doppler-velocity capability in the near-infrared (see, e.g. this recent paper by Jacob Bean and collaborators which describes the use of ammonia gas in a glass cell to imprint a forest of fixed reference lines on a K-band stellar spectrum).

A last note: Twelve-Fourteen-b is likely to become a favorite target for small-telescope observers, so I made sure to add it to the Transitsearch.org candidates table. Now that classes are done for the quarter, I’ve been going through the literature and adding or updating one or two planets a day. It’s tedious work, but I’ve noticed some interesting upcoming opportunities, which I’ll be writing about soon. For transit-themed ephemera and the latest celebrity gossip, look no further than the transitsearch twitter stream: http://twitter.com/Transitsearch.

And a postscript: In the comments, reader cwmagee points out that the implication of the post is that the HAT-P-7 and Gl1214 diagrams are to scale which eachother, but that’s not the case. He attached a version which shows a to-scale comparison of both systems:

Red dwarfs are small!