systemic

We’ve been seeing a nice increase on traffic here at oklo.org as the Sky and Telescope and American Scientist articles show up in mailboxes and on newstands. If you’re new to the site, welcome aboard, and please read the last several posts. They give a brief overview of the Systemic Project, and tell you what you need to start fitting systems.

As you may have noticed, we’re hard at work improving the usability of the site. Stefano, in particular, has done an amazing amount of work on the back-end over the past several days. It really is taking shape as a genuine research environment, and we absolutely are urging you to try it out while we’re putting the definitive users manual together. You can’t break anything, and if you post questions, we’ll make sure they get answered on a timely basis.

A few news items:

(1) There are two separate channels for registration on systemic. The first, accessed through the “login” tab on the site header above, is part of the WordPress package that runs the oklo blog. Registration on the blog allows you to comment on the oklo.org posts. The second, accessed through the “backend” tab on the site header, gives you access to the collaborative php-based environment that constitutes the systemic backend. You can register for either or both, and you don’t need to give your real name or any real-world identifying information other than an e-mail address.

(2) We’ve been working to design the first systemic challenge radial velocity data set, which will be released on Monday September 4th. The user who finds the fit with a reduced chi-square closest to unity will win a $149 Sky Atlas from Sky and Telescope. Both professional and amateur planet hunters are encouraged to participate, but given the groundswell of activity that we’re seeing on the systemic back-end, and given the console’s ability to carry out self-consistent fits, the smart money is on an amateur winner.

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Stefano (while in the midst of writing his astrophysics thesis in Bologna!) has somehow found the time to implement a whole slew of very cool improvements to the Systemic back end. New aspects include a search function, a personal “fits” library, and a variety of interactive features designed to aid collaboration and make the user experience more rewarding.

We’re working on a full user manual for both the downloadable console and the back end, but in the meantime, we’re really urging users to (1) download the console, (2) create a free account on the back end, (3) work through the systemic console tutorials one, two, and three, (4) upload fits, and (5) start collaborating. There are a number of real systems in the star catalog which can be profitably characterized and improved. I’m also very interested to see what people come up with for the datasets systemic001 and systemic002.

Do give it a try, and please give us feedback, either in the comments section on the back-end, or in the comments section for this post.

Two tips: (1) For Mac-users, Firefox provides a better interface to the back-end than does Safari. (2) At the moment, the user-interface looks better if you resize to a wider browser window.

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With the verdict in on Pluto, we here at oklo.org will have to revert to sober, scientifically rigorous posts on extrasolar planetary systems to keep our readership and ad rates up. And as soon as I can figure out how to make WordPress launch those “swing for the fences” pop-ups from our site, we’ll be increasing our revenue stream even more.

American Scientist has just published my article on planet formation and extrasolar planets in their September/October issue. The article wraps up with a description of the systemic console, and the systemic collaborative research project. If you’re an American Scientist reader visiting oklo.org for the first time, welcome aboard!

Several posts back, I put up a brief description of the immediate goals of the Systemic collaboration:

The Systemic collaboration is proceeding in three steps. In the first step, which is ongoing, we’ve been gathering all of the radial velocity data that have been published for known planet-bearing stars. These data sets are included in the downloadable systemic console, and the systemic back-end allows participants to upload their own planetary fits to this data. We want to use the data to create a uniform catalog of known planetary systems.

In the second and third phases of the systemic project, we’ll be studying synthetic data sets that have been produced using our own algorithms. “Systemic Jr.” will launch at the beginning of September, and will contain 100 synthetic data sets, four of which will be special challenge systems. The Systemic Challenge, sponsored by Sky and Telescope will be explained in more detail, and will be available at a link on their website. The challenge systems will be released on September 3, 10, 17, and 24, along with a specific set of contest rules. The first person to crack each of these systems will recieve a paperback edition of the Millennium Star Atlas (a $149.95 value). In order to prepare for the contests, go ahead and download a copy of the systemic console, and work through tutorials one, two, and three. A full technical manual for the console is in the works, and will be ready for download quite soon.

Later this Fall, when Systemic Jr. wraps up, we’ll launch the full Systemic simulation. A lot more on this will be posted in the weeks ahead. Our overall goal is to obtain an improved statistical characterization of the galactic planetary census.

The most interesting serious-planet news from the past week has been the paper by the Geneva Extrasolar Planet Search Team that releases an updated radial velocity data set for the nearby solar-type star Mu Arae (also known as HD 160691). As discussed in this post, the console can be used to quickly uncover and characterize the orbits of the four planets that have been announced for the system.

The mu Arae system is remarkable because the two middle planets (with periods P~300 days, planet “d”, and P~640 days, planet “b”) experience strong mutual gravitational interactions during the 5-year time period that the system has been observed. The presence of strong interactions indicates that a model for the system built from independant Keplerian orbits cannot provide a fully realistic fit to the system. In order to build a fully self-consistent fit, one must find an N-body model. The systemic console has this ability, which is enabled whenever the “integrate” box is checked.

N-body integrations are much more time-consuming to compute than simple evaluations of Keplerian fitting functions. The performance of the console thus slows down considerably when integration is enabled. (Note also, that this post now becomes a bit technical. If it sounds like gibberish, you can either skim the next few paragraphs, or, better yet, work through the tutorials on the use of the console.)

Read more…

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Some things don’t change. Even back in 1846, the planet detection business in our solar system was a rough-and-tumble game. No sooner had Urbain Jean Joseph LeVerrier announced his prediction of the existence and position of Neptune, and had it dramatically verified by Galle and d’Arrest, than the British tried to jump all over the discovery and claim priority for Adams! Not to mention that tricky issue of names. LeVerrier tried various jostling maneuvers with the French Academy to try to get his planet named after himself, but his machinations were unsuccesful and Neptune stuck.

At least LeVerrier didn’t have to wrangle with Nineteenth Century player haters rushing to either (1) strip his newfound world of its planet status, or (2) consign it to the marginalia of the solar system. Neptune packs 8,065.34 times the mass of Pluto and 68,286.7 times the mass of Charon. It’s a planet with a capital P.

Here’s what I find amazing. The dramatic tension of the Prague IAU meeting apparently hinges on the future nomenclature for 2003 UB-313 and its ilk. Even the New York Times, the United States paper of record, makes the episode seem like one of the scientific Big Deals of the year. Oklo dot org manages to climb out of its summer visitors slump on the basis of two chatty posts on the Pluto debate. While all this is going on, an amazing multiple-planet system orbiting the nearby solar-type star HD 160691 receives a new planet and a dramatically improved characterization, and hardly anyone notices.

The downloadable systemic console and the systemic back-end contain several data-sets for HD 169061. The exact data set used by the Geneva group in their astro-ph paper from yesterday is listed in the system menu as HD160691_M04P06CH. (No sooner had I laboriously typed in the table from the .pdf file than Eugenio pointed out that one can simply copy-paste from the text file source on astro-ph. Doh!)

The data used by the Geneva group comes from three telescopes. It includes AAT data from McCarthy et al. 2004, as well as older data from Coralie and new, extremely high-precision data from HARPS. The console therefore loads with three offset sliders.

Read more…

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The October 2006 issue of Sky and Telescope is just hitting the stands. It contains a feature article — Virtual Planet Sleuths — on the usage of the console and the Systemic collaborative project. If you’ve read the Sky and Telescope article, and are a first-time visitor to oklo.org, welcome aboard!

The Systemic collaboration is proceeding in three steps. In the first step, which is ongoing, we’ve been gathering all of the radial velocity data that have been published for known planet-bearing stars. These data sets are included in the downloadable systemic console, and the systemic back-end allows participants to upload their own planetary fits to this data. We want to use the data to create a uniform catalog of known planetary systems.

In the second and third phases of the systemic project, we’ll be studying synthetic data sets that have been produced using our own algorithms. “Systemic Jr.” will launch at the beginning of September, and will contain 100 synthetic data sets, four of which will be special challenge systems. The Systemic Challenge, sponsored by Sky and Telescope will be explained in more detail, and will be available at a link on their website. The challenge systems will be released on September 3, 10, 17, and 24, along with a specific set of contest rules. The first person to crack each of these systems will recieve a paperback edition of the Millennium Star Atlas (a $149.95 value).

Later this Fall, when Systemic Jr. wraps up, we’ll launch the full Systemic simulation. A lot more on this will be posted in the weeks ahead. Our overall goal is to obtain an improved statistical characterization of the galactic planetary census.

In the Sky and Telescope article, I made a rather bold claim that by using the console, it’s possible to find an as-yet unannounced planet around more than a dozen different stars. The 55 Cancri data set, for example, is an excellent place for aspiring planet hunters to try their hand.

The feasibility of detecting planets in the published data sets was illustrated dramatically over the past week. On August 14th, Krzysztof Gozdziewski, Andrzej Maciejewski, and Cezary Migaszewski posted a preprint on astro-ph which describes their detection of a fourth — then unknown and then unconfirmed — planet orbiting HD 160691 (also known as mu Ara). They detected the planet using their own software, which has a similar set of capabilities to the systemic console, and they used the dataset provided by the recent Butler et al. 2006 catalog paper. They found an orbital period of P~307 days for the planet, a nearly circular orbit, and a mass of 0.5 Jupiter Masses.

Today, on astro-ph, the Geneva Radial Velocity Search team published a paper with an updated set of radial velocities of HD 160691 which were obtained with the HARPS instrument at La Silla. In the abstract of their paper, they write: “We present the discovery of mu Ara d, a new planet on an almost circular 310-days period and with a mass of 0.52 Jupiter Masses”.

So there you go, folks! The planets are in the data sets. You just need to download the console, fire it up, get a good fit, and submit it to the Systemic back-end.

[Note: It’s not clear what (if any) “credit” Gozdziewski et al. will get for their discovery. I don’t want to proffer an opinion on who should get credit in a case like this, mainly because I really don’t care. The Systemic backend includes a public-record chronological list of submitted fits for each radial velocity data set. If you turn up a planetary configuration that later gets confirmed by one of the radial velocity teams, you’ll get the personal satisfaction of knowing you knew about the planet first. What you almost certainly won’t get, however, is official credit for the discovery, or the right to name the planet, etc., etc.

For the synthetic planets in phases 2 and 3 of the Systemic collaboration, however, the discoverers will receive official credit, and they will have the right to name the planets if they choose to do so.]

Looks like Geoff Marcy won the is-Pluto-a-planet debate. His stylish quote (reminiscent of Pablo Picasso’s comments to the New York Times on the occasion of Apollo 11) dramatically wrapped up Dennis Overbye’s NYT article, and made the whole brouhaha look rather foolish indeed.

I’ve been trying to take the high road too, but so far with no success. This morning, I succumbed to temptation and jumped into the fray by way of Rob Roy Britt’s cnn.com piece, snidely pointing out that eccentric satellite orbits can sometimes lead to the satellite being promoted to a planet for part of the orbit and demoted to a mere moon for the remainder:

Higher resolution version here.

Then, less than an hour later, I was talking to a departmental colleague about scientifically useful questions, when our conversation suddenly fell into the Pluto trap. We spent an enjoyable half-hour batting around a comfortably well-worn sequence of conversational bon mots. My colleague — an eminent planetary scientist — was pleased to take a tough-guy approach: Eight planets. He’s in favor of a 10-year phase-out for Pluto, now that the New Horizons probe is on its way and (presumably) safely beyond the grasp of NASA budget cuts. We agreed that a decade is more than enough time to give the kids’ plastic placemat manufacturers and textbook publishers enough time to switch the production lines over to the correct version of the solar system.

With the circulation of Alec Wilkinson’s recent New Yorker piece, planet placemats and mobiles have emerged as a topic of discussion. In Kitchenport, in downtown Santa Cruz, there are indeed plastic placemats for sale featuring the eight inner planets and Pluto. I was surprised to find Saturn listed as the “slowest planet” on the mats:

This inspired me to one-up my colleague with an even tougher-guy approach: Take a historically stringent view and limit the planets to the five classical wanderers of the heavens, thus dramatically restoring Saturn to its rightful position as the slowest planet.

Bob Naeye over at Sky and Telescope has been blogging the planet debate as well. He caught an arithmetic error in the original version of yesterday’s post. In my haste to slap the post up on the blog, I used da/dt=.374 cm/yr rather than the correct value of da/dt=3.74 cm/yr in the timescale estimation.

A first estimate for the Moon’s promotion timescale can be made with the following logic. The Moon becomes a planet when the distance to the moon is such that the Earth-moon barycenter lies at the surface of the Earth. The barycenter of the orbit at that time will be defined by

with Rm being the distance from the Earth to the Moon. The system mass ratio is

According to the IAU draft resolution, the Moon will turn into a planet at the exact moment when the barycenter moves above the surface of the Earth, which is located at R=6.378e+8 cm. Assuming a circular orbit, the Moon thus needs to be at a=5.18e+10 cm, which means that the Moon needs to recede from its current orbital radius by da=1.34e+10 cm. At the current rate of da/dt=3.8 cm/yr, this would take 3.5 billion years, a timescale that is well within the life expectancy of the Earth in the face of possible destruction by the Red Giant Sun.

This is just a first approximation, however. In reality, the time will be considerably longer, both because the tidal force (and hence the dissipation) decreases as the moon goes outward, and because the current rate of tidal dissipation is near a geological maximum, most likely because the Earth’s oceans are presently in a near-resonant, highly tidally dissipative configuration.

Assuming a constant value of the tidal quality factor Q, the time interval T, required for a satellite to recede from an initial orbital radius a_i to an orbital radius a_0 is given by

In the above, k_2=0.299 is the Earth’s Love number. Currently, Q=12 for the Earth. Plugging numbers into the above equation yields a time T=1.57 billion years for the Moon to recede to its current location. In the past, however, the average value for Q was higher, and it is likely that it will also be higher in the future. Given that the age of the Earth-Moon system is 4.5 billion years, average Q for the Earth has been more like Q=34. If we assume that Q=34 holds as a long term average value, then we arrive at a best estimate of T=26.8 billion years until the Moon is promoted to planetary status.

Sadly, though, the Moon’s reign as a planet will ultimately be limited. Planetary status is achieved when the Moon’s distance reaches 81.3 Earth radii. For the next 23 billion years thereafter, the Moon will be living the bling planetary lifestyle as it slowly continues to recede. When the Moon reaches ~87 Earth radii, the length of Earth’s rotation will have decreased to ~47 days, and the Earth and the Moon will be tidally despun. Thereafter (as described by Jeffreys, 1970), tidal interactions between the Earth, the Moon, and the Sun’s remnant white dwarf will drive the Moon back inward, eventually stripping it of planetary status, and finally destroying it by tidal breakup into a massive ring system.

You guys have all read about the recommendation of the IAU committee.

Looks like the Moon’ll be a planet soon! Tidal evolution is currently driving it outward at 3.74 cm per year. It appears that the Moon will be admitted into the planetary club in roughly 30 billion years if we aren’t destroyed by the Sun’s Red Giant phase.

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Last week, I started a series of posts that will examine the feasibility of detecting a habitable terrestrial planet orbiting Alpha Centauri B. We want to do this from the ground, using the proven radial velocity technique. Our strategy will be to build a ~1 meter telescope in (probably) Chile with a high-precision spectrometer. The telescope will be used exclusively to obtain velocities of Alpha Centauri B, night after night, whenever the star is above the horizon, and whenever the weather is good.

At La Silla, Alpha Centauri never quite sets below the horizon. From roughly October through December, however, the star is generally too low in the sky to be adequately observed. This generates a yearly periodicity in a simulated 5-year radial velocity time series:

(Note that in the original version of last week’s post, I posted an incorrect file version of this figure. The plot has now been replaced in the post with the correct plot.)

The 96076-point time series shown above was generated by Eugenio under the assumption that we can obtain the same radial velocity precision that the HARPS spectrograph obtained on HD69830 (which is a near-twin to Alpha Centauri B). The average radial velocity error is 0.8 m/s, and the observing cadence is 200 seconds. The periodogram shows crystal clear evidence of three of the four terrestrial-mass planets in the simulated system.

The large peak in the periodogram at P=347 days corresponds to a planet with half an Earth mass. The two interior peaks are produced by planets with masses similar to Mars. If the planetary masses are doubled, that is, if the largest planet in the system has one Earth mass, then the evidence from the time series is even more overwhelming (the data set is available on the downloadable console as AlphaCenB_m2Y5):

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Now I know that scientific progress is the important issue at stake here, and I’m very excited about the upcoming Kepler mission, and the fact that it will be detecting Earth-sized planets in the habitable zones of 12-14 magnitude stars. That’ll be cool. Nevertheless, we’d like to beat Kepler to the punch. We’d like to bag the first habitable Earth-mass planet from the ground. Can we do it?

Kepler is currently scheduled for launch in October 2008. To be confident of an Earth-mass planet in the habitable zone of one of their target stars, they’ll need to see four successive transits. This means that a reasonable date for their big press conference is Dec. 21, 2012. That gives us six years.

There’s a big difference between noisily posting synthetic observations on a blog, and actually observing Alpha Centauri with a purpose-built ~5 million dollar dedicated telescope in the Southern Hemisphere. It’s safe to say that we won’t be seeing first light a year from now, and therefore we won’t have a five-year data stream by the time the current long count is up.

On the other hand, the above periodogram for the Earth-mass planet constitutes an incredibly strong detection. We can be confident in the presence of the planet with considerably less data.

So consider the following example. Let’s say that instead of obtaining HARPS-like 0.8 m/s precision, we’re only able to get 3 m/s precision. This could be the result of Alpha Centauri B showing more short-term jitter than expected, or because we don’t have enough dough to commision an absolutely state-of-the-art spectrometer. Let’s also assume that we only observe for two years rather than five. In this case, the periodogram looks like this:

We’ll definitely need to do a proper statistical analysis, but from appearances alone, “chi-by-eye”, the planet is clearly still there at the many sigma level.

I’m almost too young to remember the Apollo missions. I was five years old in December 1972. Despite great protests and resolve, I had long since gone to bed when Apollo 17 blasted off in a dramatic night launch that marked the last journey into deep space. Early the next morning, Bobby Robinson came running breathless to our back door, “They’re showing the countdown again on TV!” We sprinted down the block through the cold to his house, bursting into the den. The brilliantly spotlighted Saturn V was still on the launchpad. “Four Three Two!” Billows of flame filled the screen. The slow, almost imperceptible lift-off. Shards of ice condensed from the humid Florida air fell away from the great frozen missile like waterfalls.

For days afterward, we built rockets out of legos.

One of our recurring goals here at oklo is to gain an accurate idea of what the extrasolar planets really look like. We’re working on this by connecting detailed numerical simulations to state-of-the-art rendering. The photographs brought back by the Apollo missions provide a key basis of insight into much of what we can expect to see. Inspired by Michael Light’s Full Moon, I’ve thus been spending time working through the Apollo Lunar Surface Journal, which provides a detailed commentary and a near-complete trove of images and video from all of the lunar missions. It’s easy to become engrossed to the point where hours simply disappear.

Several impressions hang in my mind. When Earth is in view, or when you’re standing on the airless lunar surface with the Sun at your back, the sky is completely black. No stars visible, no glowingly luminous nebulosity in the sky. The dynamic range vastly exceeds what the human eye can handle.

If the Sun is in view, light scattered by the optical system — be it a Hasselblad camera lens, or a gold-plated faceplate visor, or an eye lens — has a huge effect on the visual field. An understanding of the lens flare is essential to producing a realistic visual impression.

Harrison Schmitt aboard Apollo 17

When the Apollo Spacecraft arrived at the Moon, one astronaut remained alone aboard the command module, in orbit a mere 65 miles or so above the lunar surface. For the half of each orbit above the lunar farside, radio communication was impossible, with the signal regained each time the Earth rose above the horizon.

Ken Mattingly, of Apollo 16 described the experience of being alone in orbit:

I was lying there, looking out the window as we moved across the terminator. I was listening to the Symphonie Fantastique, and it was dark in the spacecraft. I was looking down at dark ground, and there was Earthshine. It was like looking at a snow-covered Earth scene under a full moon.

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Everything that we know about planet formation indicates that both Alpha Centauri A and Alpha Centauri B should be accompanied by terrestrial planet systems. Long-term integrations show that the dynamical environment is stable. Simulations using the Wetherill-Chambers method show that the accretion of terrestrial-sized bodies should proceed with an equal or greater ease than was the case in our own solar system. The metallicity of Alpha Centauri is significantly supersolar, which points toward the availability of plenty of raw material for forming terrestrial planets.

The terrestrial planets orbiting Alpha Centauri A and B were likely assembled from dried-out planetesimals. Pertubations from Proxima, however, would have stirred up Alpha Centauri’s circumbinary analog of the Kuiper belt, providing a mechanism for the delivery of volatiles to terrestrial bodies orbiting A and B.

In a string of posts last month [most recent here], we laid out the case for the existence of terrestrial planets in the Alpha Centauri system. We argued that if one of these planets has an Earth-mass and a habitable orbit, then it is detectable with a flat-out effort by the HARPS spectrograph. We based our argument on the fact that HARPS was recently used to produce an amazing detection of three Neptune-mass worlds orbiting HD 69830 — an old, chromospherically quiet K0V star that is a near-exact twin of Alpha Centauri B.

This presents quite an interesting situation. HARPS, at La Silla, and the AAT in Australia are the only instruments in the world that currently could conceivably be used to make the detection. The APF telescope can’t see the Southern Sky, and the wider astronomical community would never allow one of the VLTs to be commandered for an all-out effort on one charismatic system. Furthermore, both HARPS and AAT are currently hard at work on large-scale radial velocity surveys. This means that [1] we’re unlikely to get scooped, and [2] we’ll have to build a special-purpose telescope if we want to explore the Alpha Centauri planetary system.

Eugenio and Aaron and I have begun a detailed feasibility study of a dedicated, state-of-the-art radial velocity campaign on Alpha Centauri B. So far, the results have been encouraging — nothing resembling a showstopper has turned up yet. The purpose of the next few posts is to report what we’ve learned so far. We’ll be posting data files so that interested readers can replicate (and if they want to, extend) our work using either their own routines or the downloadable systemic console.

We’re extremely lucky to have a metal-rich KOV dwarf star lying just 1.3 parsecs away. Alpha Centauri B is roughly 100 times brighter than any other equally desirable radial velocity candidate star. The presence of Alpha Centauri A on its 80 year orbit, however, poses a complication for the fitting procedure of radial velocities from B. This problem seems readily solvable, however, and we’ll examine it in much more depth in one of the upcoming posts. Here, we’ll assume that the long-term large-amplitude radial velocity signal arising from A has been correctly filtered out of the data.

Our first step, then, was to invent some terrestrial planetary systems. Our systems have been produced with a Wetherill-Chambers method accretion code, and are both dynamically stable, and organically farmed in the Alpha Centauri AB environment.

Once a terrestrial planetary system has been created, it is observed with Eugenio’s TAC code. The TAC code is provided with a location on Earth (we’re producing synthetic data from telescopes located at La Silla and at the South Pole), and the position of the target star on the sky. Based on the readout time for the HARPS spectrograph, we assume an observing cadence of 200 seconds. Radial velocities are obtained whenever (1) the simulated weather is clear, (2) the Sun is more than 102 degrees from the zenith, and (3) Alpha Centauri is at less than 2.5 air masses. With its declination of -60 degrees, Alpha Centauri is circumpolar at La Silla, which significantly improves its overall observability. Observational errors are drawn from a normal distribution implied by the RMS residuals to the HD 69830 fit. We’re proactively aware that this is only a first approximation. (Over at my other job, we’ve been spending a fair amount of time thinking about autoregressive conditional heteroskedasticity.)

After running the TAC code, we find that 96,464 radial velocities are obtained in a trial five-year observing session. That’s one helluva RV data set. The complete time series has been added to the datafiles directory of the downloadable systemic console. You can access it by selecting “other” from the bottom of the system menu and opening the file AlphaCenB_Y5.sys. Note that because of the large size of this data set, the console function will be very slow. Patience is required. If you want to use your own software, the time series is AlphaCenB_Y5.vels.

When 96,076 velocities are all displayed in the data window, the resulting plot shows the yearly modulation of observability:

If you zoom to the highest time resolution, you can see the blocks of radial velocities obtained on successive nights:

The periodogram says it all:

The peak at 351 days corresponds to a half Earth-mass planet. The three neighboring peaks correspond to smaller planets having masses on the order of Mars.

Aaron tweaked the code for the folding window so that large datasets can be usefully manipulated. When the data is folded at 351 days, the periodicity is ever so faintly visible. Thanks to Joseph Fourier, however, the planets are clearly, unmistakeably detectable in the periodogram.

In the upcoming posts, we’ll talk in detail about the results of fitting to this data, and how the fit compares to the actual planetary system under observation. We’ll also look at modeling systematic error, non-gaussian noise, uncertainty, biases and so forth. These complications will inevitably erode the size of the peak in the above periodogram. Then we’ll implement a double-blind experiment on a set of 10 individual time series. Then we’ll talk about the confounding factors introduced by the binary companion. Then we’ll talk strategy.