The music of the spheres (sounds terrible)
After using the console for a while, you’ll notice that it’s often easy to find a reasonably good (say, chi-square of 3-5) multiple-planet fit to a given radial velocity data set. This rule of thumb tends to be especially true if you allow the planets to have large eccentricities. But how does one know whether the fit is likely to be correct?
This is one of the questions that the systemic simulation is designed to answer.
Most of the time, however, if a fit contains large enough eccentricities for the planet orbits to cross, then the trial system will be dynamically unstable. That is, the planets in the model will suffer a close encounter, which is generally followed (or directly accompanied) by a disaster. The planets collide, or one or more of them is ejected, or one of them is thrown into the central star.
While it is certainly true that such catastrophes have been reasonably common throughout galactic history, it is exceedingly unlikely that any particular planetary system that we observe will be on the verge of a dramatic instability. The stars that can be observed using the Doppler radial velocity method are billions of years old. If a star had an unstable planetary system, it is likely that the instability either occurred long ago, or that won’t happen for a long time to come.
As a result, an important requirement for any radial velocity fit is that it correspond to a dynamically stable system. Traditionally, this can be checked either by integrating the system forward in time, or by applying a technique which checks for the presence of chaos in the orbits. (Indeed, all of the planetary systems that underlie the systemic database have been integrated for one million orbits prior to being “observed”. These pre-integrations establish a strong likelihood of short-term dynamical stability for all the systemic systems.)
Here’s an idea that sounds possibly promising. If the radial velocity waveform of a planetary system is converted into an audio signal, is it possible for the human ear to rapidly detect whether a system is likely to be unstable? To test this, we’re working on bringing an audio generator into the systemic console.
More generally, what do the extrasolar planetary radial velocity reflex waveforms sound like? The short answer is, they sound terrible. There are interesting reasons for this, which we’ll pick up in a future post. For now, have a listen to these .wav’s (created by Aaron Wolf) of two of the best-known multiple planet systems: GJ 876 and Upsilon Andromedae
And try to listen for the (heavily processed voice of the better-voice-of-the-two GJ876 in the forthcoming James Alley Remix).