Some of the planets that have been detected via the radial velocity technique have been announced in the refereed literature without the supporting evidence of a published table of radial velocities. For the planets that fall in this category, the end-user gets a star name, a list of orbital elements for the planet, and a graph showing a model velocity curve running through the data points. Occasionally, the data is folded, and only a .gif file of the phased radial velocity fit is published.

In a previous post, I wrote about why I can certainly appreciate the planet detection teams’ reasons for not wanting to divulge their radial velocity data when they announce a new planet. If a star has one detectable planet, then the odds are about 50-50 that another planet will be detected after several additional years of monitoring. For a variety of reasons, multiple-planet systems are scientifically more valuable than single-planet systems. In particular, a multiple-planet system (such as GJ 876) tells a fascinating dynamical story, which in turn yields valuable information about the formation and evolution of the planetary system. Obtaining radial velocities is hard, expensive work.

The unavailability of the radial velocity data sets for some of the planet-bearing stars has led to something of a gray market industry in which the radial velocity plots of the parent stars of interesting multiple-planet systems such as HD 82943 and HD 202206 are digitized, and the radial velocities are reconstructed from the graphs. For an example of this technique, see this preprint on astro-ph.

I bear some of the responsibility for the radial velocity .gif digitization industry. In 2001, a press release was sent out announcing the discovery of eleven new planets. This bumper crop included two particularly amazing systems, HD 80606, and HD 82943. HD 80606 harbors a massive planet on an extremely eccentric orbit, and I was very interested to fit the data myself in order to estimate the uncertainties in the transit windows.

The tabulated radial velocities on which the fits were based were not published, but postscript files showing plots of the radial velocities versus time were posted. I went into the files, and by placing commands to print characters in red, I was able to figure out how the plot was encoded. I was then able to extract the exact measured radial velocities for both HD 80606, and HD 82943 from the press conference postings. I didn’t try to publish the analysis that I did with this data, since the procedure seemed a little under-the-table. I did tell people what I was doing, however, and the radial velocity plots on the websites were soon changed from postscripts to .gif files, which are much harder to reverse-engineer.

One of our initial goals with the systemic collaboration is to provide the ability for anyone who is interested to perform a uniform analysis on all of the radial velocities underlying all of the published planets that make up the current galactic planetary census. In order to do this, we need a mechanism for accurately extracting the data from image files in .gif and .jpg format. Systemic team member Eugenio Rivera has been working on this, and has been getting good results with the Dexter Java Applet (available from ADS). The ADS information page gives the following overview:

Dexter is a tool to extract data from figures on scanned pages from our article service. In order to use it, you need a browser that can execute Java Applets and has that feature enabled. Netscape users can verify this by selecting “Edit” -> “Preferences” -> “Advanced” from the top-bar menu and making sure that the button “Enable Java” is checked.

Dexter can be quite useful in generating data points from published figures containing images, plots, graphs, and histograms, whenever the original datasets used by the authors to produce figures in the papers are not available electronically.

We’ll be posting velocity sets extracted from .gif files shortly, and Eugenio will post a detailed write-up of the technique and pitfalls of “observing” the observations.

This post continues with a thread that we’ve been developing over the past several days (posts 1, 2, and 3). In brief, we’ve found interesting evidence of a second planetary companion to 51 Peg in the published radial velocity data sets.

We first used the Systemic Console to recover 51 Peg’s famous (P=4.231 d) companion from the data, and then looked at the power spectrum of the residuals to the single planet fit:

There is a startlingly large periodicity in the data at a 356.2 day period.

We then used the console to identify this periodicity with an Msin(i)= 0.32 Jupiter-mass planet in an e=0.36, P=357 day orbit.

There’s no question that the addition of this second planet reduces the scatter in the data relative to the model. The question is: can the model be taken seriously? Is 51 Peg “c” really there?

Continue reading →

In the posts for Thursday and Friday, we used the Systemic Console to explore the radial velocity variations of 51 Peg. Aside from harboring the first extrasolar planet discovered in orbit around a Sun-like star, this data set is extraordinary because it contains nearly 270 individual radial velocity measurements taken over a period of over ten years. Very few stars have published data sets that are so extensive.

After extracting the signal of the celebrated 4.231 day planet from the data, we computed a periodogram of the residuals. The calculation shows a strong concentration of power at a 356 day periodicity:

At the end of yesterday’s post, we were left hanging on the suggestion that this strong peak might represent a second planet in the 51 Peg system. Let’s have a look at this hypothesis by making a two planet fit to the data.

If you’ve gone through the systemic tutorials, and are comfortable at the controls of the console, here’s the procedure:

Launch the console and follow the directions given yesterday to obtain the best single-planet fit to the data. Next, activate a second planet, and enter 356. into the data window of the period slider for the second planet. Then, minimize the new planet’s mean anomaly, followed by a minimization on the mass. Next, send all ten orbital parameters for the two planets, along with the velocity offsets off for a polish by the Levenberg-Marquardt algorithm. Note that it’s fine to push the “polish” button several times in succession, to ensure that the algorithm has been given enough iterations to converge to the best fit in the vicinity of your choice of starting conditions.

The console shows that the addition of a second planet improves the fit to the data, dropping the chi-square to 1.7, and reducing the required jitter to 5.4 m/s.

The second planet, which we’ll call 51 Peg “c” (where c stands for “console”, huh, huh) has a period of 356.8 days, a minimum mass of 0.32 jovian masses (slightly larger than Saturn), and an orbital eccentricity, e=0.36. Here’s a link to a screenshot of the console showing all the parameters. This is also an advance look at the next version of the console which Aaron will be releasing in a few weeks.

Using the console’s zooming and scrolling sliders, we can see the modulation of the radial velocity curve. The second planet imparts a visibly non-sinusoidal envelope on the strong carrier signal created by 51 Peg b. The non-sinusoidal shape stems from the significant eccentricity of planet “c”:

Note that we still have to teach the console to draw smooth curves when the zoom level is high! Look for that improvement to show up in about 2 months or so. There’s a lot of other items ahead of it on the to-do list.

The orbits of the two planets look like this:

Does it really exist, this room-temperature Saturn? Is it really out there? Do furious anticyclonic storms spin through its cloud bands? Does it have rings? Does it loom as an enormous white crescent in the deep blue twilight sky of a habitable moon?

Maybe.

Eugenio and I have been working through the weekend to devise statistical tests which can assess the likelihood that this planet exists. We’ll check in shortly with our results

Yesterday, we supplied the Systemic Console with the published radial velocity datasets of the the planetary system that started it all, the original gangsta, 51 Peg.

It’s interesting, after more than a decade of observation, to see what happens as a radial velocity time series acquires a long baseline. Launch the Systemic Console, and select 51 Peg from the system menu. You’ll see a plot that looks like this:

With the “51peg_1.vels” offset slider, it’s easy to separate the two contributing data sets. (One was published by the California-Carnegie Planet Search Team, the other by the Geneva Extrasolar Planet Survey). The Swiss data set gives a long baseline of coverage, whereas the California-Carnegie dataset contains intensive observations taken mostly over the course of a single observing season in 1996. Click on the periodogram, and be patient while the console works through the Lomb-Scargle algorithm. While you’re waiting, you can look eagerly forward to the fact that in Aaron Wolf’s next release of the console (due in a few weeks) the periodogram calculation will be sped up by more than a factor of ten.

The periodogram has an impressive tower of power at 4.231 days. This dataset contains a whopping-strong sinusoidal signal:

To work up 51 Peg “b”, activate the first row of planetary orbital element sliders and type 4.231 into the period box. Then (1) line-minimize the mean anomaly, (2) line-minimize the mass, (3,4) line-minimize both offset sliders, and (5) line-minimize the period. (6) Activate a small eccentricity, (7) move the longitude of periastron slider off the zero point, and then (8) click the Levenberg-Marquardt boxes to the left of each entry box and polish the fit. (If this sounds like gibberish, yet also exciting, we’ve written three tutorials [here, here, and here] that go into detail regarding the use of the console. In addition, all posts marked “systemic faq” contain information about how to use and work with the console.)

When I do this, the console gives me a single planet fit with P=4.2308 days, M=0.4749 Jupiter Masses, and eccentricity e=0.014. These values are in full agreement with the orbital parameters published in the original discovery paper.

Alert readers are likely grumbling that we’ve made no mention of uncertainties in the orbital elements. This is an extremely important and interesting issue for many systems, and we’ll definitely be posting extensively on the topic and theory of computation of errors in orbital elements of extrasolar planets. The entire Systemic research collaboration, in fact, is primarily concerned with resolving the issue of how to establish confidence levels in various types of planetary system configurations.

In the meantime, however, use the console to compute a periodogram of the velocity residuals to the old-school 1-planet fit. A strong peak stands out at a period of 356.196 days. The chi-square statistic of the 1-planet fit is just over 2.00, and the required stellar jitter is about 7 meters per second. This is significantly higher than the 3-5 meters per second of long-term jitter that is expected for a quiet, old G2 IV star like 51 Peg:

Could there be another planet in the system? Could it be, that the console, by virtue of the fact that it readily combines data sets from different published sources, has found a new world (in a habitable orbit no less)? Tune in tomorrow to find out…

Most of the recent scientific papers on the general topic of extrasolar planets start with a sentence very much like this one:

Following the announcement of the planet orbiting 51 Peg (Mayor & Queloz 1995), over 170 planets have been discovered in orbit around solar type stars.

And indeed, Mayor and Queloz’s discovery of the hot Jupiter orbiting 51 Peg was truly a watershed event. Their Nature paper has racked up 764 ADS citations. Of order several billion dollars have been spent (or will shortly be spent) on the worldwide effort to locate and characterize alien solar systems. It’s thus a little weird that the Systemic Console has so far failed to include 51 Peg in its system menu. We’ve just corrected this oversight by adding the two published data sets for 51 Peg.

The closely spaced data near the beginning of the time series is from Marcy et al. (1997), who began intensively monitoring the planet from Lick Observatory as soon as the discovery was announced. The widely spaced data is from the Swiss planet hunting team (Naef et al. 2004), and contains 153 radial velocities obtained over a ~10-year period. The data is catalogued at CDS, and available at this link.

The 51 Peg data sets are interesting for a number of reasons. I’ll check in tomorrow with more details as to why. In the meantime, fire up the console and start finding fits.