As a kid I found my parents' old LP's: The Rolling Stones (Let It Bleed!), Bob Dylan (Blood on the Tracks!), Big Brother and the Holding Company (Cheap Thrills!). As a result, I feel I have a good appreciation for the roots of modern rock and roll.
So it's good to see that the kids these days are acknowledging the classics. New Penn State grad student Ben Nelson, working with Eric Ford, has been, as he put it "remastering the RV classics" by reanalyzing the LONG data streams of radial velocities for some of the longest-known and best-observed systems, like 55 Cancri (5 planets, one transiting) and GJ 876 (4 planets, probably, with strong mean-motion resonances).
My quick and usually-good-enough approach to fitting multiplanet systems measured with multiple telescopes is to use the RVLIN approach I developed with Andrew Howard (published here, code available here, parameter uncertainties available thanks to Sharon Wang's work here). But this approach does not incorporate planet-planet interactions (usually not a problem -- they are too small to detect for almost all systems) and is a strictly "frequentist" chi-squared approach, which is decidedly out of fashion in astronomy these days.
Ben, as any good Eric Ford grad student will, brings to the problem a rigorous Bayesian (Markov chain Monte Carlo, or "MCMC") approach that generates parameter posteriors. He also incorporates dynamical effects, so that planet-planet interactions are not just accounted for but can help constrain the physical parameters of the system. His code also naturally accounts for the independent radial velocity time series not just for the four telescopes that have observed these exoplanetary systems, but for potential offsets between data streams for different detectors on the same telescope. It also independently determines the quality of the data (the "instrumental jitter") for each detector/telescope.
Oh, and he also incorporates dynamical stability constraints, so that long term (108 years) unstable configurations are not part of the final posterior sample.
Oh, and he does the whole thing on a supercomputer with multithreading.
Oh, and the "supercomputer" in question is actually a cluster of graphics processor units (GPU's), which are cheap and fast but much trickier to hack into doing this sort of calculation than a "proper" supercomputer.
Really, the whole thing is a tour-de-force of how to do the problem "right".
Ben is also an old-school hip hop fan. Apparently, the coincidence of the initials of Markov Chain, Monte Carlo, and "Master of Ceremonies" has been too much to resist in astronomy. First we had "emcee: The MCMC HAMMER" (http://arxiv.org/abs/1202.3665), public code by Daniel Foreman-Mackey that samples MCMC ensembles very cleverly.
Ben's code is called RUN-DMC, for "Radial velocity Using N-body Differential evolution markov chain Monte Carlo.
Ben's paper on the 55 Cnc system is here:http://arxiv.org/abs/1311.5229
Applying RUN-DMC to 55 Cnc, Ben finds that each planet has something interesting to teach us:
- b and c are near a mean motion resonance, but not actually in the 3:1 resonance. They may, however, be apsidally locked at 180 degrees with a large libration amplitude (something Eugene Chiang refers to as the "metronome" formulation of the simple harmonic oscillator problem, as opposed to the usual "pendulum" formulation about 0 degrees). Note that the period ratio incorporating planet-planet interactions (blue) differs by many sigma from the purely Keplerian solution (orange). (The green solutions are osculating elements, I think -- you have have to average over large time intervals to determine a robust period ratio, which gives you the blue cloud).
- d's revised period and eccentricity make it one of the best Jupiter analogs known (though it has inner massive planets, so 55 Cnc is not a good Solar System analog). For reference, Jupiter has P=4332 and e=0.05.
- The transiting, e component is probably reasonably well aligned with the other 4 planets (within 60 degrees, based on dynamical stability), and has a density of 5.5 (+1.3/-1.0) g/cc, very close to Earth's (5.5, though the mass of e is at least 8 times higher than Earth's, so it probably has more volatiles and maybe a big atmosphere).
- f is in the Habitable Zone, but its amplitude is still to low to get a good handle on its eccentricity.
Incidentally, when Ben gave a talk in our department about this code, several of our department's freshmen were in attendance as part of an assignment in my First Year Seminar class to attend a department talk. They said they were confused, in particular why everyone else laughed when Ben announced the name of the code was RUN-DMC. They had never heard that term before.
Now that makes me feel old. Run was the King of Rock! There is none higher! They're in the Rock and Roll Hall of Fame for goodness' sake!
Kids just don't know their history any more.
(Though as much as I, as a classic rock fan, appreciated RUN-DMC's crossover hit Walk this Way, especially Stephen Tyler's Kool-Aid Man burst through the wall in the video, my Seattle roots make me partial to Mix -- his posse's on Broadway.)
[Update: Be sure to keep track of Ben's own explanation of the paper on his blog!]