With HAT-P-13c rapidly coming ’round the mountain, there was a very timely update on astro-ph last night. Josh Winn and his collaborators have obtained an additional slew of radial velocities which (1) demonstrate using the Rossiter-McLaughlin effect that the inner planet b’s orbit is likely well aligned with the stellar equator, (2) modify the orbital parameters, including the period of the outer massive planet, and (3) hint at a third body further out in the system.

How do these updates affect the unfolding story?

The Rossiter-McLaughlin measurement gives an estimate of the angle λ = -0.9°±8.5°, which is the angular difference between the sky-projected orbital angular momentum vector and sky-projected stellar spin vector. A non-intuitive mouthful. If we’re viewing the star edge-on, then λ = -0.9° amounts to a determination that the planet’s orbital plane is well-aligned with the star’s equator. (See this post for a discussion of what can happen if the star’s rotation axis is tipped toward the Earth). The good news from the measurement is that it’s a-priori more likely that planets b and c are coplanar — that happy state of affairs which will permit direct measurements of planet b’s interior structure and tidal quality factor. If, on the other hand, the planets b and c have a large mutual inclination, then b’s node will precess, and measurement of a small value for λ will occur only at special, relatively infrequent, times during the secular cycle. A close to co-planar configuration also increases the likelihood that the outer planet can be observed in transit.

With their beefed-up data set of out-of-transit Doppler velocities, Winn and his collaborators are able to get a better characterization of the planetary orbits. The best-fit orbital period and eccentricity of the outer planet are slightly modified when the new data are included. The best-guess center of the transit window for c has “slipped” to April 28, 2010, with a current 1-σ uncertainty of 2 days.

The later date, however, is not an excuse for procrastination! Measuring the TTV for this system is a giant opportunity for the whole ground-based photometric community, and a definitive result will require lots of good measurements of lots of transits starting now (or better yet, last month.) I’ll weigh in in detail on this point, along with the challenge posed by Mr. D very shortly…

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!

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!

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.

A quick addendum to the previous post. After a rather lengthy and undeserved “vacation”, Transitsearch.org is back on the air. The old website is running as a placeholder, and updated content will follow on soon.

I’ve moved the front-end of the transitsearch site to the hosting service that runs oklo.org, so the real URL is www.oklo.org/transitsearch/ By Dec. 10th, the domain name transfer will be complete, and the old www.transitsearch.org address should properly redirect.

Further updates can be had by subscribing to Transitsearch.org’s twitter stream: http://twitter.com/Transitsearch. We’re planning events to surround the next ’606 day, and we’re also planning to organize a campaign for the HAT-P-13c transit opportunity that’s centered on April 12, 2010.

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.

Grant-proposal season puts a crimp on one’s style. Despite many interesting developments in the field over the past few weeks, I haven’t had time to write. I’m glad that’ll change shortly.

We’re also very close to getting upgraded versions of the systemic backend and a new Transitsearch-related project on line. In the interim, here’s a link to the old transitsearch.org candidates page. I have it running on our server here at UCO/Lick, and it’s updated every 10 minutes. This information should also soon be available at JPL’s NStED site.

Full-resolution Poster-sized .pdf of the above.

The next HD 80606 transit is coming up this week. While the sky position of the star will be much more favorable during the coming January event, observers across the US have an opportunity to get photometric measurements of the ingress early Thursday morning.

The transit begins just after 11 AM UT on Sept. 24, and will unfold over the next 12 hours, meaning that observers in Japan and East Asia will be able to catch the egress.

Josh Winn of MIT is organizing a repeat of the successful June campaign (detailed in this post). If you’re a capable photometric observer, and if you’re interested in participating in the campaign, definitely get in touch with him.

Visitors to oklo.org may have noticed that the site was down for most of Sunday. I’d been neglecting to update my WordPress installation, which lead to a problem with the database, and a huge load spike for the server. Everything seems stable now, and I’m now flossin’ 2.8.4 inch rims.

In the relatively near future, I will be modernizing some aspects of the look and feel of the site, which will make it more discussion-friendly, and more smoothly slotted into the hum of the outside world. No need to worry, though. We’ll continue to roll ad-free.

I’ve updated the second systemic console tutorial which guides the user through the remarkable Upsilon Andromedae radial velocity data set. The back-end database is getting closer to its relaunch, and the systemic console (version 1.0.97) is freely available for download here.

Read on to work through the tutorial.

Console Tutorial #2 — The Ups and Downs of Ups And

The star Upsilon Andromedae lies roughly 40 light years away in the constellation Andromeda, and (unlike most of the known planet-bearing stars) is bright enough to be visible to the naked eye if you know where to look. Upsilon Andromedae is roughly 2.5 billion years old (about half the age of our Solar System), and is about 30% more massive (and roughly twice as luminous) as the Sun. Because of its relative brightness and proximity, and because it is reasonably similar to the Sun, it was among the original group of 50-odd stars surveyed for planets by Paul Butler and Geoff Marcy using the radial velocity technique. It was also one of the first stars found to be accompanied by an extrasolar planet. More than a decade on, it’s interesting to read the original discovery paper. (See Butler et al. 1997, “Three New 51-Peg Type Planets”, Astrophysical Journal Letters, 474, 115-118).

One of the several publicly available Upsilon Andromedae data sets was published by Fischer et al. 2003, and contains 253 individual radial velocity measurements that span more than 15 years of observation. It’s thus capable of giving the systemic console a very informative workout. In this tutorial, we step through the procedure for “discovering” the planets that exist in the Fischer et al. (2003) radial velocity data. We assume that you have already worked through the first tutorial, which analyzed the much less extensive data set for HD 4208, and which introduced the basic concepts that underlie the fitting of orbital models to radial velocity data.

To get started, double-click on the Console.jar icon and let the console’s initialization procedure run its course. When the console is ready for action, click on the system dialog icon (the yellow star symbol near the upper-left-hand corner of the console) and type “UpsAnd” into the text box at the upper-right-hand of the system dialog window. You’ll have a choice between a number of different data sets for Upsilon Andromedae. Because the parent star is so bright and because the planetary system is so interesting, it has been studied by nearly every active team that uses the Doppler velocity method to detect planets. For the tutorial, you’ll be using the first data set in the list. It’s labeled “upsand”.

The “upsand” data set was obtained with the venerable 3-meter Shane telescope on Mt. Hamilton. The published reference for the data and important thumbnail statistics (duration, number of observations) are shown in the lower right hand corner of the system dialog window. Click “select system” to load the data into the console, and if prompted, click “OK” to accept the default data set.

Notice how the data-taking rate increased dramatically during the time span that covered the observations. After Upsilon Andromedae was discovered to harbor a multiple-planet system in early 1999, it began to be observed much more frequently. The radial velocity surveys, with their limited budgets of observing time, continually re-balance the conflicting demands of obtaining as many observations as possible of interesting systems, while simultaneously devoting as uniform a coverage as possible to as many different stars as possible. When Upsilon Andromedae proved its worth, it started getting lots of attention.

In the case of the star HD 4208, which was the subject of tutorial #1, it was straightforward to find a decent one-planet fit to the radial velocity data set simply by manipulating the console’s sliders, and then applying a final “polish” to get a best fit. This was possible because the planet accompanying HD 4208 has only been observed for two orbits, and because it is apparently the only large planet orbiting that star. With Upsilon Andromedae, however, the complexity of the radial velocity data set hints at the presence of several significant planets with different periods. To get a foothold, we need to compute a periodogram that tells us which frequencies (that is, which potential planetary periods) are most prevalent in the data. Click the periodogram button near the top-middle of the console. After a moment, a completed, densely-sampled Lomb-Scargle periodogram will appear in its own window:

The periodogram indicates that a number of different periodicities are present in the data. The most important peaks are listed to the right of the plot. The higher the power, the more important the peak. In this case, the strongest peak is at 4.617 days. We make the hypothesis that the highest peak is due to a planet, and we therefore activate the first row of orbit sliders (using the button to the far left of the row).

By typing in the box, enter 4.6172 into the period controller for planet #1. Note that if you use the slider, you will have difficulty getting this exact value to appear.

With a 4.617 day period, the full radial velocity plot on the console window becomes totally useless. The prospective planet has executed more than a thousand orbits over the length of time (~15 years) that the star has been observed. First, click on “set curve smoothness” under the options menu, and enter 50,000, the maximum resolution available for plotting:

Then, use the zoom and scroll sliders beneath the plot to focus in on one of the well-sampled regions:

A quick inspection of the excursions of the radial velocities relative to the sinusoidal pattern produced by a single 4.617-day circular orbit suggests that more than one planet may be contributing to the overall radial velocity signal. There are trends in the distribution of points which clearly unfold over periods of hundreds of days and more. Ignore these longer-term trends for the moment, and focus on pinning down the orbit of the 4.617 day planet.

Click on the “Mean Anomaly” line minimization button for planet one:

This automatically varies the mean anomaly (defined at the epoch of the first radial velocity data point) through the full 360 degree range, and selects the value that gives the best fit to the data. The chi-square of the fit drops to something in the neighborhood of 80, and the RMS scatter drops to roughly 60 meters per second.

Next, by clicking on the line minimization buttons for Period, Mass, Mean Anomaly, and Stellar Offset, you can try to improve the one-planet fit. A few cycles of clicking brings the chi-square down to 65.8 (the exact values that you calculate might deviate slightly from this, depending on the particular history of operations that you’ve performed). A final round of improvement can be obtained by sending the Period, Mass, Mean Anomaly, and Stellar Offset parameters to the Levenberg-Marquardt multi-parameter minimization algorithm. You do this by checking the square left hand buttons and then clicking the “polish” button near the top-left of the console.

A good way to display the resulting fit is to “fold” the data by plotting it at the periodicity of the 4.617-d planet. You can do this by selecting “fold to period of planet 1″ after clicking on the fold menu button in the upper-right corner of the console.

The huge scatter indicates that the resulting model is by no means a satisfactory fit to the data! Upsilon Andromedae definitely seems to be accompanied by a ~0.7 Jupiter mass planet on a 4.167 day orbit, but there is clearly more going on. Indeed, when Paul Butler and his collaborators announced their discovery of the 4.167 d planet in 1997 on the basis of just the first 36 radial velocities, they noted that,

“The 36 velocities show evidence for variability in the gamma velocity of the sine wave on a timescale of about 2 yr with amplitude of 50 meters per second.”

Back in 1997, that was all they could say, but with the large number of additional velocities that have been published since then, we’re in much better shape to figure out what is going on. Indeed, there are several ways that one can proceed to improve the fit. One strategy might be to explore non-zero orbital eccentricities for the 4.167-day planet. (If you’re interested, you can give that a try and verify that non-circular orbits for the inner planet don’t do much to improve the fit.) An alternate, and in this case more profitable, way to proceed is to search for additional planets in the system. To do this, we want to subtract off the radial velocity signal arising from the short-period 4.617 day planet, and look for the remaining periodicities in the system. This is accomplished by clicking on the periodogram of the residuals, or “Res. Periodogram” button at the top of the console. It operates just as advertised, yielding:

In this periodogram, the strongest peak in the data occurs at 242.394 days, with the another very significant peak falling at ~1423 days. There are also peaks near exactly one day, which are aliases arising from the fact that the star was often observed with a 24-hour night-to-night cadence. Let’s assume that there is a second planet in the system with a 242.394 day period. Activate the second planet, enter the period, and then use the line minimizers to improve the fit (leave the eccentricities of both planets at zero for the moment). After a few rounds of clicking, the two-planet version of the system rolls into a local minimum of parameter space.

The fit can be improved a bit more by polishing with the Levenberg-Marquardt algorithm, but clearly, however, there may be additional bodies contributing to the radial velocity variation of the star. To find what might still be lurking, compute a periodogram of the residuals to the 2-planet fit (by clicking “update” in the residuals periodogram window).

The 242 day peak has been completely eliminated, leaving a single peak at 1290.0 days that contains a lot of power. Activate a third planet with this period, and polish the fit by line minimizations (start with the Mean Anomaly) followed by multi-parameter minimization (polish) using Levenberg-Marquardt.

With three planets on the books, the fit has improved significantly, but is not yet adequate. At this point, one could try to add a fourth planet based on the result of the residuals periodogram. Alternately, one could open the system up to eccentric orbits. To explore eccentricity, pull the eccentricity sliders of the outer two planets up to modest non-zero values (for example e=0.1 for both). Then improve the radial velocity fit with line minimization followed by another application of the Levenberg-Marquardt algorithm.

A successful model of the system has eccentricities of order e=0.27 and e=0.26 for the two outer planets, and the model radial velocity curve really does quite a good job of tracing the observations:

In an upcoming tutorial, we’ll look in more detail at how we can statistically quantify the meaning of “good job”. Here’s a (full-resolution screen-shot of the console) when the currently accepted three-planet model of the system is dialed up on the console.

Note that by using the zoom-in and zoom-out buttons on the orbital view window, you can examine the actual top-down view of the co-planar model system. The arrow button allows you to pop the orbital view out into its own separate window.

Without regard to order of likelihood, I thought it’d be interesting to lay out a few very specific scenarios by which the first extrasolar world with a 1 million+ habitability valuation could be discovered.

A favorite space-art trope is the habitable moon orbiting the giant planet (which is generally well-endowed with an impressive ring system). Smoggy frigid Titan is the best our solar system can do along these lines, but there’s nothing preventing better opportunities for habitability lying further afield.

I’ve always been intrigued by the fact that the regular satellite systems of the solar system giants each contain of order 2 parts in 10,000 of the mass of the parent planet. At present, there’s no reason to expect that this scaling is any different for extrasolar planets, and given the example of Titan, there doesn’t seem to be anything to prevent the bulk of a given planet’s satellite mass from being tied up in a single large body. Furthermore, since it’s my weblog, I’ll take the liberty of assuming that the satellite mass fraction scales with stellar metallicity.

Image source.

It’s perfectly reasonable to imagine, then, that HD 28185b is accompanied by a 0.63 M_earth, 0.86 R_earth satellite with an orbital radius of a million kilometers. HD 28185b itself has Msin(i)=5.7 Mjup, and the metallicity of HD 28185 is [Fe/H]=+0.24.

Now, for a long shot: let’s assume that on July 11th, 2009, a cadre of small telescope observers in Australia, South Africa and South America discover that HD 28185b transits its parent star. The geometric a-priori odds of the transit are ~0.5%. The expected transit depth is an eminently detectable 1%. A transit of moderate impact parameter lasts about 12 hours.

If a detection is made on July 11th, 2009, it’s a sure thing that the following transit (July 29th, 2010) will be the subject of great scrutiny. The current ground-based state of the art using orthogonal transfer arrays is demonstrating 0.4 mmag photometry with 80 second cadence. At this level, with spot filters and several observatory-class telescopes participating, the piggyback detection of the satellite transit is a many-sigma detection.The cake would be iced on Aug 16th, 2011, when the ~25 second difference in midpoint-to-midpoint intervals would be detected. We’d then be in possession of a potentially habitable terrestrial world warmed by an admirably bright and nearby parent star. Accurate mass and radius determinations would be fully forthcoming. All from the ground, and all at a total cost measured in thousands of dollars of amortized telescope time on existing facilities.

Admittedly, the odds of this specific scenario are slim. I estimate one in two thousand. The payoff, however, is massive. HD 28185bb (with the properties given above) is worth a staggering 100 million dollars. In expectation, then, that’s 50,000 dollars for fully covering the transit window this July…